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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