Contents:
Pure Tuning
Pure Tuning Unbalanced
Prime Tuning
Just intonation
Pythagorean tuning
Quarter-comma meantone temperament (1/4 syntonic comma)
Silbermann temperament (1/6 Pythagorean comma)
Gabler temperament
Werckmeister III temperament
Lehman-Bach temperament
Kirnberger III temperament
Vallotti temperament
Young temperament (Young I)
Valotti-Young temperament (Young II)
Prinz temperament
Broadwood's Best temperament
Equal temperament
Pure Tuning
C : 1 = 0 ... +0.00
C# : 19/18 = 93.603014401528 ... -6.40
D : 272/243 = 195.18040517347 ... -4.82
D# : 19/16 = 297.5130161323 ... -2.49
E : 361/288 = 391.11603053383 ... -8.88
F : 4/3 = 498.04499913461 ... -1.96
F# : 38/27 = 591.64801353614 ... -8.35
G : 256/171 = 698.57698213692 ... -1.42
G# : 19/12 = 795.55801526692 ... -4.44
A : 57/34 = 894.51260749728 ... -5.49
A# : 16/9 = 996.08999826923 ... -3.91
B : 361/192 = 1093.0710313992 ... -6.93
statistics for interval minor second:
C -> C# : 1 -> 19/18 = 19*1 / 2*3*3*1 = 19 / 18 = 93.603014401528 →
C# -> D : 19/18 -> 272/243 = 2*2*2*2*17*2*3*3 / 3*3*3*3*3*19 = 544 / 513 = 101.57739077194 →
D -> D# : 272/243 -> 19/16 = 19*3*3*3*3*3 / 2*2*2*2*2*2*2*2*17 = 4617 / 4352 = 102.33261095883 →
D# -> E : 19/16 -> 361/288 = 19*19*2*2*2*2 / 2*2*2*2*2*3*3*19 = 19 / 18 = 93.603014401528 →
E -> F : 361/288 -> 4/3 = 2*2*2*2*2*2*2*3*3 / 3*19*19 = 384 / 361 = 106.92896860078 →
F -> F# : 4/3 -> 38/27 = 2*19*3 / 3*3*3*2*2 = 19 / 18 = 93.603014401528 →
F# -> G : 38/27 -> 256/171 = 2*2*2*2*2*2*2*2*3*3*3 / 3*3*19*2*19 = 384 / 361 = 106.92896860078 →
G -> G# : 256/171 -> 19/12 = 19*3*3*19 / 2*2*3*2*2*2*2*2*2*2*2 = 1083 / 1024 = 96.981033129993 →
G# -> A : 19/12 -> 57/34 = 3*19*2*2*3 / 2*17*19 = 18 / 17 = 98.954592230368 →
A -> A# : 57/34 -> 16/9 = 2*2*2*2*2*17 / 3*3*3*19 = 544 / 513 = 101.57739077194 →
A# -> B : 16/9 -> 361/192 = 19*19*3*3 / 2*2*2*2*2*2*3*2*2*2*2 = 1083 / 1024 = 96.981033129993 →
B -> C : 361/192 -> 1 = 2*1*2*2*2*2*2*2*3 / 1*19*19 = 384 / 361 = 106.92896860078 →
3 x 93.6 2 x 97 1 x 99 2 x 101.6 1 x 102.3 3 x 106.9
statistics for interval major second:
C -> D : 1 -> 272/243 = 2*2*2*2*17*1 / 3*3*3*3*3*1 = 272 / 243 = 195.18040517347 →
C# -> D# : 19/18 -> 19/16 = 19*2*3*3 / 2*2*2*2*19 = 9 / 8 = 203.91000173077 →
D -> E : 272/243 -> 361/288 = 19*19*3*3*3*3*3 / 2*2*2*2*2*3*3*2*2*2*2*17 = 9747 / 8704 = 195.93562536036 →
D# -> F : 19/16 -> 4/3 = 2*2*2*2*2*2 / 3*19 = 64 / 57 = 200.53198300231 →
E -> F# : 361/288 -> 38/27 = 2*19*2*2*2*2*2*3*3 / 3*3*3*19*19 = 64 / 57 = 200.53198300231 →
F -> G : 4/3 -> 256/171 = 2*2*2*2*2*2*2*2*3 / 3*3*19*2*2 = 64 / 57 = 200.53198300231 →
F# -> G# : 38/27 -> 19/12 = 19*3*3*3 / 2*2*3*2*19 = 9 / 8 = 203.91000173077 →
G -> A : 256/171 -> 57/34 = 3*19*3*3*19 / 2*17*2*2*2*2*2*2*2*2 = 9747 / 8704 = 195.93562536036 →
G# -> A# : 19/12 -> 16/9 = 2*2*2*2*2*2*3 / 3*3*19 = 64 / 57 = 200.53198300231 →
A -> B : 57/34 -> 361/192 = 19*19*2*17 / 2*2*2*2*2*2*3*3*19 = 323 / 288 = 198.55842390193 →
A# -> C : 16/9 -> 1 = 2*1*3*3 / 1*2*2*2*2 = 9 / 8 = 203.91000173077 →
B -> C# : 361/192 -> 19/18 = 2*19*2*2*2*2*2*2*3 / 2*3*3*19*19 = 64 / 57 = 200.53198300231 →
1 x 195.2 2 x 195.9 1 x 198.6 5 x 200.5 3 x 203.9
statistics for interval minor third:
C -> D# : 1 -> 19/16 = 19*1 / 2*2*2*2*1 = 19 / 16 = 297.5130161323 →
C# -> E : 19/18 -> 361/288 = 19*19*2*3*3 / 2*2*2*2*2*3*3*19 = 19 / 16 = 297.5130161323 →
D -> F : 272/243 -> 4/3 = 2*2*3*3*3*3*3 / 3*2*2*2*2*17 = 81 / 68 = 302.86459396114 →
D# -> F# : 19/16 -> 38/27 = 2*19*2*2*2*2 / 3*3*3*19 = 32 / 27 = 294.13499740384 →
E -> G : 361/288 -> 256/171 = 2*2*2*2*2*2*2*2*2*2*2*2*2*3*3 / 3*3*19*19*19 = 8192 / 6859 = 307.46095160309 →
F -> G# : 4/3 -> 19/12 = 19*3 / 2*2*3*2*2 = 19 / 16 = 297.5130161323 →
F# -> A : 38/27 -> 57/34 = 3*19*3*3*3 / 2*17*2*19 = 81 / 68 = 302.86459396114 →
G -> A# : 256/171 -> 16/9 = 2*2*2*2*3*3*19 / 3*3*2*2*2*2*2*2*2*2 = 19 / 16 = 297.5130161323 →
G# -> B : 19/12 -> 361/192 = 19*19*2*2*3 / 2*2*2*2*2*2*3*19 = 19 / 16 = 297.5130161323 →
A -> C : 57/34 -> 1 = 2*1*2*17 / 1*3*19 = 68 / 57 = 305.48739250272 →
A# -> C# : 16/9 -> 19/18 = 2*19*3*3 / 2*3*3*2*2*2*2 = 19 / 16 = 297.5130161323 →
B -> D : 361/192 -> 272/243 = 2*2*2*2*2*17*2*2*2*2*2*2*3 / 3*3*3*3*3*19*19 = 34816 / 29241 = 302.10937377425 →
1 x 294.1 6 x 297.5 1 x 302.1 2 x 302.9 1 x 305.5 1 x 307.5
statistics for interval major third:
C -> E : 1 -> 361/288 = 19*19*1 / 2*2*2*2*2*3*3*1 = 361 / 288 = 391.11603053383 →
C# -> F : 19/18 -> 4/3 = 2*2*2*3*3 / 3*19 = 24 / 19 = 404.44198473308 →
D -> F# : 272/243 -> 38/27 = 2*19*3*3*3*3*3 / 3*3*3*2*2*2*2*17 = 171 / 136 = 396.46760836267 →
D# -> G : 19/16 -> 256/171 = 2*2*2*2*2*2*2*2*2*2*2*2 / 3*3*19*19 = 4096 / 3249 = 401.06396600462 →
E -> G# : 361/288 -> 19/12 = 19*2*2*2*2*2*3*3 / 2*2*3*19*19 = 24 / 19 = 404.44198473308 →
F -> A : 4/3 -> 57/34 = 3*19*3 / 2*17*2*2 = 171 / 136 = 396.46760836267 →
F# -> A# : 38/27 -> 16/9 = 2*2*2*2*3*3*3 / 3*3*2*19 = 24 / 19 = 404.44198473308 →
G -> B : 256/171 -> 361/192 = 19*19*3*3*19 / 2*2*2*2*2*2*3*2*2*2*2*2*2*2*2 = 20577 / 16384 = 394.4940492623 →
G# -> C : 19/12 -> 1 = 2*1*2*2*3 / 1*19 = 24 / 19 = 404.44198473308 →
A -> C# : 57/34 -> 19/18 = 2*19*2*17 / 2*3*3*3*19 = 34 / 27 = 399.09040690424 →
A# -> D : 16/9 -> 272/243 = 2*2*2*2*2*17*3*3 / 3*3*3*3*3*2*2*2*2 = 34 / 27 = 399.09040690425 →
B -> D# : 361/192 -> 19/16 = 2*19*2*2*2*2*2*2*3 / 2*2*2*2*19*19 = 24 / 19 = 404.44198473308 →
1 x 391.1 1 x 394.5 2 x 396.5 2 x 399.1 1 x 401.1 5 x 404.4
statistics for interval fourth:
C -> F : 1 -> 4/3 = 2*2*1 / 3*1 = 4 / 3 = 498.04499913461 →
C# -> F# : 19/18 -> 38/27 = 2*19*2*3*3 / 3*3*3*19 = 4 / 3 = 498.04499913461 →
D -> G : 272/243 -> 256/171 = 2*2*2*2*2*2*2*2*3*3*3*3*3 / 3*3*19*2*2*2*2*17 = 432 / 323 = 503.39657696345 →
D# -> G# : 19/16 -> 19/12 = 19*2*2*2*2 / 2*2*3*19 = 4 / 3 = 498.04499913461 →
E -> A : 361/288 -> 57/34 = 3*19*2*2*2*2*2*3*3 / 2*17*19*19 = 432 / 323 = 503.39657696345 →
F -> A# : 4/3 -> 16/9 = 2*2*2*2*3 / 3*3*2*2 = 4 / 3 = 498.04499913461 →
F# -> B : 38/27 -> 361/192 = 19*19*3*3*3 / 2*2*2*2*2*2*3*2*19 = 171 / 128 = 501.42301786308 →
G -> C : 256/171 -> 1 = 2*1*3*3*19 / 1*2*2*2*2*2*2*2*2 = 171 / 128 = 501.42301786308 →
G# -> C# : 19/12 -> 19/18 = 2*19*2*2*3 / 2*3*3*19 = 4 / 3 = 498.04499913461 →
A -> D : 57/34 -> 272/243 = 2*2*2*2*2*17*2*17 / 3*3*3*3*3*3*19 = 18496 / 13851 = 500.66779767619 →
A# -> D# : 16/9 -> 19/16 = 2*19*3*3 / 2*2*2*2*2*2*2*2 = 171 / 128 = 501.42301786308 →
B -> E : 361/192 -> 361/288 = 2*19*19*2*2*2*2*2*2*3 / 2*2*2*2*2*3*3*19*19 = 4 / 3 = 498.04499913461 →
6 x 498 1 x 500.7 3 x 501.4 2 x 503.4
statistics for interval tritone:
C -> F# : 1 -> 38/27 = 2*19*1 / 3*3*3*1 = 38 / 27 = 591.64801353614 →
C# -> G : 19/18 -> 256/171 = 2*2*2*2*2*2*2*2*2*3*3 / 3*3*19*19 = 512 / 361 = 604.97396773539 →
D -> G# : 272/243 -> 19/12 = 19*3*3*3*3*3 / 2*2*3*2*2*2*2*17 = 1539 / 1088 = 600.37761009345 →
D# -> A : 19/16 -> 57/34 = 3*19*2*2*2*2 / 2*17*19 = 24 / 17 = 596.99959136498 →
E -> A# : 361/288 -> 16/9 = 2*2*2*2*2*2*2*2*2*3*3 / 3*3*19*19 = 512 / 361 = 604.97396773539 →
F -> B : 4/3 -> 361/192 = 19*19*3 / 2*2*2*2*2*2*3*2*2 = 361 / 256 = 595.02603226461 →
F# -> C : 38/27 -> 1 = 2*1*3*3*3 / 1*2*19 = 27 / 19 = 608.35198646386 →
G -> C# : 256/171 -> 19/18 = 2*19*3*3*19 / 2*3*3*2*2*2*2*2*2*2*2 = 361 / 256 = 595.02603226461 →
G# -> D : 19/12 -> 272/243 = 2*2*2*2*2*17*2*2*3 / 3*3*3*3*3*19 = 2176 / 1539 = 599.62238990655 →
A -> D# : 57/34 -> 19/16 = 2*19*2*17 / 2*2*2*2*3*19 = 17 / 12 = 603.00040863502 →
A# -> E : 16/9 -> 361/288 = 2*19*19*3*3 / 2*2*2*2*2*3*3*2*2*2*2 = 361 / 256 = 595.02603226461 →
B -> F : 361/192 -> 4/3 = 2*2*2*2*2*2*2*2*2*3 / 3*19*19 = 512 / 361 = 604.97396773539 →
1 x 591.6 3 x 595 1 x 597 1 x 599.6 1 x 600.4 1 x 603 3 x 605 1 x 608.4
statistics for interval fifth:
C -> G : 1 -> 256/171 = 2*2*2*2*2*2*2*2*1 / 3*3*19*1 = 256 / 171 = 698.57698213692 →
C# -> G# : 19/18 -> 19/12 = 19*2*3*3 / 2*2*3*19 = 3 / 2 = 701.95500086539 →
D -> A : 272/243 -> 57/34 = 3*19*3*3*3*3*3 / 2*17*2*2*2*2*17 = 13851 / 9248 = 699.33220232381 →
D# -> A# : 19/16 -> 16/9 = 2*2*2*2*2*2*2*2 / 3*3*19 = 256 / 171 = 698.57698213692 →
E -> B : 361/288 -> 361/192 = 19*19*2*2*2*2*2*3*3 / 2*2*2*2*2*2*3*19*19 = 3 / 2 = 701.95500086539 →
F -> C : 4/3 -> 1 = 2*1*3 / 1*2*2 = 3 / 2 = 701.95500086539 →
F# -> C# : 38/27 -> 19/18 = 2*19*3*3*3 / 2*3*3*2*19 = 3 / 2 = 701.95500086539 →
G -> D : 256/171 -> 272/243 = 2*2*2*2*2*17*3*3*19 / 3*3*3*3*3*2*2*2*2*2*2*2*2 = 323 / 216 = 696.60342303655 →
G# -> D# : 19/12 -> 19/16 = 2*19*2*2*3 / 2*2*2*2*19 = 3 / 2 = 701.95500086539 →
A -> E : 57/34 -> 361/288 = 2*19*19*2*17 / 2*2*2*2*2*3*3*3*19 = 323 / 216 = 696.60342303655 →
A# -> F : 16/9 -> 4/3 = 2*2*2*3*3 / 3*2*2*2*2 = 3 / 2 = 701.95500086539 →
B -> F# : 361/192 -> 38/27 = 2*2*19*2*2*2*2*2*2*3 / 3*3*3*19*19 = 256 / 171 = 698.57698213692 →
2 x 696.6 3 x 698.6 1 x 699.3 6 x 702
statistics for interval minor sixth:
C -> G# : 1 -> 19/12 = 19*1 / 2*2*3*1 = 19 / 12 = 795.55801526692 →
C# -> A : 19/18 -> 57/34 = 3*19*2*3*3 / 2*17*19 = 27 / 17 = 800.90959309576 →
D -> A# : 272/243 -> 16/9 = 2*2*2*2*3*3*3*3*3 / 3*3*2*2*2*2*17 = 27 / 17 = 800.90959309575 →
D# -> B : 19/16 -> 361/192 = 19*19*2*2*2*2 / 2*2*2*2*2*2*3*19 = 19 / 12 = 795.55801526692 →
E -> C : 361/288 -> 1 = 2*1*2*2*2*2*2*3*3 / 1*19*19 = 576 / 361 = 808.88396946617 →
F -> C# : 4/3 -> 19/18 = 2*19*3 / 2*3*3*2*2 = 19 / 12 = 795.55801526692 →
F# -> D : 38/27 -> 272/243 = 2*2*2*2*2*17*3*3*3 / 3*3*3*3*3*2*19 = 272 / 171 = 803.53239163733 →
G -> D# : 256/171 -> 19/16 = 2*19*3*3*19 / 2*2*2*2*2*2*2*2*2*2*2*2 = 3249 / 2048 = 798.93603399538 →
G# -> E : 19/12 -> 361/288 = 2*19*19*2*2*3 / 2*2*2*2*2*3*3*19 = 19 / 12 = 795.55801526692 →
A -> F : 57/34 -> 4/3 = 2*2*2*2*17 / 3*3*19 = 272 / 171 = 803.53239163733 →
A# -> F# : 16/9 -> 38/27 = 2*2*19*3*3 / 3*3*3*2*2*2*2 = 19 / 12 = 795.55801526692 →
B -> G : 361/192 -> 256/171 = 2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*3 / 3*3*19*19*19 = 32768 / 20577 = 805.5059507377 →
5 x 795.6 1 x 798.9 2 x 800.9 2 x 803.5 1 x 805.5 1 x 808.9
statistics for interval major sixth:
C -> A : 1 -> 57/34 = 3*19*1 / 2*17*1 = 57 / 34 = 894.51260749728 →
C# -> A# : 19/18 -> 16/9 = 2*2*2*2*2*3*3 / 3*3*19 = 32 / 19 = 902.4869838677 →
D -> B : 272/243 -> 361/192 = 19*19*3*3*3*3*3 / 2*2*2*2*2*2*3*2*2*2*2*17 = 29241 / 17408 = 897.89062622575 →
D# -> C : 19/16 -> 1 = 2*1*2*2*2*2 / 1*19 = 32 / 19 = 902.4869838677 →
E -> C# : 361/288 -> 19/18 = 2*19*2*2*2*2*2*3*3 / 2*3*3*19*19 = 32 / 19 = 902.4869838677 →
F -> D : 4/3 -> 272/243 = 2*2*2*2*2*17*3 / 3*3*3*3*3*2*2 = 136 / 81 = 897.13540603886 →
F# -> D# : 38/27 -> 19/16 = 2*19*3*3*3 / 2*2*2*2*2*19 = 27 / 16 = 905.86500259616 →
G -> E : 256/171 -> 361/288 = 2*19*19*3*3*19 / 2*2*2*2*2*3*3*2*2*2*2*2*2*2*2 = 6859 / 4096 = 892.53904839691 →
G# -> F : 19/12 -> 4/3 = 2*2*2*2*2*3 / 3*19 = 32 / 19 = 902.4869838677 →
A -> F# : 57/34 -> 38/27 = 2*2*19*2*17 / 3*3*3*3*19 = 136 / 81 = 897.13540603886 →
A# -> G : 16/9 -> 256/171 = 2*2*2*2*2*2*2*2*2*3*3 / 3*3*19*2*2*2*2 = 32 / 19 = 902.4869838677 →
B -> G# : 361/192 -> 19/12 = 2*19*2*2*2*2*2*2*3 / 2*2*3*19*19 = 32 / 19 = 902.4869838677 →
1 x 892.5 1 x 894.5 2 x 897.1 1 x 897.9 6 x 902.5 1 x 905.9
statistics for interval minor seventh:
C -> A# : 1 -> 16/9 = 2*2*2*2*1 / 3*3*1 = 16 / 9 = 996.08999826923 →
C# -> B : 19/18 -> 361/192 = 19*19*2*3*3 / 2*2*2*2*2*2*3*19 = 57 / 32 = 999.46801699769 →
D -> C : 272/243 -> 1 = 2*1*3*3*3*3*3 / 1*2*2*2*2*17 = 243 / 136 = 1004.8195948265 →
D# -> C# : 19/16 -> 19/18 = 2*19*2*2*2*2 / 2*3*3*19 = 16 / 9 = 996.08999826923 →
E -> D : 361/288 -> 272/243 = 2*2*2*2*2*17*2*2*2*2*2*3*3 / 3*3*3*3*3*19*19 = 17408 / 9747 = 1004.0643746396 →
F -> D# : 4/3 -> 19/16 = 2*19*3 / 2*2*2*2*2*2 = 57 / 32 = 999.46801699769 →
F# -> E : 38/27 -> 361/288 = 2*19*19*3*3*3 / 2*2*2*2*2*3*3*2*19 = 57 / 32 = 999.46801699769 →
G -> F : 256/171 -> 4/3 = 2*2*2*3*3*19 / 3*2*2*2*2*2*2*2*2 = 57 / 32 = 999.46801699769 →
G# -> F# : 19/12 -> 38/27 = 2*2*19*2*2*3 / 3*3*3*19 = 16 / 9 = 996.08999826923 →
A -> G : 57/34 -> 256/171 = 2*2*2*2*2*2*2*2*2*2*17 / 3*3*19*3*19 = 17408 / 9747 = 1004.0643746396 →
A# -> G# : 16/9 -> 19/12 = 2*19*3*3 / 2*2*3*2*2*2*2 = 57 / 32 = 999.46801699769 →
B -> A : 361/192 -> 57/34 = 2*3*19*2*2*2*2*2*2*3 / 2*17*19*19 = 576 / 323 = 1001.4415760981 →
3 x 996.1 5 x 999.5 1 x 1001.4 2 x 1004.1 1 x 1004.8
statistics for interval major seventh:
C -> B : 1 -> 361/192 = 19*19*1 / 2*2*2*2*2*2*3*1 = 361 / 192 = 1093.0710313992 →
C# -> C : 19/18 -> 1 = 2*1*2*3*3 / 1*19 = 36 / 19 = 1106.3969855985 →
D -> C# : 272/243 -> 19/18 = 2*19*3*3*3*3*3 / 2*3*3*2*2*2*2*17 = 513 / 272 = 1098.4226092281 →
D# -> D : 19/16 -> 272/243 = 2*2*2*2*2*17*2*2*2*2 / 3*3*3*3*3*19 = 8704 / 4617 = 1097.6673890412 →
E -> D# : 361/288 -> 19/16 = 2*19*2*2*2*2*2*3*3 / 2*2*2*2*19*19 = 36 / 19 = 1106.3969855985 →
F -> E : 4/3 -> 361/288 = 2*19*19*3 / 2*2*2*2*2*3*3*2*2 = 361 / 192 = 1093.0710313992 →
F# -> F : 38/27 -> 4/3 = 2*2*2*3*3*3 / 3*2*19 = 36 / 19 = 1106.3969855985 →
G -> F# : 256/171 -> 38/27 = 2*2*19*3*3*19 / 3*3*3*2*2*2*2*2*2*2*2 = 361 / 192 = 1093.0710313992 →
G# -> G : 19/12 -> 256/171 = 2*2*2*2*2*2*2*2*2*2*2*3 / 3*3*19*19 = 2048 / 1083 = 1103.01896687 →
A -> G# : 57/34 -> 19/12 = 2*19*2*17 / 2*2*3*3*19 = 17 / 9 = 1101.0454077696 →
A# -> A : 16/9 -> 57/34 = 2*3*19*3*3 / 2*17*2*2*2*2 = 513 / 272 = 1098.4226092281 →
B -> A# : 361/192 -> 16/9 = 2*2*2*2*2*2*2*2*2*2*2*3 / 3*3*19*19 = 2048 / 1083 = 1103.01896687 →
3 x 1093.1 1 x 1097.7 2 x 1098.4 1 x 1101 2 x 1103 3 x 1106.4
Pure Tuning Unbalanced
C : 1 = 0 ... +0.00
C# : 20/19 = 88.800697732532 ... -11.20
D : 19/17 = 192.5576066319 ... -7.44
D# : 45/38 = 292.71069946331 ... -7.29
E : 5/4 = 386.31371386483 ... -13.69
F : 4/3 = 498.04499913461 ... -1.96
F# : 24/17 = 596.99959136498 ... -3.00
G : 3/2 = 701.95500086539 ... +1.96
G# : 30/19 = 790.75569859792 ... -9.24
A : 5/3 = 884.35871299945 ... -15.64
A# : 16/9 = 996.08999826923 ... -3.91
B : 15/8 = 1088.2687147302 ... -11.73
statistics for interval minor second:
C -> C# : 1 -> 20/19 = 2*2*5*1 / 19*1 = 20 / 19 = 88.800697732532 →
C# -> D : 20/19 -> 19/17 = 19*19 / 17*2*2*5 = 361 / 340 = 103.75690889936 →
D -> D# : 19/17 -> 45/38 = 3*3*5*17 / 2*19*19 = 765 / 722 = 100.15309283141 →
D# -> E : 45/38 -> 5/4 = 5*2*19 / 2*2*3*3*5 = 19 / 18 = 93.603014401528 →
E -> F : 5/4 -> 4/3 = 2*2*2*2 / 3*5 = 16 / 15 = 111.73128526978 →
F -> F# : 4/3 -> 24/17 = 2*2*2*3*3 / 17*2*2 = 18 / 17 = 98.954592230368 →
F# -> G : 24/17 -> 3/2 = 3*17 / 2*2*2*2*3 = 17 / 16 = 104.95540950041 →
G -> G# : 3/2 -> 30/19 = 2*3*5*2 / 19*3 = 20 / 19 = 88.800697732532 →
G# -> A : 30/19 -> 5/3 = 5*19 / 3*2*3*5 = 19 / 18 = 93.603014401528 →
A -> A# : 5/3 -> 16/9 = 2*2*2*2*3 / 3*3*5 = 16 / 15 = 111.73128526978 →
A# -> B : 16/9 -> 15/8 = 3*5*3*3 / 2*2*2*2*2*2*2 = 135 / 128 = 92.178716460997 →
B -> C : 15/8 -> 1 = 2*1*2*2*2 / 1*3*5 = 16 / 15 = 111.73128526978 →
2 x 88.8 1 x 92.2 2 x 93.6 1 x 99 1 x 100.2 1 x 103.8 1 x 105 3 x 111.7
statistics for interval major second:
C -> D : 1 -> 19/17 = 19*1 / 17*1 = 19 / 17 = 192.5576066319 →
C# -> D# : 20/19 -> 45/38 = 3*3*5*19 / 2*19*2*2*5 = 9 / 8 = 203.91000173077 →
D -> E : 19/17 -> 5/4 = 5*17 / 2*2*19 = 85 / 76 = 193.75610723294 →
D# -> F : 45/38 -> 4/3 = 2*2*2*19 / 3*3*3*5 = 152 / 135 = 205.33429967131 →
E -> F# : 5/4 -> 24/17 = 2*2*2*3*2*2 / 17*5 = 96 / 85 = 210.68587750015 →
F -> G : 4/3 -> 3/2 = 3*3 / 2*2*2 = 9 / 8 = 203.91000173077 →
F# -> G# : 24/17 -> 30/19 = 2*3*5*17 / 19*2*2*2*3 = 85 / 76 = 193.75610723294 →
G -> A : 3/2 -> 5/3 = 5*2 / 3*3 = 10 / 9 = 182.40371213406 →
G# -> A# : 30/19 -> 16/9 = 2*2*2*2*19 / 3*3*2*3*5 = 152 / 135 = 205.33429967131 →
A -> B : 5/3 -> 15/8 = 3*5*3 / 2*2*2*5 = 9 / 8 = 203.91000173077 →
A# -> C : 16/9 -> 1 = 2*1*3*3 / 1*2*2*2*2 = 9 / 8 = 203.91000173077 →
B -> C# : 15/8 -> 20/19 = 2*2*2*5*2*2*2 / 19*3*5 = 64 / 57 = 200.53198300231 →
1 x 182.4 1 x 192.6 2 x 193.8 1 x 200.5 4 x 203.9 2 x 205.3 1 x 210.7
statistics for interval minor third:
C -> D# : 1 -> 45/38 = 3*3*5*1 / 2*19*1 = 45 / 38 = 292.71069946331 →
C# -> E : 20/19 -> 5/4 = 5*19 / 2*2*2*2*5 = 19 / 16 = 297.5130161323 →
D -> F : 19/17 -> 4/3 = 2*2*17 / 3*19 = 68 / 57 = 305.48739250272 →
D# -> F# : 45/38 -> 24/17 = 2*2*2*3*2*19 / 17*3*3*5 = 304 / 255 = 304.28889190167 →
E -> G : 5/4 -> 3/2 = 3*2*2 / 2*5 = 6 / 5 = 315.64128700055 →
F -> G# : 4/3 -> 30/19 = 2*3*5*3 / 19*2*2 = 45 / 38 = 292.71069946331 →
F# -> A : 24/17 -> 5/3 = 5*17 / 3*2*2*2*3 = 85 / 72 = 287.35912163447 →
G -> A# : 3/2 -> 16/9 = 2*2*2*2*2 / 3*3*3 = 32 / 27 = 294.13499740384 →
G# -> B : 30/19 -> 15/8 = 3*5*19 / 2*2*2*2*3*5 = 19 / 16 = 297.5130161323 →
A -> C : 5/3 -> 1 = 2*1*3 / 1*5 = 6 / 5 = 315.64128700055 →
A# -> C# : 16/9 -> 20/19 = 2*2*2*5*3*3 / 19*2*2*2*2 = 45 / 38 = 292.71069946331 →
B -> D : 15/8 -> 19/17 = 2*19*2*2*2 / 17*3*5 = 304 / 255 = 304.28889190167 →
1 x 287.4 3 x 292.7 1 x 294.1 2 x 297.5 2 x 304.3 1 x 305.5 2 x 315.6
statistics for interval major third:
C -> E : 1 -> 5/4 = 5*1 / 2*2*1 = 5 / 4 = 386.31371386483 →
C# -> F : 20/19 -> 4/3 = 2*2*19 / 3*2*2*5 = 19 / 15 = 409.24430140208 →
D -> F# : 19/17 -> 24/17 = 2*2*2*3*17 / 17*19 = 24 / 19 = 404.44198473308 →
D# -> G : 45/38 -> 3/2 = 3*2*19 / 2*3*3*5 = 19 / 15 = 409.24430140208 →
E -> G# : 5/4 -> 30/19 = 2*3*5*2*2 / 19*5 = 24 / 19 = 404.44198473308 →
F -> A : 4/3 -> 5/3 = 5*3 / 3*2*2 = 5 / 4 = 386.31371386483 →
F# -> A# : 24/17 -> 16/9 = 2*2*2*2*17 / 3*3*2*2*2*3 = 34 / 27 = 399.09040690424 →
G -> B : 3/2 -> 15/8 = 3*5*2 / 2*2*2*3 = 5 / 4 = 386.31371386483 →
G# -> C : 30/19 -> 1 = 2*1*19 / 1*2*3*5 = 19 / 15 = 409.24430140208 →
A -> C# : 5/3 -> 20/19 = 2*2*2*5*3 / 19*5 = 24 / 19 = 404.44198473308 →
A# -> D : 16/9 -> 19/17 = 2*19*3*3 / 17*2*2*2*2 = 171 / 136 = 396.46760836267 →
B -> D# : 15/8 -> 45/38 = 2*3*3*5*2*2*2 / 2*19*3*5 = 24 / 19 = 404.44198473308 →
3 x 386.3 1 x 396.5 1 x 399.1 4 x 404.4 3 x 409.2
statistics for interval fourth:
C -> F : 1 -> 4/3 = 2*2*1 / 3*1 = 4 / 3 = 498.04499913461 →
C# -> F# : 20/19 -> 24/17 = 2*2*2*3*19 / 17*2*2*5 = 114 / 85 = 508.19889363245 →
D -> G : 19/17 -> 3/2 = 3*17 / 2*19 = 51 / 38 = 509.39739423349 →
D# -> G# : 45/38 -> 30/19 = 2*3*5*2*19 / 19*3*3*5 = 4 / 3 = 498.04499913461 →
E -> A : 5/4 -> 5/3 = 5*2*2 / 3*5 = 4 / 3 = 498.04499913461 →
F -> A# : 4/3 -> 16/9 = 2*2*2*2*3 / 3*3*2*2 = 4 / 3 = 498.04499913461 →
F# -> B : 24/17 -> 15/8 = 3*5*17 / 2*2*2*2*2*2*3 = 85 / 64 = 491.26912336524 →
G -> C : 3/2 -> 1 = 2*1*2 / 1*3 = 4 / 3 = 498.04499913461 →
G# -> C# : 30/19 -> 20/19 = 2*2*2*5*19 / 19*2*3*5 = 4 / 3 = 498.04499913461 →
A -> D : 5/3 -> 19/17 = 2*19*3 / 17*5 = 114 / 85 = 508.19889363245 →
A# -> D# : 16/9 -> 45/38 = 2*3*3*5*3*3 / 2*19*2*2*2*2 = 405 / 304 = 496.62070119408 →
B -> E : 15/8 -> 5/4 = 2*5*2*2*2 / 2*2*3*5 = 4 / 3 = 498.04499913461 →
1 x 491.3 1 x 496.6 7 x 498 2 x 508.2 1 x 509.4
statistics for interval tritone:
C -> F# : 1 -> 24/17 = 2*2*2*3*1 / 17*1 = 24 / 17 = 596.99959136498 →
C# -> G : 20/19 -> 3/2 = 3*19 / 2*2*2*5 = 57 / 40 = 613.15430313286 →
D -> G# : 19/17 -> 30/19 = 2*3*5*17 / 19*19 = 510 / 361 = 598.19809196602 →
D# -> A : 45/38 -> 5/3 = 5*2*19 / 3*3*3*5 = 38 / 27 = 591.64801353614 →
E -> A# : 5/4 -> 16/9 = 2*2*2*2*2*2 / 3*3*5 = 64 / 45 = 609.77628440439 →
F -> B : 4/3 -> 15/8 = 3*5*3 / 2*2*2*2*2 = 45 / 32 = 590.22371559561 →
F# -> C : 24/17 -> 1 = 2*1*17 / 1*2*2*2*3 = 17 / 12 = 603.00040863502 →
G -> C# : 3/2 -> 20/19 = 2*2*2*5*2 / 19*3 = 80 / 57 = 586.84569686714 →
G# -> D : 30/19 -> 19/17 = 2*19*19 / 17*2*3*5 = 361 / 255 = 601.80190803398 →
A -> D# : 5/3 -> 45/38 = 2*3*3*5*3 / 2*19*5 = 27 / 19 = 608.35198646386 →
A# -> E : 16/9 -> 5/4 = 2*5*3*3 / 2*2*2*2*2*2 = 45 / 32 = 590.22371559561 →
B -> F : 15/8 -> 4/3 = 2*2*2*2*2*2 / 3*3*5 = 64 / 45 = 609.77628440439 →
1 x 586.8 2 x 590.2 1 x 591.6 1 x 597 1 x 598.2 1 x 601.8 1 x 603 1 x 608.4 2 x 609.8 1 x 613.2
statistics for interval fifth:
C -> G : 1 -> 3/2 = 3*1 / 2*1 = 3 / 2 = 701.95500086539 →
C# -> G# : 20/19 -> 30/19 = 2*3*5*19 / 19*2*2*5 = 3 / 2 = 701.95500086539 →
D -> A : 19/17 -> 5/3 = 5*17 / 3*19 = 85 / 57 = 691.80110636755 →
D# -> A# : 45/38 -> 16/9 = 2*2*2*2*2*19 / 3*3*3*3*5 = 608 / 405 = 703.37929880592 →
E -> B : 5/4 -> 15/8 = 3*5*2*2 / 2*2*2*5 = 3 / 2 = 701.95500086539 →
F -> C : 4/3 -> 1 = 2*1*3 / 1*2*2 = 3 / 2 = 701.95500086539 →
F# -> C# : 24/17 -> 20/19 = 2*2*2*5*17 / 19*2*2*2*3 = 85 / 57 = 691.80110636755 →
G -> D : 3/2 -> 19/17 = 2*19*2 / 17*3 = 76 / 51 = 690.60260576651 →
G# -> D# : 30/19 -> 45/38 = 2*3*3*5*19 / 2*19*2*3*5 = 3 / 2 = 701.95500086539 →
A -> E : 5/3 -> 5/4 = 2*5*3 / 2*2*5 = 3 / 2 = 701.95500086539 →
A# -> F : 16/9 -> 4/3 = 2*2*2*3*3 / 3*2*2*2*2 = 3 / 2 = 701.95500086539 →
B -> F# : 15/8 -> 24/17 = 2*2*2*2*3*2*2*2 / 17*3*5 = 128 / 85 = 708.73087663476 →
1 x 690.6 2 x 691.8 7 x 702 1 x 703.4 1 x 708.7
statistics for interval minor sixth:
C -> G# : 1 -> 30/19 = 2*3*5*1 / 19*1 = 30 / 19 = 790.75569859792 →
C# -> A : 20/19 -> 5/3 = 5*19 / 3*2*2*5 = 19 / 12 = 795.55801526692 →
D -> A# : 19/17 -> 16/9 = 2*2*2*2*17 / 3*3*19 = 272 / 171 = 803.53239163733 →
D# -> B : 45/38 -> 15/8 = 3*5*2*19 / 2*2*2*3*3*5 = 19 / 12 = 795.55801526692 →
E -> C : 5/4 -> 1 = 2*1*2*2 / 1*5 = 8 / 5 = 813.68628613517 →
F -> C# : 4/3 -> 20/19 = 2*2*2*5*3 / 19*2*2 = 30 / 19 = 790.75569859792 →
F# -> D : 24/17 -> 19/17 = 2*19*17 / 17*2*2*2*3 = 19 / 12 = 795.55801526692 →
G -> D# : 3/2 -> 45/38 = 2*3*3*5*2 / 2*19*3 = 30 / 19 = 790.75569859792 →
G# -> E : 30/19 -> 5/4 = 2*5*19 / 2*2*2*3*5 = 19 / 12 = 795.55801526692 →
A -> F : 5/3 -> 4/3 = 2*2*2*3 / 3*5 = 8 / 5 = 813.68628613517 →
A# -> F# : 16/9 -> 24/17 = 2*2*2*2*3*3*3 / 17*2*2*2*2 = 27 / 17 = 800.90959309576 →
B -> G : 15/8 -> 3/2 = 2*3*2*2*2 / 2*3*5 = 8 / 5 = 813.68628613517 →
3 x 790.8 4 x 795.6 1 x 800.9 1 x 803.5 3 x 813.7
statistics for interval major sixth:
C -> A : 1 -> 5/3 = 5*1 / 3*1 = 5 / 3 = 884.35871299945 →
C# -> A# : 20/19 -> 16/9 = 2*2*2*2*19 / 3*3*2*2*5 = 76 / 45 = 907.28930053669 →
D -> B : 19/17 -> 15/8 = 3*5*17 / 2*2*2*19 = 255 / 152 = 895.71110809833 →
D# -> C : 45/38 -> 1 = 2*1*2*19 / 1*3*3*5 = 76 / 45 = 907.28930053669 →
E -> C# : 5/4 -> 20/19 = 2*2*2*5*2*2 / 19*5 = 32 / 19 = 902.4869838677 →
F -> D : 4/3 -> 19/17 = 2*19*3 / 17*2*2 = 57 / 34 = 894.51260749728 →
F# -> D# : 24/17 -> 45/38 = 2*3*3*5*17 / 2*19*2*2*2*3 = 255 / 152 = 895.71110809833 →
G -> E : 3/2 -> 5/4 = 2*5*2 / 2*2*3 = 5 / 3 = 884.35871299945 →
G# -> F : 30/19 -> 4/3 = 2*2*2*19 / 3*2*3*5 = 76 / 45 = 907.28930053669 →
A -> F# : 5/3 -> 24/17 = 2*2*2*2*3*3 / 17*5 = 144 / 85 = 912.64087836553 →
A# -> G : 16/9 -> 3/2 = 2*3*3*3 / 2*2*2*2*2 = 27 / 16 = 905.86500259616 →
B -> G# : 15/8 -> 30/19 = 2*2*3*5*2*2*2 / 19*3*5 = 32 / 19 = 902.4869838677 →
2 x 884.4 1 x 894.5 2 x 895.7 2 x 902.5 1 x 905.9 3 x 907.3 1 x 912.6
statistics for interval minor seventh:
C -> A# : 1 -> 16/9 = 2*2*2*2*1 / 3*3*1 = 16 / 9 = 996.08999826923 →
C# -> B : 20/19 -> 15/8 = 3*5*19 / 2*2*2*2*2*5 = 57 / 32 = 999.46801699769 →
D -> C : 19/17 -> 1 = 2*1*17 / 1*19 = 34 / 19 = 1007.4423933681 →
D# -> C# : 45/38 -> 20/19 = 2*2*2*5*2*19 / 19*3*3*5 = 16 / 9 = 996.08999826923 →
E -> D : 5/4 -> 19/17 = 2*19*2*2 / 17*5 = 152 / 85 = 1006.2438927671 →
F -> D# : 4/3 -> 45/38 = 2*3*3*5*3 / 2*19*2*2 = 135 / 76 = 994.66570032869 →
F# -> E : 24/17 -> 5/4 = 2*5*17 / 2*2*2*2*2*3 = 85 / 48 = 989.31412249985 →
G -> F : 3/2 -> 4/3 = 2*2*2*2 / 3*3 = 16 / 9 = 996.08999826923 →
G# -> F# : 30/19 -> 24/17 = 2*2*2*2*3*19 / 17*2*3*5 = 152 / 85 = 1006.2438927671 →
A -> G : 5/3 -> 3/2 = 2*3*3 / 2*5 = 9 / 5 = 1017.5962878659 →
A# -> G# : 16/9 -> 30/19 = 2*2*3*5*3*3 / 19*2*2*2*2 = 135 / 76 = 994.66570032869 →
B -> A : 15/8 -> 5/3 = 2*5*2*2*2 / 3*3*5 = 16 / 9 = 996.08999826923 →
1 x 989.3 2 x 994.7 4 x 996.1 1 x 999.5 2 x 1006.2 1 x 1007.4 1 x 1017.6
statistics for interval major seventh:
C -> B : 1 -> 15/8 = 3*5*1 / 2*2*2*1 = 15 / 8 = 1088.2687147302 →
C# -> C : 20/19 -> 1 = 2*1*19 / 1*2*2*5 = 19 / 10 = 1111.1993022675 →
D -> C# : 19/17 -> 20/19 = 2*2*2*5*17 / 19*19 = 680 / 361 = 1096.2430911006 →
D# -> D : 45/38 -> 19/17 = 2*19*2*19 / 17*3*3*5 = 1444 / 765 = 1099.8469071686 →
E -> D# : 5/4 -> 45/38 = 2*3*3*5*2*2 / 2*19*5 = 36 / 19 = 1106.3969855985 →
F -> E : 4/3 -> 5/4 = 2*5*3 / 2*2*2*2 = 15 / 8 = 1088.2687147302 →
F# -> F : 24/17 -> 4/3 = 2*2*2*17 / 3*2*2*2*3 = 17 / 9 = 1101.0454077696 →
G -> F# : 3/2 -> 24/17 = 2*2*2*2*3*2 / 17*3 = 32 / 17 = 1095.0445904996 →
G# -> G : 30/19 -> 3/2 = 2*3*19 / 2*2*3*5 = 19 / 10 = 1111.1993022675 →
A -> G# : 5/3 -> 30/19 = 2*2*3*5*3 / 19*5 = 36 / 19 = 1106.3969855985 →
A# -> A : 16/9 -> 5/3 = 2*5*3*3 / 3*2*2*2*2 = 15 / 8 = 1088.2687147302 →
B -> A# : 15/8 -> 16/9 = 2*2*2*2*2*2*2*2 / 3*3*3*5 = 256 / 135 = 1107.821283539 →
3 x 1088.3 1 x 1095 1 x 1096.2 1 x 1099.8 1 x 1101 2 x 1106.4 1 x 1107.8 2 x 1111.2
Prime Tuning
C : 1 = 0 ... +0.00
C# : 43/41 = 82.455300100817 ... -17.54
D : 19/17 = 192.5576066319 ... -7.44
D# : 13/11 = 289.20971940455 ... -10.79
E : 5/4 = 386.31371386483 ... -13.69
F : 4/3 = 498.04499913461 ... -1.96
F# : 7/5 = 582.51219260429 ... -17.49
G : 3/2 = 701.95500086539 ... +1.96
G# : 11/7 = 782.49203589563 ... -17.51
A : 5/3 = 884.35871299945 ... -15.64
A# : 23/13 = 987.7466854991 ... -12.25
B : 43/23 = 1083.2433583741 ... -16.76
statistics for interval minor second:
C -> C# : 1 -> 43/41 = 43*1 / 41*1 = 43 / 41 = 82.455300100817 →
C# -> D : 43/41 -> 19/17 = 19*41 / 17*43 = 779 / 731 = 110.10230653108 →
D -> D# : 19/17 -> 13/11 = 13*17 / 11*19 = 221 / 209 = 96.652112772659 →
D# -> E : 13/11 -> 5/4 = 5*11 / 2*2*13 = 55 / 52 = 97.103994460281 →
E -> F : 5/4 -> 4/3 = 2*2*2*2 / 3*5 = 16 / 15 = 111.73128526978 →
F -> F# : 4/3 -> 7/5 = 7*3 / 5*2*2 = 21 / 20 = 84.467193469678 →
F# -> G : 7/5 -> 3/2 = 3*5 / 2*7 = 15 / 14 = 119.4428082611 →
G -> G# : 3/2 -> 11/7 = 11*2 / 7*3 = 22 / 21 = 80.537035030244 →
G# -> A : 11/7 -> 5/3 = 5*7 / 3*11 = 35 / 33 = 101.86667710382 →
A -> A# : 5/3 -> 23/13 = 23*3 / 13*5 = 69 / 65 = 103.38797249966 →
A# -> B : 23/13 -> 43/23 = 43*13 / 23*23 = 559 / 529 = 95.496672874997 →
B -> C : 43/23 -> 1 = 2*1*23 / 1*43 = 46 / 43 = 116.7566416259 →
1 x 80.5 1 x 82.5 1 x 84.5 1 x 95.5 1 x 96.7 1 x 97.1 1 x 101.9 1 x 103.4 1 x 110.1 1 x 111.7 1 x 116.8 1 x 119.4
statistics for interval major second:
C -> D : 1 -> 19/17 = 19*1 / 17*1 = 19 / 17 = 192.5576066319 →
C# -> D# : 43/41 -> 13/11 = 13*41 / 11*43 = 533 / 473 = 206.75441930374 →
D -> E : 19/17 -> 5/4 = 5*17 / 2*2*19 = 85 / 76 = 193.75610723294 →
D# -> F : 13/11 -> 4/3 = 2*2*11 / 3*13 = 44 / 39 = 208.83527973006 →
E -> F# : 5/4 -> 7/5 = 7*2*2 / 5*5 = 28 / 25 = 196.19847873946 →
F -> G : 4/3 -> 3/2 = 3*3 / 2*2*2 = 9 / 8 = 203.91000173077 →
F# -> G# : 7/5 -> 11/7 = 11*5 / 7*7 = 55 / 49 = 199.97984329134 →
G -> A : 3/2 -> 5/3 = 5*2 / 3*3 = 10 / 9 = 182.40371213406 →
G# -> A# : 11/7 -> 23/13 = 23*7 / 13*11 = 161 / 143 = 205.25464960347 →
A -> B : 5/3 -> 43/23 = 43*3 / 23*5 = 129 / 115 = 198.88464537465 →
A# -> C : 23/13 -> 1 = 2*1*13 / 1*23 = 26 / 23 = 212.2533145009 →
B -> C# : 43/23 -> 43/41 = 2*43*23 / 41*43 = 46 / 41 = 199.21194172671 →
1 x 182.4 1 x 192.6 1 x 193.8 1 x 196.2 1 x 198.9 1 x 199.2 1 x 200 1 x 203.9 1 x 205.3 1 x 206.8 1 x 208.8 1 x 212.3
statistics for interval minor third:
C -> D# : 1 -> 13/11 = 13*1 / 11*1 = 13 / 11 = 289.20971940455 →
C# -> E : 43/41 -> 5/4 = 5*41 / 2*2*43 = 205 / 172 = 303.85841376402 →
D -> F : 19/17 -> 4/3 = 2*2*17 / 3*19 = 68 / 57 = 305.48739250272 →
D# -> F# : 13/11 -> 7/5 = 7*11 / 5*13 = 77 / 65 = 293.30247319974 →
E -> G : 5/4 -> 3/2 = 3*2*2 / 2*5 = 6 / 5 = 315.64128700055 →
F -> G# : 4/3 -> 11/7 = 11*3 / 7*2*2 = 33 / 28 = 284.44703676102 →
F# -> A : 7/5 -> 5/3 = 5*5 / 3*7 = 25 / 21 = 301.84652039516 →
G -> A# : 3/2 -> 23/13 = 23*2 / 13*3 = 46 / 39 = 285.79168463372 →
G# -> B : 11/7 -> 43/23 = 43*7 / 23*11 = 301 / 253 = 300.75132247847 →
A -> C : 5/3 -> 1 = 2*1*3 / 1*5 = 6 / 5 = 315.64128700055 →
A# -> C# : 23/13 -> 43/41 = 2*43*13 / 41*23 = 1118 / 943 = 294.70861460171 →
B -> D : 43/23 -> 19/17 = 2*19*23 / 17*43 = 874 / 731 = 309.31424825779 →
1 x 284.4 1 x 285.8 1 x 289.2 1 x 293.3 1 x 294.7 1 x 300.8 1 x 301.8 1 x 303.9 1 x 305.5 1 x 309.3 2 x 315.6
statistics for interval major third:
C -> E : 1 -> 5/4 = 5*1 / 2*2*1 = 5 / 4 = 386.31371386483 →
C# -> F : 43/41 -> 4/3 = 2*2*41 / 3*43 = 164 / 129 = 415.5896990338 →
D -> F# : 19/17 -> 7/5 = 7*17 / 5*19 = 119 / 95 = 389.95458597239 →
D# -> G : 13/11 -> 3/2 = 3*11 / 2*13 = 33 / 26 = 412.74528146083 →
E -> G# : 5/4 -> 11/7 = 11*2*2 / 7*5 = 44 / 35 = 396.1783220308 →
F -> A : 4/3 -> 5/3 = 5*3 / 3*2*2 = 5 / 4 = 386.31371386483 →
F# -> A# : 7/5 -> 23/13 = 23*5 / 13*7 = 115 / 91 = 405.23449289481 →
G -> B : 3/2 -> 43/23 = 43*2 / 23*3 = 86 / 69 = 381.28835750871 →
G# -> C : 11/7 -> 1 = 2*1*7 / 1*11 = 14 / 11 = 417.50796410437 →
A -> C# : 5/3 -> 43/41 = 2*43*3 / 41*5 = 258 / 205 = 398.09658710137 →
A# -> D : 23/13 -> 19/17 = 2*19*13 / 17*23 = 494 / 391 = 404.81092113279 →
B -> D# : 43/23 -> 13/11 = 2*13*23 / 11*43 = 598 / 473 = 405.96636103045 →
1 x 381.3 2 x 386.3 1 x 390 1 x 396.2 1 x 398.1 1 x 404.8 1 x 405.2 1 x 406 1 x 412.7 1 x 415.6 1 x 417.5
statistics for interval fourth:
C -> F : 1 -> 4/3 = 2*2*1 / 3*1 = 4 / 3 = 498.04499913461 →
C# -> F# : 43/41 -> 7/5 = 7*41 / 5*43 = 287 / 215 = 500.05689250347 →
D -> G : 19/17 -> 3/2 = 3*17 / 2*19 = 51 / 38 = 509.39739423349 →
D# -> G# : 13/11 -> 11/7 = 11*11 / 7*13 = 121 / 91 = 493.28231649108 →
E -> A : 5/4 -> 5/3 = 5*2*2 / 3*5 = 4 / 3 = 498.04499913461 →
F -> A# : 4/3 -> 23/13 = 23*3 / 13*2*2 = 69 / 52 = 489.70168636449 →
F# -> B : 7/5 -> 43/23 = 43*5 / 23*7 = 215 / 161 = 500.73116576981 →
G -> C : 3/2 -> 1 = 2*1*2 / 1*3 = 4 / 3 = 498.04499913461 →
G# -> C# : 11/7 -> 43/41 = 2*43*7 / 41*11 = 602 / 451 = 499.96326420519 →
A -> D : 5/3 -> 19/17 = 2*19*3 / 17*5 = 114 / 85 = 508.19889363245 →
A# -> D# : 23/13 -> 13/11 = 2*13*13 / 11*23 = 338 / 253 = 501.46303390545 →
B -> E : 43/23 -> 5/4 = 2*5*23 / 2*2*43 = 115 / 86 = 503.07035549073 →
1 x 489.7 1 x 493.3 3 x 498 1 x 500 1 x 500.1 1 x 500.7 1 x 501.5 1 x 503.1 1 x 508.2 1 x 509.4
statistics for interval tritone:
C -> F# : 1 -> 7/5 = 7*1 / 5*1 = 7 / 5 = 582.51219260429 →
C# -> G : 43/41 -> 3/2 = 3*41 / 2*43 = 123 / 86 = 619.49970076457 →
D -> G# : 19/17 -> 11/7 = 11*17 / 7*19 = 187 / 133 = 589.93442926374 →
D# -> A : 13/11 -> 5/3 = 5*11 / 3*13 = 55 / 39 = 595.14899359489 →
E -> A# : 5/4 -> 23/13 = 23*2*2 / 13*5 = 92 / 65 = 601.43297163427 →
F -> B : 4/3 -> 43/23 = 43*3 / 23*2*2 = 129 / 92 = 585.19835923949 →
F# -> C : 7/5 -> 1 = 2*1*5 / 1*7 = 10 / 7 = 617.48780739571 →
G -> C# : 3/2 -> 43/41 = 2*43*2 / 41*3 = 172 / 123 = 580.50029923543 →
G# -> D : 11/7 -> 19/17 = 2*19*7 / 17*11 = 266 / 187 = 610.06557073626 →
A -> D# : 5/3 -> 13/11 = 2*13*3 / 11*5 = 78 / 55 = 604.85100640511 →
A# -> E : 23/13 -> 5/4 = 2*5*13 / 2*2*23 = 65 / 46 = 598.56702836573 →
B -> F : 43/23 -> 4/3 = 2*2*2*23 / 3*43 = 184 / 129 = 614.80164076051 →
1 x 580.5 1 x 582.5 1 x 585.2 1 x 589.9 1 x 595.1 1 x 598.6 1 x 601.4 1 x 604.9 1 x 610.1 1 x 614.8 1 x 617.5 1 x 619.5
statistics for interval fifth:
C -> G : 1 -> 3/2 = 3*1 / 2*1 = 3 / 2 = 701.95500086539 →
C# -> G# : 43/41 -> 11/7 = 11*41 / 7*43 = 451 / 301 = 700.03673579481 →
D -> A : 19/17 -> 5/3 = 5*17 / 3*19 = 85 / 57 = 691.80110636755 →
D# -> A# : 13/11 -> 23/13 = 23*11 / 13*13 = 253 / 169 = 698.53696609455 →
E -> B : 5/4 -> 43/23 = 43*2*2 / 23*5 = 172 / 115 = 696.92964450927 →
F -> C : 4/3 -> 1 = 2*1*3 / 1*2*2 = 3 / 2 = 701.95500086539 →
F# -> C# : 7/5 -> 43/41 = 2*43*5 / 41*7 = 430 / 287 = 699.94310749653 →
G -> D : 3/2 -> 19/17 = 2*19*2 / 17*3 = 76 / 51 = 690.60260576651 →
G# -> D# : 11/7 -> 13/11 = 2*13*7 / 11*11 = 182 / 121 = 706.71768350892 →
A -> E : 5/3 -> 5/4 = 2*5*3 / 2*2*5 = 3 / 2 = 701.95500086539 →
A# -> F : 23/13 -> 4/3 = 2*2*2*13 / 3*23 = 104 / 69 = 710.29831363551 →
B -> F# : 43/23 -> 7/5 = 2*7*23 / 5*43 = 322 / 215 = 699.26883423019 →
1 x 690.6 1 x 691.8 1 x 696.9 1 x 698.5 1 x 699.3 1 x 699.9 1 x 700 3 x 702 1 x 706.7 1 x 710.3
statistics for interval minor sixth:
C -> G# : 1 -> 11/7 = 11*1 / 7*1 = 11 / 7 = 782.49203589563 →
C# -> A : 43/41 -> 5/3 = 5*41 / 3*43 = 205 / 129 = 801.90341289863 →
D -> A# : 19/17 -> 23/13 = 23*17 / 13*19 = 391 / 247 = 795.18907886721 →
D# -> B : 13/11 -> 43/23 = 43*11 / 23*13 = 473 / 299 = 794.03363896955 →
E -> C : 5/4 -> 1 = 2*1*2*2 / 1*5 = 8 / 5 = 813.68628613517 →
F -> C# : 4/3 -> 43/41 = 2*43*3 / 41*2*2 = 129 / 82 = 784.4103009662 →
F# -> D : 7/5 -> 19/17 = 2*19*5 / 17*7 = 190 / 119 = 810.04541402761 →
G -> D# : 3/2 -> 13/11 = 2*13*2 / 11*3 = 52 / 33 = 787.25471853917 →
G# -> E : 11/7 -> 5/4 = 2*5*7 / 2*2*11 = 35 / 22 = 803.8216779692 →
A -> F : 5/3 -> 4/3 = 2*2*2*3 / 3*5 = 8 / 5 = 813.68628613517 →
A# -> F# : 23/13 -> 7/5 = 2*7*13 / 5*23 = 182 / 115 = 794.76550710519 →
B -> G : 43/23 -> 3/2 = 2*3*23 / 2*43 = 69 / 43 = 818.71164249129 →
1 x 782.5 1 x 784.4 1 x 787.3 1 x 794 1 x 794.8 1 x 795.2 1 x 801.9 1 x 803.8 1 x 810 2 x 813.7 1 x 818.7
statistics for interval major sixth:
C -> A : 1 -> 5/3 = 5*1 / 3*1 = 5 / 3 = 884.35871299945 →
C# -> A# : 43/41 -> 23/13 = 23*41 / 13*43 = 943 / 559 = 905.29138539829 →
D -> B : 19/17 -> 43/23 = 43*17 / 23*19 = 731 / 437 = 890.68575174221 →
D# -> C : 13/11 -> 1 = 2*1*11 / 1*13 = 22 / 13 = 910.79028059545 →
E -> C# : 5/4 -> 43/41 = 2*43*2*2 / 41*5 = 344 / 205 = 896.14158623598 →
F -> D : 4/3 -> 19/17 = 2*19*3 / 17*2*2 = 57 / 34 = 894.51260749728 →
F# -> D# : 7/5 -> 13/11 = 2*13*5 / 11*7 = 130 / 77 = 906.69752680026 →
G -> E : 3/2 -> 5/4 = 2*5*2 / 2*2*3 = 5 / 3 = 884.35871299945 →
G# -> F : 11/7 -> 4/3 = 2*2*2*7 / 3*11 = 56 / 33 = 915.55296323898 →
A -> F# : 5/3 -> 7/5 = 2*7*3 / 5*5 = 42 / 25 = 898.15347960484 →
A# -> G : 23/13 -> 3/2 = 2*3*13 / 2*23 = 39 / 23 = 914.20831536628 →
B -> G# : 43/23 -> 11/7 = 2*11*23 / 7*43 = 506 / 301 = 899.24867752153 →
2 x 884.4 1 x 890.7 1 x 894.5 1 x 896.1 1 x 898.2 1 x 899.2 1 x 905.3 1 x 906.7 1 x 910.8 1 x 914.2 1 x 915.6
statistics for interval minor seventh:
C -> A# : 1 -> 23/13 = 23*1 / 13*1 = 23 / 13 = 987.7466854991 →
C# -> B : 43/41 -> 43/23 = 43*41 / 23*43 = 41 / 23 = 1000.7880582733 →
D -> C : 19/17 -> 1 = 2*1*17 / 1*19 = 34 / 19 = 1007.4423933681 →
D# -> C# : 13/11 -> 43/41 = 2*43*11 / 41*13 = 946 / 533 = 993.24558069626 →
E -> D : 5/4 -> 19/17 = 2*19*2*2 / 17*5 = 152 / 85 = 1006.2438927671 →
F -> D# : 4/3 -> 13/11 = 2*13*3 / 11*2*2 = 39 / 22 = 991.16472026994 →
F# -> E : 7/5 -> 5/4 = 2*5*5 / 2*2*7 = 25 / 14 = 1003.8015212605 →
G -> F : 3/2 -> 4/3 = 2*2*2*2 / 3*3 = 16 / 9 = 996.08999826923 →
G# -> F# : 11/7 -> 7/5 = 2*7*7 / 5*11 = 98 / 55 = 1000.0201567087 →
A -> G : 5/3 -> 3/2 = 2*3*3 / 2*5 = 9 / 5 = 1017.5962878659 →
A# -> G# : 23/13 -> 11/7 = 2*11*13 / 7*23 = 286 / 161 = 994.74535039653 →
B -> A : 43/23 -> 5/3 = 2*5*23 / 3*43 = 230 / 129 = 1001.1153546253 →
1 x 987.7 1 x 991.2 1 x 993.2 1 x 994.7 1 x 996.1 1 x 1000 1 x 1000.8 1 x 1001.1 1 x 1003.8 1 x 1006.2 1 x 1007.4 1 x 1017.6
statistics for interval major seventh:
C -> B : 1 -> 43/23 = 43*1 / 23*1 = 43 / 23 = 1083.2433583741 →
C# -> C : 43/41 -> 1 = 2*1*41 / 1*43 = 82 / 43 = 1117.5446998992 →
D -> C# : 19/17 -> 43/41 = 2*43*17 / 41*19 = 1462 / 779 = 1089.8976934689 →
D# -> D : 13/11 -> 19/17 = 2*19*11 / 17*13 = 418 / 221 = 1103.3478872273 →
E -> D# : 5/4 -> 13/11 = 2*13*2*2 / 11*5 = 104 / 55 = 1102.8960055397 →
F -> E : 4/3 -> 5/4 = 2*5*3 / 2*2*2*2 = 15 / 8 = 1088.2687147302 →
F# -> F : 7/5 -> 4/3 = 2*2*2*5 / 3*7 = 40 / 21 = 1115.5328065303 →
G -> F# : 3/2 -> 7/5 = 2*7*2 / 5*3 = 28 / 15 = 1080.5571917389 →
G# -> G : 11/7 -> 3/2 = 2*3*7 / 2*11 = 21 / 11 = 1119.4629649698 →
A -> G# : 5/3 -> 11/7 = 2*11*3 / 7*5 = 66 / 35 = 1098.1333228962 →
A# -> A : 23/13 -> 5/3 = 2*5*13 / 3*23 = 130 / 69 = 1096.6120275003 →
B -> A# : 43/23 -> 23/13 = 2*23*23 / 13*43 = 1058 / 559 = 1104.503327125 →
1 x 1080.6 1 x 1083.2 1 x 1088.3 1 x 1089.9 1 x 1096.6 1 x 1098.1 1 x 1102.9 1 x 1103.3 1 x 1104.5 1 x 1115.5 1 x 1117.5 1 x 1119.5
Just intonation
C : 1 = 0 ... +0.00
C# : 16/15 = 111.73128526978 ... +11.73
D : 9/8 = 203.91000173077 ... +3.91
D# : 6/5 = 315.64128700055 ... +15.64
E : 5/4 = 386.31371386483 ... -13.69
F : 4/3 = 498.04499913461 ... -1.96
F# : 7/5 = 582.51219260429 ... -17.49
G : 3/2 = 701.95500086539 ... +1.96
G# : 8/5 = 813.68628613517 ... +13.69
A : 5/3 = 884.35871299945 ... -15.64
A# : 16/9 = 996.08999826923 ... -3.91
B : 15/8 = 1088.2687147302 ... -11.73
statistics for interval minor second:
C -> C# : 1 -> 16/15 = 2*2*2*2*1 / 3*5*1 = 16 / 15 = 111.73128526978 →
C# -> D : 16/15 -> 9/8 = 3*3*3*5 / 2*2*2*2*2*2*2 = 135 / 128 = 92.178716460997 →
D -> D# : 9/8 -> 6/5 = 2*3*2*2*2 / 5*3*3 = 16 / 15 = 111.73128526978 →
D# -> E : 6/5 -> 5/4 = 5*5 / 2*2*2*3 = 25 / 24 = 70.672426864282 →
E -> F : 5/4 -> 4/3 = 2*2*2*2 / 3*5 = 16 / 15 = 111.73128526978 →
F -> F# : 4/3 -> 7/5 = 7*3 / 5*2*2 = 21 / 20 = 84.467193469678 →
F# -> G : 7/5 -> 3/2 = 3*5 / 2*7 = 15 / 14 = 119.4428082611 →
G -> G# : 3/2 -> 8/5 = 2*2*2*2 / 5*3 = 16 / 15 = 111.73128526978 →
G# -> A : 8/5 -> 5/3 = 5*5 / 3*2*2*2 = 25 / 24 = 70.672426864282 →
A -> A# : 5/3 -> 16/9 = 2*2*2*2*3 / 3*3*5 = 16 / 15 = 111.73128526978 →
A# -> B : 16/9 -> 15/8 = 3*5*3*3 / 2*2*2*2*2*2*2 = 135 / 128 = 92.178716460997 →
B -> C : 15/8 -> 1 = 2*1*2*2*2 / 1*3*5 = 16 / 15 = 111.73128526978 →
2 x 70.7 1 x 84.5 2 x 92.2 6 x 111.7 1 x 119.4
statistics for interval major second:
C -> D : 1 -> 9/8 = 3*3*1 / 2*2*2*1 = 9 / 8 = 203.91000173077 →
C# -> D# : 16/15 -> 6/5 = 2*3*3*5 / 5*2*2*2*2 = 9 / 8 = 203.91000173077 →
D -> E : 9/8 -> 5/4 = 5*2*2*2 / 2*2*3*3 = 10 / 9 = 182.40371213406 →
D# -> F : 6/5 -> 4/3 = 2*2*5 / 3*2*3 = 10 / 9 = 182.40371213406 →
E -> F# : 5/4 -> 7/5 = 7*2*2 / 5*5 = 28 / 25 = 196.19847873946 →
F -> G : 4/3 -> 3/2 = 3*3 / 2*2*2 = 9 / 8 = 203.91000173077 →
F# -> G# : 7/5 -> 8/5 = 2*2*2*5 / 5*7 = 8 / 7 = 231.17409353088 →
G -> A : 3/2 -> 5/3 = 5*2 / 3*3 = 10 / 9 = 182.40371213406 →
G# -> A# : 8/5 -> 16/9 = 2*2*2*2*5 / 3*3*2*2*2 = 10 / 9 = 182.40371213406 →
A -> B : 5/3 -> 15/8 = 3*5*3 / 2*2*2*5 = 9 / 8 = 203.91000173077 →
A# -> C : 16/9 -> 1 = 2*1*3*3 / 1*2*2*2*2 = 9 / 8 = 203.91000173077 →
B -> C# : 15/8 -> 16/15 = 2*2*2*2*2*2*2*2 / 3*5*3*5 = 256 / 225 = 223.46257053956 →
4 x 182.4 1 x 196.2 5 x 203.9 1 x 223.5 1 x 231.2
statistics for interval minor third:
C -> D# : 1 -> 6/5 = 2*3*1 / 5*1 = 6 / 5 = 315.64128700055 →
C# -> E : 16/15 -> 5/4 = 5*3*5 / 2*2*2*2*2*2 = 75 / 64 = 274.58242859506 →
D -> F : 9/8 -> 4/3 = 2*2*2*2*2 / 3*3*3 = 32 / 27 = 294.13499740384 →
D# -> F# : 6/5 -> 7/5 = 7*5 / 5*2*3 = 7 / 6 = 266.87090560374 →
E -> G : 5/4 -> 3/2 = 3*2*2 / 2*5 = 6 / 5 = 315.64128700055 →
F -> G# : 4/3 -> 8/5 = 2*2*2*3 / 5*2*2 = 6 / 5 = 315.64128700055 →
F# -> A : 7/5 -> 5/3 = 5*5 / 3*7 = 25 / 21 = 301.84652039516 →
G -> A# : 3/2 -> 16/9 = 2*2*2*2*2 / 3*3*3 = 32 / 27 = 294.13499740384 →
G# -> B : 8/5 -> 15/8 = 3*5*5 / 2*2*2*2*2*2 = 75 / 64 = 274.58242859506 →
A -> C : 5/3 -> 1 = 2*1*3 / 1*5 = 6 / 5 = 315.64128700055 →
A# -> C# : 16/9 -> 16/15 = 2*2*2*2*2*3*3 / 3*5*2*2*2*2 = 6 / 5 = 315.64128700055 →
B -> D : 15/8 -> 9/8 = 2*3*3*2*2*2 / 2*2*2*3*5 = 6 / 5 = 315.64128700055 →
1 x 266.9 2 x 274.6 2 x 294.1 1 x 301.8 6 x 315.6
statistics for interval major third:
C -> E : 1 -> 5/4 = 5*1 / 2*2*1 = 5 / 4 = 386.31371386483 →
C# -> F : 16/15 -> 4/3 = 2*2*3*5 / 3*2*2*2*2 = 5 / 4 = 386.31371386483 →
D -> F# : 9/8 -> 7/5 = 7*2*2*2 / 5*3*3 = 56 / 45 = 378.60219087352 →
D# -> G : 6/5 -> 3/2 = 3*5 / 2*2*3 = 5 / 4 = 386.31371386483 →
E -> G# : 5/4 -> 8/5 = 2*2*2*2*2 / 5*5 = 32 / 25 = 427.37257227033 →
F -> A : 4/3 -> 5/3 = 5*3 / 3*2*2 = 5 / 4 = 386.31371386483 →
F# -> A# : 7/5 -> 16/9 = 2*2*2*2*5 / 3*3*7 = 80 / 63 = 413.57780566494 →
G -> B : 3/2 -> 15/8 = 3*5*2 / 2*2*2*3 = 5 / 4 = 386.31371386483 →
G# -> C : 8/5 -> 1 = 2*1*5 / 1*2*2*2 = 5 / 4 = 386.31371386483 →
A -> C# : 5/3 -> 16/15 = 2*2*2*2*2*3 / 3*5*5 = 32 / 25 = 427.37257227033 →
A# -> D : 16/9 -> 9/8 = 2*3*3*3*3 / 2*2*2*2*2*2*2 = 81 / 64 = 407.82000346155 →
B -> D# : 15/8 -> 6/5 = 2*2*3*2*2*2 / 5*3*5 = 32 / 25 = 427.37257227033 →
1 x 378.6 6 x 386.3 1 x 407.8 1 x 413.6 3 x 427.4
statistics for interval fourth:
C -> F : 1 -> 4/3 = 2*2*1 / 3*1 = 4 / 3 = 498.04499913461 →
C# -> F# : 16/15 -> 7/5 = 7*3*5 / 5*2*2*2*2 = 21 / 16 = 470.78090733451 →
D -> G : 9/8 -> 3/2 = 3*2*2*2 / 2*3*3 = 4 / 3 = 498.04499913461 →
D# -> G# : 6/5 -> 8/5 = 2*2*2*5 / 5*2*3 = 4 / 3 = 498.04499913461 →
E -> A : 5/4 -> 5/3 = 5*2*2 / 3*5 = 4 / 3 = 498.04499913461 →
F -> A# : 4/3 -> 16/9 = 2*2*2*2*3 / 3*3*2*2 = 4 / 3 = 498.04499913461 →
F# -> B : 7/5 -> 15/8 = 3*5*5 / 2*2*2*7 = 75 / 56 = 505.75652212593 →
G -> C : 3/2 -> 1 = 2*1*2 / 1*3 = 4 / 3 = 498.04499913461 →
G# -> C# : 8/5 -> 16/15 = 2*2*2*2*2*5 / 3*5*2*2*2 = 4 / 3 = 498.04499913461 →
A -> D : 5/3 -> 9/8 = 2*3*3*3 / 2*2*2*5 = 27 / 20 = 519.55128873133 →
A# -> D# : 16/9 -> 6/5 = 2*2*3*3*3 / 5*2*2*2*2 = 27 / 20 = 519.55128873133 →
B -> E : 15/8 -> 5/4 = 2*5*2*2*2 / 2*2*3*5 = 4 / 3 = 498.04499913461 →
1 x 470.8 8 x 498 1 x 505.8 2 x 519.6
statistics for interval tritone:
C -> F# : 1 -> 7/5 = 7*1 / 5*1 = 7 / 5 = 582.51219260429 →
C# -> G : 16/15 -> 3/2 = 3*3*5 / 2*2*2*2*2 = 45 / 32 = 590.22371559561 →
D -> G# : 9/8 -> 8/5 = 2*2*2*2*2*2 / 5*3*3 = 64 / 45 = 609.77628440439 →
D# -> A : 6/5 -> 5/3 = 5*5 / 3*2*3 = 25 / 18 = 568.71742599889 →
E -> A# : 5/4 -> 16/9 = 2*2*2*2*2*2 / 3*3*5 = 64 / 45 = 609.77628440439 →
F -> B : 4/3 -> 15/8 = 3*5*3 / 2*2*2*2*2 = 45 / 32 = 590.22371559561 →
F# -> C : 7/5 -> 1 = 2*1*5 / 1*7 = 10 / 7 = 617.48780739571 →
G -> C# : 3/2 -> 16/15 = 2*2*2*2*2*2 / 3*5*3 = 64 / 45 = 609.77628440439 →
G# -> D : 8/5 -> 9/8 = 2*3*3*5 / 2*2*2*2*2*2 = 45 / 32 = 590.22371559561 →
A -> D# : 5/3 -> 6/5 = 2*2*3*3 / 5*5 = 36 / 25 = 631.28257400111 →
A# -> E : 16/9 -> 5/4 = 2*5*3*3 / 2*2*2*2*2*2 = 45 / 32 = 590.22371559561 →
B -> F : 15/8 -> 4/3 = 2*2*2*2*2*2 / 3*3*5 = 64 / 45 = 609.77628440439 →
1 x 568.7 1 x 582.5 4 x 590.2 4 x 609.8 1 x 617.5 1 x 631.3
statistics for interval fifth:
C -> G : 1 -> 3/2 = 3*1 / 2*1 = 3 / 2 = 701.95500086539 →
C# -> G# : 16/15 -> 8/5 = 2*2*2*3*5 / 5*2*2*2*2 = 3 / 2 = 701.95500086539 →
D -> A : 9/8 -> 5/3 = 5*2*2*2 / 3*3*3 = 40 / 27 = 680.44871126867 →
D# -> A# : 6/5 -> 16/9 = 2*2*2*2*5 / 3*3*2*3 = 40 / 27 = 680.44871126867 →
E -> B : 5/4 -> 15/8 = 3*5*2*2 / 2*2*2*5 = 3 / 2 = 701.95500086539 →
F -> C : 4/3 -> 1 = 2*1*3 / 1*2*2 = 3 / 2 = 701.95500086539 →
F# -> C# : 7/5 -> 16/15 = 2*2*2*2*2*5 / 3*5*7 = 32 / 21 = 729.21909266549 →
G -> D : 3/2 -> 9/8 = 2*3*3*2 / 2*2*2*3 = 3 / 2 = 701.95500086539 →
G# -> D# : 8/5 -> 6/5 = 2*2*3*5 / 5*2*2*2 = 3 / 2 = 701.95500086539 →
A -> E : 5/3 -> 5/4 = 2*5*3 / 2*2*5 = 3 / 2 = 701.95500086539 →
A# -> F : 16/9 -> 4/3 = 2*2*2*3*3 / 3*2*2*2*2 = 3 / 2 = 701.95500086539 →
B -> F# : 15/8 -> 7/5 = 2*7*2*2*2 / 5*3*5 = 112 / 75 = 694.24347787407 →
2 x 680.4 1 x 694.2 8 x 702 1 x 729.2
statistics for interval minor sixth:
C -> G# : 1 -> 8/5 = 2*2*2*1 / 5*1 = 8 / 5 = 813.68628613517 →
C# -> A : 16/15 -> 5/3 = 5*3*5 / 3*2*2*2*2 = 25 / 16 = 772.62742772967 →
D -> A# : 9/8 -> 16/9 = 2*2*2*2*2*2*2 / 3*3*3*3 = 128 / 81 = 792.17999653845 →
D# -> B : 6/5 -> 15/8 = 3*5*5 / 2*2*2*2*3 = 25 / 16 = 772.62742772967 →
E -> C : 5/4 -> 1 = 2*1*2*2 / 1*5 = 8 / 5 = 813.68628613517 →
F -> C# : 4/3 -> 16/15 = 2*2*2*2*2*3 / 3*5*2*2 = 8 / 5 = 813.68628613517 →
F# -> D : 7/5 -> 9/8 = 2*3*3*5 / 2*2*2*7 = 45 / 28 = 821.39780912648 →
G -> D# : 3/2 -> 6/5 = 2*2*3*2 / 5*3 = 8 / 5 = 813.68628613517 →
G# -> E : 8/5 -> 5/4 = 2*5*5 / 2*2*2*2*2 = 25 / 16 = 772.62742772967 →
A -> F : 5/3 -> 4/3 = 2*2*2*3 / 3*5 = 8 / 5 = 813.68628613517 →
A# -> F# : 16/9 -> 7/5 = 2*7*3*3 / 5*2*2*2*2 = 63 / 40 = 786.42219433506 →
B -> G : 15/8 -> 3/2 = 2*3*2*2*2 / 2*3*5 = 8 / 5 = 813.68628613517 →
3 x 772.6 1 x 786.4 1 x 792.2 6 x 813.7 1 x 821.4
statistics for interval major sixth:
C -> A : 1 -> 5/3 = 5*1 / 3*1 = 5 / 3 = 884.35871299945 →
C# -> A# : 16/15 -> 16/9 = 2*2*2*2*3*5 / 3*3*2*2*2*2 = 5 / 3 = 884.35871299945 →
D -> B : 9/8 -> 15/8 = 3*5*2*2*2 / 2*2*2*3*3 = 5 / 3 = 884.35871299945 →
D# -> C : 6/5 -> 1 = 2*1*5 / 1*2*3 = 5 / 3 = 884.35871299945 →
E -> C# : 5/4 -> 16/15 = 2*2*2*2*2*2*2 / 3*5*5 = 128 / 75 = 925.41757140494 →
F -> D : 4/3 -> 9/8 = 2*3*3*3 / 2*2*2*2*2 = 27 / 16 = 905.86500259616 →
F# -> D# : 7/5 -> 6/5 = 2*2*3*5 / 5*7 = 12 / 7 = 933.12909439626 →
G -> E : 3/2 -> 5/4 = 2*5*2 / 2*2*3 = 5 / 3 = 884.35871299945 →
G# -> F : 8/5 -> 4/3 = 2*2*2*5 / 3*2*2*2 = 5 / 3 = 884.35871299945 →
A -> F# : 5/3 -> 7/5 = 2*7*3 / 5*5 = 42 / 25 = 898.15347960484 →
A# -> G : 16/9 -> 3/2 = 2*3*3*3 / 2*2*2*2*2 = 27 / 16 = 905.86500259616 →
B -> G# : 15/8 -> 8/5 = 2*2*2*2*2*2*2 / 5*3*5 = 128 / 75 = 925.41757140494 →
6 x 884.4 1 x 898.2 2 x 905.9 2 x 925.4 1 x 933.1
statistics for interval minor seventh:
C -> A# : 1 -> 16/9 = 2*2*2*2*1 / 3*3*1 = 16 / 9 = 996.08999826923 →
C# -> B : 16/15 -> 15/8 = 3*5*3*5 / 2*2*2*2*2*2*2 = 225 / 128 = 976.53742946044 →
D -> C : 9/8 -> 1 = 2*1*2*2*2 / 1*3*3 = 16 / 9 = 996.08999826923 →
D# -> C# : 6/5 -> 16/15 = 2*2*2*2*2*5 / 3*5*2*3 = 16 / 9 = 996.08999826923 →
E -> D : 5/4 -> 9/8 = 2*3*3*2*2 / 2*2*2*5 = 9 / 5 = 1017.5962878659 →
F -> D# : 4/3 -> 6/5 = 2*2*3*3 / 5*2*2 = 9 / 5 = 1017.5962878659 →
F# -> E : 7/5 -> 5/4 = 2*5*5 / 2*2*7 = 25 / 14 = 1003.8015212605 →
G -> F : 3/2 -> 4/3 = 2*2*2*2 / 3*3 = 16 / 9 = 996.08999826923 →
G# -> F# : 8/5 -> 7/5 = 2*7*5 / 5*2*2*2 = 7 / 4 = 968.82590646912 →
A -> G : 5/3 -> 3/2 = 2*3*3 / 2*5 = 9 / 5 = 1017.5962878659 →
A# -> G# : 16/9 -> 8/5 = 2*2*2*2*3*3 / 5*2*2*2*2 = 9 / 5 = 1017.5962878659 →
B -> A : 15/8 -> 5/3 = 2*5*2*2*2 / 3*3*5 = 16 / 9 = 996.08999826923 →
1 x 968.8 1 x 976.5 5 x 996.1 1 x 1003.8 4 x 1017.6
statistics for interval major seventh:
C -> B : 1 -> 15/8 = 3*5*1 / 2*2*2*1 = 15 / 8 = 1088.2687147302 →
C# -> C : 16/15 -> 1 = 2*1*3*5 / 1*2*2*2*2 = 15 / 8 = 1088.2687147302 →
D -> C# : 9/8 -> 16/15 = 2*2*2*2*2*2*2*2 / 3*5*3*3 = 256 / 135 = 1107.821283539 →
D# -> D : 6/5 -> 9/8 = 2*3*3*5 / 2*2*2*2*3 = 15 / 8 = 1088.2687147302 →
E -> D# : 5/4 -> 6/5 = 2*2*3*2*2 / 5*5 = 48 / 25 = 1129.3275731357 →
F -> E : 4/3 -> 5/4 = 2*5*3 / 2*2*2*2 = 15 / 8 = 1088.2687147302 →
F# -> F : 7/5 -> 4/3 = 2*2*2*5 / 3*7 = 40 / 21 = 1115.5328065303 →
G -> F# : 3/2 -> 7/5 = 2*7*2 / 5*3 = 28 / 15 = 1080.5571917389 →
G# -> G : 8/5 -> 3/2 = 2*3*5 / 2*2*2*2 = 15 / 8 = 1088.2687147302 →
A -> G# : 5/3 -> 8/5 = 2*2*2*2*3 / 5*5 = 48 / 25 = 1129.3275731357 →
A# -> A : 16/9 -> 5/3 = 2*5*3*3 / 3*2*2*2*2 = 15 / 8 = 1088.2687147302 →
B -> A# : 15/8 -> 16/9 = 2*2*2*2*2*2*2*2 / 3*3*3*5 = 256 / 135 = 1107.821283539 →
1 x 1080.6 6 x 1088.3 2 x 1107.8 1 x 1115.5 2 x 1129.3
Pythagorean tuning
C : 1 = 0 ... +0.00
C# : 2187/2048 = 113.68500605771 ... +13.69
D : 9/8 = 203.91000173077 ... +3.91
D# : 32/27 = 294.13499740384 ... -5.87
E : 81/64 = 407.82000346155 ... +7.82
F : 4/3 = 498.04499913461 ... -1.96
F# : 729/512 = 611.73000519232 ... +11.73
G : 3/2 = 701.95500086539 ... +1.96
G# : 6561/4096 = 815.6400069231 ... +15.64
A : 27/16 = 905.86500259616 ... +5.87
A# : 16/9 = 996.08999826923 ... -3.91
B : 243/128 = 1109.7750043269 ... +9.78
statistics for interval minor second:
C -> C# : 1 -> 2187/2048 = 3*3*3*3*3*3*3*1 / 2*2*2*2*2*2*2*2*2*2*2*1 = 2187 / 2048 = 113.68500605771 →
C# -> D : 2187/2048 -> 9/8 = 3*3*2*2*2*2*2*2*2*2*2*2*2 / 2*2*2*3*3*3*3*3*3*3 = 256 / 243 = 90.224995673063 →
D -> D# : 9/8 -> 32/27 = 2*2*2*2*2*2*2*2 / 3*3*3*3*3 = 256 / 243 = 90.224995673063 →
D# -> E : 32/27 -> 81/64 = 3*3*3*3*3*3*3 / 2*2*2*2*2*2*2*2*2*2*2 = 2187 / 2048 = 113.68500605771 →
E -> F : 81/64 -> 4/3 = 2*2*2*2*2*2*2*2 / 3*3*3*3*3 = 256 / 243 = 90.224995673063 →
F -> F# : 4/3 -> 729/512 = 3*3*3*3*3*3*3 / 2*2*2*2*2*2*2*2*2*2*2 = 2187 / 2048 = 113.68500605771 →
F# -> G : 729/512 -> 3/2 = 3*2*2*2*2*2*2*2*2*2 / 2*3*3*3*3*3*3 = 256 / 243 = 90.224995673063 →
G -> G# : 3/2 -> 6561/4096 = 3*3*3*3*3*3*3*3*2 / 2*2*2*2*2*2*2*2*2*2*2*2*3 = 2187 / 2048 = 113.68500605771 →
G# -> A : 6561/4096 -> 27/16 = 3*3*3*2*2*2*2*2*2*2*2*2*2*2*2 / 2*2*2*2*3*3*3*3*3*3*3*3 = 256 / 243 = 90.224995673063 →
A -> A# : 27/16 -> 16/9 = 2*2*2*2*2*2*2*2 / 3*3*3*3*3 = 256 / 243 = 90.224995673063 →
A# -> B : 16/9 -> 243/128 = 3*3*3*3*3*3*3 / 2*2*2*2*2*2*2*2*2*2*2 = 2187 / 2048 = 113.68500605771 →
B -> C : 243/128 -> 1 = 2*1*2*2*2*2*2*2*2 / 1*3*3*3*3*3 = 256 / 243 = 90.224995673063 →
7 x 90.2 5 x 113.7
statistics for interval major second:
C -> D : 1 -> 9/8 = 3*3*1 / 2*2*2*1 = 9 / 8 = 203.91000173077 →
C# -> D# : 2187/2048 -> 32/27 = 2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2 / 3*3*3*3*3*3*3*3*3*3 = 65536 / 59049 = 180.44999134613 →
D -> E : 9/8 -> 81/64 = 3*3*3*3*2*2*2 / 2*2*2*2*2*2*3*3 = 9 / 8 = 203.91000173077 →
D# -> F : 32/27 -> 4/3 = 2*2*3*3*3 / 3*2*2*2*2*2 = 9 / 8 = 203.91000173077 →
E -> F# : 81/64 -> 729/512 = 3*3*3*3*3*3*2*2*2*2*2*2 / 2*2*2*2*2*2*2*2*2*3*3*3*3 = 9 / 8 = 203.91000173077 →
F -> G : 4/3 -> 3/2 = 3*3 / 2*2*2 = 9 / 8 = 203.91000173077 →
F# -> G# : 729/512 -> 6561/4096 = 3*3*3*3*3*3*3*3*2*2*2*2*2*2*2*2*2 / 2*2*2*2*2*2*2*2*2*2*2*2*3*3*3*3*3*3 = 9 / 8 = 203.91000173077 →
G -> A : 3/2 -> 27/16 = 3*3*3*2 / 2*2*2*2*3 = 9 / 8 = 203.91000173077 →
G# -> A# : 6561/4096 -> 16/9 = 2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2 / 3*3*3*3*3*3*3*3*3*3 = 65536 / 59049 = 180.44999134613 →
A -> B : 27/16 -> 243/128 = 3*3*3*3*3*2*2*2*2 / 2*2*2*2*2*2*2*3*3*3 = 9 / 8 = 203.91000173077 →
A# -> C : 16/9 -> 1 = 2*1*3*3 / 1*2*2*2*2 = 9 / 8 = 203.91000173077 →
B -> C# : 243/128 -> 2187/2048 = 2*3*3*3*3*3*3*3*2*2*2*2*2*2*2 / 2*2*2*2*2*2*2*2*2*2*2*3*3*3*3*3 = 9 / 8 = 203.91000173077 →
2 x 180.4 10 x 203.9
statistics for interval minor third:
C -> D# : 1 -> 32/27 = 2*2*2*2*2*1 / 3*3*3*1 = 32 / 27 = 294.13499740384 →
C# -> E : 2187/2048 -> 81/64 = 3*3*3*3*2*2*2*2*2*2*2*2*2*2*2 / 2*2*2*2*2*2*3*3*3*3*3*3*3 = 32 / 27 = 294.13499740384 →
D -> F : 9/8 -> 4/3 = 2*2*2*2*2 / 3*3*3 = 32 / 27 = 294.13499740384 →
D# -> F# : 32/27 -> 729/512 = 3*3*3*3*3*3*3*3*3 / 2*2*2*2*2*2*2*2*2*2*2*2*2*2 = 19683 / 16384 = 317.59500778849 →
E -> G : 81/64 -> 3/2 = 3*2*2*2*2*2*2 / 2*3*3*3*3 = 32 / 27 = 294.13499740384 →
F -> G# : 4/3 -> 6561/4096 = 3*3*3*3*3*3*3*3*3 / 2*2*2*2*2*2*2*2*2*2*2*2*2*2 = 19683 / 16384 = 317.59500778849 →
F# -> A : 729/512 -> 27/16 = 3*3*3*2*2*2*2*2*2*2*2*2 / 2*2*2*2*3*3*3*3*3*3 = 32 / 27 = 294.13499740384 →
G -> A# : 3/2 -> 16/9 = 2*2*2*2*2 / 3*3*3 = 32 / 27 = 294.13499740384 →
G# -> B : 6561/4096 -> 243/128 = 3*3*3*3*3*2*2*2*2*2*2*2*2*2*2*2*2 / 2*2*2*2*2*2*2*3*3*3*3*3*3*3*3 = 32 / 27 = 294.13499740384 →
A -> C : 27/16 -> 1 = 2*1*2*2*2*2 / 1*3*3*3 = 32 / 27 = 294.13499740384 →
A# -> C# : 16/9 -> 2187/2048 = 2*3*3*3*3*3*3*3*3*3 / 2*2*2*2*2*2*2*2*2*2*2*2*2*2*2 = 19683 / 16384 = 317.59500778849 →
B -> D : 243/128 -> 9/8 = 2*3*3*2*2*2*2*2*2*2 / 2*2*2*3*3*3*3*3 = 32 / 27 = 294.13499740384 →
9 x 294.1 3 x 317.6
statistics for interval major third:
C -> E : 1 -> 81/64 = 3*3*3*3*1 / 2*2*2*2*2*2*1 = 81 / 64 = 407.82000346155 →
C# -> F : 2187/2048 -> 4/3 = 2*2*2*2*2*2*2*2*2*2*2*2*2 / 3*3*3*3*3*3*3*3 = 8192 / 6561 = 384.3599930769 →
D -> F# : 9/8 -> 729/512 = 3*3*3*3*3*3*2*2*2 / 2*2*2*2*2*2*2*2*2*3*3 = 81 / 64 = 407.82000346155 →
D# -> G : 32/27 -> 3/2 = 3*3*3*3 / 2*2*2*2*2*2 = 81 / 64 = 407.82000346155 →
E -> G# : 81/64 -> 6561/4096 = 3*3*3*3*3*3*3*3*2*2*2*2*2*2 / 2*2*2*2*2*2*2*2*2*2*2*2*3*3*3*3 = 81 / 64 = 407.82000346155 →
F -> A : 4/3 -> 27/16 = 3*3*3*3 / 2*2*2*2*2*2 = 81 / 64 = 407.82000346155 →
F# -> A# : 729/512 -> 16/9 = 2*2*2*2*2*2*2*2*2*2*2*2*2 / 3*3*3*3*3*3*3*3 = 8192 / 6561 = 384.3599930769 →
G -> B : 3/2 -> 243/128 = 3*3*3*3*3*2 / 2*2*2*2*2*2*2*3 = 81 / 64 = 407.82000346155 →
G# -> C : 6561/4096 -> 1 = 2*1*2*2*2*2*2*2*2*2*2*2*2*2 / 1*3*3*3*3*3*3*3*3 = 8192 / 6561 = 384.3599930769 →
A -> C# : 27/16 -> 2187/2048 = 2*3*3*3*3*3*3*3*2*2*2*2 / 2*2*2*2*2*2*2*2*2*2*2*3*3*3 = 81 / 64 = 407.82000346155 →
A# -> D : 16/9 -> 9/8 = 2*3*3*3*3 / 2*2*2*2*2*2*2 = 81 / 64 = 407.82000346155 →
B -> D# : 243/128 -> 32/27 = 2*2*2*2*2*2*2*2*2*2*2*2*2 / 3*3*3*3*3*3*3*3 = 8192 / 6561 = 384.3599930769 →
4 x 384.4 8 x 407.8
statistics for interval fourth:
C -> F : 1 -> 4/3 = 2*2*1 / 3*1 = 4 / 3 = 498.04499913461 →
C# -> F# : 2187/2048 -> 729/512 = 3*3*3*3*3*3*2*2*2*2*2*2*2*2*2*2*2 / 2*2*2*2*2*2*2*2*2*3*3*3*3*3*3*3 = 4 / 3 = 498.04499913461 →
D -> G : 9/8 -> 3/2 = 3*2*2*2 / 2*3*3 = 4 / 3 = 498.04499913461 →
D# -> G# : 32/27 -> 6561/4096 = 3*3*3*3*3*3*3*3*3*3*3 / 2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2 = 177147 / 131072 = 521.50500951926 →
E -> A : 81/64 -> 27/16 = 3*3*3*2*2*2*2*2*2 / 2*2*2*2*3*3*3*3 = 4 / 3 = 498.04499913461 →
F -> A# : 4/3 -> 16/9 = 2*2*2*2*3 / 3*3*2*2 = 4 / 3 = 498.04499913461 →
F# -> B : 729/512 -> 243/128 = 3*3*3*3*3*2*2*2*2*2*2*2*2*2 / 2*2*2*2*2*2*2*3*3*3*3*3*3 = 4 / 3 = 498.04499913461 →
G -> C : 3/2 -> 1 = 2*1*2 / 1*3 = 4 / 3 = 498.04499913461 →
G# -> C# : 6561/4096 -> 2187/2048 = 2*3*3*3*3*3*3*3*2*2*2*2*2*2*2*2*2*2*2*2 / 2*2*2*2*2*2*2*2*2*2*2*3*3*3*3*3*3*3*3 = 4 / 3 = 498.04499913461 →
A -> D : 27/16 -> 9/8 = 2*3*3*2*2*2*2 / 2*2*2*3*3*3 = 4 / 3 = 498.04499913461 →
A# -> D# : 16/9 -> 32/27 = 2*2*2*2*2*2*3*3 / 3*3*3*2*2*2*2 = 4 / 3 = 498.04499913461 →
B -> E : 243/128 -> 81/64 = 2*3*3*3*3*2*2*2*2*2*2*2 / 2*2*2*2*2*2*3*3*3*3*3 = 4 / 3 = 498.04499913461 →
11 x 498 1 x 521.5
statistics for interval tritone:
C -> F# : 1 -> 729/512 = 3*3*3*3*3*3*1 / 2*2*2*2*2*2*2*2*2*1 = 729 / 512 = 611.73000519232 →
C# -> G : 2187/2048 -> 3/2 = 3*2*2*2*2*2*2*2*2*2*2*2 / 2*3*3*3*3*3*3*3 = 1024 / 729 = 588.26999480768 →
D -> G# : 9/8 -> 6561/4096 = 3*3*3*3*3*3*3*3*2*2*2 / 2*2*2*2*2*2*2*2*2*2*2*2*3*3 = 729 / 512 = 611.73000519232 →
D# -> A : 32/27 -> 27/16 = 3*3*3*3*3*3 / 2*2*2*2*2*2*2*2*2 = 729 / 512 = 611.73000519232 →
E -> A# : 81/64 -> 16/9 = 2*2*2*2*2*2*2*2*2*2 / 3*3*3*3*3*3 = 1024 / 729 = 588.26999480768 →
F -> B : 4/3 -> 243/128 = 3*3*3*3*3*3 / 2*2*2*2*2*2*2*2*2 = 729 / 512 = 611.73000519232 →
F# -> C : 729/512 -> 1 = 2*1*2*2*2*2*2*2*2*2*2 / 1*3*3*3*3*3*3 = 1024 / 729 = 588.26999480768 →
G -> C# : 3/2 -> 2187/2048 = 2*3*3*3*3*3*3*3*2 / 2*2*2*2*2*2*2*2*2*2*2*3 = 729 / 512 = 611.73000519232 →
G# -> D : 6561/4096 -> 9/8 = 2*3*3*2*2*2*2*2*2*2*2*2*2*2*2 / 2*2*2*3*3*3*3*3*3*3*3 = 1024 / 729 = 588.26999480768 →
A -> D# : 27/16 -> 32/27 = 2*2*2*2*2*2*2*2*2*2 / 3*3*3*3*3*3 = 1024 / 729 = 588.26999480768 →
A# -> E : 16/9 -> 81/64 = 2*3*3*3*3*3*3 / 2*2*2*2*2*2*2*2*2*2 = 729 / 512 = 611.73000519232 →
B -> F : 243/128 -> 4/3 = 2*2*2*2*2*2*2*2*2*2 / 3*3*3*3*3*3 = 1024 / 729 = 588.26999480768 →
6 x 588.3 6 x 611.7
statistics for interval fifth:
C -> G : 1 -> 3/2 = 3*1 / 2*1 = 3 / 2 = 701.95500086539 →
C# -> G# : 2187/2048 -> 6561/4096 = 3*3*3*3*3*3*3*3*2*2*2*2*2*2*2*2*2*2*2 / 2*2*2*2*2*2*2*2*2*2*2*2*3*3*3*3*3*3*3 = 3 / 2 = 701.95500086539 →
D -> A : 9/8 -> 27/16 = 3*3*3*2*2*2 / 2*2*2*2*3*3 = 3 / 2 = 701.95500086539 →
D# -> A# : 32/27 -> 16/9 = 2*2*2*2*3*3*3 / 3*3*2*2*2*2*2 = 3 / 2 = 701.95500086539 →
E -> B : 81/64 -> 243/128 = 3*3*3*3*3*2*2*2*2*2*2 / 2*2*2*2*2*2*2*3*3*3*3 = 3 / 2 = 701.95500086539 →
F -> C : 4/3 -> 1 = 2*1*3 / 1*2*2 = 3 / 2 = 701.95500086539 →
F# -> C# : 729/512 -> 2187/2048 = 2*3*3*3*3*3*3*3*2*2*2*2*2*2*2*2*2 / 2*2*2*2*2*2*2*2*2*2*2*3*3*3*3*3*3 = 3 / 2 = 701.95500086539 →
G -> D : 3/2 -> 9/8 = 2*3*3*2 / 2*2*2*3 = 3 / 2 = 701.95500086539 →
G# -> D# : 6561/4096 -> 32/27 = 2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2 / 3*3*3*3*3*3*3*3*3*3*3 = 262144 / 177147 = 678.49499048074 →
A -> E : 27/16 -> 81/64 = 2*3*3*3*3*2*2*2*2 / 2*2*2*2*2*2*3*3*3 = 3 / 2 = 701.95500086539 →
A# -> F : 16/9 -> 4/3 = 2*2*2*3*3 / 3*2*2*2*2 = 3 / 2 = 701.95500086539 →
B -> F# : 243/128 -> 729/512 = 2*3*3*3*3*3*3*2*2*2*2*2*2*2 / 2*2*2*2*2*2*2*2*2*3*3*3*3*3 = 3 / 2 = 701.95500086539 →
1 x 678.5 11 x 702
statistics for interval minor sixth:
C -> G# : 1 -> 6561/4096 = 3*3*3*3*3*3*3*3*1 / 2*2*2*2*2*2*2*2*2*2*2*2*1 = 6561 / 4096 = 815.6400069231 →
C# -> A : 2187/2048 -> 27/16 = 3*3*3*2*2*2*2*2*2*2*2*2*2*2 / 2*2*2*2*3*3*3*3*3*3*3 = 128 / 81 = 792.17999653845 →
D -> A# : 9/8 -> 16/9 = 2*2*2*2*2*2*2 / 3*3*3*3 = 128 / 81 = 792.17999653845 →
D# -> B : 32/27 -> 243/128 = 3*3*3*3*3*3*3*3 / 2*2*2*2*2*2*2*2*2*2*2*2 = 6561 / 4096 = 815.6400069231 →
E -> C : 81/64 -> 1 = 2*1*2*2*2*2*2*2 / 1*3*3*3*3 = 128 / 81 = 792.17999653845 →
F -> C# : 4/3 -> 2187/2048 = 2*3*3*3*3*3*3*3*3 / 2*2*2*2*2*2*2*2*2*2*2*2*2 = 6561 / 4096 = 815.6400069231 →
F# -> D : 729/512 -> 9/8 = 2*3*3*2*2*2*2*2*2*2*2*2 / 2*2*2*3*3*3*3*3*3 = 128 / 81 = 792.17999653845 →
G -> D# : 3/2 -> 32/27 = 2*2*2*2*2*2*2 / 3*3*3*3 = 128 / 81 = 792.17999653845 →
G# -> E : 6561/4096 -> 81/64 = 2*3*3*3*3*2*2*2*2*2*2*2*2*2*2*2*2 / 2*2*2*2*2*2*3*3*3*3*3*3*3*3 = 128 / 81 = 792.17999653845 →
A -> F : 27/16 -> 4/3 = 2*2*2*2*2*2*2 / 3*3*3*3 = 128 / 81 = 792.17999653845 →
A# -> F# : 16/9 -> 729/512 = 2*3*3*3*3*3*3*3*3 / 2*2*2*2*2*2*2*2*2*2*2*2*2 = 6561 / 4096 = 815.6400069231 →
B -> G : 243/128 -> 3/2 = 2*3*2*2*2*2*2*2*2 / 2*3*3*3*3*3 = 128 / 81 = 792.17999653845 →
8 x 792.2 4 x 815.6
statistics for interval major sixth:
C -> A : 1 -> 27/16 = 3*3*3*1 / 2*2*2*2*1 = 27 / 16 = 905.86500259616 →
C# -> A# : 2187/2048 -> 16/9 = 2*2*2*2*2*2*2*2*2*2*2*2*2*2*2 / 3*3*3*3*3*3*3*3*3 = 32768 / 19683 = 882.40499221151 →
D -> B : 9/8 -> 243/128 = 3*3*3*3*3*2*2*2 / 2*2*2*2*2*2*2*3*3 = 27 / 16 = 905.86500259616 →
D# -> C : 32/27 -> 1 = 2*1*3*3*3 / 1*2*2*2*2*2 = 27 / 16 = 905.86500259616 →
E -> C# : 81/64 -> 2187/2048 = 2*3*3*3*3*3*3*3*2*2*2*2*2*2 / 2*2*2*2*2*2*2*2*2*2*2*3*3*3*3 = 27 / 16 = 905.86500259616 →
F -> D : 4/3 -> 9/8 = 2*3*3*3 / 2*2*2*2*2 = 27 / 16 = 905.86500259616 →
F# -> D# : 729/512 -> 32/27 = 2*2*2*2*2*2*2*2*2*2*2*2*2*2*2 / 3*3*3*3*3*3*3*3*3 = 32768 / 19683 = 882.40499221151 →
G -> E : 3/2 -> 81/64 = 2*3*3*3*3*2 / 2*2*2*2*2*2*3 = 27 / 16 = 905.86500259616 →
G# -> F : 6561/4096 -> 4/3 = 2*2*2*2*2*2*2*2*2*2*2*2*2*2*2 / 3*3*3*3*3*3*3*3*3 = 32768 / 19683 = 882.40499221151 →
A -> F# : 27/16 -> 729/512 = 2*3*3*3*3*3*3*2*2*2*2 / 2*2*2*2*2*2*2*2*2*3*3*3 = 27 / 16 = 905.86500259616 →
A# -> G : 16/9 -> 3/2 = 2*3*3*3 / 2*2*2*2*2 = 27 / 16 = 905.86500259616 →
B -> G# : 243/128 -> 6561/4096 = 2*3*3*3*3*3*3*3*3*2*2*2*2*2*2*2 / 2*2*2*2*2*2*2*2*2*2*2*2*3*3*3*3*3 = 27 / 16 = 905.86500259616 →
3 x 882.4 9 x 905.9
statistics for interval minor seventh:
C -> A# : 1 -> 16/9 = 2*2*2*2*1 / 3*3*1 = 16 / 9 = 996.08999826923 →
C# -> B : 2187/2048 -> 243/128 = 3*3*3*3*3*2*2*2*2*2*2*2*2*2*2*2 / 2*2*2*2*2*2*2*3*3*3*3*3*3*3 = 16 / 9 = 996.08999826923 →
D -> C : 9/8 -> 1 = 2*1*2*2*2 / 1*3*3 = 16 / 9 = 996.08999826923 →
D# -> C# : 32/27 -> 2187/2048 = 2*3*3*3*3*3*3*3*3*3*3 / 2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2 = 59049 / 32768 = 1019.5500086539 →
E -> D : 81/64 -> 9/8 = 2*3*3*2*2*2*2*2*2 / 2*2*2*3*3*3*3 = 16 / 9 = 996.08999826923 →
F -> D# : 4/3 -> 32/27 = 2*2*2*2*2*2*3 / 3*3*3*2*2 = 16 / 9 = 996.08999826923 →
F# -> E : 729/512 -> 81/64 = 2*3*3*3*3*2*2*2*2*2*2*2*2*2 / 2*2*2*2*2*2*3*3*3*3*3*3 = 16 / 9 = 996.08999826923 →
G -> F : 3/2 -> 4/3 = 2*2*2*2 / 3*3 = 16 / 9 = 996.08999826923 →
G# -> F# : 6561/4096 -> 729/512 = 2*3*3*3*3*3*3*2*2*2*2*2*2*2*2*2*2*2*2 / 2*2*2*2*2*2*2*2*2*3*3*3*3*3*3*3*3 = 16 / 9 = 996.08999826923 →
A -> G : 27/16 -> 3/2 = 2*3*2*2*2*2 / 2*3*3*3 = 16 / 9 = 996.08999826923 →
A# -> G# : 16/9 -> 6561/4096 = 2*3*3*3*3*3*3*3*3*3*3 / 2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2 = 59049 / 32768 = 1019.5500086539 →
B -> A : 243/128 -> 27/16 = 2*3*3*3*2*2*2*2*2*2*2 / 2*2*2*2*3*3*3*3*3 = 16 / 9 = 996.08999826923 →
10 x 996.1 2 x 1019.6
statistics for interval major seventh:
C -> B : 1 -> 243/128 = 3*3*3*3*3*1 / 2*2*2*2*2*2*2*1 = 243 / 128 = 1109.7750043269 →
C# -> C : 2187/2048 -> 1 = 2*1*2*2*2*2*2*2*2*2*2*2*2 / 1*3*3*3*3*3*3*3 = 4096 / 2187 = 1086.3149939423 →
D -> C# : 9/8 -> 2187/2048 = 2*3*3*3*3*3*3*3*2*2*2 / 2*2*2*2*2*2*2*2*2*2*2*3*3 = 243 / 128 = 1109.7750043269 →
D# -> D : 32/27 -> 9/8 = 2*3*3*3*3*3 / 2*2*2*2*2*2*2*2 = 243 / 128 = 1109.7750043269 →
E -> D# : 81/64 -> 32/27 = 2*2*2*2*2*2*2*2*2*2*2*2 / 3*3*3*3*3*3*3 = 4096 / 2187 = 1086.3149939423 →
F -> E : 4/3 -> 81/64 = 2*3*3*3*3*3 / 2*2*2*2*2*2*2*2 = 243 / 128 = 1109.7750043269 →
F# -> F : 729/512 -> 4/3 = 2*2*2*2*2*2*2*2*2*2*2*2 / 3*3*3*3*3*3*3 = 4096 / 2187 = 1086.3149939423 →
G -> F# : 3/2 -> 729/512 = 2*3*3*3*3*3*3*2 / 2*2*2*2*2*2*2*2*2*3 = 243 / 128 = 1109.7750043269 →
G# -> G : 6561/4096 -> 3/2 = 2*3*2*2*2*2*2*2*2*2*2*2*2*2 / 2*3*3*3*3*3*3*3*3 = 4096 / 2187 = 1086.3149939423 →
A -> G# : 27/16 -> 6561/4096 = 2*3*3*3*3*3*3*3*3*2*2*2*2 / 2*2*2*2*2*2*2*2*2*2*2*2*3*3*3 = 243 / 128 = 1109.7750043269 →
A# -> A : 16/9 -> 27/16 = 2*3*3*3*3*3 / 2*2*2*2*2*2*2*2 = 243 / 128 = 1109.7750043269 →
B -> A# : 243/128 -> 16/9 = 2*2*2*2*2*2*2*2*2*2*2*2 / 3*3*3*3*3*3*3 = 4096 / 2187 = 1086.3149939423 →
5 x 1086.3 7 x 1109.8
Quarter-comma meantone temperament (1/4 syntonic comma)
C : 0 ... +0.00
C# : 76.049 ... -23.95
D : 193.15686 ... -6.84
D# : 310.26471 ... +10.26
E : 386.31371 ... -13.69
F : 503.42157 ... +3.42
F# : 579.47057 ... -20.53
G : 696.57843 ... -3.42
G# : 772.62743 ... -27.37
A : 889.73529 ... -10.26
A# : 1006.84314 ... +6.84
B : 1082.89214 ... -17.11
statistics for interval minor second:
C -> C# : 76.049 →
C# -> D : 117.10786 →
D -> D# : 117.10785 →
D# -> E : 76.049 →
E -> F : 117.10786 →
F -> F# : 76.049 →
F# -> G : 117.10786 →
G -> G# : 76.049 →
G# -> A : 117.10786 →
A -> A# : 117.10785 →
A# -> B : 76.049 →
B -> C : 117.10786 →
5 x 76 7 x 117.1
statistics for interval major second:
C -> D : 193.15686 →
C# -> D# : 234.21571 →
D -> E : 193.15685 →
D# -> F : 193.15686 →
E -> F# : 193.15686 →
F -> G : 193.15686 →
F# -> G# : 193.15686 →
G -> A : 193.15686 →
G# -> A# : 234.21571 →
A -> B : 193.15685 →
A# -> C : 193.15686 →
B -> C# : 193.15686 →
10 x 193.2 2 x 234.2
statistics for interval minor third:
C -> D# : 310.26471 →
C# -> E : 310.26471 →
D -> F : 310.26471 →
D# -> F# : 269.20586 →
E -> G : 310.26472 →
F -> G# : 269.20586 →
F# -> A : 310.26472 →
G -> A# : 310.26471 →
G# -> B : 310.26471 →
A -> C : 310.26471 →
A# -> C# : 269.20586 →
B -> D : 310.26472 →
3 x 269.2 9 x 310.3
statistics for interval major third:
C -> E : 386.31371 →
C# -> F : 427.37257 →
D -> F# : 386.31371 →
D# -> G : 386.31372 →
E -> G# : 386.31372 →
F -> A : 386.31372 →
F# -> A# : 427.37257 →
G -> B : 386.31371 →
G# -> C : 427.37257 →
A -> C# : 386.31371 →
A# -> D : 386.31372 →
B -> D# : 427.37257 →
8 x 386.3 4 x 427.4
statistics for interval fourth:
C -> F : 503.42157 →
C# -> F# : 503.42157 →
D -> G : 503.42157 →
D# -> G# : 462.36272 →
E -> A : 503.42158 →
F -> A# : 503.42157 →
F# -> B : 503.42157 →
G -> C : 503.42157 →
G# -> C# : 503.42157 →
A -> D : 503.42157 →
A# -> D# : 503.42157 →
B -> E : 503.42157 →
1 x 462.4 11 x 503.4
statistics for interval tritone:
C -> F# : 579.47057 →
C# -> G : 620.52943 →
D -> G# : 579.47057 →
D# -> A : 579.47058 →
E -> A# : 620.52943 →
F -> B : 579.47057 →
F# -> C : 620.52943 →
G -> C# : 579.47057 →
G# -> D : 620.52943 →
A -> D# : 620.52942 →
A# -> E : 579.47057 →
B -> F : 620.52943 →
6 x 579.5 6 x 620.5
statistics for interval fifth:
C -> G : 696.57843 →
C# -> G# : 696.57843 →
D -> A : 696.57843 →
D# -> A# : 696.57843 →
E -> B : 696.57843 →
F -> C : 696.57843 →
F# -> C# : 696.57843 →
G -> D : 696.57843 →
G# -> D# : 737.63728 →
A -> E : 696.57842 →
A# -> F : 696.57843 →
B -> F# : 696.57843 →
11 x 696.6 1 x 737.6
statistics for interval minor sixth:
C -> G# : 772.62743 →
C# -> A : 813.68629 →
D -> A# : 813.68628 →
D# -> B : 772.62743 →
E -> C : 813.68629 →
F -> C# : 772.62743 →
F# -> D : 813.68629 →
G -> D# : 813.68628 →
G# -> E : 813.68628 →
A -> F : 813.68628 →
A# -> F# : 772.62743 →
B -> G : 813.68629 →
4 x 772.6 8 x 813.7
statistics for interval major sixth:
C -> A : 889.73529 →
C# -> A# : 930.79414 →
D -> B : 889.73528 →
D# -> C : 889.73529 →
E -> C# : 889.73529 →
F -> D : 889.73529 →
F# -> D# : 930.79414 →
G -> E : 889.73528 →
G# -> F : 930.79414 →
A -> F# : 889.73528 →
A# -> G : 889.73529 →
B -> G# : 889.73529 →
9 x 889.7 3 x 930.8
statistics for interval minor seventh:
C -> A# : 1006.84314 →
C# -> B : 1006.84314 →
D -> C : 1006.84314 →
D# -> C# : 965.78429 →
E -> D : 1006.84315 →
F -> D# : 1006.84314 →
F# -> E : 1006.84314 →
G -> F : 1006.84314 →
G# -> F# : 1006.84314 →
A -> G : 1006.84314 →
A# -> G# : 965.78429 →
B -> A : 1006.84315 →
2 x 965.8 10 x 1006.8
statistics for interval major seventh:
C -> B : 1082.89214 →
C# -> C : 1123.951 →
D -> C# : 1082.89214 →
D# -> D : 1082.89215 →
E -> D# : 1123.951 →
F -> E : 1082.89214 →
F# -> F : 1123.951 →
G -> F# : 1082.89214 →
G# -> G : 1123.951 →
A -> G# : 1082.89214 →
A# -> A : 1082.89215 →
B -> A# : 1123.951 →
7 x 1082.9 5 x 1124
Silbermann temperament (1/6 Pythagorean comma)
C : 0 ... +0.00
C# : 86.31 ... -13.69
D : 196.09 ... -3.91
D# : 305.87 ... +5.87
E : 392.18 ... -7.82
F : 501.96 ... +1.96
F# : 588.27 ... -11.73
G : 698.04 ... -1.96
G# : 784.36 ... -15.64
A : 894.13 ... -5.87
A# : 1003.91 ... +3.91
B : 1090.22 ... -9.78
statistics for interval minor second:
C -> C# : 86.31 →
C# -> D : 109.78 →
D -> D# : 109.78 →
D# -> E : 86.31 →
E -> F : 109.78 →
F -> F# : 86.31 →
F# -> G : 109.77 →
G -> G# : 86.32 →
G# -> A : 109.77 →
A -> A# : 109.78 →
A# -> B : 86.31 →
B -> C : 109.78 →
5 x 86.3 7 x 109.8
statistics for interval major second:
C -> D : 196.09 →
C# -> D# : 219.56 →
D -> E : 196.09 →
D# -> F : 196.09 →
E -> F# : 196.09 →
F -> G : 196.08 →
F# -> G# : 196.09 →
G -> A : 196.09 →
G# -> A# : 219.55 →
A -> B : 196.09 →
A# -> C : 196.09 →
B -> C# : 196.09 →
10 x 196.1 2 x 219.6
statistics for interval minor third:
C -> D# : 305.87 →
C# -> E : 305.87 →
D -> F : 305.87 →
D# -> F# : 282.4 →
E -> G : 305.86 →
F -> G# : 282.4 →
F# -> A : 305.86 →
G -> A# : 305.87 →
G# -> B : 305.86 →
A -> C : 305.87 →
A# -> C# : 282.4 →
B -> D : 305.87 →
3 x 282.4 9 x 305.9
statistics for interval major third:
C -> E : 392.18 →
C# -> F : 415.65 →
D -> F# : 392.18 →
D# -> G : 392.17 →
E -> G# : 392.18 →
F -> A : 392.17 →
F# -> A# : 415.64 →
G -> B : 392.18 →
G# -> C : 415.64 →
A -> C# : 392.18 →
A# -> D : 392.18 →
B -> D# : 415.65 →
8 x 392.2 2 x 415.6 2 x 415.7
statistics for interval fourth:
C -> F : 501.96 →
C# -> F# : 501.96 →
D -> G : 501.95 →
D# -> G# : 478.49 →
E -> A : 501.95 →
F -> A# : 501.95 →
F# -> B : 501.95 →
G -> C : 501.96 →
G# -> C# : 501.95 →
A -> D : 501.96 →
A# -> D# : 501.96 →
B -> E : 501.96 →
1 x 478.5 11 x 502
statistics for interval tritone:
C -> F# : 588.27 →
C# -> G : 611.73 →
D -> G# : 588.27 →
D# -> A : 588.26 →
E -> A# : 611.73 →
F -> B : 588.26 →
F# -> C : 611.73 →
G -> C# : 588.27 →
G# -> D : 611.73 →
A -> D# : 611.74 →
A# -> E : 588.27 →
B -> F : 611.74 →
6 x 588.3 6 x 611.7
statistics for interval fifth:
C -> G : 698.04 →
C# -> G# : 698.05 →
D -> A : 698.04 →
D# -> A# : 698.04 →
E -> B : 698.04 →
F -> C : 698.04 →
F# -> C# : 698.04 →
G -> D : 698.05 →
G# -> D# : 721.51 →
A -> E : 698.05 →
A# -> F : 698.05 →
B -> F# : 698.05 →
6 x 698 5 x 698.1 1 x 721.5
statistics for interval minor sixth:
C -> G# : 784.36 →
C# -> A : 807.82 →
D -> A# : 807.82 →
D# -> B : 784.35 →
E -> C : 807.82 →
F -> C# : 784.35 →
F# -> D : 807.82 →
G -> D# : 807.83 →
G# -> E : 807.82 →
A -> F : 807.83 →
A# -> F# : 784.36 →
B -> G : 807.82 →
4 x 784.4 8 x 807.8
statistics for interval major sixth:
C -> A : 894.13 →
C# -> A# : 917.6 →
D -> B : 894.13 →
D# -> C : 894.13 →
E -> C# : 894.13 →
F -> D : 894.13 →
F# -> D# : 917.6 →
G -> E : 894.14 →
G# -> F : 917.6 →
A -> F# : 894.14 →
A# -> G : 894.13 →
B -> G# : 894.14 →
9 x 894.1 3 x 917.6
statistics for interval minor seventh:
C -> A# : 1003.91 →
C# -> B : 1003.91 →
D -> C : 1003.91 →
D# -> C# : 980.44 →
E -> D : 1003.91 →
F -> D# : 1003.91 →
F# -> E : 1003.91 →
G -> F : 1003.92 →
G# -> F# : 1003.91 →
A -> G : 1003.91 →
A# -> G# : 980.45 →
B -> A : 1003.91 →
1 x 980.4 1 x 980.5 10 x 1003.9
statistics for interval major seventh:
C -> B : 1090.22 →
C# -> C : 1113.69 →
D -> C# : 1090.22 →
D# -> D : 1090.22 →
E -> D# : 1113.69 →
F -> E : 1090.22 →
F# -> F : 1113.69 →
G -> F# : 1090.23 →
G# -> G : 1113.68 →
A -> G# : 1090.23 →
A# -> A : 1090.22 →
B -> A# : 1113.69 →
7 x 1090.2 5 x 1113.7
Gabler temperament
C : 0 ... +0.00
C# : 85.07009 ... -14.93
D : 195.73431 ... -4.27
D# : 306.39853 ... +6.40
E : 391.46862 ... -8.53
F : 502.13284 ... +2.13
F# : 587.20293 ... -12.80
G : 697.86716 ... -2.13
G# : 782.93724 ... -17.06
A : 893.60147 ... -6.40
A# : 1004.26569 ... +4.27
B : 1089.33578 ... -10.66
statistics for interval minor second:
C -> C# : 85.07009 →
C# -> D : 110.66422 →
D -> D# : 110.66422 →
D# -> E : 85.07009 →
E -> F : 110.66422 →
F -> F# : 85.07009 →
F# -> G : 110.66423 →
G -> G# : 85.07008 →
G# -> A : 110.66423 →
A -> A# : 110.66422 →
A# -> B : 85.07009 →
B -> C : 110.66422 →
5 x 85.1 7 x 110.7
statistics for interval major second:
C -> D : 195.73431 →
C# -> D# : 221.32844 →
D -> E : 195.73431 →
D# -> F : 195.73431 →
E -> F# : 195.73431 →
F -> G : 195.73432 →
F# -> G# : 195.73431 →
G -> A : 195.73431 →
G# -> A# : 221.32845 →
A -> B : 195.73431 →
A# -> C : 195.73431 →
B -> C# : 195.73431 →
10 x 195.7 2 x 221.3
statistics for interval minor third:
C -> D# : 306.39853 →
C# -> E : 306.39853 →
D -> F : 306.39853 →
D# -> F# : 280.8044 →
E -> G : 306.39854 →
F -> G# : 280.8044 →
F# -> A : 306.39854 →
G -> A# : 306.39853 →
G# -> B : 306.39854 →
A -> C : 306.39853 →
A# -> C# : 280.8044 →
B -> D : 306.39853 →
3 x 280.8 9 x 306.4
statistics for interval major third:
C -> E : 391.46862 →
C# -> F : 417.06275 →
D -> F# : 391.46862 →
D# -> G : 391.46863 →
E -> G# : 391.46862 →
F -> A : 391.46863 →
F# -> A# : 417.06276 →
G -> B : 391.46862 →
G# -> C : 417.06276 →
A -> C# : 391.46862 →
A# -> D : 391.46862 →
B -> D# : 417.06275 →
8 x 391.5 4 x 417.1
statistics for interval fourth:
C -> F : 502.13284 →
C# -> F# : 502.13284 →
D -> G : 502.13285 →
D# -> G# : 476.53871 →
E -> A : 502.13285 →
F -> A# : 502.13285 →
F# -> B : 502.13285 →
G -> C : 502.13284 →
G# -> C# : 502.13285 →
A -> D : 502.13284 →
A# -> D# : 502.13284 →
B -> E : 502.13284 →
1 x 476.5 11 x 502.1
statistics for interval tritone:
C -> F# : 587.20293 →
C# -> G : 612.79707 →
D -> G# : 587.20293 →
D# -> A : 587.20294 →
E -> A# : 612.79707 →
F -> B : 587.20294 →
F# -> C : 612.79707 →
G -> C# : 587.20293 →
G# -> D : 612.79707 →
A -> D# : 612.79706 →
A# -> E : 587.20293 →
B -> F : 612.79706 →
6 x 587.2 6 x 612.8
statistics for interval fifth:
C -> G : 697.86716 →
C# -> G# : 697.86715 →
D -> A : 697.86716 →
D# -> A# : 697.86716 →
E -> B : 697.86716 →
F -> C : 697.86716 →
F# -> C# : 697.86716 →
G -> D : 697.86715 →
G# -> D# : 723.46129 →
A -> E : 697.86715 →
A# -> F : 697.86715 →
B -> F# : 697.86715 →
11 x 697.9 1 x 723.5
statistics for interval minor sixth:
C -> G# : 782.93724 →
C# -> A : 808.53138 →
D -> A# : 808.53138 →
D# -> B : 782.93725 →
E -> C : 808.53138 →
F -> C# : 782.93725 →
F# -> D : 808.53138 →
G -> D# : 808.53137 →
G# -> E : 808.53138 →
A -> F : 808.53137 →
A# -> F# : 782.93724 →
B -> G : 808.53138 →
4 x 782.9 8 x 808.5
statistics for interval major sixth:
C -> A : 893.60147 →
C# -> A# : 919.1956 →
D -> B : 893.60147 →
D# -> C : 893.60147 →
E -> C# : 893.60147 →
F -> D : 893.60147 →
F# -> D# : 919.1956 →
G -> E : 893.60146 →
G# -> F : 919.1956 →
A -> F# : 893.60146 →
A# -> G : 893.60147 →
B -> G# : 893.60146 →
9 x 893.6 3 x 919.2
statistics for interval minor seventh:
C -> A# : 1004.26569 →
C# -> B : 1004.26569 →
D -> C : 1004.26569 →
D# -> C# : 978.67156 →
E -> D : 1004.26569 →
F -> D# : 1004.26569 →
F# -> E : 1004.26569 →
G -> F : 1004.26568 →
G# -> F# : 1004.26569 →
A -> G : 1004.26569 →
A# -> G# : 978.67155 →
B -> A : 1004.26569 →
2 x 978.7 10 x 1004.3
statistics for interval major seventh:
C -> B : 1089.33578 →
C# -> C : 1114.92991 →
D -> C# : 1089.33578 →
D# -> D : 1089.33578 →
E -> D# : 1114.92991 →
F -> E : 1089.33578 →
F# -> F : 1114.92991 →
G -> F# : 1089.33577 →
G# -> G : 1114.92992 →
A -> G# : 1089.33577 →
A# -> A : 1089.33578 →
B -> A# : 1114.92991 →
7 x 1089.3 5 x 1114.9
Werckmeister III temperament
C : 0 ... +0.00
C# : 90.225 ... -9.78
D : 192.18 ... -7.82
D# : 294.135 ... -5.87
E : 390.225 ... -9.77
F : 498.045 ... -1.95
F# : 588.27 ... -11.73
G : 696.09 ... -3.91
G# : 792.18 ... -7.82
A : 888.27 ... -11.73
A# : 996.09 ... -3.91
B : 1092.18 ... -7.82
statistics for interval minor second:
C -> C# : 90.225 →
C# -> D : 101.955 →
D -> D# : 101.955 →
D# -> E : 96.09 →
E -> F : 107.82 →
F -> F# : 90.225 →
F# -> G : 107.82 →
G -> G# : 96.09 →
G# -> A : 96.09 →
A -> A# : 107.82 →
A# -> B : 96.09 →
B -> C : 107.82 →
2 x 90.2 4 x 96.1 2 x 102 4 x 107.8
statistics for interval major second:
C -> D : 192.18 →
C# -> D# : 203.91 →
D -> E : 198.045 →
D# -> F : 203.91 →
E -> F# : 198.045 →
F -> G : 198.045 →
F# -> G# : 203.91 →
G -> A : 192.18 →
G# -> A# : 203.91 →
A -> B : 203.91 →
A# -> C : 203.91 →
B -> C# : 198.045 →
2 x 192.2 4 x 198 6 x 203.9
statistics for interval minor third:
C -> D# : 294.135 →
C# -> E : 300 →
D -> F : 305.865 →
D# -> F# : 294.135 →
E -> G : 305.865 →
F -> G# : 294.135 →
F# -> A : 300 →
G -> A# : 300 →
G# -> B : 300 →
A -> C : 311.73 →
A# -> C# : 294.135 →
B -> D : 300 →
4 x 294.1 5 x 300 2 x 305.9 1 x 311.7
statistics for interval major third:
C -> E : 390.225 →
C# -> F : 407.82 →
D -> F# : 396.09 →
D# -> G : 401.955 →
E -> G# : 401.955 →
F -> A : 390.225 →
F# -> A# : 407.82 →
G -> B : 396.09 →
G# -> C : 407.82 →
A -> C# : 401.955 →
A# -> D : 396.09 →
B -> D# : 401.955 →
2 x 390.2 3 x 396.1 4 x 402 3 x 407.8
statistics for interval fourth:
C -> F : 498.045 →
C# -> F# : 498.045 →
D -> G : 503.91 →
D# -> G# : 498.045 →
E -> A : 498.045 →
F -> A# : 498.045 →
F# -> B : 503.91 →
G -> C : 503.91 →
G# -> C# : 498.045 →
A -> D : 503.91 →
A# -> D# : 498.045 →
B -> E : 498.045 →
8 x 498 4 x 503.9
statistics for interval tritone:
C -> F# : 588.27 →
C# -> G : 605.865 →
D -> G# : 600 →
D# -> A : 594.135 →
E -> A# : 605.865 →
F -> B : 594.135 →
F# -> C : 611.73 →
G -> C# : 594.135 →
G# -> D : 600 →
A -> D# : 605.865 →
A# -> E : 594.135 →
B -> F : 605.865 →
1 x 588.3 4 x 594.1 2 x 600 4 x 605.9 1 x 611.7
statistics for interval fifth:
C -> G : 696.09 →
C# -> G# : 701.955 →
D -> A : 696.09 →
D# -> A# : 701.955 →
E -> B : 701.955 →
F -> C : 701.955 →
F# -> C# : 701.955 →
G -> D : 696.09 →
G# -> D# : 701.955 →
A -> E : 701.955 →
A# -> F : 701.955 →
B -> F# : 696.09 →
4 x 696.1 8 x 702
statistics for interval minor sixth:
C -> G# : 792.18 →
C# -> A : 798.045 →
D -> A# : 803.91 →
D# -> B : 798.045 →
E -> C : 809.775 →
F -> C# : 792.18 →
F# -> D : 803.91 →
G -> D# : 798.045 →
G# -> E : 798.045 →
A -> F : 809.775 →
A# -> F# : 792.18 →
B -> G : 803.91 →
3 x 792.2 4 x 798 3 x 803.9 2 x 809.8
statistics for interval major sixth:
C -> A : 888.27 →
C# -> A# : 905.865 →
D -> B : 900 →
D# -> C : 905.865 →
E -> C# : 900 →
F -> D : 894.135 →
F# -> D# : 905.865 →
G -> E : 894.135 →
G# -> F : 905.865 →
A -> F# : 900 →
A# -> G : 900 →
B -> G# : 900 →
1 x 888.3 2 x 894.1 5 x 900 4 x 905.9
statistics for interval minor seventh:
C -> A# : 996.09 →
C# -> B : 1001.955 →
D -> C : 1007.82 →
D# -> C# : 996.09 →
E -> D : 1001.955 →
F -> D# : 996.09 →
F# -> E : 1001.955 →
G -> F : 1001.955 →
G# -> F# : 996.09 →
A -> G : 1007.82 →
A# -> G# : 996.09 →
B -> A : 996.09 →
6 x 996.1 4 x 1002 2 x 1007.8
statistics for interval major seventh:
C -> B : 1092.18 →
C# -> C : 1109.775 →
D -> C# : 1098.045 →
D# -> D : 1098.045 →
E -> D# : 1103.91 →
F -> E : 1092.18 →
F# -> F : 1109.775 →
G -> F# : 1092.18 →
G# -> G : 1103.91 →
A -> G# : 1103.91 →
A# -> A : 1092.18 →
B -> A# : 1103.91 →
4 x 1092.2 2 x 1098 4 x 1103.9 2 x 1109.8
Lehman-Bach temperament
C : 0 ... +0.00
C# : 98.045 ... -1.95
D : 196.09 ... -3.91
D# : 298.045 ... -1.95
E : 392.18 ... -7.82
F : 501.955 ... +1.95
F# : 596.09 ... -3.91
G : 698.045 ... -1.96
G# : 798.045 ... -1.96
A : 894.135 ... -5.87
A# : 998.045 ... -1.96
B : 1094.135 ... -5.87
statistics for interval minor second:
C -> C# : 98.045 →
C# -> D : 98.045 →
D -> D# : 101.955 →
D# -> E : 94.135 →
E -> F : 109.775 →
F -> F# : 94.135 →
F# -> G : 101.955 →
G -> G# : 100 →
G# -> A : 96.09 →
A -> A# : 103.91 →
A# -> B : 96.09 →
B -> C : 105.865 →
2 x 94.1 2 x 96.1 2 x 98 1 x 100 2 x 102 1 x 103.9 1 x 105.9 1 x 109.8
statistics for interval major second:
C -> D : 196.09 →
C# -> D# : 200 →
D -> E : 196.09 →
D# -> F : 203.91 →
E -> F# : 203.91 →
F -> G : 196.09 →
F# -> G# : 201.955 →
G -> A : 196.09 →
G# -> A# : 200 →
A -> B : 200 →
A# -> C : 201.955 →
B -> C# : 203.91 →
4 x 196.1 3 x 200 2 x 202 3 x 203.9
statistics for interval minor third:
C -> D# : 298.045 →
C# -> E : 294.135 →
D -> F : 305.865 →
D# -> F# : 298.045 →
E -> G : 305.865 →
F -> G# : 296.09 →
F# -> A : 298.045 →
G -> A# : 300 →
G# -> B : 296.09 →
A -> C : 305.865 →
A# -> C# : 300 →
B -> D : 301.955 →
1 x 294.1 2 x 296.1 3 x 298 2 x 300 1 x 302 3 x 305.9
statistics for interval major third:
C -> E : 392.18 →
C# -> F : 403.91 →
D -> F# : 400 →
D# -> G : 400 →
E -> G# : 405.865 →
F -> A : 392.18 →
F# -> A# : 401.955 →
G -> B : 396.09 →
G# -> C : 401.955 →
A -> C# : 403.91 →
A# -> D : 398.045 →
B -> D# : 403.91 →
2 x 392.2 1 x 396.1 1 x 398 2 x 400 2 x 402 3 x 403.9 1 x 405.9
statistics for interval fourth:
C -> F : 501.955 →
C# -> F# : 498.045 →
D -> G : 501.955 →
D# -> G# : 500 →
E -> A : 501.955 →
F -> A# : 496.09 →
F# -> B : 498.045 →
G -> C : 501.955 →
G# -> C# : 500 →
A -> D : 501.955 →
A# -> D# : 500 →
B -> E : 498.045 →
1 x 496.1 3 x 498 3 x 500 5 x 502
statistics for interval tritone:
C -> F# : 596.09 →
C# -> G : 600 →
D -> G# : 601.955 →
D# -> A : 596.09 →
E -> A# : 605.865 →
F -> B : 592.18 →
F# -> C : 603.91 →
G -> C# : 600 →
G# -> D : 598.045 →
A -> D# : 603.91 →
A# -> E : 594.135 →
B -> F : 607.82 →
1 x 592.2 1 x 594.1 2 x 596.1 1 x 598 2 x 600 1 x 602 2 x 603.9 1 x 605.9 1 x 607.8
statistics for interval fifth:
C -> G : 698.045 →
C# -> G# : 700 →
D -> A : 698.045 →
D# -> A# : 700 →
E -> B : 701.955 →
F -> C : 698.045 →
F# -> C# : 701.955 →
G -> D : 698.045 →
G# -> D# : 700 →
A -> E : 698.045 →
A# -> F : 703.91 →
B -> F# : 701.955 →
5 x 698 3 x 700 3 x 702 1 x 703.9
statistics for interval minor sixth:
C -> G# : 798.045 →
C# -> A : 796.09 →
D -> A# : 801.955 →
D# -> B : 796.09 →
E -> C : 807.82 →
F -> C# : 796.09 →
F# -> D : 800 →
G -> D# : 800 →
G# -> E : 794.135 →
A -> F : 807.82 →
A# -> F# : 798.045 →
B -> G : 803.91 →
1 x 794.1 3 x 796.1 2 x 798 2 x 800 1 x 802 1 x 803.9 2 x 807.8
statistics for interval major sixth:
C -> A : 894.135 →
C# -> A# : 900 →
D -> B : 898.045 →
D# -> C : 901.955 →
E -> C# : 905.865 →
F -> D : 894.135 →
F# -> D# : 901.955 →
G -> E : 894.135 →
G# -> F : 903.91 →
A -> F# : 901.955 →
A# -> G : 900 →
B -> G# : 903.91 →
3 x 894.1 1 x 898 2 x 900 3 x 902 2 x 903.9 1 x 905.9
statistics for interval minor seventh:
C -> A# : 998.045 →
C# -> B : 996.09 →
D -> C : 1003.91 →
D# -> C# : 1000 →
E -> D : 1003.91 →
F -> D# : 996.09 →
F# -> E : 996.09 →
G -> F : 1003.91 →
G# -> F# : 998.045 →
A -> G : 1003.91 →
A# -> G# : 1000 →
B -> A : 1000 →
3 x 996.1 2 x 998 3 x 1000 4 x 1003.9
statistics for interval major seventh:
C -> B : 1094.135 →
C# -> C : 1101.955 →
D -> C# : 1101.955 →
D# -> D : 1098.045 →
E -> D# : 1105.865 →
F -> E : 1090.225 →
F# -> F : 1105.865 →
G -> F# : 1098.045 →
G# -> G : 1100 →
A -> G# : 1103.91 →
A# -> A : 1096.09 →
B -> A# : 1103.91 →
1 x 1090.2 1 x 1094.1 1 x 1096.1 2 x 1098 1 x 1100 2 x 1102 2 x 1103.9 2 x 1105.9
Kirnberger III temperament
C : 1 = 0 ... +0.00
C# : 135/128 = 92.178716460997 ... -7.82
D : 193.15686 ... -6.84
D# : 32/27 = 294.13499740384 ... -5.87
E : 5/4 = 386.31371386483 ... -13.69
F : 4/3 = 498.04499913461 ... -1.96
F# : 45/32 = 590.22371559561 ... -9.78
G : 696.57843 ... -3.42
G# : 405/256 = 794.13371732638 ... -5.87
A : 889.73529 ... -10.26
A# : 16/9 = 996.08999826923 ... -3.91
B : 15/8 = 1088.2687147302 ... -11.73
statistics for interval minor second:
C -> C# : 1 -> 135/128 = 3*3*3*5*1 / 2*2*2*2*2*2*2*1 = 135 / 128 = 92.178716460997 →
C# -> D : 135/128 -> 193.15686 = 193*1.000812746114*2*2*2*2*2*2*2 / 1*3*3*3*5 = 24724.07808 / 135 = 100.978143539 →
D -> D# : 193.15686 -> 32/27 = 2*2*2*2*2*1 / 3*3*3*193*1.000812746114 = 31.974013244986 / 5211 = 100.97813740384 →
D# -> E : 32/27 -> 5/4 = 5*3*3*3 / 2*2*2*2*2*2*2 = 135 / 128 = 92.178716460997 →
E -> F : 5/4 -> 4/3 = 2*2*2*2 / 3*5 = 16 / 15 = 111.73128526978 →
F -> F# : 4/3 -> 45/32 = 3*3*5*3 / 2*2*2*2*2*2*2 = 135 / 128 = 92.178716460997 →
F# -> G : 45/32 -> 696.57843 = 2*2*2*3*29*1.0008310775862*2*2*2*2*2 / 1*3*3*5 = 1486.033984 / 3 = 106.35471440439 →
G -> G# : 696.57843 -> 405/256 = 3*3*3*3*5*1 / 2*2*2*2*2*2*2*2*2*2*2*3*29*1.0008310775862 = 67.443948845789 / 29696 = 97.555287326385 →
G# -> A : 405/256 -> 889.73529 = 7*127*1.0008270978628*2*2*2*2*2*2*2*2 / 1*3*3*3*3*5 = 2812.0028918519 / 5 = 95.601572673615 →
A -> A# : 889.73529 -> 16/9 = 2*2*2*2*1 / 3*3*7*127*1.0008270978628 = 5.3289257902014 / 2667 = 106.35470826923 →
A# -> B : 16/9 -> 15/8 = 3*5*3*3 / 2*2*2*2*2*2*2 = 135 / 128 = 92.178716460997 →
B -> C : 15/8 -> 1 = 2*1*2*2*2 / 1*3*5 = 16 / 15 = 111.73128526978 →
4 x 92.2 1 x 95.6 1 x 97.6 2 x 101 2 x 106.4 2 x 111.7
statistics for interval major second:
C -> D : 1 -> 193.15686 = 193*1.000812746114*1 / 1*1 = 193.15686 / 1 = 193.15686 →
C# -> D# : 135/128 -> 32/27 = 2*2*2*2*2*2*2*2*2*2*2*2 / 3*3*3*3*3*3*5 = 4096 / 3645 = 201.95628094284 →
D -> E : 193.15686 -> 5/4 = 5*1 / 2*2*193*1.000812746114 = 1.2489848923823 / 193 = 193.15685386483 →
D# -> F : 32/27 -> 4/3 = 2*2*3*3*3 / 3*2*2*2*2*2 = 9 / 8 = 203.91000173077 →
E -> F# : 5/4 -> 45/32 = 3*3*5*2*2 / 2*2*2*2*2*5 = 9 / 8 = 203.91000173077 →
F -> G : 4/3 -> 696.57843 = 2*2*2*3*29*1.0008310775862*3 / 1*2*2 = 2089.73529 / 4 = 198.53343086539 →
F# -> G# : 45/32 -> 405/256 = 3*3*3*3*5*2*2*2*2*2 / 2*2*2*2*2*2*2*2*3*3*5 = 9 / 8 = 203.91000173077 →
G -> A : 696.57843 -> 889.73529 = 7*127*1.0008270978628*1 / 1*2*2*2*3*29*1.0008310775862 = 888.99646496375 / 696 = 193.15686 →
G# -> A# : 405/256 -> 16/9 = 2*2*2*2*2*2*2*2*2*2*2*2 / 3*3*3*3*3*3*5 = 4096 / 3645 = 201.95628094284 →
A -> B : 889.73529 -> 15/8 = 3*5*1 / 2*2*2*7*127*1.0008270978628 = 7.4938018924707 / 3556 = 198.53342473022 →
A# -> C : 16/9 -> 1 = 2*1*3*3 / 1*2*2*2*2 = 9 / 8 = 203.91000173077 →
B -> C# : 15/8 -> 135/128 = 2*3*3*3*5*2*2*2 / 2*2*2*2*2*2*2*3*5 = 9 / 8 = 203.91000173077 →
3 x 193.2 2 x 198.5 2 x 202 5 x 203.9
statistics for interval minor third:
C -> D# : 1 -> 32/27 = 2*2*2*2*2*1 / 3*3*3*1 = 32 / 27 = 294.13499740384 →
C# -> E : 135/128 -> 5/4 = 5*2*2*2*2*2*2*2 / 2*2*3*3*3*5 = 32 / 27 = 294.13499740384 →
D -> F : 193.15686 -> 4/3 = 2*2*1 / 3*193*1.000812746114 = 1.3322505518744 / 193 = 304.88813913461 →
D# -> F# : 32/27 -> 45/32 = 3*3*5*3*3*3 / 2*2*2*2*2*2*2*2*2*2 = 1215 / 1024 = 296.08871819177 →
E -> G : 5/4 -> 696.57843 = 2*2*2*3*29*1.0008310775862*2*2 / 1*5 = 2786.31372 / 5 = 310.26471613517 →
F -> G# : 4/3 -> 405/256 = 3*3*3*3*5*3 / 2*2*2*2*2*2*2*2*2*2 = 1215 / 1024 = 296.08871819177 →
F# -> A : 45/32 -> 889.73529 = 7*127*1.0008270978628*2*2*2*2*2 / 1*3*3*5 = 28471.52928 / 45 = 299.51157440439 →
G -> A# : 696.57843 -> 16/9 = 2*2*2*2*1 / 3*3*2*2*2*3*29*1.0008310775862 = 1.9983392250604 / 783 = 299.51156826923 →
G# -> B : 405/256 -> 15/8 = 3*5*2*2*2*2*2*2*2*2 / 2*2*2*3*3*3*3*5 = 32 / 27 = 294.13499740384 →
A -> C : 889.73529 -> 1 = 2*1*1 / 1*7*127*1.0008270978628 = 1.9983471713255 / 889 = 310.26471 →
A# -> C# : 16/9 -> 135/128 = 2*3*3*3*5*3*3 / 2*2*2*2*2*2*2*2*2*2*2 = 1215 / 1024 = 296.08871819177 →
B -> D : 15/8 -> 193.15686 = 2*193*1.000812746114*2*2*2 / 1*3*5 = 206.033984 / 1 = 304.88814526978 →
3 x 294.1 3 x 296.1 2 x 299.5 2 x 304.9 2 x 310.3
statistics for interval major third:
C -> E : 1 -> 5/4 = 5*1 / 2*2*1 = 5 / 4 = 386.31371386483 →
C# -> F : 135/128 -> 4/3 = 2*2*2*2*2*2*2*2*2 / 3*3*3*3*5 = 512 / 405 = 405.86628267362 →
D -> F# : 193.15686 -> 45/32 = 3*3*5*1 / 2*2*2*2*2*193*1.000812746114 = 11.240864031441 / 1544 = 397.06685559561 →
D# -> G : 32/27 -> 696.57843 = 2*2*2*3*29*1.0008310775862*3*3*3 / 1*2*2*2*2*2 = 18807.61761 / 32 = 402.44343259616 →
E -> G# : 5/4 -> 405/256 = 3*3*3*3*5*2*2 / 2*2*2*2*2*2*2*2*5 = 81 / 64 = 407.82000346155 →
F -> A : 4/3 -> 889.73529 = 7*127*1.0008270978628*3 / 1*2*2 = 2669.20587 / 4 = 391.69029086539 →
F# -> A# : 45/32 -> 16/9 = 2*2*2*2*2*2*2*2*2 / 3*3*3*3*5 = 512 / 405 = 405.86628267362 →
G -> B : 696.57843 -> 15/8 = 3*5*1 / 2*2*2*2*2*2*3*29*1.0008310775862 = 1.2489620156628 / 464 = 391.69028473022 →
G# -> C : 405/256 -> 1 = 2*1*2*2*2*2*2*2*2*2 / 1*3*3*3*3*5 = 512 / 405 = 405.86628267362 →
A -> C# : 889.73529 -> 135/128 = 2*3*3*3*5*1 / 2*2*2*2*2*2*2*7*127*1.0008270978628 = 67.444217032237 / 28448 = 402.443426461 →
A# -> D : 16/9 -> 193.15686 = 2*193*1.000812746114*3*3 / 1*2*2*2*2 = 869.20587 / 4 = 397.06686173077 →
B -> D# : 15/8 -> 32/27 = 2*2*2*2*2*2*2*2*2 / 3*3*3*3*5 = 512 / 405 = 405.86628267362 →
1 x 386.3 2 x 391.7 2 x 397.1 2 x 402.4 4 x 405.9 1 x 407.8
statistics for interval fourth:
C -> F : 1 -> 4/3 = 2*2*1 / 3*1 = 4 / 3 = 498.04499913461 →
C# -> F# : 135/128 -> 45/32 = 3*3*5*2*2*2*2*2*2*2 / 2*2*2*2*2*3*3*3*5 = 4 / 3 = 498.04499913461 →
D -> G : 193.15686 -> 696.57843 = 2*2*2*3*29*1.0008310775862*1 / 1*193*1.000812746114 = 696.0127483435 / 193 = 503.42157 →
D# -> G# : 32/27 -> 405/256 = 3*3*3*3*5*3*3*3 / 2*2*2*2*2*2*2*2*2*2*2*2*2 = 10935 / 8192 = 499.99871992255 →
E -> A : 5/4 -> 889.73529 = 7*127*1.0008270978628*2*2 / 1*5 = 3558.94116 / 5 = 503.42157613517 →
F -> A# : 4/3 -> 16/9 = 2*2*2*2*3 / 3*3*2*2 = 4 / 3 = 498.04499913461 →
F# -> B : 45/32 -> 15/8 = 3*5*2*2*2*2*2 / 2*2*2*3*3*5 = 4 / 3 = 498.04499913461 →
G -> C : 696.57843 -> 1 = 2*1*1 / 1*2*2*2*3*29*1.0008310775862 = 0.99916961253021 / 348 = 503.42157 →
G# -> C# : 405/256 -> 135/128 = 2*3*3*3*5*2*2*2*2*2*2*2*2 / 2*2*2*2*2*2*2*3*3*3*3*5 = 4 / 3 = 498.04499913461 →
A -> D : 889.73529 -> 193.15686 = 2*193*1.000812746114*1 / 1*7*127*1.0008270978628 = 385.99446480312 / 889 = 503.42157 →
A# -> D# : 16/9 -> 32/27 = 2*2*2*2*2*2*3*3 / 3*3*3*2*2*2*2 = 4 / 3 = 498.04499913461 →
B -> E : 15/8 -> 5/4 = 2*5*2*2*2 / 2*2*3*5 = 4 / 3 = 498.04499913461 →
7 x 498 1 x 500 4 x 503.4
statistics for interval tritone:
C -> F# : 1 -> 45/32 = 3*3*5*1 / 2*2*2*2*2*1 = 45 / 32 = 590.22371559561 →
C# -> G : 135/128 -> 696.57843 = 2*2*2*3*29*1.0008310775862*2*2*2*2*2*2*2 / 1*3*3*3*5 = 89162.03904 / 135 = 604.399713539 →
D -> G# : 193.15686 -> 405/256 = 3*3*3*3*5*1 / 2*2*2*2*2*2*2*2*193*1.000812746114 = 101.16777628297 / 12352 = 600.97685732638 →
D# -> A : 32/27 -> 889.73529 = 7*127*1.0008270978628*3*3*3 / 1*2*2*2*2*2 = 12011.426415 / 16 = 595.60029259616 →
E -> A# : 5/4 -> 16/9 = 2*2*2*2*2*2 / 3*3*5 = 64 / 45 = 609.77628440439 →
F -> B : 4/3 -> 15/8 = 3*5*3 / 2*2*2*2*2 = 45 / 32 = 590.22371559561 →
F# -> C : 45/32 -> 1 = 2*1*2*2*2*2*2 / 1*3*3*5 = 64 / 45 = 609.77628440439 →
G -> C# : 696.57843 -> 135/128 = 2*3*3*3*5*1 / 2*2*2*2*2*2*2*2*2*2*3*29*1.0008310775862 = 11.240658140965 / 3712 = 595.600286461 →
G# -> D : 405/256 -> 193.15686 = 2*193*1.000812746114*2*2*2*2*2*2*2*2 / 1*3*3*3*3*5 = 98896.31232 / 405 = 599.02314267362 →
A -> D# : 889.73529 -> 32/27 = 2*2*2*2*2*2*1 / 3*3*3*7*127*1.0008270978628 = 63.947109482417 / 24003 = 604.39970740384 →
A# -> E : 16/9 -> 5/4 = 2*5*3*3 / 2*2*2*2*2*2 = 45 / 32 = 590.22371559561 →
B -> F : 15/8 -> 4/3 = 2*2*2*2*2*2 / 3*3*5 = 64 / 45 = 609.77628440439 →
3 x 590.2 2 x 595.6 1 x 599 1 x 601 2 x 604.4 3 x 609.8
statistics for interval fifth:
C -> G : 1 -> 696.57843 = 2*2*2*3*29*1.0008310775862*1 / 1*1 = 696.57843 / 1 = 696.57843 →
C# -> G# : 135/128 -> 405/256 = 3*3*3*3*5*2*2*2*2*2*2*2 / 2*2*2*2*2*2*2*2*3*3*3*5 = 3 / 2 = 701.95500086539 →
D -> A : 193.15686 -> 889.73529 = 7*127*1.0008270978628*1 / 1*193*1.000812746114 = 889.0127483435 / 193 = 696.57843 →
D# -> A# : 32/27 -> 16/9 = 2*2*2*2*3*3*3 / 3*3*2*2*2*2*2 = 3 / 2 = 701.95500086539 →
E -> B : 5/4 -> 15/8 = 3*5*2*2 / 2*2*2*5 = 3 / 2 = 701.95500086539 →
F -> C : 4/3 -> 1 = 2*1*3 / 1*2*2 = 3 / 2 = 701.95500086539 →
F# -> C# : 45/32 -> 135/128 = 2*3*3*3*5*2*2*2*2*2 / 2*2*2*2*2*2*2*3*3*5 = 3 / 2 = 701.95500086539 →
G -> D : 696.57843 -> 193.15686 = 2*193*1.000812746114*1 / 1*2*2*2*3*29*1.0008310775862 = 192.99646496375 / 348 = 696.57843 →
G# -> D# : 405/256 -> 32/27 = 2*2*2*2*2*2*2*2*2*2*2*2*2*2 / 3*3*3*3*3*3*3*5 = 16384 / 10935 = 700.00128007745 →
A -> E : 889.73529 -> 5/4 = 2*5*1 / 2*2*7*127*1.0008270978628 = 2.4979339641569 / 889 = 696.57842386483 →
A# -> F : 16/9 -> 4/3 = 2*2*2*3*3 / 3*2*2*2*2 = 3 / 2 = 701.95500086539 →
B -> F# : 15/8 -> 45/32 = 2*3*3*5*2*2*2 / 2*2*2*2*2*3*5 = 3 / 2 = 701.95500086539 →
4 x 696.6 1 x 700 7 x 702
statistics for interval minor sixth:
C -> G# : 1 -> 405/256 = 3*3*3*3*5*1 / 2*2*2*2*2*2*2*2*1 = 405 / 256 = 794.13371732638 →
C# -> A : 135/128 -> 889.73529 = 7*127*1.0008270978628*2*2*2*2*2*2*2 / 1*3*3*3*5 = 4218.0043377778 / 5 = 797.556573539 →
D -> A# : 193.15686 -> 16/9 = 2*2*2*2*1 / 3*3*193*1.000812746114 = 5.3290022074977 / 579 = 802.93313826923 →
D# -> B : 32/27 -> 15/8 = 3*5*3*3*3 / 2*2*2*2*2*2*2*2 = 405 / 256 = 794.13371732638 →
E -> C : 5/4 -> 1 = 2*1*2*2 / 1*5 = 8 / 5 = 813.68628613517 →
F -> C# : 4/3 -> 135/128 = 2*3*3*3*5*3 / 2*2*2*2*2*2*2*2*2 = 405 / 256 = 794.13371732638 →
F# -> D : 45/32 -> 193.15686 = 2*193*1.000812746114*2*2*2*2*2 / 1*3*3*5 = 12362.03904 / 45 = 802.93314440439 →
G -> D# : 696.57843 -> 32/27 = 2*2*2*2*2*2*1 / 3*3*3*2*2*2*3*29*1.0008310775862 = 2.6644523000806 / 783 = 797.55656740384 →
G# -> E : 405/256 -> 5/4 = 2*5*2*2*2*2*2*2*2*2 / 2*2*3*3*3*3*5 = 128 / 81 = 792.17999653845 →
A -> F : 889.73529 -> 4/3 = 2*2*2*1 / 3*7*127*1.0008270978628 = 2.6644628951007 / 889 = 808.30970913461 →
A# -> F# : 16/9 -> 45/32 = 2*3*3*5*3*3 / 2*2*2*2*2*2*2*2*2 = 405 / 256 = 794.13371732638 →
B -> G : 15/8 -> 696.57843 = 2*2*2*2*3*29*1.0008310775862*2*2*2 / 1*3*5 = 11145.25488 / 15 = 808.30971526978 →
1 x 792.2 4 x 794.1 2 x 797.6 2 x 802.9 2 x 808.3 1 x 813.7
statistics for interval major sixth:
C -> A : 1 -> 889.73529 = 7*127*1.0008270978628*1 / 1*1 = 889.73529 / 1 = 889.73529 →
C# -> A# : 135/128 -> 16/9 = 2*2*2*2*2*2*2*2*2*2*2 / 3*3*3*3*3*5 = 2048 / 1215 = 903.91128180823 →
D -> B : 193.15686 -> 15/8 = 3*5*1 / 2*2*2*193*1.000812746114 = 7.4939093542937 / 772 = 895.11185473022 →
D# -> C : 32/27 -> 1 = 2*1*3*3*3 / 1*2*2*2*2*2 = 27 / 16 = 905.86500259616 →
E -> C# : 5/4 -> 135/128 = 2*3*3*3*5*2*2 / 2*2*2*2*2*2*2*5 = 27 / 16 = 905.86500259616 →
F -> D : 4/3 -> 193.15686 = 2*193*1.000812746114*3 / 1*2*2 = 579.47058 / 2 = 895.11186086539 →
F# -> D# : 45/32 -> 32/27 = 2*2*2*2*2*2*2*2*2*2*2 / 3*3*3*3*3*5 = 2048 / 1215 = 903.91128180823 →
G -> E : 696.57843 -> 5/4 = 2*5*1 / 2*2*2*2*2*3*29*1.0008310775862 = 1.2489620156628 / 348 = 889.73528386483 →
G# -> F : 405/256 -> 4/3 = 2*2*2*2*2*2*2*2*2*2*2 / 3*3*3*3*3*5 = 2048 / 1215 = 903.91128180823 →
A -> F# : 889.73529 -> 45/32 = 2*3*3*5*1 / 2*2*2*2*2*7*127*1.0008270978628 = 11.240702838706 / 3556 = 900.48842559561 →
A# -> G : 16/9 -> 696.57843 = 2*2*2*2*3*29*1.0008310775862*3*3 / 1*2*2*2*2 = 6269.20587 / 8 = 900.48843173077 →
B -> G# : 15/8 -> 405/256 = 2*3*3*3*3*5*2*2*2 / 2*2*2*2*2*2*2*2*3*5 = 27 / 16 = 905.86500259616 →
2 x 889.7 2 x 895.1 2 x 900.5 3 x 903.9 3 x 905.9
statistics for interval minor seventh:
C -> A# : 1 -> 16/9 = 2*2*2*2*1 / 3*3*1 = 16 / 9 = 996.08999826923 →
C# -> B : 135/128 -> 15/8 = 3*5*2*2*2*2*2*2*2 / 2*2*2*3*3*3*5 = 16 / 9 = 996.08999826923 →
D -> C : 193.15686 -> 1 = 2*1*1 / 1*193*1.000812746114 = 1.9983758278117 / 193 = 1006.84314 →
D# -> C# : 32/27 -> 135/128 = 2*3*3*3*5*3*3*3 / 2*2*2*2*2*2*2*2*2*2*2*2 = 3645 / 2048 = 998.04371905716 →
E -> D : 5/4 -> 193.15686 = 2*193*1.000812746114*2*2 / 1*5 = 1545.25488 / 5 = 1006.8431461352 →
F -> D# : 4/3 -> 32/27 = 2*2*2*2*2*2*3 / 3*3*3*2*2 = 16 / 9 = 996.08999826923 →
F# -> E : 45/32 -> 5/4 = 2*5*2*2*2*2*2 / 2*2*3*3*5 = 16 / 9 = 996.08999826923 →
G -> F : 696.57843 -> 4/3 = 2*2*2*1 / 3*2*2*2*3*29*1.0008310775862 = 0.33305653751007 / 87 = 1001.4665691346 →
G# -> F# : 405/256 -> 45/32 = 2*3*3*5*2*2*2*2*2*2*2*2 / 2*2*2*2*2*3*3*3*3*5 = 16 / 9 = 996.08999826923 →
A -> G : 889.73529 -> 696.57843 = 2*2*2*2*3*29*1.0008310775862*1 / 1*7*127*1.0008270978628 = 1392.0055351969 / 889 = 1006.84314 →
A# -> G# : 16/9 -> 405/256 = 2*3*3*3*3*5*3*3 / 2*2*2*2*2*2*2*2*2*2*2*2 = 3645 / 2048 = 998.04371905716 →
B -> A : 15/8 -> 889.73529 = 2*7*127*1.0008270978628*2*2*2 / 1*3*5 = 14235.76464 / 15 = 1001.4665752698 →
5 x 996.1 2 x 998 2 x 1001.5 3 x 1006.8
statistics for interval major seventh:
C -> B : 1 -> 15/8 = 3*5*1 / 2*2*2*1 = 15 / 8 = 1088.2687147302 →
C# -> C : 135/128 -> 1 = 2*1*2*2*2*2*2*2*2 / 1*3*3*3*5 = 256 / 135 = 1107.821283539 →
D -> C# : 193.15686 -> 135/128 = 2*3*3*3*5*1 / 2*2*2*2*2*2*2*193*1.000812746114 = 67.445184188643 / 6176 = 1099.021856461 →
D# -> D : 32/27 -> 193.15686 = 2*193*1.000812746114*3*3*3 / 1*2*2*2*2*2 = 5215.23522 / 16 = 1099.0218625962 →
E -> D# : 5/4 -> 32/27 = 2*2*2*2*2*2*2*2 / 3*3*3*5 = 256 / 135 = 1107.821283539 →
F -> E : 4/3 -> 5/4 = 2*5*3 / 2*2*2*2 = 15 / 8 = 1088.2687147302 →
F# -> F : 45/32 -> 4/3 = 2*2*2*2*2*2*2*2 / 3*3*3*5 = 256 / 135 = 1107.821283539 →
G -> F# : 696.57843 -> 45/32 = 2*3*3*5*1 / 2*2*2*2*2*2*2*2*3*29*1.0008310775862 = 7.4937720939766 / 1856 = 1093.6452855956 →
G# -> G : 405/256 -> 696.57843 = 2*2*2*2*3*29*1.0008310775862*2*2*2*2*2*2*2*2 / 1*3*3*3*3*5 = 356648.15616 / 405 = 1102.4447126736 →
A -> G# : 889.73529 -> 405/256 = 2*3*3*3*3*5*1 / 2*2*2*2*2*2*2*2*7*127*1.0008270978628 = 101.16632554835 / 28448 = 1104.3984273264 →
A# -> A : 16/9 -> 889.73529 = 2*7*127*1.0008270978628*3*3 / 1*2*2*2*2 = 8007.61761 / 8 = 1093.6452917308 →
B -> A# : 15/8 -> 16/9 = 2*2*2*2*2*2*2*2 / 3*3*3*5 = 256 / 135 = 1107.821283539 →
2 x 1088.3 2 x 1093.6 2 x 1099 1 x 1102.4 1 x 1104.4 4 x 1107.8
Vallotti temperament
C : 0 ... +0.00
C# : 94.135 ... -5.86
D : 196.09 ... -3.91
D# : 298.045 ... -1.95
E : 392.18 ... -7.82
F : 501.955 ... +1.95
F# : 592.18 ... -7.82
G : 698.045 ... -1.96
G# : 796.09 ... -3.91
A : 894.135 ... -5.87
A# : 1000 ... +0.00
B : 1090.225 ... -9.78
statistics for interval minor second:
C -> C# : 94.135 →
C# -> D : 101.955 →
D -> D# : 101.955 →
D# -> E : 94.135 →
E -> F : 109.775 →
F -> F# : 90.225 →
F# -> G : 105.865 →
G -> G# : 98.045 →
G# -> A : 98.045 →
A -> A# : 105.865 →
A# -> B : 90.225 →
B -> C : 109.775 →
2 x 90.2 2 x 94.1 2 x 98 2 x 102 2 x 105.9 2 x 109.8
statistics for interval major second:
C -> D : 196.09 →
C# -> D# : 203.91 →
D -> E : 196.09 →
D# -> F : 203.91 →
E -> F# : 200 →
F -> G : 196.09 →
F# -> G# : 203.91 →
G -> A : 196.09 →
G# -> A# : 203.91 →
A -> B : 196.09 →
A# -> C : 200 →
B -> C# : 203.91 →
5 x 196.1 2 x 200 5 x 203.9
statistics for interval minor third:
C -> D# : 298.045 →
C# -> E : 298.045 →
D -> F : 305.865 →
D# -> F# : 294.135 →
E -> G : 305.865 →
F -> G# : 294.135 →
F# -> A : 301.955 →
G -> A# : 301.955 →
G# -> B : 294.135 →
A -> C : 305.865 →
A# -> C# : 294.135 →
B -> D : 305.865 →
4 x 294.1 2 x 298 2 x 302 4 x 305.9
statistics for interval major third:
C -> E : 392.18 →
C# -> F : 407.82 →
D -> F# : 396.09 →
D# -> G : 400 →
E -> G# : 403.91 →
F -> A : 392.18 →
F# -> A# : 407.82 →
G -> B : 392.18 →
G# -> C : 403.91 →
A -> C# : 400 →
A# -> D : 396.09 →
B -> D# : 407.82 →
3 x 392.2 2 x 396.1 2 x 400 2 x 403.9 3 x 407.8
statistics for interval fourth:
C -> F : 501.955 →
C# -> F# : 498.045 →
D -> G : 501.955 →
D# -> G# : 498.045 →
E -> A : 501.955 →
F -> A# : 498.045 →
F# -> B : 498.045 →
G -> C : 501.955 →
G# -> C# : 498.045 →
A -> D : 501.955 →
A# -> D# : 498.045 →
B -> E : 501.955 →
6 x 498 6 x 502
statistics for interval tritone:
C -> F# : 592.18 →
C# -> G : 603.91 →
D -> G# : 600 →
D# -> A : 596.09 →
E -> A# : 607.82 →
F -> B : 588.27 →
F# -> C : 607.82 →
G -> C# : 596.09 →
G# -> D : 600 →
A -> D# : 603.91 →
A# -> E : 592.18 →
B -> F : 611.73 →
1 x 588.3 2 x 592.2 2 x 596.1 2 x 600 2 x 603.9 2 x 607.8 1 x 611.7
statistics for interval fifth:
C -> G : 698.045 →
C# -> G# : 701.955 →
D -> A : 698.045 →
D# -> A# : 701.955 →
E -> B : 698.045 →
F -> C : 698.045 →
F# -> C# : 701.955 →
G -> D : 698.045 →
G# -> D# : 701.955 →
A -> E : 698.045 →
A# -> F : 701.955 →
B -> F# : 701.955 →
6 x 698 6 x 702
statistics for interval minor sixth:
C -> G# : 796.09 →
C# -> A : 800 →
D -> A# : 803.91 →
D# -> B : 792.18 →
E -> C : 807.82 →
F -> C# : 792.18 →
F# -> D : 803.91 →
G -> D# : 800 →
G# -> E : 796.09 →
A -> F : 807.82 →
A# -> F# : 792.18 →
B -> G : 807.82 →
3 x 792.2 2 x 796.1 2 x 800 2 x 803.9 3 x 807.8
statistics for interval major sixth:
C -> A : 894.135 →
C# -> A# : 905.865 →
D -> B : 894.135 →
D# -> C : 901.955 →
E -> C# : 901.955 →
F -> D : 894.135 →
F# -> D# : 905.865 →
G -> E : 894.135 →
G# -> F : 905.865 →
A -> F# : 898.045 →
A# -> G : 898.045 →
B -> G# : 905.865 →
4 x 894.1 2 x 898 2 x 902 4 x 905.9
statistics for interval minor seventh:
C -> A# : 1000 →
C# -> B : 996.09 →
D -> C : 1003.91 →
D# -> C# : 996.09 →
E -> D : 1003.91 →
F -> D# : 996.09 →
F# -> E : 1000 →
G -> F : 1003.91 →
G# -> F# : 996.09 →
A -> G : 1003.91 →
A# -> G# : 996.09 →
B -> A : 1003.91 →
5 x 996.1 2 x 1000 5 x 1003.9
statistics for interval major seventh:
C -> B : 1090.225 →
C# -> C : 1105.865 →
D -> C# : 1098.045 →
D# -> D : 1098.045 →
E -> D# : 1105.865 →
F -> E : 1090.225 →
F# -> F : 1109.775 →
G -> F# : 1094.135 →
G# -> G : 1101.955 →
A -> G# : 1101.955 →
A# -> A : 1094.135 →
B -> A# : 1109.775 →
2 x 1090.2 2 x 1094.1 2 x 1098 2 x 1102 2 x 1105.9 2 x 1109.8
Young temperament (Young I)
C : 1 = 0 ... +0.00
C# : 100000/94723 = 93.855985413418 ... -6.14
D : 100000/89304 = 195.84395830786 ... -4.16
D# : 100000/84197 = 297.79111793708 ... -2.21
E : 100000/79752 = 391.68887522835 ... -8.31
F : 100000/74921 = 499.86952675296 ... -0.13
F# : 100000/71041 = 591.93144616207 ... -8.07
G : 100000/66822 = 697.9259175924 ... -2.07
G# : 100000/63148 = 795.82926318291 ... -4.17
A : 100000/59676 = 893.73270949547 ... -6.27
A# : 100000/56131 = 999.75639968653 ... -0.24
B : 100000/53224 = 1091.8213872656 ... -8.18
statistics for interval minor second:
C -> C# : 1 -> 100000/94723 = 2*2*2*2*2*5*5*5*5*5*1 / 94723*1 = 100000 / 94723 = 93.855985413418 →
C# -> D : 100000/94723 -> 100000/89304 = 2*2*2*2*2*5*5*5*5*5*94723 / 2*2*2*3*61*61*2*2*2*2*2*5*5*5*5*5 = 94723 / 89304 = 101.98797289444 →
D -> D# : 100000/89304 -> 100000/84197 = 2*2*2*2*2*5*5*5*5*5*2*2*2*3*61*61 / 269*313*2*2*2*2*2*5*5*5*5*5 = 89304 / 84197 = 101.94715962922 →
D# -> E : 100000/84197 -> 100000/79752 = 2*2*2*2*2*5*5*5*5*5*269*313 / 2*2*2*3*3323*2*2*2*2*2*5*5*5*5*5 = 84197 / 79752 = 93.897757291266 →
E -> F : 100000/79752 -> 100000/74921 = 2*2*2*2*2*5*5*5*5*5*2*2*2*3*3323 / 7*7*11*139*2*2*2*2*2*5*5*5*5*5 = 79752 / 74921 = 108.18065152461 →
F -> F# : 100000/74921 -> 100000/71041 = 2*2*2*2*2*5*5*5*5*5*7*7*11*139 / 19*3739*2*2*2*2*2*5*5*5*5*5 = 74921 / 71041 = 92.06191940911 →
F# -> G : 100000/71041 -> 100000/66822 = 2*2*2*2*2*5*5*5*5*5*19*3739 / 2*3*7*37*43*2*2*2*2*2*5*5*5*5*5 = 71041 / 66822 = 105.99447143034 →
G -> G# : 100000/66822 -> 100000/63148 = 2*2*2*2*2*5*5*5*5*5*2*3*7*37*43 / 2*2*15787*2*2*2*2*2*5*5*5*5*5 = 33411 / 31574 = 97.903345590506 →
G# -> A : 100000/63148 -> 100000/59676 = 2*2*2*2*2*5*5*5*5*5*2*2*15787 / 2*2*3*4973*2*2*2*2*2*5*5*5*5*5 = 15787 / 14919 = 97.903446312562 →
A -> A# : 100000/59676 -> 100000/56131 = 2*2*2*2*2*5*5*5*5*5*2*2*3*4973 / 56131*2*2*2*2*2*5*5*5*5*5 = 59676 / 56131 = 106.02369019105 →
A# -> B : 100000/56131 -> 100000/53224 = 2*2*2*2*2*5*5*5*5*5*56131 / 2*2*2*6653*2*2*2*2*2*5*5*5*5*5 = 56131 / 53224 = 92.064987579085 →
B -> C : 100000/53224 -> 1 = 2*1*2*2*2*6653 / 1*2*2*2*2*2*5*5*5*5*5 = 6653 / 6250 = 108.17861273439 →
2 x 92.1 2 x 93.9 2 x 97.9 1 x 101.9 1 x 102 2 x 106 2 x 108.2
statistics for interval major second:
C -> D : 1 -> 100000/89304 = 2*2*2*2*2*5*5*5*5*5*1 / 2*2*2*3*61*61*1 = 12500 / 11163 = 195.84395830786 →
C# -> D# : 100000/94723 -> 100000/84197 = 2*2*2*2*2*5*5*5*5*5*94723 / 269*313*2*2*2*2*2*5*5*5*5*5 = 94723 / 84197 = 203.93513252366 →
D -> E : 100000/89304 -> 100000/79752 = 2*2*2*2*2*5*5*5*5*5*2*2*2*3*61*61 / 2*2*2*3*3323*2*2*2*2*2*5*5*5*5*5 = 3721 / 3323 = 195.84491692049 →
D# -> F : 100000/84197 -> 100000/74921 = 2*2*2*2*2*5*5*5*5*5*269*313 / 7*7*11*139*2*2*2*2*2*5*5*5*5*5 = 84197 / 74921 = 202.07840881588 →
E -> F# : 100000/79752 -> 100000/71041 = 2*2*2*2*2*5*5*5*5*5*2*2*2*3*3323 / 19*3739*2*2*2*2*2*5*5*5*5*5 = 79752 / 71041 = 200.24257093372 →
F -> G : 100000/74921 -> 100000/66822 = 2*2*2*2*2*5*5*5*5*5*7*7*11*139 / 2*3*7*37*43*2*2*2*2*2*5*5*5*5*5 = 10703 / 9546 = 198.05639083945 →
F# -> G# : 100000/71041 -> 100000/63148 = 2*2*2*2*2*5*5*5*5*5*19*3739 / 2*2*15787*2*2*2*2*2*5*5*5*5*5 = 71041 / 63148 = 203.89781702084 →
G -> A : 100000/66822 -> 100000/59676 = 2*2*2*2*2*5*5*5*5*5*2*3*7*37*43 / 2*2*3*4973*2*2*2*2*2*5*5*5*5*5 = 11137 / 9946 = 195.80679190307 →
G# -> A# : 100000/63148 -> 100000/56131 = 2*2*2*2*2*5*5*5*5*5*2*2*15787 / 56131*2*2*2*2*2*5*5*5*5*5 = 63148 / 56131 = 203.92713650361 →
A -> B : 100000/59676 -> 100000/53224 = 2*2*2*2*2*5*5*5*5*5*2*2*3*4973 / 2*2*2*6653*2*2*2*2*2*5*5*5*5*5 = 14919 / 13306 = 198.08867777014 →
A# -> C : 100000/56131 -> 1 = 2*1*56131 / 1*2*2*2*2*2*5*5*5*5*5 = 56131 / 50000 = 200.24360031347 →
B -> C# : 100000/53224 -> 100000/94723 = 2*2*2*2*2*2*5*5*5*5*5*2*2*2*6653 / 94723*2*2*2*2*2*5*5*5*5*5 = 106448 / 94723 = 202.03459814781 →
3 x 195.8 2 x 198.1 2 x 200.2 1 x 202 1 x 202.1 3 x 203.9
statistics for interval minor third:
C -> D# : 1 -> 100000/84197 = 2*2*2*2*2*5*5*5*5*5*1 / 269*313*1 = 100000 / 84197 = 297.79111793708 →
C# -> E : 100000/94723 -> 100000/79752 = 2*2*2*2*2*5*5*5*5*5*94723 / 2*2*2*3*3323*2*2*2*2*2*5*5*5*5*5 = 94723 / 79752 = 297.83288981493 →
D -> F : 100000/89304 -> 100000/74921 = 2*2*2*2*2*5*5*5*5*5*2*2*2*3*61*61 / 7*7*11*139*2*2*2*2*2*5*5*5*5*5 = 89304 / 74921 = 304.0255684451 →
D# -> F# : 100000/84197 -> 100000/71041 = 2*2*2*2*2*5*5*5*5*5*269*313 / 19*3739*2*2*2*2*2*5*5*5*5*5 = 84197 / 71041 = 294.14032822499 →
E -> G : 100000/79752 -> 100000/66822 = 2*2*2*2*2*5*5*5*5*5*2*2*2*3*3323 / 2*3*7*37*43*2*2*2*2*2*5*5*5*5*5 = 13292 / 11137 = 306.23704236406 →
F -> G# : 100000/74921 -> 100000/63148 = 2*2*2*2*2*5*5*5*5*5*7*7*11*139 / 2*2*15787*2*2*2*2*2*5*5*5*5*5 = 74921 / 63148 = 295.95973642995 →
F# -> A : 100000/71041 -> 100000/59676 = 2*2*2*2*2*5*5*5*5*5*19*3739 / 2*2*3*4973*2*2*2*2*2*5*5*5*5*5 = 71041 / 59676 = 301.8012633334 →
G -> A# : 100000/66822 -> 100000/56131 = 2*2*2*2*2*5*5*5*5*5*2*3*7*37*43 / 56131*2*2*2*2*2*5*5*5*5*5 = 66822 / 56131 = 301.83048209412 →
G# -> B : 100000/63148 -> 100000/53224 = 2*2*2*2*2*5*5*5*5*5*2*2*15787 / 2*2*2*6653*2*2*2*2*2*5*5*5*5*5 = 15787 / 13306 = 295.9921240827 →
A -> C : 100000/59676 -> 1 = 2*1*2*2*3*4973 / 1*2*2*2*2*2*5*5*5*5*5 = 14919 / 12500 = 306.26729050453 →
A# -> C# : 100000/56131 -> 100000/94723 = 2*2*2*2*2*2*5*5*5*5*5*56131 / 94723*2*2*2*2*2*5*5*5*5*5 = 112262 / 94723 = 294.09958572689 →
B -> D : 100000/53224 -> 100000/89304 = 2*2*2*2*2*2*5*5*5*5*5*2*2*2*6653 / 2*2*2*3*61*61*2*2*2*2*2*5*5*5*5*5 = 13306 / 11163 = 304.02257104225 →
2 x 294.1 2 x 296 2 x 297.8 2 x 301.8 2 x 304 1 x 306.2 1 x 306.3
statistics for interval major third:
C -> E : 1 -> 100000/79752 = 2*2*2*2*2*5*5*5*5*5*1 / 2*2*2*3*3323*1 = 12500 / 9969 = 391.68887522835 →
C# -> F : 100000/94723 -> 100000/74921 = 2*2*2*2*2*5*5*5*5*5*94723 / 7*7*11*139*2*2*2*2*2*5*5*5*5*5 = 94723 / 74921 = 406.01354133954 →
D -> F# : 100000/89304 -> 100000/71041 = 2*2*2*2*2*5*5*5*5*5*2*2*2*3*61*61 / 19*3739*2*2*2*2*2*5*5*5*5*5 = 89304 / 71041 = 396.08748785421 →
D# -> G : 100000/84197 -> 100000/66822 = 2*2*2*2*2*5*5*5*5*5*269*313 / 2*3*7*37*43*2*2*2*2*2*5*5*5*5*5 = 84197 / 66822 = 400.13479965532 →
E -> G# : 100000/79752 -> 100000/63148 = 2*2*2*2*2*5*5*5*5*5*2*2*2*3*3323 / 2*2*15787*2*2*2*2*2*5*5*5*5*5 = 19938 / 15787 = 404.14038795456 →
F -> A : 100000/74921 -> 100000/59676 = 2*2*2*2*2*5*5*5*5*5*7*7*11*139 / 2*2*3*4973*2*2*2*2*2*5*5*5*5*5 = 74921 / 59676 = 393.86318274251 →
F# -> A# : 100000/71041 -> 100000/56131 = 2*2*2*2*2*5*5*5*5*5*19*3739 / 56131*2*2*2*2*2*5*5*5*5*5 = 71041 / 56131 = 407.82495352446 →
G -> B : 100000/66822 -> 100000/53224 = 2*2*2*2*2*5*5*5*5*5*2*3*7*37*43 / 2*2*2*6653*2*2*2*2*2*5*5*5*5*5 = 33411 / 26612 = 393.89546967321 →
G# -> C : 100000/63148 -> 1 = 2*1*2*2*15787 / 1*2*2*2*2*2*5*5*5*5*5 = 15787 / 12500 = 404.17073681709 →
A -> C# : 100000/59676 -> 100000/94723 = 2*2*2*2*2*2*5*5*5*5*5*2*2*3*4973 / 94723*2*2*2*2*2*5*5*5*5*5 = 119352 / 94723 = 400.12327591795 →
A# -> D : 100000/56131 -> 100000/89304 = 2*2*2*2*2*2*5*5*5*5*5*56131 / 2*2*2*3*61*61*2*2*2*2*2*5*5*5*5*5 = 56131 / 44652 = 396.08755862133 →
B -> D# : 100000/53224 -> 100000/84197 = 2*2*2*2*2*2*5*5*5*5*5*2*2*2*6653 / 269*313*2*2*2*2*2*5*5*5*5*5 = 106448 / 84197 = 405.96973067147 →
1 x 391.7 2 x 393.9 2 x 396.1 2 x 400.1 1 x 404.1 1 x 404.2 2 x 406 1 x 407.8
statistics for interval fourth:
C -> F : 1 -> 100000/74921 = 2*2*2*2*2*5*5*5*5*5*1 / 7*7*11*139*1 = 100000 / 74921 = 499.86952675296 →
C# -> F# : 100000/94723 -> 100000/71041 = 2*2*2*2*2*5*5*5*5*5*94723 / 19*3739*2*2*2*2*2*5*5*5*5*5 = 94723 / 71041 = 498.07546074865 →
D -> G : 100000/89304 -> 100000/66822 = 2*2*2*2*2*5*5*5*5*5*2*2*2*3*61*61 / 2*3*7*37*43*2*2*2*2*2*5*5*5*5*5 = 14884 / 11137 = 502.08195928454 →
D# -> G# : 100000/84197 -> 100000/63148 = 2*2*2*2*2*5*5*5*5*5*269*313 / 2*2*15787*2*2*2*2*2*5*5*5*5*5 = 84197 / 63148 = 498.03814524583 →
E -> A : 100000/79752 -> 100000/59676 = 2*2*2*2*2*5*5*5*5*5*2*2*2*3*3323 / 2*2*3*4973*2*2*2*2*2*5*5*5*5*5 = 6646 / 4973 = 502.04383426712 →
F -> A# : 100000/74921 -> 100000/56131 = 2*2*2*2*2*5*5*5*5*5*7*7*11*139 / 56131*2*2*2*2*2*5*5*5*5*5 = 74921 / 56131 = 499.88687293357 →
F# -> B : 100000/71041 -> 100000/53224 = 2*2*2*2*2*5*5*5*5*5*19*3739 / 2*2*2*6653*2*2*2*2*2*5*5*5*5*5 = 71041 / 53224 = 499.88994110354 →
G -> C : 100000/66822 -> 1 = 2*1*2*3*7*37*43 / 1*2*2*2*2*2*5*5*5*5*5 = 33411 / 25000 = 502.0740824076 →
G# -> C# : 100000/63148 -> 100000/94723 = 2*2*2*2*2*2*5*5*5*5*5*2*2*15787 / 94723*2*2*2*2*2*5*5*5*5*5 = 126296 / 94723 = 498.02672223051 →
A -> D : 100000/59676 -> 100000/89304 = 2*2*2*2*2*2*5*5*5*5*5*2*2*3*4973 / 2*2*2*3*61*61*2*2*2*2*2*5*5*5*5*5 = 4973 / 3721 = 502.11124881239 →
A# -> D# : 100000/56131 -> 100000/84197 = 2*2*2*2*2*2*5*5*5*5*5*56131 / 269*313*2*2*2*2*2*5*5*5*5*5 = 112262 / 84197 = 498.03471825056 →
B -> E : 100000/53224 -> 100000/79752 = 2*2*2*2*2*2*5*5*5*5*5*2*2*2*6653 / 2*2*2*3*3323*2*2*2*2*2*5*5*5*5*5 = 13306 / 9969 = 499.86748796274 →
3 x 498 1 x 498.1 4 x 499.9 1 x 502 3 x 502.1
statistics for interval tritone:
C -> F# : 1 -> 100000/71041 = 2*2*2*2*2*5*5*5*5*5*1 / 19*3739*1 = 100000 / 71041 = 591.93144616207 →
C# -> G : 100000/94723 -> 100000/66822 = 2*2*2*2*2*5*5*5*5*5*94723 / 2*3*7*37*43*2*2*2*2*2*5*5*5*5*5 = 94723 / 66822 = 604.06993217899 →
D -> G# : 100000/89304 -> 100000/63148 = 2*2*2*2*2*5*5*5*5*5*2*2*2*3*61*61 / 2*2*15787*2*2*2*2*2*5*5*5*5*5 = 22326 / 15787 = 599.98530487505 →
D# -> A : 100000/84197 -> 100000/59676 = 2*2*2*2*2*5*5*5*5*5*269*313 / 2*2*3*4973*2*2*2*2*2*5*5*5*5*5 = 84197 / 59676 = 595.94159155839 →
E -> A# : 100000/79752 -> 100000/56131 = 2*2*2*2*2*5*5*5*5*5*2*2*2*3*3323 / 56131*2*2*2*2*2*5*5*5*5*5 = 79752 / 56131 = 608.06752445818 →
F -> B : 100000/74921 -> 100000/53224 = 2*2*2*2*2*5*5*5*5*5*7*7*11*139 / 2*2*2*6653*2*2*2*2*2*5*5*5*5*5 = 74921 / 53224 = 591.95186051265 →
F# -> C : 100000/71041 -> 1 = 2*1*19*3739 / 1*2*2*2*2*2*5*5*5*5*5 = 71041 / 50000 = 608.06855383793 →
G -> C# : 100000/66822 -> 100000/94723 = 2*2*2*2*2*2*5*5*5*5*5*2*3*7*37*43 / 94723*2*2*2*2*2*5*5*5*5*5 = 133644 / 94723 = 595.93006782101 →
G# -> D : 100000/63148 -> 100000/89304 = 2*2*2*2*2*2*5*5*5*5*5*2*2*15787 / 2*2*2*3*61*61*2*2*2*2*2*5*5*5*5*5 = 15787 / 11163 = 600.01469512495 →
A -> D# : 100000/59676 -> 100000/84197 = 2*2*2*2*2*2*5*5*5*5*5*2*2*3*4973 / 269*313*2*2*2*2*2*5*5*5*5*5 = 119352 / 84197 = 604.05840844161 →
A# -> E : 100000/56131 -> 100000/79752 = 2*2*2*2*2*2*5*5*5*5*5*56131 / 2*2*2*3*3323*2*2*2*2*2*5*5*5*5*5 = 56131 / 39876 = 591.93247554182 →
B -> F : 100000/53224 -> 100000/74921 = 2*2*2*2*2*2*5*5*5*5*5*2*2*2*6653 / 7*7*11*139*2*2*2*2*2*5*5*5*5*5 = 106448 / 74921 = 608.04813948735 →
2 x 591.9 1 x 592 2 x 595.9 2 x 600 2 x 604.1 1 x 608 2 x 608.1
statistics for interval fifth:
C -> G : 1 -> 100000/66822 = 2*2*2*2*2*5*5*5*5*5*1 / 2*3*7*37*43*1 = 50000 / 33411 = 697.9259175924 →
C# -> G# : 100000/94723 -> 100000/63148 = 2*2*2*2*2*5*5*5*5*5*94723 / 2*2*15787*2*2*2*2*2*5*5*5*5*5 = 94723 / 63148 = 701.97327776949 →
D -> A : 100000/89304 -> 100000/59676 = 2*2*2*2*2*5*5*5*5*5*2*2*2*3*61*61 / 2*2*3*4973*2*2*2*2*2*5*5*5*5*5 = 7442 / 4973 = 697.88875118761 →
D# -> A# : 100000/84197 -> 100000/56131 = 2*2*2*2*2*5*5*5*5*5*269*313 / 56131*2*2*2*2*2*5*5*5*5*5 = 84197 / 56131 = 701.96528174944 →
E -> B : 100000/79752 -> 100000/53224 = 2*2*2*2*2*5*5*5*5*5*2*2*2*3*3323 / 2*2*2*6653*2*2*2*2*2*5*5*5*5*5 = 9969 / 6653 = 700.13251203726 →
F -> C : 100000/74921 -> 1 = 2*1*7*7*11*139 / 1*2*2*2*2*2*5*5*5*5*5 = 74921 / 50000 = 700.13047324704 →
F# -> C# : 100000/71041 -> 100000/94723 = 2*2*2*2*2*2*5*5*5*5*5*19*3739 / 94723*2*2*2*2*2*5*5*5*5*5 = 142082 / 94723 = 701.92453925135 →
G -> D : 100000/66822 -> 100000/89304 = 2*2*2*2*2*2*5*5*5*5*5*2*3*7*37*43 / 2*2*2*3*61*61*2*2*2*2*2*5*5*5*5*5 = 11137 / 7442 = 697.91804071546 →
G# -> D# : 100000/63148 -> 100000/84197 = 2*2*2*2*2*2*5*5*5*5*5*2*2*15787 / 269*313*2*2*2*2*2*5*5*5*5*5 = 126296 / 84197 = 701.96185475417 →
A -> E : 100000/59676 -> 100000/79752 = 2*2*2*2*2*2*5*5*5*5*5*2*2*3*4973 / 2*2*2*3*3323*2*2*2*2*2*5*5*5*5*5 = 4973 / 3323 = 697.95616573288 →
A# -> F : 100000/56131 -> 100000/74921 = 2*2*2*2*2*2*5*5*5*5*5*56131 / 7*7*11*139*2*2*2*2*2*5*5*5*5*5 = 112262 / 74921 = 700.11312706643 →
B -> F# : 100000/53224 -> 100000/71041 = 2*2*2*2*2*2*5*5*5*5*5*2*2*2*6653 / 19*3739*2*2*2*2*2*5*5*5*5*5 = 106448 / 71041 = 700.11005889646 →
3 x 697.9 1 x 698 4 x 700.1 1 x 701.9 3 x 702
statistics for interval minor sixth:
C -> G# : 1 -> 100000/63148 = 2*2*2*2*2*5*5*5*5*5*1 / 2*2*15787*1 = 25000 / 15787 = 795.82926318291 →
C# -> A : 100000/94723 -> 100000/59676 = 2*2*2*2*2*5*5*5*5*5*94723 / 2*2*3*4973*2*2*2*2*2*5*5*5*5*5 = 94723 / 59676 = 799.87672408205 →
D -> A# : 100000/89304 -> 100000/56131 = 2*2*2*2*2*5*5*5*5*5*2*2*2*3*61*61 / 56131*2*2*2*2*2*5*5*5*5*5 = 89304 / 56131 = 803.91244137867 →
D# -> B : 100000/84197 -> 100000/53224 = 2*2*2*2*2*5*5*5*5*5*269*313 / 2*2*2*6653*2*2*2*2*2*5*5*5*5*5 = 84197 / 53224 = 794.03026932853 →
E -> C : 100000/79752 -> 1 = 2*1*2*2*2*3*3323 / 1*2*2*2*2*2*5*5*5*5*5 = 9969 / 6250 = 808.31112477165 →
F -> C# : 100000/74921 -> 100000/94723 = 2*2*2*2*2*2*5*5*5*5*5*7*7*11*139 / 94723*2*2*2*2*2*5*5*5*5*5 = 149842 / 94723 = 793.98645866046 →
F# -> D : 100000/71041 -> 100000/89304 = 2*2*2*2*2*2*5*5*5*5*5*19*3739 / 2*2*2*3*61*61*2*2*2*2*2*5*5*5*5*5 = 71041 / 44652 = 803.91251214579 →
G -> D# : 100000/66822 -> 100000/84197 = 2*2*2*2*2*2*5*5*5*5*5*2*3*7*37*43 / 269*313*2*2*2*2*2*5*5*5*5*5 = 133644 / 84197 = 799.86520034468 →
G# -> E : 100000/63148 -> 100000/79752 = 2*2*2*2*2*2*5*5*5*5*5*2*2*15787 / 2*2*2*3*3323*2*2*2*2*2*5*5*5*5*5 = 15787 / 9969 = 795.85961204544 →
A -> F : 100000/59676 -> 100000/74921 = 2*2*2*2*2*2*5*5*5*5*5*2*2*3*4973 / 7*7*11*139*2*2*2*2*2*5*5*5*5*5 = 119352 / 74921 = 806.13681725749 →
A# -> F# : 100000/56131 -> 100000/71041 = 2*2*2*2*2*2*5*5*5*5*5*56131 / 19*3739*2*2*2*2*2*5*5*5*5*5 = 112262 / 71041 = 792.17504647554 →
B -> G : 100000/53224 -> 100000/66822 = 2*2*2*2*2*2*5*5*5*5*5*2*2*2*6653 / 2*3*7*37*43*2*2*2*2*2*5*5*5*5*5 = 53224 / 33411 = 806.10453032679 →
1 x 792.2 2 x 794 1 x 795.8 1 x 795.9 2 x 799.9 2 x 803.9 2 x 806.1 1 x 808.3
statistics for interval major sixth:
C -> A : 1 -> 100000/59676 = 2*2*2*2*2*5*5*5*5*5*1 / 2*2*3*4973*1 = 25000 / 14919 = 893.73270949547 →
C# -> A# : 100000/94723 -> 100000/56131 = 2*2*2*2*2*5*5*5*5*5*94723 / 56131*2*2*2*2*2*5*5*5*5*5 = 94723 / 56131 = 905.90041427311 →
D -> B : 100000/89304 -> 100000/53224 = 2*2*2*2*2*5*5*5*5*5*2*2*2*3*61*61 / 2*2*2*6653*2*2*2*2*2*5*5*5*5*5 = 11163 / 6653 = 895.97742895775 →
D# -> C : 100000/84197 -> 1 = 2*1*269*313 / 1*2*2*2*2*2*5*5*5*5*5 = 84197 / 50000 = 902.20888206292 →
E -> C# : 100000/79752 -> 100000/94723 = 2*2*2*2*2*2*5*5*5*5*5*2*2*2*3*3323 / 94723*2*2*2*2*2*5*5*5*5*5 = 159504 / 94723 = 902.16711018507 →
F -> D : 100000/74921 -> 100000/89304 = 2*2*2*2*2*2*5*5*5*5*5*7*7*11*139 / 2*2*2*3*61*61*2*2*2*2*2*5*5*5*5*5 = 74921 / 44652 = 895.9744315549 →
F# -> D# : 100000/71041 -> 100000/84197 = 2*2*2*2*2*2*5*5*5*5*5*19*3739 / 269*313*2*2*2*2*2*5*5*5*5*5 = 142082 / 84197 = 905.85967177501 →
G -> E : 100000/66822 -> 100000/79752 = 2*2*2*2*2*2*5*5*5*5*5*2*3*7*37*43 / 2*2*2*3*3323*2*2*2*2*2*5*5*5*5*5 = 11137 / 6646 = 893.76295763594 →
G# -> F : 100000/63148 -> 100000/74921 = 2*2*2*2*2*2*5*5*5*5*5*2*2*15787 / 7*7*11*139*2*2*2*2*2*5*5*5*5*5 = 126296 / 74921 = 904.04026357005 →
A -> F# : 100000/59676 -> 100000/71041 = 2*2*2*2*2*2*5*5*5*5*5*2*2*3*4973 / 19*3739*2*2*2*2*2*5*5*5*5*5 = 119352 / 71041 = 898.1987366666 →
A# -> G : 100000/56131 -> 100000/66822 = 2*2*2*2*2*2*5*5*5*5*5*56131 / 2*3*7*37*43*2*2*2*2*2*5*5*5*5*5 = 56131 / 33411 = 898.16951790588 →
B -> G# : 100000/53224 -> 100000/63148 = 2*2*2*2*2*2*5*5*5*5*5*2*2*2*6653 / 2*2*15787*2*2*2*2*2*5*5*5*5*5 = 26612 / 15787 = 904.0078759173 →
1 x 893.7 1 x 893.8 2 x 896 2 x 898.2 2 x 902.2 2 x 904 2 x 905.9
statistics for interval minor seventh:
C -> A# : 1 -> 100000/56131 = 2*2*2*2*2*5*5*5*5*5*1 / 56131*1 = 100000 / 56131 = 999.75639968653 →
C# -> B : 100000/94723 -> 100000/53224 = 2*2*2*2*2*5*5*5*5*5*94723 / 2*2*2*6653*2*2*2*2*2*5*5*5*5*5 = 94723 / 53224 = 997.96540185219 →
D -> C : 100000/89304 -> 1 = 2*1*2*2*2*3*61*61 / 1*2*2*2*2*2*5*5*5*5*5 = 11163 / 6250 = 1004.1560416921 →
D# -> C# : 100000/84197 -> 100000/94723 = 2*2*2*2*2*2*5*5*5*5*5*269*313 / 94723*2*2*2*2*2*5*5*5*5*5 = 168394 / 94723 = 996.06486747634 →
E -> D : 100000/79752 -> 100000/89304 = 2*2*2*2*2*2*5*5*5*5*5*2*2*2*3*3323 / 2*2*2*3*61*61*2*2*2*2*2*5*5*5*5*5 = 6646 / 3721 = 1004.1550830795 →
F -> D# : 100000/74921 -> 100000/84197 = 2*2*2*2*2*2*5*5*5*5*5*7*7*11*139 / 269*313*2*2*2*2*2*5*5*5*5*5 = 149842 / 84197 = 997.92159118412 →
F# -> E : 100000/71041 -> 100000/79752 = 2*2*2*2*2*2*5*5*5*5*5*19*3739 / 2*2*2*3*3323*2*2*2*2*2*5*5*5*5*5 = 71041 / 39876 = 999.75742906628 →
G -> F : 100000/66822 -> 100000/74921 = 2*2*2*2*2*2*5*5*5*5*5*2*3*7*37*43 / 7*7*11*139*2*2*2*2*2*5*5*5*5*5 = 19092 / 10703 = 1001.9436091606 →
G# -> F# : 100000/63148 -> 100000/71041 = 2*2*2*2*2*2*5*5*5*5*5*2*2*15787 / 19*3739*2*2*2*2*2*5*5*5*5*5 = 126296 / 71041 = 996.10218297916 →
A -> G : 100000/59676 -> 100000/66822 = 2*2*2*2*2*2*5*5*5*5*5*2*2*3*4973 / 2*3*7*37*43*2*2*2*2*2*5*5*5*5*5 = 19892 / 11137 = 1004.1932080969 →
A# -> G# : 100000/56131 -> 100000/63148 = 2*2*2*2*2*2*5*5*5*5*5*56131 / 2*2*15787*2*2*2*2*2*5*5*5*5*5 = 56131 / 31574 = 996.07286349639 →
B -> A : 100000/53224 -> 100000/59676 = 2*2*2*2*2*2*5*5*5*5*5*2*2*2*6653 / 2*2*3*4973*2*2*2*2*2*5*5*5*5*5 = 26612 / 14919 = 1001.9113222299 →
3 x 996.1 1 x 997.9 1 x 998 2 x 999.8 2 x 1001.9 3 x 1004.2
statistics for interval major seventh:
C -> B : 1 -> 100000/53224 = 2*2*2*2*2*5*5*5*5*5*1 / 2*2*2*6653*1 = 12500 / 6653 = 1091.8213872656 →
C# -> C : 100000/94723 -> 1 = 2*1*94723 / 1*2*2*2*2*2*5*5*5*5*5 = 94723 / 50000 = 1106.1440145866 →
D -> C# : 100000/89304 -> 100000/94723 = 2*2*2*2*2*2*5*5*5*5*5*2*2*2*3*61*61 / 94723*2*2*2*2*2*5*5*5*5*5 = 178608 / 94723 = 1098.0120271056 →
D# -> D : 100000/84197 -> 100000/89304 = 2*2*2*2*2*2*5*5*5*5*5*269*313 / 2*2*2*3*61*61*2*2*2*2*2*5*5*5*5*5 = 84197 / 44652 = 1098.0528403708 →
E -> D# : 100000/79752 -> 100000/84197 = 2*2*2*2*2*2*5*5*5*5*5*2*2*2*3*3323 / 269*313*2*2*2*2*2*5*5*5*5*5 = 159504 / 84197 = 1106.1022427087 →
F -> E : 100000/74921 -> 100000/79752 = 2*2*2*2*2*2*5*5*5*5*5*7*7*11*139 / 2*2*2*3*3323*2*2*2*2*2*5*5*5*5*5 = 74921 / 39876 = 1091.8193484754 →
F# -> F : 100000/71041 -> 100000/74921 = 2*2*2*2*2*2*5*5*5*5*5*19*3739 / 7*7*11*139*2*2*2*2*2*5*5*5*5*5 = 142082 / 74921 = 1107.9380805909 →
G -> F# : 100000/66822 -> 100000/71041 = 2*2*2*2*2*2*5*5*5*5*5*2*3*7*37*43 / 19*3739*2*2*2*2*2*5*5*5*5*5 = 133644 / 71041 = 1094.0055285697 →
G# -> G : 100000/63148 -> 100000/66822 = 2*2*2*2*2*2*5*5*5*5*5*2*2*15787 / 2*3*7*37*43*2*2*2*2*2*5*5*5*5*5 = 63148 / 33411 = 1102.0966544095 →
A -> G# : 100000/59676 -> 100000/63148 = 2*2*2*2*2*2*5*5*5*5*5*2*2*3*4973 / 2*2*15787*2*2*2*2*2*5*5*5*5*5 = 29838 / 15787 = 1102.0965536874 →
A# -> A : 100000/56131 -> 100000/59676 = 2*2*2*2*2*2*5*5*5*5*5*56131 / 2*2*3*4973*2*2*2*2*2*5*5*5*5*5 = 56131 / 29838 = 1093.9763098089 →
B -> A# : 100000/53224 -> 100000/56131 = 2*2*2*2*2*2*5*5*5*5*5*2*2*2*6653 / 56131*2*2*2*2*2*5*5*5*5*5 = 106448 / 56131 = 1107.9350124209 →
2 x 1091.8 2 x 1094 1 x 1098 1 x 1098.1 2 x 1102.1 2 x 1106.1 2 x 1107.9
Valotti-Young temperament (Young II)
C : 1 = 0 ... +0.00
C# : 256/243 = 90.224995673063 ... -9.78
D : 196.09000 ... -3.91
D# : 32/27 = 294.13499740384 ... -5.87
E : 392.18000 ... -7.82
F : 4/3 = 498.04499913461 ... -1.96
F# : 1024/729 = 588.26999480768 ... -11.73
G : 698.04500 ... -1.96
G# : 128/81 = 792.17999653845 ... -7.82
A : 894.13500 ... -5.87
A# : 16/9 = 996.08999826923 ... -3.91
B : 1090.22500 ... -9.78
statistics for interval minor second:
C -> C# : 1 -> 256/243 = 2*2*2*2*2*2*2*2*1 / 3*3*3*3*3*1 = 256 / 243 = 90.224995673063 →
C# -> D : 256/243 -> 196.09000 = 2*2*7*7*1.0004591836735*3*3*3*3*3 / 1*2*2*2*2*2*2*2*2 = 47649.87 / 256 = 105.86500432694 →
D -> D# : 196.09000 -> 32/27 = 2*2*2*2*2*1 / 3*3*3*2*2*7*7*1.0004591836735 = 7.9963282166352 / 1323 = 98.044997403838 →
D# -> E : 32/27 -> 392.18000 = 2*2*2*7*7*1.0004591836735*3*3*3 / 1*2*2*2*2*2 = 2647.215 / 8 = 98.045002596162 →
E -> F : 392.18000 -> 4/3 = 2*2*1 / 3*2*2*2*7*7*1.0004591836735 = 0.3331803423598 / 98 = 105.86499913461 →
F -> F# : 4/3 -> 1024/729 = 2*2*2*2*2*2*2*2*2*2*3 / 3*3*3*3*3*3*2*2 = 256 / 243 = 90.224995673063 →
F# -> G : 1024/729 -> 698.04500 = 2*349*1.000064469914*3*3*3*3*3*3 / 1*2*2*2*2*2*2*2*2*2*2 = 254437.4025 / 512 = 109.77500519232 →
G -> G# : 698.04500 -> 128/81 = 2*2*2*2*2*2*2*1 / 3*3*3*3*2*349*1.000064469914 = 7.1106526879436 / 3141 = 94.13499653845 →
G# -> A : 128/81 -> 894.13500 = 2*3*149*1.0001510067114*3*3*3*3 / 1*2*2*2*2*2*2*2 = 9053.116875 / 16 = 101.95500346155 →
A -> A# : 894.13500 -> 16/9 = 2*2*2*2*1 / 3*3*2*3*149*1.0001510067114 = 7.9987921287054 / 4023 = 101.95499826923 →
A# -> B : 16/9 -> 1090.22500 = 2*5*109*1.0002064220183*3*3 / 1*2*2*2*2 = 2453.00625 / 4 = 94.135001730775 →
B -> C : 1090.22500 -> 1 = 2*1*1 / 1*2*5*109*1.0002064220183 = 0.99979362058291 / 545 = 109.775 →
2 x 90.2 2 x 94.1 2 x 98 2 x 102 2 x 105.9 2 x 109.8
statistics for interval major second:
C -> D : 1 -> 196.09000 = 2*2*7*7*1.0004591836735*1 / 1*1 = 196.09 / 1 = 196.09 →
C# -> D# : 256/243 -> 32/27 = 2*2*2*2*2*3*3*3*3*3 / 3*3*3*2*2*2*2*2*2*2*2 = 9 / 8 = 203.91000173077 →
D -> E : 196.09000 -> 392.18000 = 2*2*2*7*7*1.0004591836735*1 / 1*2*2*7*7*1.0004591836735 = 2 / 1 = 196.09 →
D# -> F : 32/27 -> 4/3 = 2*2*3*3*3 / 3*2*2*2*2*2 = 9 / 8 = 203.91000173077 →
E -> F# : 392.18000 -> 1024/729 = 2*2*2*2*2*2*2*2*2*2*1 / 3*3*3*3*3*3*2*2*2*7*7*1.0004591836735 = 127.94125146616 / 35721 = 196.08999480768 →
F -> G : 4/3 -> 698.04500 = 2*349*1.000064469914*3 / 1*2*2 = 1047.0675 / 2 = 200.00000086539 →
F# -> G# : 1024/729 -> 128/81 = 2*2*2*2*2*2*2*3*3*3*3*3*3 / 3*3*3*3*2*2*2*2*2*2*2*2*2*2 = 9 / 8 = 203.91000173077 →
G -> A : 698.04500 -> 894.13500 = 2*3*149*1.0001510067114*1 / 1*2*349*1.000064469914 = 447.03867945476 / 349 = 196.09 →
G# -> A# : 128/81 -> 16/9 = 2*2*2*2*3*3*3*3 / 3*3*2*2*2*2*2*2*2 = 9 / 8 = 203.91000173077 →
A -> B : 894.13500 -> 1090.22500 = 2*5*109*1.0002064220183*1 / 1*2*3*149*1.0001510067114 = 545.03019678237 / 447 = 196.09 →
A# -> C : 16/9 -> 1 = 2*1*3*3 / 1*2*2*2*2 = 9 / 8 = 203.91000173077 →
B -> C# : 1090.22500 -> 256/243 = 2*2*2*2*2*2*2*2*2*1 / 3*3*3*3*3*2*5*109*1.0002064220183 = 255.94716686922 / 132435 = 199.99999567306 →
5 x 196.1 2 x 200 5 x 203.9
statistics for interval minor third:
C -> D# : 1 -> 32/27 = 2*2*2*2*2*1 / 3*3*3*1 = 32 / 27 = 294.13499740384 →
C# -> E : 256/243 -> 392.18000 = 2*2*2*7*7*1.0004591836735*3*3*3*3*3 / 1*2*2*2*2*2*2*2*2 = 95299.74 / 256 = 301.95500432694 →
D -> F : 196.09000 -> 4/3 = 2*2*1 / 3*2*2*7*7*1.0004591836735 = 0.3331803423598 / 49 = 301.95499913461 →
D# -> F# : 32/27 -> 1024/729 = 2*2*2*2*2*2*2*2*2*2*3*3*3 / 3*3*3*3*3*3*2*2*2*2*2 = 32 / 27 = 294.13499740384 →
E -> G : 392.18000 -> 698.04500 = 2*349*1.000064469914*1 / 1*2*2*2*7*7*1.0004591836735 = 348.86230812382 / 196 = 305.865 →
F -> G# : 4/3 -> 128/81 = 2*2*2*2*2*2*2*3 / 3*3*3*3*2*2 = 32 / 27 = 294.13499740384 →
F# -> A : 1024/729 -> 894.13500 = 2*3*149*1.0001510067114*3*3*3*3*3*3 / 1*2*2*2*2*2*2*2*2*2*2 = 40739.0259375 / 64 = 305.86500519232 →
G -> A# : 698.04500 -> 16/9 = 2*2*2*2*1 / 3*3*2*349*1.000064469914 = 7.9994842739365 / 3141 = 298.04499826923 →
G# -> B : 128/81 -> 1090.22500 = 2*5*109*1.0002064220183*3*3*3*3 / 1*2*2*2*2*2*2*2 = 22077.05625 / 32 = 298.04500346155 →
A -> C : 894.13500 -> 1 = 2*1*1 / 1*2*3*149*1.0001510067114 = 0.99984901608817 / 447 = 305.865 →
A# -> C# : 16/9 -> 256/243 = 2*2*2*2*2*2*2*2*2*3*3 / 3*3*3*3*3*2*2*2*2 = 32 / 27 = 294.13499740384 →
B -> D : 1090.22500 -> 196.09000 = 2*2*2*7*7*1.0004591836735*1 / 1*2*5*109*1.0002064220183 = 196.0495310601 / 545 = 305.865 →
4 x 294.1 2 x 298 2 x 302 4 x 305.9
statistics for interval major third:
C -> E : 1 -> 392.18000 = 2*2*2*7*7*1.0004591836735*1 / 1*1 = 392.18 / 1 = 392.18 →
C# -> F : 256/243 -> 4/3 = 2*2*3*3*3*3*3 / 3*2*2*2*2*2*2*2*2 = 81 / 64 = 407.82000346155 →
D -> F# : 196.09000 -> 1024/729 = 2*2*2*2*2*2*2*2*2*2*1 / 3*3*3*3*3*3*2*2*7*7*1.0004591836735 = 85.294167644109 / 11907 = 392.17999480768 →
D# -> G : 32/27 -> 698.04500 = 2*349*1.000064469914*3*3*3 / 1*2*2*2*2*2 = 18847.215 / 32 = 403.91000259616 →
E -> G# : 392.18000 -> 128/81 = 2*2*2*2*2*2*2*1 / 3*3*3*3*2*2*2*7*7*1.0004591836735 = 5.3308854777568 / 1323 = 399.99999653845 →
F -> A : 4/3 -> 894.13500 = 2*3*149*1.0001510067114*3 / 1*2*2 = 1341.2025 / 2 = 396.09000086539 →
F# -> A# : 1024/729 -> 16/9 = 2*2*2*2*3*3*3*3*3*3 / 3*3*2*2*2*2*2*2*2*2*2*2 = 81 / 64 = 407.82000346155 →
G -> B : 698.04500 -> 1090.22500 = 2*5*109*1.0002064220183*1 / 1*2*349*1.000064469914 = 545.07735890953 / 349 = 392.18 →
G# -> C : 128/81 -> 1 = 2*1*3*3*3*3 / 1*2*2*2*2*2*2*2 = 81 / 64 = 407.82000346155 →
A -> C# : 894.13500 -> 256/243 = 2*2*2*2*2*2*2*2*2*1 / 3*3*3*3*3*2*3*149*1.0001510067114 = 255.96134811857 / 108621 = 396.08999567306 →
A# -> D : 16/9 -> 196.09000 = 2*2*2*7*7*1.0004591836735*3*3 / 1*2*2*2*2 = 441.2025 / 2 = 400.00000173077 →
B -> D# : 1090.22500 -> 32/27 = 2*2*2*2*2*2*1 / 3*3*3*2*5*109*1.0002064220183 = 10.664465286218 / 4905 = 403.90999740384 →
3 x 392.2 2 x 396.1 2 x 400 2 x 403.9 3 x 407.8
statistics for interval fourth:
C -> F : 1 -> 4/3 = 2*2*1 / 3*1 = 4 / 3 = 498.04499913461 →
C# -> F# : 256/243 -> 1024/729 = 2*2*2*2*2*2*2*2*2*2*3*3*3*3*3 / 3*3*3*3*3*3*2*2*2*2*2*2*2*2 = 4 / 3 = 498.04499913461 →
D -> G : 196.09000 -> 698.04500 = 2*349*1.000064469914*1 / 1*2*2*7*7*1.0004591836735 = 348.86230812382 / 98 = 501.955 →
D# -> G# : 32/27 -> 128/81 = 2*2*2*2*2*2*2*3*3*3 / 3*3*3*3*2*2*2*2*2 = 4 / 3 = 498.04499913461 →
E -> A : 392.18000 -> 894.13500 = 2*3*149*1.0001510067114*1 / 1*2*2*2*7*7*1.0004591836735 = 446.86230812382 / 196 = 501.955 →
F -> A# : 4/3 -> 16/9 = 2*2*2*2*3 / 3*3*2*2 = 4 / 3 = 498.04499913461 →
F# -> B : 1024/729 -> 1090.22500 = 2*5*109*1.0002064220183*3*3*3*3*3*3 / 1*2*2*2*2*2*2*2*2*2*2 = 397387.0125 / 512 = 501.95500519232 →
G -> C : 698.04500 -> 1 = 2*1*1 / 1*2*349*1.000064469914 = 0.99993553424206 / 349 = 501.955 →
G# -> C# : 128/81 -> 256/243 = 2*2*2*2*2*2*2*2*2*3*3*3*3 / 3*3*3*3*3*2*2*2*2*2*2*2 = 4 / 3 = 498.04499913461 →
A -> D : 894.13500 -> 196.09000 = 2*2*2*7*7*1.0004591836735*1 / 1*2*3*149*1.0001510067114 = 196.06039356473 / 447 = 501.955 →
A# -> D# : 16/9 -> 32/27 = 2*2*2*2*2*2*3*3 / 3*3*3*2*2*2*2 = 4 / 3 = 498.04499913461 →
B -> E : 1090.22500 -> 392.18000 = 2*2*2*2*7*7*1.0004591836735*1 / 1*2*5*109*1.0002064220183 = 392.0990621202 / 545 = 501.955 →
6 x 498 6 x 502
statistics for interval tritone:
C -> F# : 1 -> 1024/729 = 2*2*2*2*2*2*2*2*2*2*1 / 3*3*3*3*3*3*1 = 1024 / 729 = 588.26999480768 →
C# -> G : 256/243 -> 698.04500 = 2*349*1.000064469914*3*3*3*3*3 / 1*2*2*2*2*2*2*2*2 = 21203.116875 / 32 = 607.82000432694 →
D -> G# : 196.09000 -> 128/81 = 2*2*2*2*2*2*2*1 / 3*3*3*3*2*2*7*7*1.0004591836735 = 31.985312866541 / 3969 = 596.08999653845 →
D# -> A : 32/27 -> 894.13500 = 2*3*149*1.0001510067114*3*3*3 / 1*2*2*2*2*2 = 24141.645 / 32 = 600.00000259616 →
E -> A# : 392.18000 -> 16/9 = 2*2*2*2*1 / 3*3*2*2*2*7*7*1.0004591836735 = 1.9990820541588 / 441 = 603.90999826923 →
F -> B : 4/3 -> 1090.22500 = 2*5*109*1.0002064220183*3 / 1*2*2 = 1635.3375 / 2 = 592.18000086539 →
F# -> C : 1024/729 -> 1 = 2*1*3*3*3*3*3*3 / 1*2*2*2*2*2*2*2*2*2*2 = 729 / 512 = 611.73000519232 →
G -> C# : 698.04500 -> 256/243 = 2*2*2*2*2*2*2*2*2*1 / 3*3*3*3*3*2*349*1.000064469914 = 255.98349676597 / 84807 = 592.17999567306 →
G# -> D : 128/81 -> 196.09000 = 2*2*2*7*7*1.0004591836735*3*3*3*3 / 1*2*2*2*2*2*2*2 = 15883.29 / 64 = 603.91000346155 →
A -> D# : 894.13500 -> 32/27 = 2*2*2*2*2*2*1 / 3*3*3*2*3*149*1.0001510067114 = 10.665056171607 / 4023 = 599.99999740384 →
A# -> E : 16/9 -> 392.18000 = 2*2*2*2*7*7*1.0004591836735*3*3 / 1*2*2*2*2 = 3529.62 / 8 = 596.09000173077 →
B -> F : 1090.22500 -> 4/3 = 2*2*2*1 / 3*2*5*109*1.0002064220183 = 3.9991744823316 / 1635 = 607.81999913461 →
1 x 588.3 2 x 592.2 2 x 596.1 2 x 600 2 x 603.9 2 x 607.8 1 x 611.7
statistics for interval fifth:
C -> G : 1 -> 698.04500 = 2*349*1.000064469914*1 / 1*1 = 698.045 / 1 = 698.045 →
C# -> G# : 256/243 -> 128/81 = 2*2*2*2*2*2*2*3*3*3*3*3 / 3*3*3*3*2*2*2*2*2*2*2*2 = 3 / 2 = 701.95500086539 →
D -> A : 196.09000 -> 894.13500 = 2*3*149*1.0001510067114*1 / 1*2*2*7*7*1.0004591836735 = 446.86230812382 / 98 = 698.045 →
D# -> A# : 32/27 -> 16/9 = 2*2*2*2*3*3*3 / 3*3*2*2*2*2*2 = 3 / 2 = 701.95500086539 →
E -> B : 392.18000 -> 1090.22500 = 2*5*109*1.0002064220183*1 / 1*2*2*2*7*7*1.0004591836735 = 544.86230812382 / 196 = 698.045 →
F -> C : 4/3 -> 1 = 2*1*3 / 1*2*2 = 3 / 2 = 701.95500086539 →
F# -> C# : 1024/729 -> 256/243 = 2*2*2*2*2*2*2*2*2*3*3*3*3*3*3 / 3*3*3*3*3*2*2*2*2*2*2*2*2*2*2 = 3 / 2 = 701.95500086539 →
G -> D : 698.04500 -> 196.09000 = 2*2*2*7*7*1.0004591836735*1 / 1*2*349*1.000064469914 = 196.07735890953 / 349 = 698.045 →
G# -> D# : 128/81 -> 32/27 = 2*2*2*2*2*2*3*3*3*3 / 3*3*3*2*2*2*2*2*2*2 = 3 / 2 = 701.95500086539 →
A -> E : 894.13500 -> 392.18000 = 2*2*2*2*7*7*1.0004591836735*1 / 1*2*3*149*1.0001510067114 = 392.12078712946 / 447 = 698.045 →
A# -> F : 16/9 -> 4/3 = 2*2*2*3*3 / 3*2*2*2*2 = 3 / 2 = 701.95500086539 →
B -> F# : 1090.22500 -> 1024/729 = 2*2*2*2*2*2*2*2*2*2*2*1 / 3*3*3*3*3*3*2*5*109*1.0002064220183 = 1023.7886674769 / 397305 = 698.04499480768 →
6 x 698 6 x 702
statistics for interval minor sixth:
C -> G# : 1 -> 128/81 = 2*2*2*2*2*2*2*1 / 3*3*3*3*1 = 128 / 81 = 792.17999653845 →
C# -> A : 256/243 -> 894.13500 = 2*3*149*1.0001510067114*3*3*3*3*3 / 1*2*2*2*2*2*2*2*2 = 108637.4025 / 128 = 803.91000432694 →
D -> A# : 196.09000 -> 16/9 = 2*2*2*2*1 / 3*3*2*2*7*7*1.0004591836735 = 1.3327213694392 / 147 = 799.99999826923 →
D# -> B : 32/27 -> 1090.22500 = 2*5*109*1.0002064220183*3*3*3 / 1*2*2*2*2*2 = 7359.01875 / 8 = 796.09000259616 →
E -> C : 392.18000 -> 1 = 2*1*1 / 1*2*2*2*7*7*1.0004591836735 = 0.9995410270794 / 196 = 807.82 →
F -> C# : 4/3 -> 256/243 = 2*2*2*2*2*2*2*2*2*3 / 3*3*3*3*3*2*2 = 128 / 81 = 792.17999653845 →
F# -> D : 1024/729 -> 196.09000 = 2*2*2*7*7*1.0004591836735*3*3*3*3*3*3 / 1*2*2*2*2*2*2*2*2*2*2 = 142949.61 / 512 = 807.82000519232 →
G -> D# : 698.04500 -> 32/27 = 2*2*2*2*2*2*1 / 3*3*3*2*349*1.000064469914 = 10.665979031915 / 3141 = 796.08999740384 →
G# -> E : 128/81 -> 392.18000 = 2*2*2*2*7*7*1.0004591836735*3*3*3*3 / 1*2*2*2*2*2*2*2 = 15883.29 / 32 = 800.00000346155 →
A -> F : 894.13500 -> 4/3 = 2*2*2*1 / 3*2*3*149*1.0001510067114 = 3.9993960643527 / 1341 = 803.90999913461 →
A# -> F# : 16/9 -> 1024/729 = 2*2*2*2*2*2*2*2*2*2*2*3*3 / 3*3*3*3*3*3*2*2*2*2 = 128 / 81 = 792.17999653845 →
B -> G : 1090.22500 -> 698.04500 = 2*2*349*1.000064469914*1 / 1*2*5*109*1.0002064220183 = 697.9009378798 / 545 = 807.82 →
3 x 792.2 2 x 796.1 2 x 800 2 x 803.9 3 x 807.8
statistics for interval major sixth:
C -> A : 1 -> 894.13500 = 2*3*149*1.0001510067114*1 / 1*1 = 894.135 / 1 = 894.135 →
C# -> A# : 256/243 -> 16/9 = 2*2*2*2*3*3*3*3*3 / 3*3*2*2*2*2*2*2*2*2 = 27 / 16 = 905.86500259616 →
D -> B : 196.09000 -> 1090.22500 = 2*5*109*1.0002064220183*1 / 1*2*2*7*7*1.0004591836735 = 544.86230812382 / 98 = 894.135 →
D# -> C : 32/27 -> 1 = 2*1*3*3*3 / 1*2*2*2*2*2 = 27 / 16 = 905.86500259616 →
E -> C# : 392.18000 -> 256/243 = 2*2*2*2*2*2*2*2*2*1 / 3*3*3*3*3*2*2*2*7*7*1.0004591836735 = 63.970625733082 / 11907 = 898.04499567306 →
F -> D : 4/3 -> 196.09000 = 2*2*2*7*7*1.0004591836735*3 / 1*2*2 = 294.135 / 1 = 898.04500086539 →
F# -> D# : 1024/729 -> 32/27 = 2*2*2*2*2*2*3*3*3*3*3*3 / 3*3*3*2*2*2*2*2*2*2*2*2*2 = 27 / 16 = 905.86500259616 →
G -> E : 698.04500 -> 392.18000 = 2*2*2*2*7*7*1.0004591836735*1 / 1*2*349*1.000064469914 = 392.15471781905 / 349 = 894.135 →
G# -> F : 128/81 -> 4/3 = 2*2*2*3*3*3*3 / 3*2*2*2*2*2*2*2 = 27 / 16 = 905.86500259616 →
A -> F# : 894.13500 -> 1024/729 = 2*2*2*2*2*2*2*2*2*2*2*1 / 3*3*3*3*3*3*2*3*149*1.0001510067114 = 1023.8453924743 / 325863 = 894.13499480768 →
A# -> G : 16/9 -> 698.04500 = 2*2*349*1.000064469914*3*3 / 1*2*2*2*2 = 3141.2025 / 4 = 901.95500173077 →
B -> G# : 1090.22500 -> 128/81 = 2*2*2*2*2*2*2*2*1 / 3*3*3*3*2*5*109*1.0002064220183 = 14.21928704829 / 4905 = 901.95499653845 →
4 x 894.1 2 x 898 2 x 902 4 x 905.9
statistics for interval minor seventh:
C -> A# : 1 -> 16/9 = 2*2*2*2*1 / 3*3*1 = 16 / 9 = 996.08999826923 →
C# -> B : 256/243 -> 1090.22500 = 2*5*109*1.0002064220183*3*3*3*3*3 / 1*2*2*2*2*2*2*2*2 = 66231.16875 / 64 = 1000.0000043269 →
D -> C : 196.09000 -> 1 = 2*1*1 / 1*2*2*7*7*1.0004591836735 = 0.9995410270794 / 98 = 1003.91 →
D# -> C# : 32/27 -> 256/243 = 2*2*2*2*2*2*2*2*2*3*3*3 / 3*3*3*3*3*2*2*2*2*2 = 16 / 9 = 996.08999826923 →
E -> D : 392.18000 -> 196.09000 = 2*2*2*7*7*1.0004591836735*1 / 1*2*2*2*7*7*1.0004591836735 = 1 / 1 = 1003.91 →
F -> D# : 4/3 -> 32/27 = 2*2*2*2*2*2*3 / 3*3*3*2*2 = 16 / 9 = 996.08999826923 →
F# -> E : 1024/729 -> 392.18000 = 2*2*2*2*7*7*1.0004591836735*3*3*3*3*3*3 / 1*2*2*2*2*2*2*2*2*2*2 = 285899.22 / 512 = 1003.9100051923 →
G -> F : 698.04500 -> 4/3 = 2*2*2*1 / 3*2*349*1.000064469914 = 3.9997421369682 / 1047 = 999.99999913461 →
G# -> F# : 128/81 -> 1024/729 = 2*2*2*2*2*2*2*2*2*2*2*3*3*3*3 / 3*3*3*3*3*3*2*2*2*2*2*2*2 = 16 / 9 = 996.08999826923 →
A -> G : 894.13500 -> 698.04500 = 2*2*349*1.000064469914*1 / 1*2*3*149*1.0001510067114 = 697.93960643527 / 447 = 1003.91 →
A# -> G# : 16/9 -> 128/81 = 2*2*2*2*2*2*2*2*3*3 / 3*3*3*3*2*2*2*2 = 16 / 9 = 996.08999826923 →
B -> A : 1090.22500 -> 894.13500 = 2*2*3*149*1.0001510067114*1 / 1*2*5*109*1.0002064220183 = 893.9504689399 / 545 = 1003.91 →
5 x 996.1 2 x 1000 5 x 1003.9
statistics for interval major seventh:
C -> B : 1 -> 1090.22500 = 2*5*109*1.0002064220183*1 / 1*1 = 1090.225 / 1 = 1090.225 →
C# -> C : 256/243 -> 1 = 2*1*3*3*3*3*3 / 1*2*2*2*2*2*2*2*2 = 243 / 128 = 1109.7750043269 →
D -> C# : 196.09000 -> 256/243 = 2*2*2*2*2*2*2*2*2*1 / 3*3*3*3*3*2*2*7*7*1.0004591836735 = 14.215694607352 / 1323 = 1094.1349956731 →
D# -> D : 32/27 -> 196.09000 = 2*2*2*7*7*1.0004591836735*3*3*3 / 1*2*2*2*2*2 = 2647.215 / 8 = 1101.9550025962 →
E -> D# : 392.18000 -> 32/27 = 2*2*2*2*2*2*1 / 3*3*3*2*2*2*7*7*1.0004591836735 = 2.6654427388784 / 441 = 1101.9549974038 →
F -> E : 4/3 -> 392.18000 = 2*2*2*2*7*7*1.0004591836735*3 / 1*2*2 = 588.27 / 1 = 1094.1350008654 →
F# -> F : 1024/729 -> 4/3 = 2*2*2*3*3*3*3*3*3 / 3*2*2*2*2*2*2*2*2*2*2 = 243 / 128 = 1109.7750043269 →
G -> F# : 698.04500 -> 1024/729 = 2*2*2*2*2*2*2*2*2*2*2*1 / 3*3*3*3*3*3*2*349*1.000064469914 = 1023.9339870639 / 254421 = 1090.2249948077 →
G# -> G : 128/81 -> 698.04500 = 2*2*349*1.000064469914*3*3*3*3 / 1*2*2*2*2*2*2*2 = 56541.645 / 64 = 1105.8650034615 →
A -> G# : 894.13500 -> 128/81 = 2*2*2*2*2*2*2*2*1 / 3*3*3*3*2*3*149*1.0001510067114 = 14.220074895476 / 4023 = 1098.0449965385 →
A# -> A : 16/9 -> 894.13500 = 2*2*3*149*1.0001510067114*3*3 / 1*2*2*2*2 = 8047.215 / 8 = 1098.0450017308 →
B -> A# : 1090.22500 -> 16/9 = 2*2*2*2*2*1 / 3*3*2*5*109*1.0002064220183 = 15.996697929327 / 4905 = 1105.8649982692 →
2 x 1090.2 2 x 1094.1 2 x 1098 2 x 1102 2 x 1105.9 2 x 1109.8
Prinz temperament
C : 1 = 0 ... +0.00
C# : 256/243 = 90.224995673063 ... -9.78
D : 193.15686 ... -6.84
D# : 32/27 = 294.13499740384 ... -5.87
E : 5/4 = 386.31371386483 ... -13.69
F : 4/3 = 498.04499913461 ... -1.96
F# : 1024/729 = 588.26999480768 ... -11.73
G : 696.57843 ... -3.42
G# : 128/81 = 792.17999653845 ... -7.82
A : 889.73529 ... -10.26
A# : 16/9 = 996.08999826923 ... -3.91
B : 15/8 = 1088.2687147302 ... -11.73
statistics for interval minor second:
C -> C# : 1 -> 256/243 = 2*2*2*2*2*2*2*2*1 / 3*3*3*3*3*1 = 256 / 243 = 90.224995673063 →
C# -> D : 256/243 -> 193.15686 = 193*1.000812746114*3*3*3*3*3 / 1*2*2*2*2*2*2*2*2 = 46937.11698 / 256 = 102.93186432694 →
D -> D# : 193.15686 -> 32/27 = 2*2*2*2*2*1 / 3*3*3*193*1.000812746114 = 31.974013244986 / 5211 = 100.97813740384 →
D# -> E : 32/27 -> 5/4 = 5*3*3*3 / 2*2*2*2*2*2*2 = 135 / 128 = 92.178716460997 →
E -> F : 5/4 -> 4/3 = 2*2*2*2 / 3*5 = 16 / 15 = 111.73128526978 →
F -> F# : 4/3 -> 1024/729 = 2*2*2*2*2*2*2*2*2*2*3 / 3*3*3*3*3*3*2*2 = 256 / 243 = 90.224995673063 →
F# -> G : 1024/729 -> 696.57843 = 2*2*2*3*29*1.0008310775862*3*3*3*3*3*3 / 1*2*2*2*2*2*2*2*2*2*2 = 507805.67547 / 1024 = 108.30843519232 →
G -> G# : 696.57843 -> 128/81 = 2*2*2*2*2*2*2*1 / 3*3*3*3*2*2*2*3*29*1.0008310775862 = 5.3289046001611 / 2349 = 95.60156653845 →
G# -> A : 128/81 -> 889.73529 = 7*127*1.0008270978628*3*3*3*3 / 1*2*2*2*2*2*2*2 = 18017.1396225 / 32 = 97.55529346155 →
A -> A# : 889.73529 -> 16/9 = 2*2*2*2*1 / 3*3*7*127*1.0008270978628 = 5.3289257902014 / 2667 = 106.35470826923 →
A# -> B : 16/9 -> 15/8 = 3*5*3*3 / 2*2*2*2*2*2*2 = 135 / 128 = 92.178716460997 →
B -> C : 15/8 -> 1 = 2*1*2*2*2 / 1*3*5 = 16 / 15 = 111.73128526978 →
2 x 90.2 2 x 92.2 1 x 95.6 1 x 97.6 1 x 101 1 x 102.9 1 x 106.4 1 x 108.3 2 x 111.7
statistics for interval major second:
C -> D : 1 -> 193.15686 = 193*1.000812746114*1 / 1*1 = 193.15686 / 1 = 193.15686 →
C# -> D# : 256/243 -> 32/27 = 2*2*2*2*2*3*3*3*3*3 / 3*3*3*2*2*2*2*2*2*2*2 = 9 / 8 = 203.91000173077 →
D -> E : 193.15686 -> 5/4 = 5*1 / 2*2*193*1.000812746114 = 1.2489848923823 / 193 = 193.15685386483 →
D# -> F : 32/27 -> 4/3 = 2*2*3*3*3 / 3*2*2*2*2*2 = 9 / 8 = 203.91000173077 →
E -> F# : 5/4 -> 1024/729 = 2*2*2*2*2*2*2*2*2*2*2*2 / 3*3*3*3*3*3*5 = 4096 / 3645 = 201.95628094284 →
F -> G : 4/3 -> 696.57843 = 2*2*2*3*29*1.0008310775862*3 / 1*2*2 = 2089.73529 / 4 = 198.53343086539 →
F# -> G# : 1024/729 -> 128/81 = 2*2*2*2*2*2*2*3*3*3*3*3*3 / 3*3*3*3*2*2*2*2*2*2*2*2*2*2 = 9 / 8 = 203.91000173077 →
G -> A : 696.57843 -> 889.73529 = 7*127*1.0008270978628*1 / 1*2*2*2*3*29*1.0008310775862 = 888.99646496375 / 696 = 193.15686 →
G# -> A# : 128/81 -> 16/9 = 2*2*2*2*3*3*3*3 / 3*3*2*2*2*2*2*2*2 = 9 / 8 = 203.91000173077 →
A -> B : 889.73529 -> 15/8 = 3*5*1 / 2*2*2*7*127*1.0008270978628 = 7.4938018924707 / 3556 = 198.53342473022 →
A# -> C : 16/9 -> 1 = 2*1*3*3 / 1*2*2*2*2 = 9 / 8 = 203.91000173077 →
B -> C# : 15/8 -> 256/243 = 2*2*2*2*2*2*2*2*2*2*2*2 / 3*3*3*3*3*3*5 = 4096 / 3645 = 201.95628094284 →
3 x 193.2 2 x 198.5 2 x 202 5 x 203.9
statistics for interval minor third:
C -> D# : 1 -> 32/27 = 2*2*2*2*2*1 / 3*3*3*1 = 32 / 27 = 294.13499740384 →
C# -> E : 256/243 -> 5/4 = 5*3*3*3*3*3 / 2*2*2*2*2*2*2*2*2*2 = 1215 / 1024 = 296.08871819177 →
D -> F : 193.15686 -> 4/3 = 2*2*1 / 3*193*1.000812746114 = 1.3322505518744 / 193 = 304.88813913461 →
D# -> F# : 32/27 -> 1024/729 = 2*2*2*2*2*2*2*2*2*2*3*3*3 / 3*3*3*3*3*3*2*2*2*2*2 = 32 / 27 = 294.13499740384 →
E -> G : 5/4 -> 696.57843 = 2*2*2*3*29*1.0008310775862*2*2 / 1*5 = 2786.31372 / 5 = 310.26471613517 →
F -> G# : 4/3 -> 128/81 = 2*2*2*2*2*2*2*3 / 3*3*3*3*2*2 = 32 / 27 = 294.13499740384 →
F# -> A : 1024/729 -> 889.73529 = 7*127*1.0008270978628*3*3*3*3*3*3 / 1*2*2*2*2*2*2*2*2*2*2 = 648617.02641 / 1024 = 301.46529519232 →
G -> A# : 696.57843 -> 16/9 = 2*2*2*2*1 / 3*3*2*2*2*3*29*1.0008310775862 = 1.9983392250604 / 783 = 299.51156826923 →
G# -> B : 128/81 -> 15/8 = 3*5*3*3*3*3 / 2*2*2*2*2*2*2*2*2*2 = 1215 / 1024 = 296.08871819177 →
A -> C : 889.73529 -> 1 = 2*1*1 / 1*7*127*1.0008270978628 = 1.9983471713255 / 889 = 310.26471 →
A# -> C# : 16/9 -> 256/243 = 2*2*2*2*2*2*2*2*2*3*3 / 3*3*3*3*3*2*2*2*2 = 32 / 27 = 294.13499740384 →
B -> D : 15/8 -> 193.15686 = 2*193*1.000812746114*2*2*2 / 1*3*5 = 206.033984 / 1 = 304.88814526978 →
4 x 294.1 2 x 296.1 1 x 299.5 1 x 301.5 2 x 304.9 2 x 310.3
statistics for interval major third:
C -> E : 1 -> 5/4 = 5*1 / 2*2*1 = 5 / 4 = 386.31371386483 →
C# -> F : 256/243 -> 4/3 = 2*2*3*3*3*3*3 / 3*2*2*2*2*2*2*2*2 = 81 / 64 = 407.82000346155 →
D -> F# : 193.15686 -> 1024/729 = 2*2*2*2*2*2*2*2*2*2*1 / 3*3*3*3*3*3*193*1.000812746114 = 341.05614127986 / 46899 = 395.11313480768 →
D# -> G : 32/27 -> 696.57843 = 2*2*2*3*29*1.0008310775862*3*3*3 / 1*2*2*2*2*2 = 18807.61761 / 32 = 402.44343259616 →
E -> G# : 5/4 -> 128/81 = 2*2*2*2*2*2*2*2*2 / 3*3*3*3*5 = 512 / 405 = 405.86628267362 →
F -> A : 4/3 -> 889.73529 = 7*127*1.0008270978628*3 / 1*2*2 = 2669.20587 / 4 = 391.69029086539 →
F# -> A# : 1024/729 -> 16/9 = 2*2*2*2*3*3*3*3*3*3 / 3*3*2*2*2*2*2*2*2*2*2*2 = 81 / 64 = 407.82000346155 →
G -> B : 696.57843 -> 15/8 = 3*5*1 / 2*2*2*2*2*2*3*29*1.0008310775862 = 1.2489620156628 / 464 = 391.69028473022 →
G# -> C : 128/81 -> 1 = 2*1*3*3*3*3 / 1*2*2*2*2*2*2*2 = 81 / 64 = 407.82000346155 →
A -> C# : 889.73529 -> 256/243 = 2*2*2*2*2*2*2*2*2*1 / 3*3*3*3*3*7*127*1.0008270978628 = 170.52562528645 / 72009 = 400.48970567306 →
A# -> D : 16/9 -> 193.15686 = 2*193*1.000812746114*3*3 / 1*2*2*2*2 = 869.20587 / 4 = 397.06686173077 →
B -> D# : 15/8 -> 32/27 = 2*2*2*2*2*2*2*2*2 / 3*3*3*3*5 = 512 / 405 = 405.86628267362 →
1 x 386.3 2 x 391.7 1 x 395.1 1 x 397.1 1 x 400.5 1 x 402.4 2 x 405.9 3 x 407.8
statistics for interval fourth:
C -> F : 1 -> 4/3 = 2*2*1 / 3*1 = 4 / 3 = 498.04499913461 →
C# -> F# : 256/243 -> 1024/729 = 2*2*2*2*2*2*2*2*2*2*3*3*3*3*3 / 3*3*3*3*3*3*2*2*2*2*2*2*2*2 = 4 / 3 = 498.04499913461 →
D -> G : 193.15686 -> 696.57843 = 2*2*2*3*29*1.0008310775862*1 / 1*193*1.000812746114 = 696.0127483435 / 193 = 503.42157 →
D# -> G# : 32/27 -> 128/81 = 2*2*2*2*2*2*2*3*3*3 / 3*3*3*3*2*2*2*2*2 = 4 / 3 = 498.04499913461 →
E -> A : 5/4 -> 889.73529 = 7*127*1.0008270978628*2*2 / 1*5 = 3558.94116 / 5 = 503.42157613517 →
F -> A# : 4/3 -> 16/9 = 2*2*2*2*3 / 3*3*2*2 = 4 / 3 = 498.04499913461 →
F# -> B : 1024/729 -> 15/8 = 3*5*3*3*3*3*3*3 / 2*2*2*2*2*2*2*2*2*2*2*2*2 = 10935 / 8192 = 499.99871992255 →
G -> C : 696.57843 -> 1 = 2*1*1 / 1*2*2*2*3*29*1.0008310775862 = 0.99916961253021 / 348 = 503.42157 →
G# -> C# : 128/81 -> 256/243 = 2*2*2*2*2*2*2*2*2*3*3*3*3 / 3*3*3*3*3*2*2*2*2*2*2*2 = 4 / 3 = 498.04499913461 →
A -> D : 889.73529 -> 193.15686 = 2*193*1.000812746114*1 / 1*7*127*1.0008270978628 = 385.99446480312 / 889 = 503.42157 →
A# -> D# : 16/9 -> 32/27 = 2*2*2*2*2*2*3*3 / 3*3*3*2*2*2*2 = 4 / 3 = 498.04499913461 →
B -> E : 15/8 -> 5/4 = 2*5*2*2*2 / 2*2*3*5 = 4 / 3 = 498.04499913461 →
7 x 498 1 x 500 4 x 503.4
statistics for interval tritone:
C -> F# : 1 -> 1024/729 = 2*2*2*2*2*2*2*2*2*2*1 / 3*3*3*3*3*3*1 = 1024 / 729 = 588.26999480768 →
C# -> G : 256/243 -> 696.57843 = 2*2*2*3*29*1.0008310775862*3*3*3*3*3 / 1*2*2*2*2*2*2*2*2 = 42317.1396225 / 64 = 606.35343432694 →
D -> G# : 193.15686 -> 128/81 = 2*2*2*2*2*2*2*1 / 3*3*3*3*193*1.000812746114 = 127.89605297995 / 15633 = 599.02313653845 →
D# -> A : 32/27 -> 889.73529 = 7*127*1.0008270978628*3*3*3 / 1*2*2*2*2*2 = 12011.426415 / 16 = 595.60029259616 →
E -> A# : 5/4 -> 16/9 = 2*2*2*2*2*2 / 3*3*5 = 64 / 45 = 609.77628440439 →
F -> B : 4/3 -> 15/8 = 3*5*3 / 2*2*2*2*2 = 45 / 32 = 590.22371559561 →
F# -> C : 1024/729 -> 1 = 2*1*3*3*3*3*3*3 / 1*2*2*2*2*2*2*2*2*2*2 = 729 / 512 = 611.73000519232 →
G -> C# : 696.57843 -> 256/243 = 2*2*2*2*2*2*2*2*2*1 / 3*3*3*3*3*2*2*2*3*29*1.0008310775862 = 63.946855201933 / 21141 = 593.64656567306 →
G# -> D : 128/81 -> 193.15686 = 2*193*1.000812746114*3*3*3*3 / 1*2*2*2*2*2*2*2 = 15645.70566 / 64 = 600.97686346155 →
A -> D# : 889.73529 -> 32/27 = 2*2*2*2*2*2*1 / 3*3*3*7*127*1.0008270978628 = 63.947109482417 / 24003 = 604.39970740384 →
A# -> E : 16/9 -> 5/4 = 2*5*3*3 / 2*2*2*2*2*2 = 45 / 32 = 590.22371559561 →
B -> F : 15/8 -> 4/3 = 2*2*2*2*2*2 / 3*3*5 = 64 / 45 = 609.77628440439 →
1 x 588.3 2 x 590.2 1 x 593.6 1 x 595.6 1 x 599 1 x 601 1 x 604.4 1 x 606.4 2 x 609.8 1 x 611.7
statistics for interval fifth:
C -> G : 1 -> 696.57843 = 2*2*2*3*29*1.0008310775862*1 / 1*1 = 696.57843 / 1 = 696.57843 →
C# -> G# : 256/243 -> 128/81 = 2*2*2*2*2*2*2*3*3*3*3*3 / 3*3*3*3*2*2*2*2*2*2*2*2 = 3 / 2 = 701.95500086539 →
D -> A : 193.15686 -> 889.73529 = 7*127*1.0008270978628*1 / 1*193*1.000812746114 = 889.0127483435 / 193 = 696.57843 →
D# -> A# : 32/27 -> 16/9 = 2*2*2*2*3*3*3 / 3*3*2*2*2*2*2 = 3 / 2 = 701.95500086539 →
E -> B : 5/4 -> 15/8 = 3*5*2*2 / 2*2*2*5 = 3 / 2 = 701.95500086539 →
F -> C : 4/3 -> 1 = 2*1*3 / 1*2*2 = 3 / 2 = 701.95500086539 →
F# -> C# : 1024/729 -> 256/243 = 2*2*2*2*2*2*2*2*2*3*3*3*3*3*3 / 3*3*3*3*3*2*2*2*2*2*2*2*2*2*2 = 3 / 2 = 701.95500086539 →
G -> D : 696.57843 -> 193.15686 = 2*193*1.000812746114*1 / 1*2*2*2*3*29*1.0008310775862 = 192.99646496375 / 348 = 696.57843 →
G# -> D# : 128/81 -> 32/27 = 2*2*2*2*2*2*3*3*3*3 / 3*3*3*2*2*2*2*2*2*2 = 3 / 2 = 701.95500086539 →
A -> E : 889.73529 -> 5/4 = 2*5*1 / 2*2*7*127*1.0008270978628 = 2.4979339641569 / 889 = 696.57842386483 →
A# -> F : 16/9 -> 4/3 = 2*2*2*3*3 / 3*2*2*2*2 = 3 / 2 = 701.95500086539 →
B -> F# : 15/8 -> 1024/729 = 2*2*2*2*2*2*2*2*2*2*2*2*2*2 / 3*3*3*3*3*3*3*5 = 16384 / 10935 = 700.00128007745 →
4 x 696.6 1 x 700 7 x 702
statistics for interval minor sixth:
C -> G# : 1 -> 128/81 = 2*2*2*2*2*2*2*1 / 3*3*3*3*1 = 128 / 81 = 792.17999653845 →
C# -> A : 256/243 -> 889.73529 = 7*127*1.0008270978628*3*3*3*3*3 / 1*2*2*2*2*2*2*2*2 = 216205.67547 / 256 = 799.51029432694 →
D -> A# : 193.15686 -> 16/9 = 2*2*2*2*1 / 3*3*193*1.000812746114 = 5.3290022074977 / 579 = 802.93313826923 →
D# -> B : 32/27 -> 15/8 = 3*5*3*3*3 / 2*2*2*2*2*2*2*2 = 405 / 256 = 794.13371732638 →
E -> C : 5/4 -> 1 = 2*1*2*2 / 1*5 = 8 / 5 = 813.68628613517 →
F -> C# : 4/3 -> 256/243 = 2*2*2*2*2*2*2*2*2*3 / 3*3*3*3*3*2*2 = 128 / 81 = 792.17999653845 →
F# -> D : 1024/729 -> 193.15686 = 2*193*1.000812746114*3*3*3*3*3*3 / 1*2*2*2*2*2*2*2*2*2*2 = 140811.35094 / 512 = 804.88686519232 →
G -> D# : 696.57843 -> 32/27 = 2*2*2*2*2*2*1 / 3*3*3*2*2*2*3*29*1.0008310775862 = 2.6644523000806 / 783 = 797.55656740384 →
G# -> E : 128/81 -> 5/4 = 2*5*3*3*3*3 / 2*2*2*2*2*2*2*2*2 = 405 / 256 = 794.13371732638 →
A -> F : 889.73529 -> 4/3 = 2*2*2*1 / 3*7*127*1.0008270978628 = 2.6644628951007 / 889 = 808.30970913461 →
A# -> F# : 16/9 -> 1024/729 = 2*2*2*2*2*2*2*2*2*2*2*3*3 / 3*3*3*3*3*3*2*2*2*2 = 128 / 81 = 792.17999653845 →
B -> G : 15/8 -> 696.57843 = 2*2*2*2*3*29*1.0008310775862*2*2*2 / 1*3*5 = 11145.25488 / 15 = 808.30971526978 →
3 x 792.2 2 x 794.1 1 x 797.6 1 x 799.5 1 x 802.9 1 x 804.9 2 x 808.3 1 x 813.7
statistics for interval major sixth:
C -> A : 1 -> 889.73529 = 7*127*1.0008270978628*1 / 1*1 = 889.73529 / 1 = 889.73529 →
C# -> A# : 256/243 -> 16/9 = 2*2*2*2*3*3*3*3*3 / 3*3*2*2*2*2*2*2*2*2 = 27 / 16 = 905.86500259616 →
D -> B : 193.15686 -> 15/8 = 3*5*1 / 2*2*2*193*1.000812746114 = 7.4939093542937 / 772 = 895.11185473022 →
D# -> C : 32/27 -> 1 = 2*1*3*3*3 / 1*2*2*2*2*2 = 27 / 16 = 905.86500259616 →
E -> C# : 5/4 -> 256/243 = 2*2*2*2*2*2*2*2*2*2*2 / 3*3*3*3*3*5 = 2048 / 1215 = 903.91128180823 →
F -> D : 4/3 -> 193.15686 = 2*193*1.000812746114*3 / 1*2*2 = 579.47058 / 2 = 895.11186086539 →
F# -> D# : 1024/729 -> 32/27 = 2*2*2*2*2*2*3*3*3*3*3*3 / 3*3*3*2*2*2*2*2*2*2*2*2*2 = 27 / 16 = 905.86500259616 →
G -> E : 696.57843 -> 5/4 = 2*5*1 / 2*2*2*2*2*3*29*1.0008310775862 = 1.2489620156628 / 348 = 889.73528386483 →
G# -> F : 128/81 -> 4/3 = 2*2*2*3*3*3*3 / 3*2*2*2*2*2*2*2 = 27 / 16 = 905.86500259616 →
A -> F# : 889.73529 -> 1024/729 = 2*2*2*2*2*2*2*2*2*2*2*1 / 3*3*3*3*3*3*7*127*1.0008270978628 = 682.10250114578 / 216027 = 898.53470480768 →
A# -> G : 16/9 -> 696.57843 = 2*2*2*2*3*29*1.0008310775862*3*3 / 1*2*2*2*2 = 6269.20587 / 8 = 900.48843173077 →
B -> G# : 15/8 -> 128/81 = 2*2*2*2*2*2*2*2*2*2*2 / 3*3*3*3*3*5 = 2048 / 1215 = 903.91128180823 →
2 x 889.7 2 x 895.1 1 x 898.5 1 x 900.5 2 x 903.9 4 x 905.9
statistics for interval minor seventh:
C -> A# : 1 -> 16/9 = 2*2*2*2*1 / 3*3*1 = 16 / 9 = 996.08999826923 →
C# -> B : 256/243 -> 15/8 = 3*5*3*3*3*3*3 / 2*2*2*2*2*2*2*2*2*2*2 = 3645 / 2048 = 998.04371905716 →
D -> C : 193.15686 -> 1 = 2*1*1 / 1*193*1.000812746114 = 1.9983758278117 / 193 = 1006.84314 →
D# -> C# : 32/27 -> 256/243 = 2*2*2*2*2*2*2*2*2*3*3*3 / 3*3*3*3*3*2*2*2*2*2 = 16 / 9 = 996.08999826923 →
E -> D : 5/4 -> 193.15686 = 2*193*1.000812746114*2*2 / 1*5 = 1545.25488 / 5 = 1006.8431461352 →
F -> D# : 4/3 -> 32/27 = 2*2*2*2*2*2*3 / 3*3*3*2*2 = 16 / 9 = 996.08999826923 →
F# -> E : 1024/729 -> 5/4 = 2*5*3*3*3*3*3*3 / 2*2*2*2*2*2*2*2*2*2*2*2 = 3645 / 2048 = 998.04371905716 →
G -> F : 696.57843 -> 4/3 = 2*2*2*1 / 3*2*2*2*3*29*1.0008310775862 = 0.33305653751007 / 87 = 1001.4665691346 →
G# -> F# : 128/81 -> 1024/729 = 2*2*2*2*2*2*2*2*2*2*2*3*3*3*3 / 3*3*3*3*3*3*2*2*2*2*2*2*2 = 16 / 9 = 996.08999826923 →
A -> G : 889.73529 -> 696.57843 = 2*2*2*2*3*29*1.0008310775862*1 / 1*7*127*1.0008270978628 = 1392.0055351969 / 889 = 1006.84314 →
A# -> G# : 16/9 -> 128/81 = 2*2*2*2*2*2*2*2*3*3 / 3*3*3*3*2*2*2*2 = 16 / 9 = 996.08999826923 →
B -> A : 15/8 -> 889.73529 = 2*7*127*1.0008270978628*2*2*2 / 1*3*5 = 14235.76464 / 15 = 1001.4665752698 →
5 x 996.1 2 x 998 2 x 1001.5 3 x 1006.8
statistics for interval major seventh:
C -> B : 1 -> 15/8 = 3*5*1 / 2*2*2*1 = 15 / 8 = 1088.2687147302 →
C# -> C : 256/243 -> 1 = 2*1*3*3*3*3*3 / 1*2*2*2*2*2*2*2*2 = 243 / 128 = 1109.7750043269 →
D -> C# : 193.15686 -> 256/243 = 2*2*2*2*2*2*2*2*2*1 / 3*3*3*3*3*193*1.000812746114 = 170.52807063993 / 15633 = 1097.0681356731 →
D# -> D : 32/27 -> 193.15686 = 2*193*1.000812746114*3*3*3 / 1*2*2*2*2*2 = 5215.23522 / 16 = 1099.0218625962 →
E -> D# : 5/4 -> 32/27 = 2*2*2*2*2*2*2*2 / 3*3*3*5 = 256 / 135 = 1107.821283539 →
F -> E : 4/3 -> 5/4 = 2*5*3 / 2*2*2*2 = 15 / 8 = 1088.2687147302 →
F# -> F : 1024/729 -> 4/3 = 2*2*2*3*3*3*3*3*3 / 3*2*2*2*2*2*2*2*2*2*2 = 243 / 128 = 1109.7750043269 →
G -> F# : 696.57843 -> 1024/729 = 2*2*2*2*2*2*2*2*2*2*2*1 / 3*3*3*3*3*3*2*2*2*3*29*1.0008310775862 = 255.78742080773 / 63423 = 1091.6915648077 →
G# -> G : 128/81 -> 696.57843 = 2*2*2*2*3*29*1.0008310775862*3*3*3*3 / 1*2*2*2*2*2*2*2 = 28211.426415 / 32 = 1104.3984334615 →
A -> G# : 889.73529 -> 128/81 = 2*2*2*2*2*2*2*2*1 / 3*3*3*3*7*127*1.0008270978628 = 255.78843792967 / 72009 = 1102.4447065385 →
A# -> A : 16/9 -> 889.73529 = 2*7*127*1.0008270978628*3*3 / 1*2*2*2*2 = 8007.61761 / 8 = 1093.6452917308 →
B -> A# : 15/8 -> 16/9 = 2*2*2*2*2*2*2*2 / 3*3*3*5 = 256 / 135 = 1107.821283539 →
2 x 1088.3 1 x 1091.7 1 x 1093.6 1 x 1097.1 1 x 1099 1 x 1102.4 1 x 1104.4 2 x 1107.8 2 x 1109.8
Broadwood's Best temperament
C : 0 ... +0.00
C# : 95.965 ... -4.03
D : 197.99 ... -2.01
D# : 297.955 ... -2.05
E : 392.98 ... -7.02
F : 498.945 ... -1.06
F# : 594.97 ... -5.03
G : 699.995 ... -0.00
G# : 796.96 ... -3.04
A : 894.985 ... -5.01
A# : 998.95 ... -1.05
B : 1093.975 ... -6.03
statistics for interval minor second:
C -> C# : 95.965 →
C# -> D : 102.025 →
D -> D# : 99.965 →
D# -> E : 95.025 →
E -> F : 105.965 →
F -> F# : 96.025 →
F# -> G : 105.025 →
G -> G# : 96.965 →
G# -> A : 98.025 →
A -> A# : 103.965 →
A# -> B : 95.025 →
B -> C : 106.025 →
2 x 95 2 x 96 1 x 97 1 x 98 1 x 100 1 x 102 1 x 104 1 x 105 2 x 106
statistics for interval major second:
C -> D : 197.99 →
C# -> D# : 201.99 →
D -> E : 194.99 →
D# -> F : 200.99 →
E -> F# : 201.99 →
F -> G : 201.05 →
F# -> G# : 201.99 →
G -> A : 194.99 →
G# -> A# : 201.99 →
A -> B : 198.99 →
A# -> C : 201.05 →
B -> C# : 201.99 →
2 x 195 1 x 198 1 x 199 1 x 201 2 x 201.1 5 x 202
statistics for interval minor third:
C -> D# : 297.955 →
C# -> E : 297.015 →
D -> F : 300.955 →
D# -> F# : 297.015 →
E -> G : 307.015 →
F -> G# : 298.015 →
F# -> A : 300.015 →
G -> A# : 298.955 →
G# -> B : 297.015 →
A -> C : 305.015 →
A# -> C# : 297.015 →
B -> D : 304.015 →
4 x 297 2 x 298 1 x 299 1 x 300 1 x 301 1 x 304 1 x 305 1 x 307
statistics for interval major third:
C -> E : 392.98 →
C# -> F : 402.98 →
D -> F# : 396.98 →
D# -> G : 402.04 →
E -> G# : 403.98 →
F -> A : 396.04 →
F# -> A# : 403.98 →
G -> B : 393.98 →
G# -> C : 403.04 →
A -> C# : 400.98 →
A# -> D : 399.04 →
B -> D# : 403.98 →
1 x 393 1 x 394 1 x 396 1 x 397 1 x 399 1 x 401 1 x 402 2 x 403 3 x 404
statistics for interval fourth:
C -> F : 498.945 →
C# -> F# : 499.005 →
D -> G : 502.005 →
D# -> G# : 499.005 →
E -> A : 502.005 →
F -> A# : 500.005 →
F# -> B : 499.005 →
G -> C : 500.005 →
G# -> C# : 499.005 →
A -> D : 503.005 →
A# -> D# : 499.005 →
B -> E : 499.005 →
1 x 498.9 6 x 499 2 x 500 2 x 502 1 x 503
statistics for interval tritone:
C -> F# : 594.97 →
C# -> G : 604.03 →
D -> G# : 598.97 →
D# -> A : 597.03 →
E -> A# : 605.97 →
F -> B : 595.03 →
F# -> C : 605.03 →
G -> C# : 595.97 →
G# -> D : 601.03 →
A -> D# : 602.97 →
A# -> E : 594.03 →
B -> F : 604.97 →
1 x 594 2 x 595 1 x 596 1 x 597 1 x 599 1 x 601 1 x 603 1 x 604 2 x 605 1 x 606
statistics for interval fifth:
C -> G : 699.995 →
C# -> G# : 700.995 →
D -> A : 696.995 →
D# -> A# : 700.995 →
E -> B : 700.995 →
F -> C : 701.055 →
F# -> C# : 700.995 →
G -> D : 697.995 →
G# -> D# : 700.995 →
A -> E : 697.995 →
A# -> F : 699.995 →
B -> F# : 700.995 →
1 x 697 2 x 698 2 x 700 6 x 701 1 x 701.1
statistics for interval minor sixth:
C -> G# : 796.96 →
C# -> A : 799.02 →
D -> A# : 800.96 →
D# -> B : 796.02 →
E -> C : 807.02 →
F -> C# : 797.02 →
F# -> D : 803.02 →
G -> D# : 797.96 →
G# -> E : 796.02 →
A -> F : 803.96 →
A# -> F# : 796.02 →
B -> G : 806.02 →
3 x 796 2 x 797 1 x 798 1 x 799 1 x 801 1 x 803 1 x 804 1 x 806 1 x 807
statistics for interval major sixth:
C -> A : 894.985 →
C# -> A# : 902.985 →
D -> B : 895.985 →
D# -> C : 902.045 →
E -> C# : 902.985 →
F -> D : 899.045 →
F# -> D# : 902.985 →
G -> E : 892.985 →
G# -> F : 901.985 →
A -> F# : 899.985 →
A# -> G : 901.045 →
B -> G# : 902.985 →
1 x 893 1 x 895 1 x 896 1 x 899 1 x 900 1 x 901 2 x 902 4 x 903
statistics for interval minor seventh:
C -> A# : 998.95 →
C# -> B : 998.01 →
D -> C : 1002.01 →
D# -> C# : 998.01 →
E -> D : 1005.01 →
F -> D# : 999.01 →
F# -> E : 998.01 →
G -> F : 998.95 →
G# -> F# : 998.01 →
A -> G : 1005.01 →
A# -> G# : 998.01 →
B -> A : 1001.01 →
5 x 998 3 x 999 1 x 1001 1 x 1002 2 x 1005
statistics for interval major seventh:
C -> B : 1093.975 →
C# -> C : 1104.035 →
D -> C# : 1097.975 →
D# -> D : 1100.035 →
E -> D# : 1104.975 →
F -> E : 1094.035 →
F# -> F : 1103.975 →
G -> F# : 1094.975 →
G# -> G : 1103.035 →
A -> G# : 1101.975 →
A# -> A : 1096.035 →
B -> A# : 1104.975 →
2 x 1094 1 x 1095 1 x 1096 1 x 1098 1 x 1100 1 x 1102 1 x 1103 2 x 1104 2 x 1105
Equal temperament
C : 0 ... +0.00
C# : 100 ... +0.00
D : 200 ... +0.00
D# : 300 ... +0.00
E : 400 ... +0.00
F : 500 ... +0.00
F# : 600 ... +0.00
G : 700 ... +0.00
G# : 800 ... +0.00
A : 900 ... +0.00
A# : 1000 ... +0.00
B : 1100 ... +0.00
statistics for interval minor second:
C -> C# : 100 →
C# -> D : 100 →
D -> D# : 100 →
D# -> E : 100 →
E -> F : 100 →
F -> F# : 100 →
F# -> G : 100 →
G -> G# : 100 →
G# -> A : 100 →
A -> A# : 100 →
A# -> B : 100 →
B -> C : 100 →
12 x 100
statistics for interval major second:
C -> D : 200 →
C# -> D# : 200 →
D -> E : 200 →
D# -> F : 200 →
E -> F# : 200 →
F -> G : 200 →
F# -> G# : 200 →
G -> A : 200 →
G# -> A# : 200 →
A -> B : 200 →
A# -> C : 200 →
B -> C# : 200 →
12 x 200
statistics for interval minor third:
C -> D# : 300 →
C# -> E : 300 →
D -> F : 300 →
D# -> F# : 300 →
E -> G : 300 →
F -> G# : 300 →
F# -> A : 300 →
G -> A# : 300 →
G# -> B : 300 →
A -> C : 300 →
A# -> C# : 300 →
B -> D : 300 →
12 x 300
statistics for interval major third:
C -> E : 400 →
C# -> F : 400 →
D -> F# : 400 →
D# -> G : 400 →
E -> G# : 400 →
F -> A : 400 →
F# -> A# : 400 →
G -> B : 400 →
G# -> C : 400 →
A -> C# : 400 →
A# -> D : 400 →
B -> D# : 400 →
12 x 400
statistics for interval fourth:
C -> F : 500 →
C# -> F# : 500 →
D -> G : 500 →
D# -> G# : 500 →
E -> A : 500 →
F -> A# : 500 →
F# -> B : 500 →
G -> C : 500 →
G# -> C# : 500 →
A -> D : 500 →
A# -> D# : 500 →
B -> E : 500 →
12 x 500
statistics for interval tritone:
C -> F# : 600 →
C# -> G : 600 →
D -> G# : 600 →
D# -> A : 600 →
E -> A# : 600 →
F -> B : 600 →
F# -> C : 600 →
G -> C# : 600 →
G# -> D : 600 →
A -> D# : 600 →
A# -> E : 600 →
B -> F : 600 →
12 x 600
statistics for interval fifth:
C -> G : 700 →
C# -> G# : 700 →
D -> A : 700 →
D# -> A# : 700 →
E -> B : 700 →
F -> C : 700 →
F# -> C# : 700 →
G -> D : 700 →
G# -> D# : 700 →
A -> E : 700 →
A# -> F : 700 →
B -> F# : 700 →
12 x 700
statistics for interval minor sixth:
C -> G# : 800 →
C# -> A : 800 →
D -> A# : 800 →
D# -> B : 800 →
E -> C : 800 →
F -> C# : 800 →
F# -> D : 800 →
G -> D# : 800 →
G# -> E : 800 →
A -> F : 800 →
A# -> F# : 800 →
B -> G : 800 →
12 x 800
statistics for interval major sixth:
C -> A : 900 →
C# -> A# : 900 →
D -> B : 900 →
D# -> C : 900 →
E -> C# : 900 →
F -> D : 900 →
F# -> D# : 900 →
G -> E : 900 →
G# -> F : 900 →
A -> F# : 900 →
A# -> G : 900 →
B -> G# : 900 →
12 x 900
statistics for interval minor seventh:
C -> A# : 1000 →
C# -> B : 1000 →
D -> C : 1000 →
D# -> C# : 1000 →
E -> D : 1000 →
F -> D# : 1000 →
F# -> E : 1000 →
G -> F : 1000 →
G# -> F# : 1000 →
A -> G : 1000 →
A# -> G# : 1000 →
B -> A : 1000 →
12 x 1000
statistics for interval major seventh:
C -> B : 1100 →
C# -> C : 1100 →
D -> C# : 1100 →
D# -> D : 1100 →
E -> D# : 1100 →
F -> E : 1100 →
F# -> F : 1100 →
G -> F# : 1100 →
G# -> G : 1100 →
A -> G# : 1100 →
A# -> A : 1100 →
B -> A# : 1100 →
12 x 1100