Overview of harmonic intervals.

Overview of harmonic intervals.

redundant ratio

new ratio

Just intonation

Septimal tuning

Bohlen-Pierce scale

Neutral/undecimal/tridecimal/Pythagorean/other

harmonic ratio

P = perfect, M = major, m = minor, A = augmented, d = diminished, n = neutral

Chromatic semitones:

0
P1
1
m2
2
M2
3
m3
4
M3

5
P4
6
tri
7
P5
8
m6
9
M6
10
m7
11
M7

24
2P8

36
3P8

48
4P8

60
5P8

72
6P8

Frequency interval ratios:

1:1

P1

P1

BP0

Fundamental tone, 1st harmonic, 0 cents

2:2

2:1

P8

P8

1 octave, 2nd harmonic, 1st overtone, 1200 cents

3:3

3:2

P5

P5

Perfect fifth, 702 cents

3:1

P12(P5)

BP13 (1 tritave)

3rd harmonic, 2nd overtone

4:4

4:3

P4

P4

Perfect fourth, 498 cents

4:2 = 2:1

4:1

P15(2P8)

2 octaves, 4th harmonic, 3rd overtone

5:5

5:4

M3

386 cents

5:3

M6

BP6

884 cents

5:2

M10(M3)

5:1

M17(M3)

BP19(6)

5th harm, 4th over

6:6

6:5

m3

6:4 = 3:2

6:3 = 2:1

6:2 = 3:1

6:1

P19(P5)

6th harm, 5th over

7:7

7:6

m3

7:5

tritone (lesser)

BP4

7:4

m7

7:3

m10(m3)

BP10

7:2

m14(m7)

7:1

m21(m7)

BP23(10)

7th harm, 6th over

8:8

8:7

M2

8:6 = 4:3

8:5

m6

8:4 = 2:1

8:3

P11(P4)

8:2 = 4:1

8:1

P22(3P8)

3 octaves, h8

9:9

9:8

M2

204 cents

9:7

M3

BP3

9:6 = 3:2

9:5

m7

BP7

9:4

M9(M2)

9:3 = 3:1

9:2

M16(M2)

9:1

M23(M2)

BP26 (2 tritaves)

h9

10:10

10:9

M2 (lesser)

10:8 = 5:4

10:7

tritone (greater)

10:6 = 5:3

10:5 = 2:1

10:4 = 5:2

10:3

M13(M6)

10:2 = 5:1

10:1

M24(M3)

h10

11:11

11:10

n2

11:9

n3

11:8

und. semi-A4

11:7

und. A5

11:6

n7

11:5

n9

11:4

11:3

11:2

11:1

h11

12:12

12:10

n2

12:10 = 6:5

12:9 = 4:3

12:8 = 3:2

12:7

M6

12:6 = 2:1

12:5

m10(m3)

12:4 = 3:1

12:3 = 4:1

12:2 = 6:1

12:1

P26(P5)

h12

13:13

13:12

trid. 2/3

13:11

trid. m3

13:10

trid. semi-d4

13:9

trid. d5

13:8

trid. n6

13:7

13:6

13:5

13:4

13:3

13:2

13:1

h13

14:14

14:13

14:12 = 7:6

14:11

und. M3/d4

14:10 = 7:5

14:9

m6

14:8 = 7:4

14:7 = 2:1

14:6 = 7:3

14:5

tritone (lesser)

14:4 = 7:2

14:3

m17(m3)

14:2 = 7:1

14:1

m28(m7)

h14

15:15

15:14

m2

15:13

trid. 5/4

15:12 = 5:4

15:11

und. A4

15:10 = 3:2

15:9 = 5:3

15:8

M7

15:7

m9(m2)

BP9

15:6 = 5:2

15:5 = 3:1

15:4

M14(M7)

15:3 = 5:1

15:2

M21(M7)

15:1

M28(M7)

BP32(6)

h15

16:16

16:15

m2

16:14 = 8:7

16:13

n3

16:12 = 4:3

16:11

und. semi-d5

16:10 = 8:5

16:9

Pyth. m7

16:8 = 2:1

16:7

M9(M2)

16:6 = 8:3

16:5

m13(m6)

16:4 = 4:1

16:3

P18(P4)

16:2 = 8:1

16:1

P29(4P8)

4 octaves, h16

⋮

⋮

18:11

n6

18:7

M10(M3)

18:5

m14(m7)

18:1

M30(M2)

25:21

BP2

25:9

BP12

25:7

BP15(2)

25:3

BP25(12)

25:1

BP38(12)

27:25

BP1

27:14

M7

27:7

M14(M7)

BP16(3)

27:1

BP39 (3 tritaves)

32:15

m9(m2)

32:7

M16(M2)

32:5

m20(m6)

32:3

P25(P4)

32:1

P36(5P8)