Tuning Systems
Pythagorean Intonation
|
Interval Size
|
Cents
|
Ratio
|
|
minor 2
|
182.404
|
10 : 9
|
|
major 2
|
203.910
|
9 : 8
|
|
minor 3
|
315.641
|
6 : 5
|
|
major 3
|
386.314
|
5 : 4
|
|
perfect 4
|
498.045
|
4 : 3
|
|
augmented 4
|
590.224
|
45 : 32
|
|
diminished 5
|
609.777
|
64 : 45
|
|
perfect 5
|
701.955
|
3 : 2
|
|
minor 6
|
792.180
|
128.81
|
|
major 6
|
813.687
|
8 : 5
|
|
minor 7
|
996.091
|
16 : 9
|
|
major 7
|
1088.269
|
15 : 8
|
-- 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.
Twelve Tone Equal Temperament
|
Interval Size
|
Cents
|
Ratio
|
|
minor 2
|
100.000
|
89 : 84
|
|
major 2/diminshed 3
|
200.000
|
449 : 400
|
|
minor 3/augmented 2
|
300.000
|
44 : 37
|
|
major 3/diminished 4
|
400.000
|
63 : 50
|
|
perfect 4/augmented 3
|
500.000
|
303 : 227
|
|
augmented 4/diminished 5
|
600.000
|
140 : 99
|
|
perfect 5
|
700.000
|
433 : 289
|
|
minor 6/ augmented 5
|
800.000
|
100 : 63
|
|
major 6/diminished 7
|
900.000
|
37 : 22
|
|
minor 7/augmented 6
|
1000.000
|
98 : 55
|
|
major 7
|
1100.000
|
168 : 89
|
-- unlike the Pythagorean system this one 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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