List of pitch intervals

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Template:Short description

File:Meantone comparison.png
Comparison between tunings: Pythagorean, equal-tempered, quarter-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 ATemplate:Music (at the left) is at 792 cents, GTemplate:Music (at the right) at 816 cents; the difference is the Pythagorean comma. Equal temperament by definition is such that ATemplate:Music and GTemplate:Music are at the same level. Template:1/4-comma meantone produces the "just" major third (5:4, 386 cents, a syntonic comma lower than the Pythagorean one of 408 cents). Template: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 ATemplate:Music and GTemplate:Music, is much larger than in Pythagorean, and with the flat degree higher than the sharp one.
File:Music intervals frequency ratio equal tempered pythagorean comparison.svg
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 Template:Section link.

Terminology

  • 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 factored into 2 × 5 (and 9 into 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 Template: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. Template:Sfrac, the mean of the major third Template:Sfrac, and the fifth (3:2) is not tempered; and the Template: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 Template: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.
  • Superparticular ratios are intervals that can be expressed as the ratio of two consecutive integers.

List

Column Legend
TET X-tone equal temperament (12-tet, etc.).
Limit 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.
Higher limits.
M Meantone temperament or tuning.
S Superparticular ratio (no separate color code).
List of musical intervals
Cents Note (from C) Freq. ratio Prime factors Interval name TET Limit M S
0.00
 C[2] 1 : 1 1 : 1 Template:Splitspan 1, 12 3 M
0.03
65537 : 65536 65537 : 216 Template:Splitspan 65537 S
0.40
 CTemplate:MusicTemplate:Music− 4375 : 4374 54×7 : 2×37 Template:Splitspan 7 S
0.72
 ETemplate:MusicTemplate:MusicTemplate:MusicTemplate:MusicTemplate:Music+ 2401 : 2400 74 : 25×3×52 Template:Splitspan 7 S
1.00
21/1200 21/1200 Template:Splitspan 1200
1.20
21/1000 21/1000 Template:Splitspan 1000
1.95
BTemplate:Music++ 32805 : 32768 38×5 : 215 Template:Splitspan 5
1.96
3:2÷(27/12) 3 : 219/12 Template:Splitspan
3.99
101/1000 21/1000×51/1000 Template:Splitspan 301.03
7.71
BTemplate:MusicTemplate:Music 225 : 224 32×52 : 25×7 Template:Splitspan 7 S
8.11
BTemplate:Music− 15625 : 15552 56 : 26×35 Template:Splitspan 5
10.06
ATemplate:MusicTemplate:Music++ 2109375 : 2097152 33×57 : 221 Template:Splitspan 5
10.85
CTemplate:Music 160 : 159 25×5 : 3×53 Template:Splitspan 53 S
11.98
 CTemplate:Music 145 : 144 5×29 : 24×32 Template:Splitspan 29 S
12.50
21/96 21/96 Template:Splitspan 96
13.07
 BTemplate:MusicTemplate:MusicTemplate:Music− 1728 : 1715 26×33 : 5×73 Template:Splitspan 7
13.47
 CTemplate:Music 129 : 128 3×43 : 27 Template:Splitspan 43 S
13.79
DTemplate:MusicTemplate:Music 126 : 125 2×32×7 : 53 Template:Splitspan 7 S
14.37
CTemplate:MusicTemplate:MusicTemplate:Music− 121 : 120 112 : 23×3×5 Template:Splitspan 11 S
16.67
CTemplate:MusicTemplate:Efn 21/72 21/72 Template:Splitspan 72
18.13
CTemplate:Music 96 : 95 25×3 : 5×19 Template:Splitspan 19 S
19.55
DTemplate:Music--[2] 2048 : 2025 211 : 34×52 Template:Splitspan 5
21.51
C+[2] 81 : 80 34 : 24×5 Template:Splitspan 5 S
22.64
21/53 21/53 Template:Splitspan 53
23.46
BTemplate:Music+++ 531441 : 524288 312 : 219 Template:Splitspan 3
25.00
21/48 21/48 Template:Splitspan 48
26.84
CTemplate:Music 65 : 64 5×13 : 26 Template:Splitspan 13 S
27.26
CTemplate:Music− 64 : 63 26 : 32×7 Template:Splitspan 7 S
29.27
 21/41 21/41 Template:Splitspan 41
31.19
DTemplate:MusicTemplate:MusicTemplate:Music 56 : 55 23×7 : 5×11 Template:Splitspan 11 S
33.33
 CTemplate:Music/DTemplate:MusicTemplate:MusicTemplate:MusicTemplate:Efn 21/36 21/36 Template:Splitspan 36, 72
34.28
CTemplate:Music 51 : 50 3×17 : 2×52 Template:Splitspan 17 S
34.98
BTemplate:MusicTemplate:MusicTemplate:Music- 50 : 49 2×52 : 72 Template:Splitspan 7 S
35.70
DTemplate:MusicTemplate:MusicTemplate:Music 49 : 48 72 : 24×3 Template:Splitspan 7 S
38.05
CTemplate:Music 46 : 45 2×23 : 32×5 Template:Splitspan 23 S
38.71
21/31 21/31 Template:Splitspan 31
38.91
CTemplate:MusicTemplate:MusicTemplate:Music 45 : 44 32×5 : 4×11 Template:Splitspan 11 S
40.00
21/30 21/30 Template:Splitspan 30
41.06
DTemplate:Music− 128 : 125 27 : 53 Template:Splitspan 5
41.72
DTemplate:MusicTemplate:MusicTemplate:Music 42 : 41 2×3×7 : 41 Template:Splitspan 41 S
42.75
CTemplate:Music 41 : 40 41 : 23×5 Template:Splitspan 41 S
43.83
CTemplate:MusicTemplate:Music 40 : 39 23×5 : 3×13 Template:Splitspan 13 S
44.97
CTemplate:MusicTemplate:Music 39 : 38 3×13 : 2×19 Template:Splitspan 19 S
46.17
DTemplate:MusicTemplate:MusicTemplate:MusicTemplate:Music 38 : 37 2×19 : 37 Template:Splitspan 37 S
47.43
CTemplate:MusicTemplate:Music 37 : 36 37 : 22×32 Template:Splitspan 37 S
48.77
CTemplate:Music 36 : 35 22×32 : 5×7 Template:Splitspan 7 S
49.98
246 : 239 3×41 : 239 Template:Splitspan 239
50.00
CTemplate:Music/DTemplate:Music 21/24 21/24 Template:Splitspan 24
50.18
DTemplate:MusicTemplate:MusicTemplate:Music 35 : 34 5×7 : 2×17 Template:Splitspan 17 S
50.72
BTemplate:MusicTemplate:MusicTemplate:MusicTemplate:Music 59049 : 57344 310 : 213×7 Template:Splitspan 7
51.68
CTemplate:MusicTemplate:MusicTemplate:Music 34 : 33 2×17 : 3×11 Template:Splitspan 17 S
53.27
CTemplate:Music 33 : 32 3×11 : 25 Template:Splitspan 11 S
54.96
DTemplate:MusicTemplate:MusicTemplate:Music 32 : 31 25 : 31 Template:Splitspan 31 S
56.55
BTemplate:MusicTemplate:MusicTemplate:MusicTemplate:Music 529 : 512 232 : 29 Template:Splitspan 23
56.77
CTemplate:Music 31 : 30 31 : 2×3×5 Template:Splitspan 31 S
58.69
CTemplate:MusicTemplate:Music 30 : 29 2×3×5 : 29 Template:Splitspan 29 S
60.75
CTemplate:MusicTemplate:Music 29 : 28 29 : 22×7 Template:Splitspan 29 S
62.96
DTemplate:MusicTemplate:MusicTemplate:Music 28 : 27 22×7 : 33 Template:Splitspan 7 S
63.81
(3 : 2)1/11 31/11 : 21/11 Template:Splitspan 18.80
65.34
CTemplate:MusicTemplate:Music+ 27 : 26 33 : 2×13 Template:Splitspan 13 S
66.34
DTemplate:MusicTemplate:MusicTemplate:Music 133 : 128 7×19 : 27 Template:Splitspan 19
66.67
CTemplate:MusicTemplate:Music/CTemplate:MusicTemplate:MusicTemplate:Efn 21/18 21/18 Template:Splitspan 18, 36, 72
67.90
DTemplate:MusicTemplate:MusicTemplate:Music 26 : 25 2×13 : 52 Template:Splitspan 13 S
70.67
CTemplate:Music[2] 25 : 24 52 : 23×3 Template:Splitspan 5 S
73.68
DTemplate:MusicTemplate:MusicTemplate:Music 24 : 23 23×3 : 23 Template:Splitspan 23 S
75.00
21/16 23/48 Template:Splitspan 16, 48
76.96
CTemplate:MusicTemplate:MusicTemplate:MusicTemplate:Music 23 : 22 23 : 2×11 Template:Splitspan 23 S
78.00
(3 : 2)1/9 31/9 : 21/9 Template:Splitspan 15.39
79.31
67 : 64 67 : 26 Template:Splitspan 67
80.54
CTemplate:MusicTemplate:MusicTemplate:Music 22 : 21 2×11 : 3×7 Template:Splitspan 11 S
84.47
DTemplate:MusicTemplate:Music 21 : 20 3×7 : 22×5 Template:Splitspan 7 S
88.80
CTemplate:MusicTemplate:Music 20 : 19 22×5 : 19 Template:Splitspan 19 S
90.22
DTemplate:Music−−[2] 256 : 243 28 : 35 Template:Splitspan 3
92.18
CTemplate:Music+[2] 135 : 128 33×5 : 27 Template:Splitspan 5
93.60
DTemplate:MusicTemplate:MusicTemplate:Music 19 : 18 19 : 2×32 Template:Splitspan 19 S
97.36
D↓↓ 128 : 121 27 : 112 Template:Splitspan 11
98.95
DTemplate:MusicTemplate:Music 18 : 17 2×32 : 17 Template:Splitspan 17 S
100.00
CTemplate:Music/DTemplate:Music 21/12 21/12 Template:Splitspan 12 M
104.96
CTemplate:MusicTemplate:Music[2] 17 : 16 17 : 24 Template:Splitspan 17 S
111.45
  1. REDIRECT Template:Radic

Template:Rcat shell || (5 : 1)1/25|| bgcolor="#EFCFCF" |Template:Splitspan || 10.77 || || ||

111.73
DTemplate:MusicTemplate:Music[2] 16 : 15 24 : 3×5 Template:Splitspan 5 S
113.69
CTemplate:Music++ 2187 : 2048 37 : 211 Template:Splitspan 3
116.72
(18 : 5)1/19 21/19×32/19 : 51/19 Template:Splitspan 10.28
119.44
CTemplate:MusicTemplate:Music 15 : 14 3×5 : 2×7 Template:Splitspan 7 S
125.00
25/48 25/48 Template:Splitspan 48
128.30
DTemplate:MusicTemplate:Music 14 : 13 2×7 : 13 Template:Splitspan 13 S
130.23
CTemplate:MusicTemplate:Music+ 69 : 64 3×23 : 26 Template:Splitspan 23
133.24
DTemplate:Music 27 : 25 33 : 52 Template:Splitspan 5
133.33
CTemplate:MusicTemplate:Music/DTemplate:MusicTemplate:MusicTemplate:Efn 21/9 22/18 Template:Splitspan 9, 18, 36, 72
138.57
DTemplate:MusicTemplate:MusicTemplate:Music 13 : 12 13 : 22×3 Template:Splitspan 13 S
150.00
CTemplate:Music/DTemplate:Music 23/24 21/8 Template:Splitspan 8, 24
150.64
D↓[2] 12 : 11 22×3 : 11 Template:Splitspan 11 S
155.14
DTemplate:Music 35 : 32 5×7 : 25 Template:Splitspan 7
160.90
D−− 800 : 729 25×52 : 36 Template:Splitspan 5
165.00
DTemplate:MusicTemplate:Music−[2] 11 : 10 11 : 2×5 Template:Splitspan 11 S
171.43
21/7 21/7 Template:Splitspan 7
175.00
27/48 27/48 Template:Splitspan 48
179.70
71 : 64 71 : 26 Template:Splitspan 71
180.45
ETemplate:Music−−− 65536 : 59049 216 : 310 Template:Splitspan 3
182.40
D−[2] 10 : 9 2×5 : 32 Template:Splitspan 5 S
200.00
D 22/12 21/6 Template:Splitspan 6, 12 M
203.91
D[2] 9 : 8 32 : 23 Template:Splitspan 3 S
215.89
DTemplate:Music 145 : 128 5×29 : 27 Template:Splitspan 29
223.46
ETemplate:Music−[2] 256 : 225 28 : 32×52 Template:Splitspan 5
225.00
23/16 29/48 Template:Splitspan 16, 48
227.79
73 : 64 73 : 26 Template:Splitspan 73
231.17
DTemplate:Music−[2] 8 : 7 23 : 7 Template:Splitspan 7 S
240.00
21/5 21/5 Template:Splitspan 5
247.74
DTemplate:MusicTemplate:Music 15 : 13 3×5 : 13 Template:Splitspan 13
250.00
DTemplate:Music/ETemplate:Music 25/24 25/24 Template:Splitspan 24
251.34
DTemplate:MusicTemplate:Music 37 : 32 37 : 25 Template:Splitspan 37
253.08
DTemplate:Music− 125 : 108 53 : 22×33 Template:Splitspan 5
262.37
E↓Template:Music 64 : 55 26 : 5×11 Template:Splitspan 11
266.87
ETemplate:MusicTemplate:Music[2] 7 : 6 7 : 2×3 Template:Splitspan 7 S
268.80
DTemplate:MusicTemplate:Music 299 : 256 13×23 : 28 Template:Splitspan 23
274.58
DTemplate:Music[2] 75 : 64 3×52 : 26 Template:Splitspan 5
275.00
211/48 211/48 Template:Splitspan 48
289.21
ETemplate:MusicTemplate:MusicTemplate:Music 13 : 11 13 : 11 Template:Splitspan 13
294.13
ETemplate:Music−[2] 32 : 27 25 : 33 Template:Splitspan 3
297.51
ETemplate:MusicTemplate:Music[2] 19 : 16 19 : 24 Template:Splitspan 19
300.00
DTemplate:Music/ETemplate:Music 23/12 21/4 Template:Splitspan 4, 12 M
301.85
DTemplate:MusicTemplate:MusicTemplate:Music 25 : 21[3] 52 : 3×7 Template:Splitspan 7
310.26
6:5÷(81:80)1/4 22 : 53/4 Template:Splitspan M
311.98
(3 : 2)4/9 34/9 : 24/9 Template:Splitspan 15.39
315.64
ETemplate:Music[2] 6 : 5 2×3 : 5 Template:Splitspan 5 M S
317.60
DTemplate:Music++ 19683 : 16384 39 : 214 Template:Splitspan 3
320.14
ETemplate:MusicTemplate:MusicTemplate:Music 77 : 64 7×11 : 26 Template:Splitspan 11
325.00
213/48 213/48 Template:Splitspan 48
336.13
DTemplate:MusicTemplate:MusicTemplate:MusicTemplate:Music 17 : 14 17 : 2×7 Template:Splitspan 17
337.15
ETemplate:Music+ 243 : 200 35 : 23×52 Template:Splitspan 5
342.48
ETemplate:MusicTemplate:Music 39 : 32 3×13 : 25 Template:Splitspan 13
342.86
22/7 22/7 Template:Splitspan 7
342.91
ETemplate:MusicTemplate:MusicTemplate:Music 128 : 105 27 : 3×5×7 Template:Splitspan 7
347.41
ETemplate:MusicTemplate:Music−[2] 11 : 9 11 : 32 Template:Splitspan 11
350.00
DTemplate:Music/ETemplate:Music 27/24 27/24 Template:Splitspan 24
354.55
ETemplate:MusicTemplate:Music 27 : 22 33 : 2×11 Template:Splitspan 11
359.47
ETemplate:Music[2] 16 : 13 24 : 13 Template:Splitspan 13
364.54
79 : 64 79 : 26 Template:Splitspan 79
364.81
E− 100 : 81 22×52 : 34 Template:Splitspan 5
375.00
25/16 215/48 Template:Splitspan 16, 48
384.36
FTemplate:Music−− 8192 : 6561 213 : 38 Template:Splitspan 3
386.31
E[2] 5 : 4 5 : 22 Template:Splitspan 5 M S
397.10
ETemplate:MusicTemplate:MusicTemplate:Music 161 : 128 7×23 : 27 Template:Splitspan 23
400.00
E 24/12 21/3 Template:Splitspan 3, 12 M
402.47
ETemplate:MusicTemplate:Music 323 : 256 17×19 : 28 Template:Splitspan 19
407.82
E+[2] 81 : 64 34 : 26 Template:Splitspan 3
417.51
FTemplate:MusicTemplate:Music+[2] 14 : 11 2×7 : 11 Template:Splitspan 11
425.00
217/48 217/48 Template:Splitspan 48
427.37
FTemplate:Music[2] 32 : 25 25 : 52 Template:Splitspan 5
429.06
ETemplate:Music 41 : 32 41 : 25 Template:Splitspan 41
435.08
ETemplate:Music[2] 9 : 7 32 : 7 Template:Splitspan 7
444.77
F↓ 128 : 99 27 : 32×11 Template:Splitspan 11
450.00
ETemplate:Music/FTemplate:Music 29/24 29/24 Template:Splitspan 8, 24
450.05
83 : 64 83 : 26 Template:Splitspan 83
454.21
FTemplate:MusicTemplate:Music 13 : 10 13 : 2×5 Template:Splitspan 13
456.99
ETemplate:Music[2] 125 : 96 53 : 25×3 Template:Splitspan 5
462.35
ETemplate:MusicTemplate:MusicTemplate:Music 64 : 49 26 : 72 Template:Splitspan 7
470.78
FTemplate:Music+[2] 21 : 16 3×7 : 24 Template:Splitspan 7
475.00
219/48 219/48 Template:Splitspan 48
478.49
ETemplate:Music+ 675 : 512 33×52 : 29 Template:Splitspan 5
480.00
22/5 22/5 Template:Splitspan 5
491.27
ETemplate:MusicTemplate:Music 85 : 64 5×17 : 26 Template:Splitspan 17
498.04
F[2] 4 : 3 22 : 3 Template:Splitspan 3 S
500.00
F 25/12 25/12 Template:Splitspan 12 M
501.42
FTemplate:MusicTemplate:Music 171 : 128 32×19 : 27 Template:Splitspan 19
510.51
(3 : 2)8/11 38/11 : 28/11 Template:Splitspan 18.80
511.52
FTemplate:Music 43 : 32 43 : 25 Template:Splitspan 43
514.29
23/7 23/7 Template:Splitspan 7
519.55
F+[2] 27 : 20 33 : 22×5 Template:Splitspan 5
521.51
ETemplate:Music+++ 177147 : 131072 311 : 217 Template:Splitspan 3
525.00
27/16 221/48 Template:Splitspan 16, 48
531.53
FTemplate:Music+ 87 : 64 3×29 : 26 Template:Splitspan 29
536.95
FTemplate:MusicTemplate:MusicTemplate:Music 15 : 11 3×5 : 11 Template:Splitspan 11
550.00
FTemplate:Music/GTemplate:Music 211/24 211/24 Template:Splitspan 24
551.32
FTemplate:Music[2] 11 : 8 11 : 23 Template:Splitspan 11
563.38
FTemplate:MusicTemplate:MusicTemplate:Music 18 : 13 2×9 : 13 Template:Splitspan 13
568.72
FTemplate:Music[2] 25 : 18 52 : 2×32 Template:Splitspan 5
570.88
89 : 64 89 : 26 Template:Splitspan 89
575.00
223/48 223/48 Template:Splitspan 48
582.51
GTemplate:MusicTemplate:Music[2] 7 : 5 7 : 5 Template:Splitspan 7
588.27
GTemplate:Music−− 1024 : 729 210 : 36 Template:Splitspan 3
590.22
FTemplate:Music+[2] 45 : 32 32×5 : 25 Template:Splitspan 5
595.03
GTemplate:MusicTemplate:MusicTemplate:Music 361 : 256 192 : 28 Template:Splitspan 19
600.00
FTemplate:Music/GTemplate:Music 26/12 21/2=Template:Radic Template:Splitspan 2, 12 M
609.35
GTemplate:MusicTemplate:MusicTemplate:Music 91 : 64 7×13 : 26 Template:Splitspan 13
609.78
GTemplate:Music−[2] 64 : 45 26 : 32×5 Template:Splitspan 5
611.73
FTemplate:Music++ 729 : 512 36 : 29 Template:Splitspan 3
617.49
FTemplate:MusicTemplate:Music[2] 10 : 7 2×5 : 7 Template:Splitspan 7
625.00
225/48 225/48 Template:Splitspan 48
628.27
FTemplate:MusicTemplate:Music+ 23 : 16 23 : 24 Template:Splitspan 23
631.28
GTemplate:Music[2] 36 : 25 22×32 : 52 Template:Splitspan 5
646.99
FTemplate:MusicTemplate:Music+ 93 : 64 3×31 : 26 Template:Splitspan 31
648.68
G↓[2] 16 : 11 24 : 11 Template:Splitspan 11
650.00
FTemplate:Music/GTemplate:Music 213/24 213/24 Template:Splitspan 24
665.51
GTemplate:Music 47 : 32 47 : 25 Template:Splitspan 47
675.00
29/16 227/48 Template:Splitspan 16, 48
678.49
ATemplate:Music−−− 262144 : 177147 218 : 311 Template:Splitspan 3
680.45
G− 40 : 27 23×5 : 33 Template:Splitspan 5
683.83
GTemplate:Music 95 : 64 5×19 : 26 Template:Splitspan 19
684.82
ETemplate:MusicTemplate:MusicTemplate:MusicTemplate:MusicTemplate:MusicTemplate:Music 12167 : 8192 233 : 213 Template:Splitspan 23
685.71
24/7 : 1 Template:Splitspan 7
691.20
3:2÷(81:80)1/2 2×51/2 : 3 Template:Splitspan M
694.79
3:2÷(81:80)1/3 21/3×51/3 : 31/3 Template:Splitspan M
695.81
3:2÷(81:80)2/7 21/7×52/7 : 31/7 Template:Splitspan M
696.58
3:2÷(81:80)1/4 51/4 Template:Splitspan M
697.65
3:2÷(81:80)1/5 31/5×51/5 : 21/5 Template:Splitspan M
698.37
3:2÷(81:80)1/6 31/3×51/6 : 21/3 Template:Splitspan M
700.00
G 27/12 27/12 Template:Splitspan 12 M
701.89
231/53 231/53 Template:Splitspan 53
701.96
G[2] 3 : 2 3 : 2 Template:Splitspan 3 S
702.44
224/41 224/41 Template:Splitspan 41
703.45
217/29 217/29 Template:Splitspan 29
719.90
97 : 64 97 : 26 Template:Splitspan 97
720.00
23/5 : 1 Template:Splitspan 5
721.51
ATemplate:Music− 1024 : 675 210 : 33×52 Template:Splitspan 5
725.00
229/48 229/48 Template:Splitspan 48
729.22
GTemplate:MusicTemplate:Music 32 : 21 24 : 3×7 Template:Splitspan 7
733.23
FTemplate:MusicTemplate:MusicTemplate:MusicTemplate:Music 391 : 256 17×23 : 28 Template:Splitspan 23
737.65
ATemplate:MusicTemplate:MusicTemplate:Music+ 49 : 32 7×7 : 25 Template:Splitspan 7
743.01
ATemplate:Music 192 : 125 26×3 : 53 Template:Splitspan 5
750.00
GTemplate:Music/ATemplate:Music 215/24 215/24 Template:Splitspan 8, 24
755.23
GTemplate:Music 99 : 64 32×11 : 26 Template:Splitspan 11
764.92
ATemplate:MusicTemplate:Music[2] 14 : 9 2×7 : 32 Template:Splitspan 7
772.63
GTemplate:Music 25 : 16 52 : 24 Template:Splitspan 5
775.00
231/48 231/48 Template:Splitspan 48
781.79
[[pi|Template:Pi]] : 2 Template:Splitspan
782.49
GTemplate:MusicTemplate:Music-[2] 11 : 7 11 : 7 Template:Splitspan 11
789.85
101 : 64 101 : 26 Template:Splitspan 101
792.18
ATemplate:Music−[2] 128 : 81 27 : 34 Template:Splitspan 3
798.40
ATemplate:MusicTemplate:MusicTemplate:MusicTemplate:Music 203 : 128 7×29 : 27 Template:Splitspan 29
800.00
GTemplate:Music/ATemplate:Music 28/12 22/3 Template:Splitspan 3, 12 M
806.91
GTemplate:MusicTemplate:Music 51 : 32 3×17 : 25 Template:Splitspan 17
813.69
ATemplate:Music[2] 8 : 5 23 : 5 Template:Splitspan 5
815.64
GTemplate:Music++ 6561 : 4096 38 : 212 Template:Splitspan 3
823.80
103 : 64 103 : 26 Template:Splitspan 103
825.00
211/16 233/48 Template:Splitspan 16, 48
832.18
GTemplate:MusicTemplate:MusicTemplate:Music 207 : 128 32×23 : 27 Template:Splitspan 23
833.09
(51/2+1)/2 Template:Mvar : 1 Template:Splitspan
835.19
ATemplate:Music+ 81 : 50 34 : 2×52 Template:Splitspan 5
840.53
ATemplate:MusicTemplate:Music[2] 13 : 8 13 : 23 Template:Splitspan 13
848.83
ATemplate:MusicTemplate:MusicTemplate:Music 209 : 128 11×19 : 27 Template:Splitspan 19
850.00
GTemplate:Music/ATemplate:Music 217/24 217/24 Template:Splitspan 24
852.59
A↓+[2] 18 : 11 2×32 : 11 Template:Splitspan 11
857.09
ATemplate:Music+ 105 : 64 3×5×7 : 26 Template:Splitspan 7
857.14
25/7 25/7 Template:Splitspan 7
862.85
A− 400 : 243 24×52 : 35 Template:Splitspan 5
873.50
ATemplate:Music 53 : 32 53 : 25 Template:Splitspan 53
875.00
235/48 235/48 Template:Splitspan 48
879.86
A↓Template:Music 128 : 77 27 : 7×11 Template:Splitspan 11
882.40
BTemplate:Music−−− 32768 : 19683 215 : 39 Template:Splitspan 3
884.36
A[2] 5 : 3 5 : 3 Template:Splitspan 5 M
889.76
107 : 64 107 : 26 Template:Splitspan 107
892.54
BTemplate:MusicTemplate:MusicTemplate:MusicTemplate:Music 6859 : 4096 193 : 212 Template:Splitspan 19
900.00
A 29/12 23/4 Template:Splitspan 4, 12 M
902.49
ATemplate:Music 32 : 19 25 : 19 Template:Splitspan 19
905.87
A+[2] 27 : 16 33 : 24 Template:Splitspan 3
921.82
109 : 64 109 : 26 Template:Splitspan 109
925.00
237/48 237/48 Template:Splitspan 48
925.42
BTemplate:Music−[2] 128 : 75 27 : 3×52 Template:Splitspan 5
925.79
ATemplate:MusicTemplate:MusicTemplate:Music 437 : 256 19×23 : 28 Template:Splitspan 23
933.13
ATemplate:Music[2] 12 : 7 22×3 : 7 Template:Splitspan 7
937.63
ATemplate:Music 55 : 32 5×11 : 25 Template:Splitspan 11
950.00
ATemplate:Music/BTemplate:Music 219/24 219/24 Template:Splitspan 24
953.30
ATemplate:MusicTemplate:MusicTemplate:Music 111 : 64 3×37 : 26 Template:Splitspan 37
955.03
ATemplate:Music[2] 125 : 72 53 : 23×32 Template:Splitspan 5
957.21
(3 : 2)15/11 315/11 : 215/11 Template:Splitspan 18.80
960.00
24/5 24/5 Template:Splitspan 5
968.83
BTemplate:MusicTemplate:Music[2] 7 : 4 7 : 22 Template:Splitspan 7
975.00
213/16 239/48 Template:Splitspan 16, 48
976.54
ATemplate:Music+[2] 225 : 128 32×52 : 27 Template:Splitspan 5
984.21
113 : 64 113 : 26 Template:Splitspan 113
996.09
 BTemplate:Music−[2] 16 : 9 24 : 32 Template:Splitspan 3
999.47
BTemplate:MusicTemplate:Music 57 : 32 3×19 : 25 Template:Splitspan 19
1000.00
 ATemplate:Music/BTemplate:Music 210/12 25/6 Template:Splitspan 6, 12 M
1014.59
ATemplate:MusicTemplate:Music+ 115 : 64 5×23 : 26 Template:Splitspan 23
1017.60
 BTemplate:Music[2] 9 : 5 32 : 5 Template:Splitspan 5
1019.55
ATemplate:Music+++ 59049 : 32768 310 : 215 Template:Splitspan 3
1025.00
241/48 241/48 Template:Splitspan 48
1028.57
26/7 26/7 Template:Splitspan 7
1029.58
BTemplate:MusicTemplate:Music 29 : 16 29 : 24 Template:Splitspan 29
1035.00
 B↓[2] 20 : 11 22×5 : 11 Template:Splitspan 11
1039.10
BTemplate:Music+ 729 : 400 36 : 24×52 Template:Splitspan 5
1044.44
BTemplate:MusicTemplate:Music 117 : 64 32×13 : 26 Template:Splitspan 13
1044.86
BTemplate:MusicTemplate:MusicTemplate:Music 64 : 35 26 : 5×7 Template:Splitspan 7
1049.36
 BTemplate:MusicTemplate:Music−[2] 11 : 6 11 : 2×3 Template:Splitspan 11
1050.00
ATemplate:Music/BTemplate:Music 221/24 27/8 Template:Splitspan 8, 24
1059.17
59 : 32 59 : 25 Template:Splitspan 59
1066.76
B− 50 : 27 2×52 : 33 Template:Splitspan 5
1071.70
BTemplate:MusicTemplate:MusicTemplate:MusicTemplate:Music 13 : 7 13 : 7 Template:Splitspan 13
1073.78
BTemplate:MusicTemplate:Music 119 : 64 7×17 : 26 Template:Splitspan 17
1075.00
243/48 243/48 Template:Splitspan 48
1086.31
C′Template:Music−− 4096 : 2187 212 : 37 Template:Splitspan 3
1088.27
B[2] 15 : 8 3×5 : 23 Template:Splitspan 5
1095.04
CTemplate:MusicTemplate:Music 32 : 17 25 : 17 Template:Splitspan 17
1100.00
B 211/12 211/12 Template:Splitspan 12 M
1102.64
BTemplate:MusicTemplate:MusicTemplate:Music- 121 : 64 112 : 26 Template:Splitspan 11
1107.82
C′Template:Music− 256 : 135 28 : 33×5 Template:Splitspan 5
1109.78
B+[2] 243 : 128 35 : 27 Template:Splitspan 3
1116.88
61 : 32 61 : 25 Template:Splitspan 61
1125.00
215/16 245/48 Template:Splitspan 16, 48
1129.33
C′Template:Music[2] 48 : 25 24×3 : 52 Template:Splitspan 5
1131.02
BTemplate:Music 123 : 64 3×41 : 26 Template:Splitspan 41
1137.04
BTemplate:Music 27 : 14 33 : 2×7 Template:Splitspan 7
1138.04
CTemplate:MusicTemplate:MusicTemplate:Music 247 : 128 13×19 : 27 Template:Splitspan 19
1145.04
BTemplate:Music 31 : 16 31 : 24 Template:Splitspan 31
1146.73
C↓ 64 : 33 26 : 3×11 Template:Splitspan 11
1150.00
BTemplate:Music/CTemplate:Music 223/24 223/24 Template:Splitspan 24
1151.23
CTemplate:Music 35 : 18 5×7 : 2×32 Template:Splitspan 7
1158.94
BTemplate:Music[2] 125 : 64 53 : 26 Template:Splitspan 5
1172.74
CTemplate:Music+ 63 : 32 32×7 : 25 Template:Splitspan 7
1175.00
247/48 247/48 Template:Splitspan 48
1178.49
C′− 160 : 81 25×5 : 34 Template:Splitspan 5
1179.59
BTemplate:MusicTemplate:Music 253 : 128 11×23 : 27 Template:Splitspan 23
1186.42
127 : 64 127 : 26 Template:Splitspan 127
1200.00
C′ 2 : 1 2 : 1 Template:Splitspan 1, 12 3 M S

See also

Notes

Template:Notelist

References

Template:Reflist

External links

Template:Consonance and dissonance Script error: No such module "Navbox". Script error: No such module "Navbox". Template:Music theory lists

  1. ↑ a b Fox, Christopher (2003). "Microtones and Microtonalities", Contemporary Music Review, v. 22, pt. 1–2. (Abingdon, Oxfordshire, UK: Routledge): p. 13.
  2. ↑ a b c d e f g h i j k l m n o p q r s t u v w x y z aa ab ac ad ae af ag ah ai aj ak al am an ao ap aq ar as at au av aw ax ay az ba bb bc bd be bf bg bh Fonville, John. 1991. "Ben Johnston's Extended Just Intonation: A Guide for Interpreters". Perspectives of New Music 29, no. 2 (Summer): 106–137.
  3. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Gann
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