Comparison between tunings: Pythagorean , equal-tempered , 1/4-comma meantone , and others. For each, the common origin is arbitrarily chosen as C. The degrees are arranged in the order or the cycle of fifths; as in each of these tunings except just intonation all fifths are of the same size, the tunings appear as straight lines, the slope indicating the relative tempering with respect to Pythagorean, which has pure fifths (3:2, 702 cents). The Pythagorean A♭ (at the left) is at 792 cents, G♯ (at the right) at 816 cents; the difference is the Pythagorean comma. Equal temperament by definition is such that A♭ and G♯ are at the same level. 1/4 comma meantone produces the "just" major third (5:4, 386 cents, a syntonic comma lower than the Pythagorean one of 408 cents). 1/3 comma meantone produces the "just" minor third (6:5, 316 cents, a syntonic comma higher than the Pythagorean one of 294 cents). In both these meantone temperaments, the enharmony, here the difference between A♭ and G♯ , is much larger than in Pythagorean, and with the flat degree higher than the sharp one.
Comparison of two sets of musical intervals. The equal-tempered intervals are black; the Pythagorean intervals are green.
Below is a list of intervals expressible in terms of a prime limit (see Terminology ), completed by a choice of intervals in various equal subdivisions of the octave or of other intervals.
For commonly encountered harmonic or melodic intervals between pairs of notes in contemporary Western music theory , without consideration of the way in which they are tuned, see Interval (music) § Main intervals .
The prime limit [1] henceforth referred to simply as the limit , is the largest prime number occurring in the factorizations of the numerator and denominator of the frequency ratio describing a rational interval. For instance, the limit of the just perfect fourth (4 : 3) is 3, but the just minor tone (10 : 9) has a limit of 5, because 10 can be factorized into 2·5 (and 9 in 3·3). There exists another type of limit, the odd limit , a concept used by Harry Partch (bigger of odd numbers obtained after dividing numerator and denominator by highest possible powers of 2), but it is not used here. The term "limit" was devised by Partch.[1]
By definition, every interval in a given limit can also be part of a limit of higher order. For instance, a 3-limit unit can also be part of a 5-limit tuning and so on. By sorting the limit columns in the table below, all intervals of a given limit can be brought together (sort backwards by clicking the button twice).
Pythagorean tuning means 3-limit intonation—a ratio of numbers with prime factors no higher than three.
Just intonation means 5-limit intonation—a ratio of numbers with prime factors no higher than five.
Septimal , undecimal , tridecimal , and septendecimal mean, respectively, 7, 11, 13, and 17-limit intonation.
Meantone refers to meantone temperament , where the whole tone is the mean of the major third. In general, a meantone is constructed in the same way as Pythagorean tuning, as a stack of fifths: the tone is reached after two fifths, the major third after four, so that as all fifths are the same, the tone is the mean of the third. In a meantone temperament, each fifth is narrowed ("tempered") by the same small amount. The most common of meantone temperaments is the quarter-comma meantone , in which each fifth is tempered by 1/4 of the syntonic comma, so that after four steps the major third (as C-G-D-A-E) is a full syntonic comma lower than the Pythagorean one. The extremes of the meantone systems encountered in historical practice are the Pythagorean tuning, where the whole tone corresponds to 9:8, i.e. (3:2)2 /2, the mean of the major third (3:2)4 /4, and the fifth (3:2) is not tempered; and the 1/3-comma meantone, where the fifth is tempered to the extent that three ascending fifths produce a pure minor third.(See Meantone temperaments ). The music program Logic Pro uses also 1/2-comma meantone temperament.
Equal-tempered refers to X -tone equal temperament with intervals corresponding to X divisions per octave.
Tempered intervals however cannot be expressed in terms of prime limits and, unless exceptions, are not found in the table below.
The table can also be sorted by frequency ratio, by cents, or alphabetically.
Column
Legend
TET
X -tone equal temperament (12-tet, etc.).
Limit
2 -limit intonation, or octave(s) .
3 -limit intonation, or Pythagorean .
5 -limit "just" intonation, or just .
7 -limit intonation, or septimal .
11 -limit intonation, or undecimal .
13 -limit intonation, or tridecimal .
17 -limit intonation, or septendecimal .
19 -limit intonation, or novendecimal .
H igher limits.
M
M eantone temperament or tuning.
S
S uperparticular ratio (no separate color code).
List of musical intervals
Cents
Note (from C)
Freq. ratio
Prime factors
Interval name
TET
Limit
M
S
Template:Right
C[2]
1 : 1
1 : 1
Template:Splitspan
1, 12
2
M
Template:Right
65537 : 65536
65537 : 216
Template:Splitspan
65537
S
Template:Right
C♯ -
4375 : 4374
54 ·7 : 2·37
Template:Splitspan
7
S
Template:Right
E +
2401 : 2400
74 : 25 ·3·52
Template:Splitspan
7
S
Template:Right
21/1200
21/1200
Template:Splitspan
1200
Template:Right
21/1000
21/1000
Template:Splitspan
1000
Template:Right
B♯ ++
32805 : 32768
38 ·5 : 215
Template:Splitspan
5
Template:Right
101/1000
21/1000 ·51/1000
Template:Splitspan
301.03
Template:Right
B♯
225 : 224
32 ·52 : 25 ·7
Template:Splitspan
7
S
Template:Right
B -
15625 : 15552
56 : 26 ·35
Template:Splitspan
5
Template:Right
A ++
2109375 : 2097152
33 ·57 : 221
Template:Splitspan
5
Template:Right
C
160 : 159
25 ·5 : 3·53
Template:Splitspan
53
S
Template:Right
C
145 : 144
5·29 : 24 ·32
Template:Splitspan
29
S
Template:Right
21/96
21/96
Template:Splitspan
96
Template:Right
B -
1728 : 1715
26 ·33 : 5·73
Template:Splitspan
7
Template:Right
C
129 : 128
3·43 : 27
Template:Splitspan
43
S
Template:Right
D
126 : 125
2·32 ·7 : 53
Template:Splitspan
7
S
Template:Right
C♭ ↑ ↑ -
121 : 120
112 : 23 ·3·5
Template:Splitspan
11
S
Template:Right
C↑ [lower-alpha 1]
21/72
21/72
Template:Splitspan
72
Template:Right
C
96 : 95
25 ·3 : 5·19
Template:Splitspan
19
S
Template:Right
D --[2]
2048 : 2025
211 : 34 ·52
Template:Splitspan
5
Template:Right
C+[2]
81 : 80
34 : 24 ·5
Template:Splitspan
5
S
Template:Right
21/53
21/53
Template:Splitspan
53
Template:Right
B♯ +++
531441 : 524288
312 : 219
Template:Splitspan
3
Template:Right
21/48
21/48
Template:Splitspan
48
Template:Right
C
65 : 64
5·13 : 26
Template:Splitspan
13
S
Template:Right
C -
64 : 63
26 : 32 ·7
Template:Splitspan
7
S
Template:Right
21/41
21/41
Template:Splitspan
41
Template:Right
D♭ ↓
56 : 55
23 ·7 : 5·11
Template:Splitspan
11
S
Template:Right
C /D♭ [lower-alpha 1]
21/36
21/36
Template:Splitspan
36, 72
Template:Right
C
51 : 50
3·17 : 2·52
Template:Splitspan
17
S
Template:Right
B♯ -
50 : 49
2·52 : 72
Template:Splitspan
7
S
Template:Right
D♭
49 : 48
72 : 24 ·3
Template:Splitspan
7
S
Template:Right
C
46 : 45
2·23 : 32 ·5
Template:Splitspan
23
S
Template:Right
21/31
21/31
Template:Splitspan
31
Template:Right
C↓ ♯ +
45 : 44
32 ·5 : 4·11
Template:Splitspan
11
S
Template:Right
21/30
21/30
Template:Splitspan
30
Template:Right
D -
128 : 125
27 : 53
Template:Splitspan
5
Template:Right
D♭
42 : 41
2·3·7 : 41
Template:Splitspan
41
S
Template:Right
C
41 : 40
41 : 23 ·5
Template:Splitspan
41
S
Template:Right
C♯
40 : 39
23 ·5 : 3·13
Template:Splitspan
13
S
Template:Right
C
39 : 38
3·13 : 2·19
Template:Splitspan
19
S
Template:Right
D-
38 : 37
2·19 : 37
Template:Splitspan
37
S
Template:Right
C♯
37 : 36
37 : 22 ·32
Template:Splitspan
37
S
Template:Right
C
36 : 35
22 ·32 : 5·7
Template:Splitspan
7
S
Template:Right
246 : 239
3·41 : 239
Template:Splitspan
239
Template:Right
C /D
21/24
21/24
Template:Splitspan
24
Template:Right
D♭
35 : 34
5·7 : 2·17
Template:Splitspan
17
S
Template:Right
B♯ + +
59049 : 57344
310 : 213 ·7
Template:Splitspan
7
Template:Right
C↓ ♯
34 : 33
2·17 : 3·11
Template:Splitspan
17
S
Template:Right
C↑
33 : 32
3·11 : 25
Template:Splitspan
11
S
Template:Right
D♭ -
32 : 31
25 : 31
Template:Splitspan
31
S
Template:Right
B♯ +
529 : 512
232 : 29
Template:Splitspan
23
Template:Right
C
31 : 30
31 : 2·3·5
Template:Splitspan
31
S
Template:Right
C♯
30 : 29
2·3·5 : 29
Template:Splitspan
29
S
Template:Right
C
29 : 28
29 : 22 ·7
Template:Splitspan
29
S
Template:Right
D♭ -
28 : 27
22 ·7 : 33
Template:Splitspan
7
S
Template:Right
(3 : 2)1/11
31/11 : 21/11
Template:Splitspan
18.75
Template:Right
C♯ +
27 : 26
33 : 2·13
Template:Splitspan
13
S
Template:Right
D♭
133 : 128
7·19 : 27
Template:Splitspan
19
Template:Right
C↑ /C♯ [lower-alpha 1]
21/18
21/18
Template:Splitspan
18, 36, 72
Template:Right
D-
26 : 25
2·13 : 52
Template:Splitspan
13
S
Template:Right
C♯ [2]
25 : 24
52 : 23 ·3
Template:Splitspan
5
S
Template:Right
D♭ -
24 : 23
23 ·3 : 23
Template:Splitspan
23
S
Template:Right
21/16
23/48
Template:Splitspan
16, 48
Template:Right
C↓ ♯ +
23 : 22
23 : 2·11
Template:Splitspan
23
S
Template:Right
(3 : 2)1/9
31/9 : 21/9
Template:Splitspan
15.39
Template:Right
67 : 64
67 : 26
Template:Splitspan
67
Template:Right
C↑ -
22 : 21
2·11 : 3·7
Template:Splitspan
11
S
Template:Right
D♭
21 : 20
3·7 : 22 ·5
Template:Splitspan
7
S
Template:Right
C♯
20 : 19
22 ·5 : 19
Template:Splitspan
19
S
Template:Right
D♭ --[2]
256 : 243
28 : 35
Template:Splitspan
3
Template:Right
C♯ +[2]
135 : 128
33 ·5 : 27
Template:Splitspan
5
Template:Right
D♭ -
19 : 18
19 : 2·9
Template:Splitspan
19
S
Template:Right
D↓↓
128 : 121
27 : 112
Template:Splitspan
11
Template:Right
D♭
18 : 17
2·32 : 17
Template:Splitspan
17
S
Template:Right
C♯ /D♭
21/12
21/12
Template:Splitspan
12
M
Template:Right
C♯ [2]
17 : 16
17 : 24
Template:Splitspan
17
S
Template:Right
5
25
{\displaystyle {\sqrt[{25}]{5}}}
(5 : 1)1/25
Template:Splitspan
25
Template:Right
D♭ - [2]
16 : 15
24 : 3·5
Template:Splitspan
5
S
Template:Right
C♯ ++
2187 : 2048
37 : 211
Template:Splitspan
3
Template:Right
(18 : 5)1/19
21/19 ·32/19 : 51/19
Template:Splitspan
10.28
Template:Right
C♯
15 : 14
3·5 : 2·7
Template:Splitspan
7
S
Template:Right
25/48
25/48
Template:Splitspan
48
Template:Right
D
14 : 13
2·7 : 13
Template:Splitspan
13
S
Template:Right
C♯ +
69 : 64
3·23 : 26
Template:Splitspan
23
Template:Right
D♭
27 : 25
33 : 52
Template:Splitspan
5
Template:Right
C♯ /D♭ [lower-alpha 1]
21/9
22/18
Template:Splitspan
9, 18, 36, 72
Template:Right
D♭ -
13 : 12
13 : 22 ·3
Template:Splitspan
13
S
Template:Right
C /D
23/24
21/8
Template:Splitspan
8, 24
Template:Right
D↓[2]
12 : 11
22 ·3 : 11
Template:Splitspan
11
S
Template:Right
D
35 : 32
5·7 : 25
Template:Splitspan
7
Template:Right
D--
800 : 729
25 ·52 : 36
Template:Splitspan
5
Template:Right
D↑ ♭ -[2]
11 : 10
11 : 2·5
Template:Splitspan
11
S
Template:Right
21/7
21/7
Template:Splitspan
7
Template:Right
27/48
27/48
Template:Splitspan
48
Template:Right
71 : 64
71 : 26
Template:Splitspan
71
Template:Right
E ---
65536 : 59049
216 : 310
Template:Splitspan
3
Template:Right
D-[2]
10 : 9
2·5 : 32
Template:Splitspan
5
S
Template:Right
D
22/12
21/6
Template:Splitspan
6, 12
M
Template:Right
D[2]
9 : 8
32 : 23
Template:Splitspan
3
S
Template:Right
D
145 : 128
5·29 : 27
Template:Splitspan
29
Template:Right
E -[2]
256 : 225
28 : 32 ·52
Template:Splitspan
5
Template:Right
23/16
29/48
Template:Splitspan
16, 48
Template:Right
73 : 64
73 : 26
Template:Splitspan
73
Template:Right
D -[2]
8 : 7
23 : 7
Template:Splitspan
7
S
Template:Right
21/5
21/5
Template:Splitspan
5
Template:Right
D♯
15 : 13
3·5 : 13
Template:Splitspan
13
Template:Right
25/24
25/24
Template:Splitspan
24
Template:Right
D♯
37 : 32
37 : 25
Template:Splitspan
37
Template:Right
D♯ -
125 : 108
53 : 22 ·33
Template:Splitspan
5
Template:Right
E↓♭
64 : 55
26 : 5·11
Template:Splitspan
11
Template:Right
D
299 : 256
13·23 : 28
Template:Splitspan
23
Template:Right
E♭ [2]
7 : 6
7 : 2·3
Template:Splitspan
7
S
Template:Right
D♯ [2]
75 : 64
3·52 : 26
Template:Splitspan
5
Template:Right
211/48
211/48
Template:Splitspan
48
Template:Right
E↓ ♭
13 : 11
13 : 11
Template:Splitspan
13
S
Template:Right
E♭ -[2]
32 : 27
25 : 33
Template:Splitspan
3
Template:Right
E♭ [2]
19 : 16
19 : 24
Template:Splitspan
19
Template:Right
D♯ /E♭
23/12
21/4
Template:Splitspan
4, 12
M
Template:Right
D♯ -
25 : 21[3]
52 : 3·7
Template:Splitspan
7
Template:Right
6:5÷(81:80)1/4
22 : 53/4
Template:Splitspan
M
Template:Right
(3 : 2)4/9
34/9 : 24/9
Template:Splitspan
3.85
Template:Right
E♭ [2]
6 : 5
2·3 : 5
Template:Splitspan
5
M
S
Template:Right
D♯ ++
19683 : 16384
39 : 214
Template:Splitspan
3
Template:Right
E♭ ↑
77 : 64
7·11 : 26
Template:Splitspan
11
Template:Right
213/48
213/48
Template:Splitspan
48
Template:Right
D♯ -
17 : 14
17 : 2·7
Template:Splitspan
17
Template:Right
E♭ +
243 : 200
35 : 23 ·52
Template:Splitspan
5
Template:Right
E♭
39 : 32
3·13 : 25
Template:Splitspan
13
Template:Right
22/7
22/7
Template:Splitspan
7
Template:Right
E♭ -
128 : 105
27 : 3·5·7
Template:Splitspan
7
Template:Right
E↑ ♭ -[2]
11 : 9
11 : 32
Template:Splitspan
11
Template:Right
D /E
27/24
27/24
Template:Splitspan
24
Template:Right
E↓ +
27 : 22
33 : 2·11
Template:Splitspan
11
Template:Right
E[2]
16 : 13
24 : 13
Template:Splitspan
13
Template:Right
79 : 64
79 : 26
Template:Splitspan
79
Template:Right
E-
100 : 81
22 ·52 : 34
Template:Splitspan
5
Template:Right
25/16
215/48
Template:Splitspan
16, 48
Template:Right
F♭ --
8192 : 6561
213 : 38
Template:Splitspan
3
Template:Right
E[2]
5 : 4
5 : 22
Template:Splitspan
5
M
S
Template:Right
E+
161 : 128
7·23 : 27
Template:Splitspan
23
Template:Right
E
24/12
21/3
Template:Splitspan
3, 12
M
Template:Right
E
323 : 256
17·19 : 28
Template:Splitspan
19
Template:Right
E+[2]
81 : 64
34 : 26
Template:Splitspan
3
Template:Right
F↓ +[2]
14 : 11
2·7 : 11
Template:Splitspan
11
Template:Right
217/48
217/48
Template:Splitspan
48
Template:Right
F♭ [2]
32 : 25
25 : 52
Template:Splitspan
5
Template:Right
E
41 : 32
41 : 25
Template:Splitspan
41
Template:Right
E[2]
9 : 7
32 : 7
Template:Splitspan
7
Template:Right
F↓
128 : 99
27 : 9·11
Template:Splitspan
11
Template:Right
29/24
29/24
Template:Splitspan
24
Template:Right
83 : 64
83 : 26
Template:Splitspan
83
Template:Right
F♭
13 : 10
13 : 2·5
Template:Splitspan
13
Template:Right
E♯ [2]
125 : 96
53 : 25 ·3
Template:Splitspan
5
Template:Right
E-
64 : 49
26 : 72
Template:Splitspan
7
Template:Right
F +[2]
21 : 16
3·7 : 24
Template:Splitspan
7
Template:Right
219/48
219/48
Template:Splitspan
48
Template:Right
E♯ +
675 : 512
33 ·52 : 29
Template:Splitspan
5
Template:Right
22/5
22/5
Template:Splitspan
5
Template:Right
E♯
85 : 64
5·17 : 26
Template:Splitspan
17
Template:Right
F[2]
4 : 3
22 : 3
Template:Splitspan
3
S
Template:Right
F
25/12
25/12
Template:Splitspan
12
M
Template:Right
F+
171 : 128
32 ·19 : 27
Template:Splitspan
19
Template:Right
(3 : 2)8/11
38/11 : 28/11
Template:Splitspan
18.75
Template:Right
F
43 : 32
43 : 25
Template:Splitspan
43
Template:Right
23/7
23/7
Template:Splitspan
7
Template:Right
F+[2]
27 : 20
33 : 22 ·5
Template:Splitspan
5
Template:Right
E♯ +++
177147 : 131072
311 : 217
Template:Splitspan
3
Template:Right
27/16
221/48
Template:Splitspan
16, 48
Template:Right
F +
87 : 64
3·29 : 26
Template:Splitspan
29
Template:Right
F↓ ♯ +
15 : 11
3·5 : 11
Template:Splitspan
11
Template:Right
211/24
211/24
Template:Splitspan
24
Template:Right
F↑ [2]
11 : 8
11 : 23
Template:Splitspan
11
Template:Right
F♯ +
18 : 13
2·9 : 13
Template:Splitspan
13
Template:Right
F♯ [2]
25 : 18
52 : 2·32
Template:Splitspan
5
Template:Right
89 : 64
89 : 26
Template:Splitspan
89
Template:Right
223/48
223/48
Template:Splitspan
48
Template:Right
G♭ [2]
7 : 5
7 : 5
Template:Splitspan
7
Template:Right
G♭ --
1024 : 729
210 : 36
Template:Splitspan
3
Template:Right
F♯ +[2]
45 : 32
32 ·5 : 25
Template:Splitspan
5
Template:Right
G♭
361 : 256
192 : 28
Template:Splitspan
19
Template:Right
F♯ /G♭
26/12
21/2 =√2
Template:Splitspan
2, 12
M
Template:Right
G♭
91 : 64
7·13 : 26
Template:Splitspan
13
Template:Right
G♭ -[2]
64 : 45
26 : 32 ·5
Template:Splitspan
5
Template:Right
F♯ ++
729 : 512
36 : 29
Template:Splitspan
3
Template:Right
F♯ [2]
10 : 7
2·5 : 7
Template:Splitspan
7
Template:Right
225/48
225/48
Template:Splitspan
48
Template:Right
F♯ +
23 : 16
23 : 24
Template:Splitspan
23
Template:Right
G♭ [2]
36 : 25
22 ·32 : 52
Template:Splitspan
5
Template:Right
F♯ +
93 : 64
3·31 : 26
Template:Splitspan
31
Template:Right
G↓[2]
16 : 11
24 : 11
Template:Splitspan
11
Template:Right
213/24
213/24
Template:Splitspan
24
Template:Right
G
47 : 32
47 : 25
Template:Splitspan
47
Template:Right
29/16
227/48
Template:Splitspan
16, 48
Template:Right
A ---
262144 : 177147
218 : 311
Template:Splitspan
3
Template:Right
G-
40 : 27
23 ·5 : 33
Template:Splitspan
5
Template:Right
G
95 : 64
5·19 : 26
Template:Splitspan
19
Template:Right
E+ +
12167 : 8192
233 : 213
Template:Splitspan
23
Template:Right
24/7 : 1
Template:Splitspan
Template:Right
3:2÷(81:80)1/2
2·51/2 : 3
Template:Splitspan
M
Template:Right
3:2÷(81:80)1/3
21/3 ·51/3 : 31/3
Template:Splitspan
M
Template:Right
3:2÷(81:80)2/7
21/7 ·52/7 : 31/7
Template:Splitspan
M
Template:Right
3:2÷(81:80)1/4
51/4
Template:Splitspan
M
Template:Right
3:2÷(81:80)1/5
31/5 ·51/5 : 21/5
Template:Splitspan
M
Template:Right
3:2÷(81:80)1/6
31/3 ·51/6 : 21/3
Template:Splitspan
M
Template:Right
G
27/12
27/12
Template:Splitspan
12
M
Template:Right
231/53
231/53
Template:Splitspan
53
Template:Right
G[2]
3 : 2
3 : 2
Template:Splitspan
3
S
Template:Right
224/41
224/41
Template:Splitspan
41
Template:Right
217/29
217/29
Template:Splitspan
29
Template:Right
97 : 64
97 : 26
Template:Splitspan
97
Template:Right
23/5 : 1
Template:Splitspan
5
Template:Right
A -
1024 : 675
210 : 33 ·52
Template:Splitspan
5
Template:Right
229/48
229/48
Template:Splitspan
48
Template:Right
G-
32 : 21
24 : 3·7
Template:Splitspan
7
Template:Right
F+
391 : 256
17·23 : 28
Template:Splitspan
23
Template:Right
A♭ +
49 : 32
7·7 : 25
Template:Splitspan
7
Template:Right
A
192 : 125
26 ·3 : 53
Template:Splitspan
5
Template:Right
215/24
215/24
Template:Splitspan
24
Template:Right
G↑
99 : 64
32 ·11 : 26
Template:Splitspan
11
Template:Right
A♭ [2]
14 : 9
2·7 : 32
Template:Splitspan
7
Template:Right
G♯
25 : 16
52 : 24
Template:Splitspan
Template:Right
231/48
231/48
Template:Splitspan
48
Template:Right
[[pi|Template:Pi ]] : 2
Template:Splitspan
Template:Right
G↑ -[2]
11 : 7
11 : 7
Template:Splitspan
11
Template:Right
101 : 64
101 : 26
Template:Splitspan
101
Template:Right
A♭ -[2]
128 : 81
27 : 34
Template:Splitspan
3
Template:Right
A♭ +
203 : 128
7·29 : 27
Template:Splitspan
29
Template:Right
G♯ /A♭
28/12
22/3
Template:Splitspan
3, 12
M
Template:Right
G♯
51 : 32
3·17 : 25
Template:Splitspan
17
Template:Right
A♭ [2]
8 : 5
23 : 5
Template:Splitspan
5
Template:Right
G♯ ++
6561 : 4096
38 : 212
Template:Splitspan
3
Template:Right
103 : 64
103 : 26
Template:Splitspan
103
Template:Right
211/16
233/48
Template:Splitspan
16, 48
Template:Right
G♯ +
207 : 128
32 ·23 : 27
Template:Splitspan
23
Template:Right
51/2 +1 : 2
φ
{\displaystyle {\varphi }}
: 2
Template:Splitspan
Template:Right
233 : 144
233 : 24 ·32
Template:Splitspan
233
Template:Right
A♭ +
81 : 50
34 : 2·52
Template:Splitspan
5
Template:Right
A♭ [2]
13 : 8
13 : 23
Template:Splitspan
13
Template:Right
A♭ ↑
209 : 128
11·19 : 27
Template:Splitspan
19
Template:Right
G /A
217/24
217/24
Template:Splitspan
24
Template:Right
A↓+[2]
18 : 11
2·32 : 11
Template:Splitspan
11
Template:Right
A +
105 : 64
3·5·7 : 26
Template:Splitspan
7
Template:Right
25/7
25/7
Template:Splitspan
7
Template:Right
A-
400 : 243
24 ·52 : 35
Template:Splitspan
5
Template:Right
A
53 : 32
53 : 25
Template:Splitspan
53
Template:Right
235/48
235/48
Template:Splitspan
48
Template:Right
A↓
128 : 77
27 : 7·11
Template:Splitspan
11
Template:Right
B ---
32768 : 19683
215 : 39
Template:Splitspan
3
Template:Right
A[2]
5 : 3
5 : 3
Template:Splitspan
5
M
Template:Right
107 : 64
107 : 26
Template:Splitspan
107
Template:Right
B
6859 : 4096
193 : 212
Template:Splitspan
19
Template:Right
A
29/12
23/4
Template:Splitspan
4, 12
M
Template:Right
A
32 : 19
25 : 19
Template:Splitspan
19
Template:Right
A+[2]
27 : 16
33 : 24
Template:Splitspan
3
Template:Right
109 : 64
109 : 26
Template:Splitspan
109
Template:Right
237/48
237/48
Template:Splitspan
48
Template:Right
B -[2]
128 : 75
27 : 3·52
Template:Splitspan
5
Template:Right
A+
437 : 256
19·23 : 28
Template:Splitspan
23
Template:Right
A[2]
12 : 7
22 ·3 : 7
Template:Splitspan
7
Template:Right
A↑
55 : 32
5·11 : 25
Template:Splitspan
11
Template:Right
219/24
219/24
Template:Splitspan
24
Template:Right
A♯ +
111 : 64
3·37 : 26
Template:Splitspan
37
Template:Right
A♯ [2]
125 : 72
53 : 23 ·32
Template:Splitspan
5
Template:Right
(3 : 2)15/11
315/11 : 215/11
Template:Splitspan
18.75
Template:Right
24/5
24/5
Template:Splitspan
5
Template:Right
B♭ [2]
7 : 4
7 : 22
Template:Splitspan
7
Template:Right
213/16
239/48
Template:Splitspan
16, 48
Template:Right
A♯ +[2]
225 : 128
32 ·52 : 27
Template:Splitspan
5
Template:Right
113 : 64
113 : 26
Template:Splitspan
113
Template:Right
B♭ -[2]
16 : 9
24 : 32
Template:Splitspan
3
Template:Right
B♭
57 : 32
3·19 : 25
Template:Splitspan
19
Template:Right
A♯ /B♭
210/12
25/6
Template:Splitspan
6, 12
M
Template:Right
A♯ +
115 : 64
5·23 : 26
Template:Splitspan
23
Template:Right
B♭ [2]
9 : 5
32 : 5
Template:Splitspan
5
Template:Right
A♯ +++
59049 : 32768
310 : 215
Template:Splitspan
3
Template:Right
241/48
241/48
Template:Splitspan
48
Template:Right
26/7
26/7
Template:Splitspan
7
Template:Right
B♭
29 : 16
29 : 24
Template:Splitspan
29
Template:Right
B↓[2]
20 : 11
22 ·5 : 11
Template:Splitspan
11
Template:Right
B♭ +
729 : 400
36 : 24 ·52
Template:Splitspan
5
Template:Right
B♭
117 : 64
32 ·13 : 26
Template:Splitspan
13
Template:Right
B♭ -
64 : 35
26 : 5·7
Template:Splitspan
7
Template:Right
B↑ ♭ -[2]
11 : 6
11 : 2·3
Template:Splitspan
11
Template:Right
A /B
221/24
27/8
Template:Splitspan
8, 24
Template:Right
59 : 32
59 : 25
Template:Splitspan
59
Template:Right
B-
50 : 27
2·52 : 33
Template:Splitspan
5
Template:Right
B♭ -
13 : 7
13 : 7
Template:Splitspan
13
Template:Right
B
119 : 64
7·17 : 26
Template:Splitspan
17
Template:Right
243/48
243/48
Template:Splitspan
48
Template:Right
C♭ --
4096 : 2187
212 : 37
Template:Splitspan
3
Template:Right
B[2]
15 : 8
3·5 : 23
Template:Splitspan
5
Template:Right
C♭
32 : 17
25 : 17
Template:Splitspan
17
Template:Right
B
211/12
211/12
Template:Splitspan
12
M
Template:Right
B↑ ↑ ♭ -
121 : 64
112 : 26
Template:Splitspan
11
Template:Right
C'♭ -
256 : 135
28 : 33 ·5
Template:Splitspan
5
Template:Right
B+[2]
243 : 128
35 : 27
Template:Splitspan
3
Template:Right
61 : 32
61 : 25
Template:Splitspan
61
Template:Right
215/16
245/48
Template:Splitspan
16, 48
Template:Right
C'♭ [2]
48 : 25
24 ·3 : 52
Template:Splitspan
5
Template:Right
B
123 : 64
3·41 : 26
Template:Splitspan
41
Template:Right
B
27 : 14
33 : 2·7
Template:Splitspan
7
Template:Right
C♭
247 : 128
13·19 : 27
Template:Splitspan
19
Template:Right
B
31 : 16
31 : 24
Template:Splitspan
31
Template:Right
C↓
64 : 33
26 : 3·11
Template:Splitspan
11
Template:Right
223/24
223/24
Template:Splitspan
24
Template:Right
C
35 : 18
5·7 : 2·32
Template:Splitspan
7
Template:Right
B♯ [2]
125 : 64
53 : 26
Template:Splitspan
5
Template:Right
C +
63 : 32
32 ·7 : 25
Template:Splitspan
7
Template:Right
247/48
247/48
Template:Splitspan
48
Template:Right
C'-
160 : 81
25 ·5 : 34
Template:Splitspan
5
Template:Right
B↑
253 : 128
11·23 : 27
Template:Splitspan
23
Template:Right
127 : 64
127 : 26
Template:Splitspan
127
Template:Right
C'
2 : 1
2 : 1
Template:Splitspan
1, 12
2
M
S
Template:Right
B♯ +++
531441 : 262144
312 : 218
Template:Splitspan
3
Template:Right
21/2 +1
Template:Splitspan
Template:Right
G'
3 : 1
3 : 1
Template:Splitspan
3
Template:Right
C"
4 : 1
22 : 1
Template:Splitspan
1, 12
2
M
Template:Right
E'''
10 : 1
5·2 : 1
Template:Splitspan
5
M
Template:Consonance and dissonance
Numbers in brackets are the number of semitones in the interval. Fractional semitones are approximate. Twelve- semitone (Western)
Other systems
Other intervals
Template:Music theory lists
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