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TUNING SYSTEMS
Pythagorean Intonation
-- it should be noted that this tuning system is a linear system, meaning that the intervals do not point back to themselves. The systems just continues up or down. If you start on a given note and travel in the same direction with the same interval you won't return to the starting note.
INTERVAL SIZE
minor 2
major 2/diminshed 3
minor 3/augmented 2
major 3/diminished 4
perfect 4/augmented 3
augmented 4/dim 5
perfect 5
minor 6/ augmented 5
major 6/diminished 7
minor 7/augmented 6
major 7
TWELVE TONE
INTERVAL SIZE
minor 2
major 2
minor 3
major 3
perfect 4
augmented 4
diminished 5
perfect 5
minor 6
major 6
minor 7
major 7
-- unlike the Pythagorean system, Equal Temperment is cyclic, meaning the the intervals will return to where it started, just in a different register. If you start on a note and continue in the same direction with the same interval you will end up on the same note, just in a different location.
Other Commonly Used Tuning Systems
The Cycle of 53
Mean Tone Temperament (Various Forms)
The Skhismic Temperament
Helmholtzian
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CENTS
100.000
200.000
300.000
400.000
500.000
600.000
700.000
800.000
900.000
1000.000
1100.000
EQUAL TEMPERMENT
CENTS
182.404
203.910
315.641
386.314
498.045
590.224
609.777
701.955
792.180
813.687
996.091
1088.269
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RATIO
89 : 84
449 : 400
44 : 37
63 : 50
303 : 227
140 : 99
433 : 289
100 : 63
37 : 22
98 : 55
168 : 89
EQUAL TEMPERMENT
RATIO
10 : 9
9 : 8
6 : 5
5 : 4
4 : 3
45 : 32
64 : 45
3 : 2
128.81
8 : 5
16 : 9
15 : 8
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