Interval Ratios

Semitones Intervals Frequency Ratio Equal Temperment
(cents)
Just Intonation
(cents)
12 octave 2:1 1200 1200
11 major 7th 15:8 1088 1100
10 minor 7th 9:5 1018 1000
9 major 6th 5:3 884 900
8 minor 6th 8:5 814 800
7 perfect 5th 3:2 702 700
6 tritone 7:5 583 600
5 perfect 4th 4:3 498 500
4 major 3rd 5:4 386 400
3 minor 3rd 6:5 316 300
2 major 2nd 9:8 204 200
1 minor 2nd 16:15 112 100
0 unison 1:1 0 0

Valve Combinations

Valves Harmonic Note Ratio Cents Cents from 12ET Just tuning Cents from just
○○○ 2 C 1:1 0 0 1:1 0
●●● 3 C/D 180:167 130 30 16:15 18
●○● 3 D 60:53 215 15 9:8 11
○●● 3 D/E 45:38 293 −7 6:5 −23
●●○ 3 E 180:143 398 −2 5:4 12
●○○ 3 F 4:3 498 −2 4:3 0
○●○ 3 F/G 45:32 590 −10 45:32 0
○○○ 3 G 3:2 702 2 3:2 0
○●● 4 G/A 30:19 791 −9 8:5 −23
●●○ 4 A 240:143 896 −4 5:3 12
●○○ 4 A/B 16:9 996 −4 9:5 −22
○●○ 4 B 15:8 1088 −12 15:8 0
○○○ 4 C 2:1 1200 0 2:1 0
●●○ 5 C/D 300:143 1283 −17 32:15 −29
●○○ 5 D 20:9 1382 −18 9:4 −22
○●○ 5 D/E 75:32 1475 −25 12:5 −41
○○○ 5 E 5:2 1586 −14 5:2 0

Diatonic Scale

Note C D E F G A B C
Ratio 1:1 9:8 5:4 4:3 3:2 5:3 15:8 2:1
Cents 0 204 386 498 702 884 1088 1200
Interval   M2 M2 m2 M2 M2 M2 m2  
Ratio 9:8 10:9 16:15 9:8 10:9 9:8 16:15
Cents 0 204 182 112 204 182 204 112

Valve Combinations

Valve combination and effect on pitch
Valve combination Effect on pitch Interval Tuning problems
2 12 step Minor second
1 1 step Major second
1+2 or 3 1 12 step Minor third Very slightly sharp
2+3 2 steps Major third Slightly sharp
1+3 or 4 2 12 steps Perfect fourth Sharp (1+3 only)
1+2+3 or 2+4 3 steps Tritone Very sharp (1+2+3 only)
1+4 3 12 steps Perfect fifth
1+2+4 or 3+4 4 steps Augmented fifth Flat
2+3+4 4 12 steps Major sixth Slightly sharp
1+3+4 5 steps Minor seventh Sharp
1+2+3+4 5 12 steps Major seventh Very sharp
Harmonics and tuning
Harmonic 12TET Interval Note Variance cents
1 2 4 8 16 prime (octave) C 0
17 minor second C, D +5
9 18 major second D +4
19 minor third D, E −2
5 10 20 major third E −14
21 fourth F −29
11 22 tritone F, G −49
23 +28
3 6 12 24 fifth G +2
25 minor sixth G, A −27
13 26 +41
27 major sixth A +6
7 14 28 minor seventh A, B −31
29 +30
15 30 major seventh B −12
31 +45

Interval Ratios

Ratios from the harmonic series.

Interval Ratios
# of Semitones Interval Frequency Ratio Equal Temperment
(cents)
Just Intonation
(cents)
12 octave 2:1 1200 1200
11 major 7th 15:8 1088 1100
10 minor 7th 9:5 1018 1000
9 major 6th 5:3 884 900
8 minor 6th 8:5 814 800
7 perfect 5th 3:2 702 700
6 tritone 7:5 583 600
5 perfect 4th 4:3 498 500
4 major 3rd 5:4 386 400
3 minor 3rd 6:5 316 300
2 major 2nd 9:8 204 200
1 minor 2nd 16:15 112 100
0 unison 1:1 0 0