List of pitch intervals

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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.

Terminology[edit | edit source]

  • 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.

List[edit | edit source]

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.
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
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 C7- 4375 : 4374 54·7 : 2·37 Template:Splitspan 7 S
Template:Right E7777triple flat+ 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 B7 upside-down 225 : 224 32·52 : 25·7 Template:Splitspan 7 S
Template:Right Bdouble sharp- 15625 : 15552 56 : 26·35 Template:Splitspan 5
Template:Right Adouble sharpdouble sharp++ 2109375 : 2097152 33·57 : 221 Template:Splitspan 5
Template:Right C43U 160 : 159 25·5 : 3·53 Template:Splitspan 53 S
Template:Right C29 145 : 144 5·29 : 24·32 Template:Splitspan 29 S
Template:Right 21/96 21/96 Template:Splitspan 96
Template:Right B7 upside-down7 upside-down7 upside-down- 1728 : 1715 26·33 : 5·73 Template:Splitspan 7
Template:Right C43 129 : 128 3·43 : 27 Template:Splitspan 43 S
Template:Right Ddouble flat7 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 C19U 96 : 95 25·3 : 5·19 Template:Splitspan 19 S
Template:Right Ddouble flat--[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 C13 65 : 64 5·13 : 26 Template:Splitspan 13 S
Template:Right C7 upside-down- 64 : 63 26 : 32·7 Template:Splitspan 7 S
Template:Right 21/41 21/41 Template:Splitspan 41
Template:Right D7 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 C17 51 : 50 3·17 : 2·52 Template:Splitspan 17 S
Template:Right B7 upside-down7 upside-down- 50 : 49 2·52 : 72 Template:Splitspan 7 S
Template:Right D77 49 : 48 72 : 24·3 Template:Splitspan 7 S
Template:Right C23 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 Ddouble flat- 128 : 125 27 : 53 Template:Splitspan 5
Template:Right D41U7 42 : 41 2·3·7 : 41 Template:Splitspan 41 S
Template:Right C41 41 : 40 41 : 23·5 Template:Splitspan 41 S
Template:Right C13 upside down 40 : 39 23·5 : 3·13 Template:Splitspan 13 S
Template:Right C19U13 39 : 38 3·13 : 2·19 Template:Splitspan 19 S
Template:Right D37U19double flat- 38 : 37 2·19 : 37 Template:Splitspan 37 S
Template:Right C37 37 : 36 37 : 22·32 Template:Splitspan 37 S
Template:Right C7 upside-down 36 : 35 22·32 : 5·7 Template:Splitspan 7 S
Template:Right 246 : 239 3·41 : 239 Template:Splitspan 239
Template:Right Chalf sharp/Dthree quarter flat 21/24 21/24 Template:Splitspan 24
Template:Right D17 upside down7 35 : 34 5·7 : 2·17 Template:Splitspan 17 S
Template:Right B7 upside-down++ 59049 : 57344 310 : 213·7 Template:Splitspan 7
Template:Right C17 34 : 33 2·17 : 3·11 Template:Splitspan 17 S
Template:Right C 33 : 32 3·11 : 25 Template:Splitspan 11 S
Template:Right D31U- 32 : 31 25 : 31 Template:Splitspan 31 S
Template:Right B2323+ 529 : 512 232 : 29 Template:Splitspan 23
Template:Right C31 31 : 30 31 : 2·3·5 Template:Splitspan 31 S
Template:Right C29U 30 : 29 2·3·5 : 29 Template:Splitspan 29 S
Template:Right C297 upside-down 29 : 28 29 : 22·7 Template:Splitspan 29 S
Template:Right D7- 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 C13 upside down+ 27 : 26 33 : 2·13 Template:Splitspan 13 S
Template:Right D197 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 D13double flat- 26 : 25 2·13 : 52 Template:Splitspan 13 S
Template:Right C[2] 25 : 24 52 : 23·3 Template:Splitspan 5 S
Template:Right D23U- 24 : 23 23·3 : 23 Template:Splitspan 23 S
Template:Right 21/16 23/48 Template:Splitspan 16, 48
Template:Right C23+ 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 C7 upside-down- 22 : 21 2·11 : 3·7 Template:Splitspan 11 S
Template:Right D7 21 : 20 3·7 : 22·5 Template:Splitspan 7 S
Template:Right C19U 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 D19- 19 : 18 19 : 2·9 Template:Splitspan 19 S
Template:Right D↓↓ 128 : 121 27 : 112 Template:Splitspan 11
Template:Right D17 upside down 18 : 17 2·32 : 17 Template:Splitspan 17 S
Template:Right C/D 21/12 21/12 Template:Splitspan 12 M
Template:Right C17[2] 17 : 16 17 : 24 Template:Splitspan 17 S
Template:Right (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 C7 upside-down 15 : 14 3·5 : 2·7 Template:Splitspan 7 S
Template:Right 25/48 25/48 Template:Splitspan 48
Template:Right D13 upside down7 14 : 13 2·7 : 13 Template:Splitspan 13 S
Template:Right C23+ 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 D13- 13 : 12 13 : 22·3 Template:Splitspan 13 S
Template:Right Cthree quarter sharp/Dhalf flat 23/24 21/8 Template:Splitspan 8, 24
Template:Right D↓[2] 12 : 11 22·3 : 11 Template:Splitspan 11 S
Template:Right D7 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 Edouble flat--- 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 D29 145 : 128 5·29 : 27 Template:Splitspan 29
Template:Right Edouble flat-[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 D7 upside-down-[2] 8 : 7 23 : 7 Template:Splitspan 7 S
Template:Right 21/5 21/5 Template:Splitspan 5
Template:Right D13 upside down 15 : 13 3·5 : 13 Template:Splitspan 13
Template:Right 25/24 25/24 Template:Splitspan 24
Template:Right D37 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 D2313 299 : 256 13·23 : 28 Template:Splitspan 23
Template:Right E7[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 E13 13 : 11 13 : 11 Template:Splitspan 13 S
Template:Right E-[2] 32 : 27 25 : 33 Template:Splitspan 3
Template:Right E19[2] 19 : 16 19 : 24 Template:Splitspan 19
Template:Right D/E 23/12 21/4 Template:Splitspan 4, 12 M
Template:Right D7 upside-down- 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 E7 77 : 64 7·11 : 26 Template:Splitspan 11
Template:Right 213/48 213/48 Template:Splitspan 48
Template:Right D177 upside-down- 17 : 14 17 : 2·7 Template:Splitspan 17
Template:Right E+ 243 : 200 35 : 23·52 Template:Splitspan 5
Template:Right E13 39 : 32 3·13 : 25 Template:Splitspan 13
Template:Right 22/7 22/7 Template:Splitspan 7
Template:Right E7 upside-down- 128 : 105 27 : 3·5·7 Template:Splitspan 7
Template:Right E-[2] 11 : 9 11 : 32 Template:Splitspan 11
Template:Right Dthree quarter sharp/Ehalf flat 27/24 27/24 Template:Splitspan 24
Template:Right E+ 27 : 22 33 : 2·11 Template:Splitspan 11
Template:Right E13 upside down[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 E237+ 161 : 128 7·23 : 27 Template:Splitspan 23
Template:Right E 24/12 21/3 Template:Splitspan 3, 12 M
Template:Right E1917 323 : 256 17·19 : 28 Template:Splitspan 19
Template:Right E+[2] 81 : 64 34 : 26 Template:Splitspan 3
Template:Right F7+[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 E41 41 : 32 41 : 25 Template:Splitspan 41
Template:Right E7 upside-down[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 F13 13 : 10 13 : 2·5 Template:Splitspan 13
Template:Right E[2] 125 : 96 53 : 25·3 Template:Splitspan 5
Template:Right E7 upside-down7 upside-down- 64 : 49 26 : 72 Template:Splitspan 7
Template:Right F7+[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 E17 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 F19+ 171 : 128 32·19 : 27 Template:Splitspan 19
Template:Right (3 : 2)8/11 38/11 : 28/11 Template:Splitspan 18.75
Template:Right F43 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 F29+ 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 F13 upside down+ 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 G7[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 G1919 361 : 256 192 : 28 Template:Splitspan 19
Template:Right F/G 26/12 21/2=2 Template:Splitspan 2, 12 M
Template:Right G137 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 F7 upside-down[2] 10 : 7 2·5 : 7 Template:Splitspan 7
Template:Right 225/48 225/48 Template:Splitspan 48
Template:Right F23+ 23 : 16 23 : 24 Template:Splitspan 23
Template:Right G[2] 36 : 25 22·32 : 52 Template:Splitspan 5
Template:Right F31+ 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 G43U 47 : 32 47 : 25 Template:Splitspan 47
Template:Right 29/16 227/48 Template:Splitspan 16, 48
Template:Right Adouble flat--- 262144 : 177147 218 : 311 Template:Splitspan 3
Template:Right G- 40 : 27 23·5 : 33 Template:Splitspan 5
Template:Right G19 95 : 64 5·19 : 26 Template:Splitspan 19
Template:Right E232323double sharp++ 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 Adouble flat- 1024 : 675 210 : 33·52 Template:Splitspan 5
Template:Right 229/48 229/48 Template:Splitspan 48
Template:Right G7 upside-down- 32 : 21 24 : 3·7 Template:Splitspan 7
Template:Right F2317double sharp+ 391 : 256 17·23 : 28 Template:Splitspan 23
Template:Right A77+ 49 : 32 7·7 : 25 Template:Splitspan 7
Template:Right Adouble flat 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 A7[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 G7 upside-down-[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 A297+ 203 : 128 7·29 : 27 Template:Splitspan 29
Template:Right G/A 28/12 22/3 Template:Splitspan 3, 12 M
Template:Right G17 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 G23+ 207 : 128 32·23 : 27 Template:Splitspan 23
Template:Right 51/2+1 : 2  : 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 A13[2] 13 : 8 13 : 23 Template:Splitspan 13
Template:Right A19 209 : 128 11·19 : 27 Template:Splitspan 19
Template:Right Gthree quarter sharp/Ahalf flat 217/24 217/24 Template:Splitspan 24
Template:Right A↓+[2] 18 : 11 2·32 : 11 Template:Splitspan 11
Template:Right A7+ 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 A43U 53 : 32 53 : 25 Template:Splitspan 53
Template:Right 235/48 235/48 Template:Splitspan 48
Template:Right A↓7 upside-down 128 : 77 27 : 7·11 Template:Splitspan 11
Template:Right Bdouble flat--- 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 B191919double flat 6859 : 4096 193 : 212 Template:Splitspan 19
Template:Right A 29/12 23/4 Template:Splitspan 4, 12 M
Template:Right A19U 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 Bdouble flat-[2] 128 : 75 27 : 3·52 Template:Splitspan 5
Template:Right A2319+ 437 : 256 19·23 : 28 Template:Splitspan 23
Template:Right A7 upside-down[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 A37+ 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 B7[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 B19 57 : 32 3·19 : 25 Template:Splitspan 19
Template:Right A/B 210/12 25/6 Template:Splitspan 6, 12 M
Template:Right A23+ 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 B29 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 B13 117 : 64 32·13 : 26 Template:Splitspan 13
Template:Right B7 upside-down- 64 : 35 26 : 5·7 Template:Splitspan 7
Template:Right B-[2] 11 : 6 11 : 2·3 Template:Splitspan 11
Template:Right Athree quarter sharp/Bhalf flat 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 B137 upside-down- 13 : 7 13 : 7 Template:Splitspan 13
Template:Right B717 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 C17 upside down 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 B41 123 : 64 3·41 : 26 Template:Splitspan 41
Template:Right B7 upside-down 27 : 14 33 : 2·7 Template:Splitspan 7
Template:Right C1913 247 : 128 13·19 : 27 Template:Splitspan 19
Template:Right B31 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 C7 35 : 18 5·7 : 2·32 Template:Splitspan 7
Template:Right B[2] 125 : 64 53 : 26 Template:Splitspan 5
Template:Right C7+ 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 B23 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

See also[edit | edit source]

Notes[edit | edit source]

  1. 1.0 1.1 1.2 1.3 Maneri-Sims notation

References[edit | edit source]

  1. 1.0 1.1 Fox, Christopher (2003). "Microtones and Microtonalities", Contemporary Music Review, v. 22, pt. 1-2. (Abingdon, Oxfordshire, UK: Routledge): p.13.
  2. 2.00 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 2.20 2.21 2.22 2.23 2.24 2.25 2.26 2.27 2.28 2.29 2.30 2.31 2.32 2.33 2.34 2.35 2.36 2.37 2.38 2.39 2.40 2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.49 2.50 2.51 2.52 2.53 2.54 2.55 2.56 2.57 2.58 2.59 Fonville, John. 1991. "Ben Johnston's Extended Just Intonation: A Guide for Interpreters". Perspectives of New Music 29, no. 2 (Summer): 106–37.
  3. Cite error: Invalid <ref> tag; no text was provided for refs named Gann

External links[edit | edit source]

Template:Consonance and dissonance

Template:Music theory lists

This article uses material from List of pitch intervals on Wikipedia (view authors). License under CC BY-SA 3.0. Wikipedia logo
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