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List of pitch intervals

January 01, 1970

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.

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 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.

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

  • 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 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.
  • Superparticular ratios are intervals that can be expressed as the ratio of two consecutive integers.

List edit

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 playⓘ Unison,[3] monophony,[4] perfect prime,[3] tonic,[5] or fundamental 1, 12 3 M
0.03
65537 : 65536 65537 : 216 playⓘ Sixty-five-thousand-five-hundred-thirty-seventh harmonic 65537 S
0.40
 C ♯− 4375 : 4374 54×7 : 2×37 playⓘ Ragisma[3][6] 7 S
0.72
 E     + 2401 : 2400 74 : 25×3×52 playⓘ Breedsma[3][6] 7 S
1.00
21/1200 21/1200 playⓘ Cent[7] 1200
1.20
21/1000 21/1000 playⓘ Millioctave 1000
1.95
B♯++ 32805 : 32768 38×5 : 215 playⓘ Schisma[3][5] 5
1.96
3:2÷(27/12) 3 : 219/12 Grad, Werckmeister[8]
3.99
101/1000 21/1000×51/1000 playⓘ Savart or eptaméride 301.03
7.71
B ♯ 225 : 224 32×52 : 25×7 playⓘ Septimal kleisma,[3][6] marvel comma 7 S
8.11
B − 15625 : 15552 56 : 26×35 playⓘ Kleisma or semicomma majeur[3][6] 5
10.06
A  ++ 2109375 : 2097152 33×57 : 221 playⓘ Semicomma,[3][6] Fokker's comma[3] 5
10.85
C  160 : 159 25×5 : 3×53 playⓘ Difference between 5:3 & 53:32 53 S
11.98
 C  145 : 144 5×29 : 24×32 playⓘ Difference between 29:16 & 9:5 29 S
12.50
21/96 21/96 playⓘ Sixteenth tone 96
13.07
 B   − 1728 : 1715 26×33 : 5×73 playⓘ Orwell comma[3][9] 7
13.47
 C  129 : 128 3×43 : 27 playⓘ Hundred-twenty-ninth harmonic 43 S
13.79
D   126 : 125 2×32×7 : 53 playⓘ Small septimal semicomma,[6] small septimal comma,[3] starling comma 7 S
14.37
C♭↑↑− 121 : 120 112 : 23×3×5 playⓘ Undecimal seconds comma[3] 11 S
16.67
C↑[a] 21/72 21/72 playⓘ 1 step in 72 equal temperament 72
18.13
C  96 : 95 25×3 : 5×19 playⓘ Difference between 19:16 & 6:5 19 S
19.55
D --[2] 2048 : 2025 211 : 34×52 playⓘ Diaschisma,[3][6] minor comma 5
21.51
C+[2] 81 : 80 34 : 24×5 playⓘ Syntonic comma,[3][5][6] major comma, komma, chromatic diesis, or comma of Didymus[3][6][10][11] 5 S
22.64
21/53 21/53 playⓘ Holdrian comma, Holder's comma, 1 step in 53 equal temperament 53
23.46
B♯+++ 531441 : 524288 312 : 219 playⓘ Pythagorean comma,[3][5][6][10][11] ditonic comma[3][6] 3
25.00
21/48 21/48 playⓘ Eighth tone 48
26.84
C  65 : 64 5×13 : 26 playⓘ Sixty-fifth harmonic,[5] 13th-partial chroma[3] 13 S
27.26
C − 64 : 63 26 : 32×7 playⓘ Septimal comma,[3][6][11] Archytas' comma,[3] 63rd subharmonic 7 S
29.27
 21/41 21/41 playⓘ 1 step in 41 equal temperament 41
31.19
D ♭↓ 56 : 55 23×7 : 5×11 playⓘ Undecimal diesis,[3] Ptolemy's enharmonic:[5] difference between (11 : 8) and (7 : 5) tritone 11 S
33.33
 C /D♭  [a] 21/36 21/36 playⓘ Sixth tone 36, 72
34.28
C  51 : 50 3×17 : 2×52 playⓘ Difference between 17:16 & 25:24 17 S
34.98
B  ♯- 50 : 49 2×52 : 72 playⓘ Septimal sixth tone or jubilisma, Erlich's decatonic comma or tritonic diesis[3][6] 7 S
35.70
D  ♭ 49 : 48 72 : 24×3 playⓘ Septimal diesis, slendro diesis or septimal 1/6-tone[3] 7 S
38.05
C  46 : 45 2×23 : 32×5 playⓘ Inferior quarter tone,[5] difference between 23:16 & 45:32 23 S
38.71
21/31 21/31 playⓘ 1 step in 31 equal temperament 31
38.91
C↓♯+ 45 : 44 32×5 : 4×11 playⓘ Undecimal diesis or undecimal fifth tone 11 S
40.00
21/30 21/30 playⓘ Fifth tone 30
41.06
D − 128 : 125 27 : 53 playⓘ Enharmonic diesis or 5-limit limma, minor diesis,[6] diminished second,[5][6] minor diesis or diesis,[3] 125th subharmonic 5
41.72
D  ♭ 42 : 41 2×3×7 : 41 playⓘ Lesser 41-limit fifth tone 41 S
42.75
C  41 : 40 41 : 23×5 playⓘ Greater 41-limit fifth tone 41 S
43.83
C ♯ 40 : 39 23×5 : 3×13 playⓘ Tridecimal fifth tone 13 S
44.97
C   39 : 38 3×13 : 2×19 playⓘ Superior quarter-tone,[5] novendecimal fifth tone 19 S
46.17
D   - 38 : 37 2×19 : 37 playⓘ Lesser 37-limit quarter tone 37 S
47.43
C ♯ 37 : 36 37 : 22×32 playⓘ Greater 37-limit quarter tone 37 S
48.77
C  36 : 35 22×32 : 5×7 playⓘ Septimal quarter tone, septimal diesis,[3][6] septimal chroma,[2] superior quarter tone[5] 7 S
49.98
246 : 239 3×41 : 239 playⓘ Just quarter tone[11] 239
50.00
C /D  21/24 21/24 playⓘ Equal-tempered quarter tone 24
50.18
D  ♭ 35 : 34 5×7 : 2×17 playⓘ ET quarter-tone approximation,[5] lesser 17-limit quarter tone 17 S
50.72
B ♯++ 59049 : 57344 310 : 213×7 playⓘ Harrison's comma (10 P5s – 1 H7)[3] 7
51.68
C ↓♯ 34 : 33 2×17 : 3×11 playⓘ Greater 17-limit quarter tone 17 S
53.27
C↑ 33 : 32 3×11 : 25 playⓘ Thirty-third harmonic,[5] undecimal comma, undecimal quarter tone 11 S
54.96
D ♭- 32 : 31 25 : 31 playⓘ Inferior quarter-tone,[5] thirty-first subharmonic 31 S
56.55
B  ♯+ 529 : 512 232 : 29 playⓘ Five-hundred-twenty-ninth harmonic 23
56.77
C  31 : 30 31 : 2×3×5 playⓘ Greater quarter-tone,[5] difference between 31:16 & 15:8 31 S
58.69
C ♯ 30 : 29 2×3×5 : 29 playⓘ Lesser 29-limit quarter tone 29 S
60.75
C   29 : 28 29 : 22×7 playⓘ Greater 29-limit quarter tone 29 S
62.96
D ♭- 28 : 27 22×7 : 33 playⓘ Septimal minor second, small minor second, inferior quarter tone[5] 7 S
63.81
(3 : 2)1/11 31/11 : 21/11 playⓘ Beta scale step 18.75
65.34
C ♯+ 27 : 26 33 : 2×13 playⓘ Chromatic diesis,[12] tridecimal comma[3] 13 S
66.34
D  ♭ 133 : 128 7×19 : 27 playⓘ One-hundred-thirty-third harmonic 19
66.67
C ↑/C♯ [a] 21/18 21/18 playⓘ Third tone 18, 36, 72
67.90
D  - 26 : 25 2×13 : 52 playⓘ Tridecimal third tone, third tone[5] 13 S
70.67
C♯[2] 25 : 24 52 : 23×3 playⓘ Just chromatic semitone or minor chroma,[3] lesser chromatic semitone, small (just) semitone[11] or minor second,[4] minor chromatic semitone,[13] or minor semitone,[5] 2⁄7-comma meantone chromatic semitone, augmented unison 5 S
73.68
D ♭- 24 : 23 23×3 : 23 playⓘ Lesser 23-limit semitone 23 S
75.00
21/16 23/48 playⓘ 1 step in 16 equal temperament, 3 steps in 48 16, 48
76.96
C ↓♯+ 23 : 22 23 : 2×11 playⓘ Greater 23-limit semitone 23 S
78.00
(3 : 2)1/9 31/9 : 21/9 playⓘ Alpha scale step 15.39
79.31
67 : 64 67 : 26 playⓘ Sixty-seventh harmonic[5] 67
80.54
C↑ - 22 : 21 2×11 : 3×7 playⓘ Hard semitone,[5] two-fifth tone small semitone 11 S
84.47
D ♭ 21 : 20 3×7 : 22×5 playⓘ Septimal chromatic semitone, minor semitone[3] 7 S
88.80
C ♯ 20 : 19 22×5 : 19 playⓘ Novendecimal augmented unison 19 S
90.22
D♭−−[2] 256 : 243 28 : 35 playⓘ Pythagorean minor second or limma,[3][6][11] Pythagorean diatonic semitone, Low Semitone[14] 3
92.18
C♯+[2] 135 : 128 33×5 : 27 playⓘ Greater chromatic semitone, chromatic semitone, semitone medius, major chroma or major limma,[3] small limma,[11] major chromatic semitone,[13] limma ascendant[5] 5
93.60
D ♭- 19 : 18 19 : 2×9 Novendecimal minor secondplayⓘ 19 S
97.36
D↓↓ 128 : 121 27 : 112 playⓘ 121st subharmonic,[5][6] undecimal minor second 11
98.95
D ♭ 18 : 17 2×32 : 17 playⓘ Just minor semitone, Arabic lute index finger[3] 17 S
100.00
C♯/D♭ 21/12 21/12 playⓘ Equal-tempered minor second or semitone 12 M
104.96
C ♯[2] 17 : 16 17 : 24 playⓘ Minor diatonic semitone, just major semitone, overtone semitone,[5] 17th harmonic,[3] limma[citation needed] 17 S
111.45
25√5 (5 : 1)1/25 playⓘ Studie II interval (compound just major third, 5:1, divided into 25 equal parts) 25
111.73
D♭-[2] 16 : 15 24 : 3×5 playⓘ Just minor second,[15] just diatonic semitone, large just semitone or major second,[4] major semitone,[5] limma, minor diatonic semitone,[3] diatonic second[16] semitone,[14] diatonic semitone,[11] 1⁄6-comma meantone minor second 5 S
113.69
C♯++ 2187 : 2048 37 : 211 playⓘ Apotome[3][11] or Pythagorean major semitone,[6] Pythagorean augmented unison, Pythagorean chromatic semitone, or Pythagorean apotome 3
116.72
(18 : 5)1/19 21/19×32/19 : 51/19 playⓘ Secor 10.28
119.44
C ♯ 15 : 14 3×5 : 2×7 playⓘ Septimal diatonic semitone, major diatonic semitone,[3] Cowell semitone[5] 7 S
125.00
25/48 25/48 playⓘ 5 steps in 48 equal temperament 48
128.30
D   14 : 13 2×7 : 13 playⓘ Lesser tridecimal 2/3-tone[17] 13 S
130.23
C ♯+ 69 : 64 3×23 : 26 playⓘ Sixty-ninth harmonic[5] 23
133.24
D♭ 27 : 25 33 : 52 playⓘ Semitone maximus, minor second, large limma or Bohlen-Pierce small semitone,[3] high semitone,[14] alternate Renaissance half-step,[5] large limma, acute minor second[citation needed] 5
133.33
C♯ /D♭ [a] 21/9 22/18 playⓘ Two-third tone 9, 18, 36, 72
138.57
D ♭- 13 : 12 13 : 22×3 playⓘ Greater tridecimal 2/3-tone,[17] Three-quarter tone[5] 13 S
150.00
C /D  23/24 21/8 playⓘ Equal-tempered neutral second 8, 24
150.64
D↓[2] 12 : 11 22×3 : 11 playⓘ 3⁄4 tone or Undecimal neutral second,[3][5] trumpet three-quarter tone,[11] middle finger [between frets][14] 11 S
155.14
D  35 : 32 5×7 : 25 playⓘ Thirty-fifth harmonic[5] 7
160.90
D−− 800 : 729 25×52 : 36 playⓘ Grave whole tone,[3] neutral second, grave major second[citation needed] 5
165.00
D↑♭−[2] 11 : 10 11 : 2×5 playⓘ Greater undecimal minor/major/neutral second, 4/5-tone[6] or Ptolemy's second[3] 11 S
171.43
21/7 21/7 playⓘ 1 step in 7 equal temperament 7
175.00
27/48 27/48 playⓘ 7 steps in 48 equal temperament 48
179.70
71 : 64 71 : 26 playⓘ Seventy-first harmonic[5] 71
180.45
E −−− 65536 : 59049 216 : 310 playⓘ Pythagorean diminished third,[3][6] Pythagorean minor tone 3
182.40
D−[2] 10 : 9 2×5 : 32 playⓘ Small just whole tone or major second,[4] minor whole tone,[3][5] lesser whole tone,[16] minor tone,[14] minor second,[11] half-comma meantone major second 5 S
200.00
D 22/12 21/6 playⓘ Equal-tempered major second 6, 12 M
203.91
D[2] 9 : 8 32 : 23 playⓘ Pythagorean major second, Large just whole tone or major second[11] (sesquioctavan),[4] tonus, major whole tone,[3][5] greater whole tone,[16] major tone[14] 3 S
215.89
D  145 : 128 5×29 : 27 playⓘ Hundred-forty-fifth harmonic 29
223.46
E −[2] 256 : 225 28 : 32×52 playⓘ Just diminished third,[16] 225th subharmonic 5
225.00
23/16 29/48 playⓘ 9 steps in 48 equal temperament 16, 48
227.79
73 : 64 73 : 26 playⓘ Seventy-third harmonic[5] 73
231.17
D −[2] 8 : 7 23 : 7 playⓘ Septimal major second,[4] septimal whole tone[3][5] 7 S
240.00
21/5 21/5 playⓘ 1 step in 5 equal temperament 5
247.74
D ♯ 15 : 13 3×5 : 13 playⓘ Tridecimal 5⁄4 tone[3] 13
250.00
D /E  25/24 25/24 playⓘ 5 steps in 24 equal temperament 24
251.34
D ♯ 37 : 32 37 : 25 playⓘ Thirty-seventh harmonic[5] 37
253.08
D♯− 125 : 108 53 : 22×33 playⓘ Semi-augmented whole tone,[3] semi-augmented second[citation needed] 5
262.37
E↓♭ 64 : 55 26 : 5×11 playⓘ 55th subharmonic[5][6] 11
266.87
E ♭[2] 7 : 6 7 : 2×3 playⓘ Septimal minor third[3][4][11] or Sub minor third[14] 7 S
268.80
D   299 : 256 13×23 : 28 playⓘ Two-hundred-ninety-ninth harmonic 23
274.58
D♯[2] 75 : 64 3×52 : 26 playⓘ Just augmented second,[16] Augmented tone,[14] augmented second[5][13] 5
275.00
211/48 211/48 playⓘ 11 steps in 48 equal temperament 48
289.21
E ↓♭ 13 : 11 13 : 11 playⓘ Tridecimal minor third[3] 13
294.13
E♭−[2] 32 : 27 25 : 33 playⓘ Pythagorean minor third[3][5][6][14][16] semiditone, or 27th subharmonic 3
297.51
E ♭[2] 19 : 16 19 : 24 playⓘ 19th harmonic,[3] 19-limit minor third, overtone minor third[5] 19
300.00
D♯/E♭ 23/12 21/4 playⓘ Equal-tempered minor third 4, 12 M
301.85
D ♯- 25 : 21[5] 52 : 3×7 playⓘ Quasi-equal-tempered minor third, 2nd 7-limit minor third, Bohlen-Pierce second[3][6] 7
310.26
6:5÷(81:80)1/4 22 : 53/4 playⓘ Quarter-comma meantone minor third M
311.98
(3 : 2)4/9 34/9 : 24/9 playⓘ Alpha scale minor third 3.85
315.64
E♭[2] 6 : 5 2×3 : 5 playⓘ Just minor third,[3][4][5][11][16] minor third,[14] 1⁄3-comma meantone minor third 5 M S
317.60
D♯++ 19683 : 16384 39 : 214 playⓘ Pythagorean augmented second[3][6] 3
320.14
E ♭↑ 77 : 64 7×11 : 26 playⓘ Seventy-seventh harmonic[5] 11
325.00
213/48 213/48 playⓘ 13 steps in 48 equal temperament 48
336.13
D  ♯- 17 : 14 17 : 2×7 playⓘ Superminor third[18] 17
337.15
E♭+ 243 : 200 35 : 23×52 playⓘ Acute minor third[3] 5
342.48
E ♭ 39 : 32 3×13 : 25 playⓘ Thirty-ninth harmonic[5] 13
342.86
22/7 22/7 playⓘ 2 steps in 7 equal temperament 7
342.91
E ♭- 128 : 105 27 : 3×5×7 playⓘ 105th subharmonic,[5] septimal neutral third[6] 7
347.41
E↑♭−[2] 11 : 9 11 : 32 playⓘ Undecimal neutral third[3][5] 11
350.00
D /E  27/24 27/24 playⓘ Equal-tempered neutral third 24
354.55
E↓+ 27 : 22 33 : 2×11 playⓘ Zalzal's wosta[6] 12:11 X 9:8[14] 11
359.47
E [2] 16 : 13 24 : 13 playⓘ Tridecimal neutral third[3] 13
364.54
79 : 64 79 : 26 playⓘ Seventy-ninth harmonic[5] 79
364.81
E− 100 : 81 22×52 : 34 playⓘ Grave major third[3] 5
375.00
25/16 215/48 playⓘ 15 steps in 48 equal temperament 16, 48
384.36
F♭−− 8192 : 6561 213 : 38 playⓘ Pythagorean diminished fourth,[3][6] Pythagorean 'schismatic' third[5] 3
386.31
E[2] 5 : 4 5 : 22 playⓘ Just major third,[3][4][5][11][16] major third,[14] quarter-comma meantone major third 5 M S
397.10
E  + 161 : 128 7×23 : 27 playⓘ One-hundred-sixty-first harmonic 23
400.00
E 24/12 21/3 playⓘ Equal-tempered major third 3, 12 M
402.47
E   323 : 256 17×19 : 28 playⓘ Three-hundred-twenty-third harmonic 19
407.82
E+[2] 81 : 64 34 : 26 playⓘ Pythagorean major third,[3][5][6][14][16] ditone 3
417.51
F ↓+[2] 14 : 11 2×7 : 11 playⓘ Undecimal diminished fourth or major third[3] 11
425.00
217/48 217/48 playⓘ 17 steps in 48 equal temperament 48
427.37
F♭[2] 32 : 25 25 : 52 playⓘ Just diminished fourth,[16] diminished fourth,[5][13] 25th subharmonic 5
429.06
E  41 : 32 41 : 25 playⓘ Forty-first harmonic[5] 41
435.08
E [2] 9 : 7 32 : 7 playⓘ Septimal major third,[3][5] Bohlen-Pierce third,[3] Super major Third[14] 7
444.77
F↓ 128 : 99 27 : 9×11 playⓘ 99th subharmonic[5][6] 11
450.00
E /F  29/24 29/24 playⓘ 9 steps in 24 equal temperament 24
450.05
83 : 64 83 : 26 playⓘ Eighty-third harmonic[5] 83
454.21
F♭  13 : 10 13 : 2×5 playⓘ Tridecimal major third or diminished fourth 13
456.99
E♯[2] 125 : 96 53 : 25×3 playⓘ Just augmented third, augmented third[5] 5
462.35
E  - 64 : 49 26 : 72 playⓘ 49th subharmonic[5][6] 7
470.78
F +[2] 21 : 16 3×7 : 24 playⓘ Twenty-first harmonic, narrow fourth,[3] septimal fourth,[5] wide augmented third,[citation needed] H7 on G 7
475.00
219/48 219/48 playⓘ 19 steps in 48 equal temperament 48
478.49
E♯+ 675 : 512 33×52 : 29 playⓘ Six-hundred-seventy-fifth harmonic, wide augmented third[3] 5
480.00
22/5 22/5 playⓘ 2 steps in 5 equal temperament 5
491.27
E ♯ 85 : 64 5×17 : 26 playⓘ Eighty-fifth harmonic[5] 17
498.04
F[2] 4 : 3 22 : 3 playⓘ Perfect fourth,[3][5][16] Pythagorean perfect fourth, Just perfect fourth or diatessaron[4] 3 S
500.00
F 25/12 25/12 playⓘ Equal-tempered perfect fourth 12 M
501.42
F + 171 : 128 32×19 : 27 playⓘ One-hundred-seventy-first harmonic 19
510.51
(3 : 2)8/11 38/11 : 28/11 playⓘ Beta scale perfect fourth 18.75
511.52
F  43 : 32 43 : 25 playⓘ Forty-third harmonic[5] 43
514.29
23/7 23/7 playⓘ 3 steps in 7 equal temperament 7
519.55
F+[2] 27 : 20 33 : 22×5 playⓘ 5-limit wolf fourth, acute fourth,[3] imperfect fourth[16] 5
521.51
E♯+++ 177147 : 131072 311 : 217 playⓘ Pythagorean augmented third[3][6] (F+ (pitch)) 3
525.00
27/16 221/48 playⓘ 21 steps in 48 equal temperament 16, 48
531.53
F + 87 : 64 3×29 : 26 playⓘ Eighty-seventh harmonic[5] 29
536.95
F↓♯+ 15 : 11 3×5 : 11 playⓘ Undecimal augmented fourth[3] 11
550.00
F /G  211/24 211/24 playⓘ 11 steps in 24 equal temperament 24
551.32
F↑[2] 11 : 8 11 : 23 playⓘ eleventh harmonic,[5] undecimal tritone,[5] lesser undecimal tritone, undecimal semi-augmented fourth[3] 11
563.38
F ♯+ 18 : 13 2×9 : 13 playⓘ Tridecimal augmented fourth[3] 13
568.72
F♯[2] 25 : 18 52 : 2×32 playⓘ Just augmented fourth[3][5] 5
570.88
89 : 64 89 : 26 playⓘ Eighty-ninth harmonic[5] 89
575.00
223/48 223/48 playⓘ 23 steps in 48 equal temperament 48
582.51
G ♭[2] 7 : 5 7 : 5 playⓘ Lesser septimal tritone, septimal tritone[3][4][5] Huygens' tritone or Bohlen-Pierce fourth,[3] septimal fifth,[11] septimal diminished fifth[19] 7
588.27
G♭−− 1024 : 729 210 : 36 playⓘ Pythagorean diminished fifth,[3][6] low Pythagorean tritone[5] 3
590.22
F♯+[2] 45 : 32 32×5 : 25 playⓘ Just augmented fourth, just tritone,[4][11] tritone,[6] diatonic tritone,[3] 'augmented' or 'false' fourth,[16] high 5-limit tritone,[5] 1⁄6-comma meantone augmented fourth 5
595.03
G  ♭ 361 : 256 192 : 28 playⓘ Three-hundred-sixty-first harmonic 19
600.00
F♯/G♭ 26/12 21/2=√2 playⓘ Equal-tempered tritone 2, 12 M
609.35
G  ♭ 91 : 64 7×13 : 26 playⓘ Ninety-first harmonic[5] 13
609.78
G♭−[2] 64 : 45 26 : 32×5 playⓘ Just tritone,[4] 2nd tritone,[6] 'false' fifth,[16] diminished fifth,[13] low 5-limit tritone,[5] 45th subharmonic 5
611.73
F♯++ 729 : 512 36 : 29 playⓘ Pythagorean tritone,[3][6] Pythagorean augmented fourth, high Pythagorean tritone[5] 3
617.49
F♯ [2] 10 : 7 2×5 : 7 playⓘ Greater septimal tritone, septimal tritone,[4][5] Euler's tritone[3] 7
625.00
225/48 225/48 playⓘ 25 steps in 48 equal temperament 48
628.27
F ♯+ 23 : 16 23 : 24 playⓘ Twenty-third harmonic,[5] classic diminished fifth[citation needed] 23
631.28
G♭[2] 36 : 25 22×32 : 52 playⓘ Just diminished fifth[5] 5
646.99
F ♯+ 93 : 64 3×31 : 26 playⓘ Ninety-third harmonic[5] 31
648.68
G↓[2] 16 : 11 24 : 11 playⓘ ` undecimal semi-diminished fifth[3] 11
650.00
F /G  213/24 213/24 playⓘ 13 steps in 24 equal temperament 24
665.51
G  47 : 32 47 : 25 playⓘ Forty-seventh harmonic[5] 47
675.00
29/16 227/48 playⓘ 27 steps in 48 equal temperament 16, 48
678.49
A −−− 262144 : 177147 218 : 311 playⓘ Pythagorean diminished sixth[3][6] 3
680.45
G− 40 : 27 23×5 : 33 playⓘ 5-limit wolf fifth,[5] or diminished sixth, grave fifth,[3][6][11] imperfect fifth,[16] 5
683.83
G  95 : 64 5×19 : 26 playⓘ Ninety-fifth harmonic[5] 19
684.82
E    ++ 12167 : 8192 233 : 213 playⓘ 12167th harmonic 23
685.71
24/7 : 1 playⓘ 4 steps in 7 equal temperament
691.20
3:2÷(81:80)1/2 2×51/2 : 3 playⓘ Half-comma meantone perfect fifth M
694.79
3:2÷(81:80)1/3 21/3×51/3 : 31/3 playⓘ 1⁄3-comma meantone perfect fifth M
695.81
3:2÷(81:80)2/7 21/7×52/7 : 31/7 playⓘ 2⁄7-comma meantone perfect fifth M
696.58
3:2÷(81:80)1/4 51/4 playⓘ Quarter-comma meantone perfect fifth M
697.65
3:2÷(81:80)1/5 31/5×51/5 : 21/5 playⓘ 1⁄5-comma meantone perfect fifth M
698.37
3:2÷(81:80)1/6 31/3×51/6 : 21/3 playⓘ 1⁄6-comma meantone perfect fifth M
700.00
G 27/12 27/12 playⓘ Equal-tempered perfect fifth 12 M
701.89
231/53 231/53 playⓘ 53-TET perfect fifth 53
701.96
G[2] 3 : 2 3 : 2 playⓘ Perfect fifth,[3][5][16] Pythagorean perfect fifth, Just perfect fifth or diapente,[4] fifth,[14] Just fifth[11] 3 S
702.44
224/41 224/41 playⓘ 41-TET perfect fifth 41
703.45
217/29 217/29 playⓘ 29-TET perfect fifth 29
719.90
97 : 64 97 : 26 playⓘ Ninety-seventh harmonic[5] 97
720.00
23/5 : 1 playⓘ 3 steps in 5 equal temperament 5
721.51
A − 1024 : 675 210 : 33×52 playⓘ Narrow diminished sixth[3] 5
725.00
229/48 229/48 playⓘ 29 steps in 48 equal temperament 48
729.22
G - 32 : 21 24

January 01, 1970
list, pitch, intervals, below, list, intervals, expressible, terms, prime, limit, terminology, completed, choice, intervals, various, equal, subdivisions, octave, other, intervals, comparison, between, tunings, pythagorean, equal, tempered, quarter, comma, mea. 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 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 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 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 Contents 1 Terminology 2 List 3 See also 4 Notes 5 References 6 External linksTerminology editThe 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 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 Superparticular ratios are intervals that can be expressed as the ratio of two consecutive integers List editColumn 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 play Unison 3 monophony 4 perfect prime 3 tonic 5 or fundamental 1 12 3 M 0 03 65537 65536 65537 216 play Sixty five thousand five hundred thirty seventh harmonic 65537 S 0 40 C nbsp 4375 4374 54 7 2 37 play Ragisma 3 6 7 S 0 72 E nbsp nbsp nbsp nbsp nbsp 2401 2400 74 25 3 52 play Breedsma 3 6 7 S 1 00 21 1200 21 1200 play Cent 7 1200 1 20 21 1000 21 1000 play Millioctave 1000 1 95 B 32805 32768 38 5 215 play Schisma 3 5 5 1 96 3 2 27 12 3 219 12 Grad Werckmeister 8 3 99 101 1000 21 1000 51 1000 play Savart or eptameride 301 03 7 71 B nbsp 225 224 32 52 25 7 play Septimal kleisma 3 6 marvel comma 7 S 8 11 B nbsp 15625 15552 56 26 35 play Kleisma or semicomma majeur 3 6 5 10 06 A nbsp nbsp 2109375 2097152 33 57 221 play Semicomma 3 6 Fokker s comma 3 5 10 85 C nbsp 160 159 25 5 3 53 play Difference between 5 3 amp 53 32 53 S 11 98 C nbsp 145 144 5 29 24 32 play Difference between 29 16 amp 9 5 29 S 12 50 21 96 21 96 play Sixteenth tone 96 13 07 B nbsp nbsp nbsp 1728 1715 26 33 5 73 play Orwell comma 3 9 7 13 47 C nbsp 129 128 3 43 27 play Hundred twenty ninth harmonic 43 S 13 79 D nbsp nbsp 126 125 2 32 7 53 play Small septimal semicomma 6 small septimal comma 3 starling comma 7 S 14 37 C 121 120 112 23 3 5 play Undecimal seconds comma 3 11 S 16 67 C a 21 72 21 72 play 1 step in 72 equal temperament 72 18 13 C nbsp 96 95 25 3 5 19 play Difference between 19 16 amp 6 5 19 S 19 55 D nbsp 2 2048 2025 211 34 52 play Diaschisma 3 6 minor comma 5 21 51 C 2 81 80 34 24 5 play Syntonic comma 3 5 6 major comma komma chromatic diesis or comma of Didymus 3 6 10 11 5 S 22 64 21 53 21 53 play Holdrian comma Holder s comma 1 step in 53 equal temperament 53 23 46 B 531441 524288 312 219 play Pythagorean comma 3 5 6 10 11 ditonic comma 3 6 3 25 00 21 48 21 48 play Eighth tone 48 26 84 C nbsp 65 64 5 13 26 play Sixty fifth harmonic 5 13th partial chroma 3 13 S 27 26 C nbsp 64 63 26 32 7 play Septimal comma 3 6 11 Archytas comma 3 63rd subharmonic 7 S 29 27 21 41 21 41 play 1 step in 41 equal temperament 41 31 19 D nbsp 56 55 23 7 5 11 play Undecimal diesis 3 Ptolemy s enharmonic 5 difference between 11 8 and 7 5 tritone 11 S 33 33 C nbsp D nbsp nbsp a 21 36 21 36 play Sixth tone 36 72 34 28 C nbsp 51 50 3 17 2 52 play Difference between 17 16 amp 25 24 17 S 34 98 B nbsp nbsp 50 49 2 52 72 play Septimal sixth tone or jubilisma Erlich s decatonic comma or tritonic diesis 3 6 7 S 35 70 D nbsp nbsp 49 48 72 24 3 play Septimal diesis slendro diesis or septimal 1 6 tone 3 7 S 38 05 C nbsp 46 45 2 23 32 5 play Inferior quarter tone 5 difference between 23 16 amp 45 32 23 S 38 71 21 31 21 31 play 1 step in 31 equal temperament 31 38 91 C 45 44 32 5 4 11 play Undecimal diesis or undecimal fifth tone 11 S 40 00 21 30 21 30 play Fifth tone 30 41 06 D nbsp 128 125 27 53 play Enharmonic diesis or 5 limit limma minor diesis 6 diminished second 5 6 minor diesis or diesis 3 125th subharmonic 5 41 72 D nbsp nbsp 42 41 2 3 7 41 play Lesser 41 limit fifth tone 41 S 42 75 C nbsp 41 40 41 23 5 play Greater 41 limit fifth tone 41 S 43 83 C nbsp 40 39 23 5 3 13 play Tridecimal fifth tone 13 S 44 97 C nbsp nbsp 39 38 3 13 2 19 play Superior quarter tone 5 novendecimal fifth tone 19 S 46 17 D nbsp nbsp nbsp 38 37 2 19 37 play Lesser 37 limit quarter tone 37 S 47 43 C nbsp 37 36 37 22 32 play Greater 37 limit quarter tone 37 S 48 77 C nbsp 36 35 22 32 5 7 play Septimal quarter tone septimal diesis 3 6 septimal chroma 2 superior quarter tone 5 7 S 49 98 246 239 3 41 239 play Just quarter tone 11 239 50 00 C nbsp D nbsp 21 24 21 24 play Equal tempered quarter tone 24 50 18 D nbsp nbsp 35 34 5 7 2 17 play ET quarter tone approximation 5 lesser 17 limit quarter tone 17 S 50 72 B nbsp 59049 57344 310 213 7 play Harrison s comma 10 P5s 1 H7 3 7 51 68 C nbsp 34 33 2 17 3 11 play Greater 17 limit quarter tone 17 S 53 27 C 33 32 3 11 25 play Thirty third harmonic 5 undecimal comma undecimal quarter tone 11 S 54 96 D nbsp 32 31 25 31 play Inferior quarter tone 5 thirty first subharmonic 31 S 56 55 B nbsp nbsp 529 512 232 29 play Five hundred twenty ninth harmonic 23 56 77 C nbsp 31 30 31 2 3 5 play Greater quarter tone 5 difference between 31 16 amp 15 8 31 S 58 69 C nbsp 30 29 2 3 5 29 play Lesser 29 limit quarter tone 29 S 60 75 C nbsp nbsp 29 28 29 22 7 play Greater 29 limit quarter tone 29 S 62 96 D nbsp 28 27 22 7 33 play Septimal minor second small minor second inferior quarter tone 5 7 S 63 81 3 2 1 11 31 11 21 11 play Beta scale step 18 75 65 34 C nbsp 27 26 33 2 13 play Chromatic diesis 12 tridecimal comma 3 13 S 66 34 D nbsp nbsp 133 128 7 19 27 play One hundred thirty third harmonic 19 66 67 C nbsp C nbsp a 21 18 21 18 play Third tone 18 36 72 67 90 D nbsp nbsp 26 25 2 13 52 play Tridecimal third tone third tone 5 13 S 70 67 C 2 25 24 52 23 3 play Just chromatic semitone or minor chroma 3 lesser chromatic semitone small just semitone 11 or minor second 4 minor chromatic semitone 13 or minor semitone 5 2 7 comma meantone chromatic semitone augmented unison 5 S 73 68 D nbsp 24 23 23 3 23 play Lesser 23 limit semitone 23 S 75 00 21 16 23 48 play 1 step in 16 equal temperament 3 steps in 48 16 48 76 96 C nbsp 23 22 23 2 11 play Greater 23 limit semitone 23 S 78 00 3 2 1 9 31 9 21 9 play Alpha scale step 15 39 79 31 67 64 67 26 play Sixty seventh harmonic 5 67 80 54 C nbsp 22 21 2 11 3 7 play Hard semitone 5 two fifth tone small semitone 11 S 84 47 D nbsp 21 20 3 7 22 5 play Septimal chromatic semitone minor semitone 3 7 S 88 80 C nbsp 20 19 22 5 19 play Novendecimal augmented unison 19 S 90 22 D 2 256 243 28 35 play Pythagorean minor second or limma 3 6 11 Pythagorean diatonic semitone Low Semitone 14 3 92 18 C 2 135 128 33 5 27 play Greater chromatic semitone chromatic semitone semitone medius major chroma or major limma 3 small limma 11 major chromatic semitone 13 limma ascendant 5 5 93 60 D nbsp 19 18 19 2 9 Novendecimal minor secondplay 19 S 97 36 D 128 121 27 112 play 121st subharmonic 5 6 undecimal minor second 11 98 95 D nbsp 18 17 2 32 17 play Just minor semitone Arabic lute index finger 3 17 S 100 00 C D 21 12 21 12 play Equal tempered minor second or semitone 12 M 104 96 C nbsp 2 17 16 17 24 play Minor diatonic semitone just major semitone overtone semitone 5 17th harmonic 3 limma citation needed 17 S 111 45 25 5 5 1 1 25 play Studie II interval compound just major third 5 1 divided into 25 equal parts 25 111 73 D 2 16 15 24 3 5 play Just minor second 15 just diatonic semitone large just semitone or major second 4 major semitone 5 limma minor diatonic semitone 3 diatonic second 16 semitone 14 diatonic semitone 11 1 6 comma meantone minor second 5 S 113 69 C 2187 2048 37 211 play Apotome 3 11 or Pythagorean major semitone 6 Pythagorean augmented unison Pythagorean chromatic semitone or Pythagorean apotome 3 116 72 18 5 1 19 21 19 32 19 51 19 play Secor 10 28 119 44 C nbsp 15 14 3 5 2 7 play Septimal diatonic semitone major diatonic semitone 3 Cowell semitone 5 7 S 125 00 25 48 25 48 play 5 steps in 48 equal temperament 48 128 30 D nbsp nbsp 14 13 2 7 13 play Lesser tridecimal 2 3 tone 17 13 S 130 23 C nbsp 69 64 3 23 26 play Sixty ninth harmonic 5 23 133 24 D 27 25 33 52 play Semitone maximus minor second large limma or Bohlen Pierce small semitone 3 high semitone 14 alternate Renaissance half step 5 large limma acute minor second citation needed 5 133 33 C nbsp D nbsp a 21 9 22 18 play Two third tone 9 18 36 72 138 57 D nbsp 13 12 13 22 3 play Greater tridecimal 2 3 tone 17 Three quarter tone 5 13 S 150 00 C nbsp D nbsp 23 24 21 8 play Equal tempered neutral second 8 24 150 64 D 2 12 11 22 3 11 play 3 4 tone or Undecimal neutral second 3 5 trumpet three quarter tone 11 middle finger between frets 14 11 S 155 14 D nbsp 35 32 5 7 25 play Thirty fifth harmonic 5 7 160 90 D 800 729 25 52 36 play Grave whole tone 3 neutral second grave major second citation needed 5 165 00 D 2 11 10 11 2 5 play Greater undecimal minor major neutral second 4 5 tone 6 or Ptolemy s second 3 11 S 171 43 21 7 21 7 play 1 step in 7 equal temperament 7 175 00 27 48 27 48 play 7 steps in 48 equal temperament 48 179 70 71 64 71 26 play Seventy first harmonic 5 71 180 45 E nbsp 65536 59049 216 310 play Pythagorean diminished third 3 6 Pythagorean minor tone 3 182 40 D 2 10 9 2 5 32 play Small just whole tone or major second 4 minor whole tone 3 5 lesser whole tone 16 minor tone 14 minor second 11 half comma meantone major second 5 S 200 00 D 22 12 21 6 play Equal tempered major second 6 12 M 203 91 D 2 9 8 32 23 play Pythagorean major second Large just whole tone or major second 11 sesquioctavan 4 tonus major whole tone 3 5 greater whole tone 16 major tone 14 3 S 215 89 D nbsp 145 128 5 29 27 play Hundred forty fifth harmonic 29 223 46 E nbsp 2 256 225 28 32 52 play Just diminished third 16 225th subharmonic 5 225 00 23 16 29 48 play 9 steps in 48 equal temperament 16 48 227 79 73 64 73 26 play Seventy third harmonic 5 73 231 17 D nbsp 2 8 7 23 7 play Septimal major second 4 septimal whole tone 3 5 7 S 240 00 21 5 21 5 play 1 step in 5 equal temperament 5 247 74 D nbsp 15 13 3 5 13 play Tridecimal 5 4 tone 3 13 250 00 D nbsp E nbsp 25 24 25 24 play 5 steps in 24 equal temperament 24 251 34 D nbsp 37 32 37 25 play Thirty seventh harmonic 5 37 253 08 D 125 108 53 22 33 play Semi augmented whole tone 3 semi augmented second citation needed 5 262 37 E 64 55 26 5 11 play 55th subharmonic 5 6 11 266 87 E nbsp 2 7 6 7 2 3 play Septimal minor third 3 4 11 or Sub minor third 14 7 S 268 80 D nbsp nbsp 299 256 13 23 28 play Two hundred ninety ninth harmonic 23 274 58 D 2 75 64 3 52 26 play Just augmented second 16 Augmented tone 14 augmented second 5 13 5 275 00 211 48 211 48 play 11 steps in 48 equal temperament 48 289 21 E nbsp 13 11 13 11 play Tridecimal minor third 3 13 294 13 E 2 32 27 25 33 play Pythagorean minor third 3 5 6 14 16 semiditone or 27th subharmonic 3 297 51 E nbsp 2 19 16 19 24 play 19th harmonic 3 19 limit minor third overtone minor third 5 19 300 00 D E 23 12 21 4 play Equal tempered minor third 4 12 M 301 85 D nbsp 25 21 5 52 3 7 play Quasi equal tempered minor third 2nd 7 limit minor third Bohlen Pierce second 3 6 7 310 26 6 5 81 80 1 4 22 53 4 play Quarter comma meantone minor third M 311 98 3 2 4 9 34 9 24 9 play Alpha scale minor third 3 85 315 64 E 2 6 5 2 3 5 play Just minor third 3 4 5 11 16 minor third 14 1 3 comma meantone minor third 5 M S 317 60 D 19683 16384 39 214 play Pythagorean augmented second 3 6 3 320 14 E nbsp 77 64 7 11 26 play Seventy seventh harmonic 5 11 325 00 213 48 213 48 play 13 steps in 48 equal temperament 48 336 13 D nbsp nbsp 17 14 17 2 7 play Superminor third 18 17 337 15 E 243 200 35 23 52 play Acute minor third 3 5 342 48 E nbsp 39 32 3 13 25 play Thirty ninth harmonic 5 13 342 86 22 7 22 7 play 2 steps in 7 equal temperament 7 342 91 E nbsp 128 105 27 3 5 7 play 105th subharmonic 5 septimal neutral third 6 7 347 41 E 2 11 9 11 32 play Undecimal neutral third 3 5 11 350 00 D nbsp E nbsp 27 24 27 24 play Equal tempered neutral third 24 354 55 E 27 22 33 2 11 play Zalzal s wosta 6 12 11 X 9 8 14 11 359 47 E nbsp 2 16 13 24 13 play Tridecimal neutral third 3 13 364 54 79 64 79 26 play Seventy ninth harmonic 5 79 364 81 E 100 81 22 52 34 play Grave major third 3 5 375 00 25 16 215 48 play 15 steps in 48 equal temperament 16 48 384 36 F 8192 6561 213 38 play Pythagorean diminished fourth 3 6 Pythagorean schismatic third 5 3 386 31 E 2 5 4 5 22 play Just major third 3 4 5 11 16 major third 14 quarter comma meantone major third 5 M S 397 10 E nbsp nbsp 161 128 7 23 27 play One hundred sixty first harmonic 23 400 00 E 24 12 21 3 play Equal tempered major third 3 12 M 402 47 E nbsp nbsp 323 256 17 19 28 play Three hundred twenty third harmonic 19 407 82 E 2 81 64 34 26 play Pythagorean major third 3 5 6 14 16 ditone 3 417 51 F nbsp 2 14 11 2 7 11 play Undecimal diminished fourth or major third 3 11 425 00 217 48 217 48 play 17 steps in 48 equal temperament 48 427 37 F 2 32 25 25 52 play Just diminished fourth 16 diminished fourth 5 13 25th subharmonic 5 429 06 E nbsp 41 32 41 25 play Forty first harmonic 5 41 435 08 E nbsp 2 9 7 32 7 play Septimal major third 3 5 Bohlen Pierce third 3 Super major Third 14 7 444 77 F 128 99 27 9 11 play 99th subharmonic 5 6 11 450 00 E nbsp F nbsp 29 24 29 24 play 9 steps in 24 equal temperament 24 450 05 83 64 83 26 play Eighty third harmonic 5 83 454 21 F nbsp 13 10 13 2 5 play Tridecimal major third or diminished fourth 13 456 99 E 2 125 96 53 25 3 play Just augmented third augmented third 5 5 462 35 E nbsp nbsp 64 49 26 72 play 49th subharmonic 5 6 7 470 78 F nbsp 2 21 16 3 7 24 play Twenty first harmonic narrow fourth 3 septimal fourth 5 wide augmented third citation needed H7 on G 7 475 00 219 48 219 48 play 19 steps in 48 equal temperament 48 478 49 E 675 512 33 52 29 play Six hundred seventy fifth harmonic wide augmented third 3 5 480 00 22 5 22 5 play 2 steps in 5 equal temperament 5 491 27 E nbsp 85 64 5 17 26 play Eighty fifth harmonic 5 17 498 04 F 2 4 3 22 3 play Perfect fourth 3 5 16 Pythagorean perfect fourth Just perfect fourth or diatessaron 4 3 S 500 00 F 25 12 25 12 play Equal tempered perfect fourth 12 M 501 42 F nbsp 171 128 32 19 27 play One hundred seventy first harmonic 19 510 51 3 2 8 11 38 11 28 11 play Beta scale perfect fourth 18 75 511 52 F nbsp 43 32 43 25 play Forty third harmonic 5 43 514 29 23 7 23 7 play 3 steps in 7 equal temperament 7 519 55 F 2 27 20 33 22 5 play 5 limit wolf fourth acute fourth 3 imperfect fourth 16 5 521 51 E 177147 131072 311 217 play Pythagorean augmented third 3 6 F pitch 3 525 00 27 16 221 48 play 21 steps in 48 equal temperament 16 48 531 53 F nbsp 87 64 3 29 26 play Eighty seventh harmonic 5 29 536 95 F 15 11 3 5 11 play Undecimal augmented fourth 3 11 550 00 F nbsp G nbsp 211 24 211 24 play 11 steps in 24 equal temperament 24 551 32 F 2 11 8 11 23 play eleventh harmonic 5 undecimal tritone 5 lesser undecimal tritone undecimal semi augmented fourth 3 11 563 38 F nbsp 18 13 2 9 13 play Tridecimal augmented fourth 3 13 568 72 F 2 25 18 52 2 32 play Just augmented fourth 3 5 5 570 88 89 64 89 26 play Eighty ninth harmonic 5 89 575 00 223 48 223 48 play 23 steps in 48 equal temperament 48 582 51 G nbsp 2 7 5 7 5 play Lesser septimal tritone septimal tritone 3 4 5 Huygens tritone or Bohlen Pierce fourth 3 septimal fifth 11 septimal diminished fifth 19 7 588 27 G 1024 729 210 36 play Pythagorean diminished fifth 3 6 low Pythagorean tritone 5 3 590 22 F 2 45 32 32 5 25 play Just augmented fourth just tritone 4 11 tritone 6 diatonic tritone 3 augmented or false fourth 16 high 5 limit tritone 5 1 6 comma meantone augmented fourth 5 595 03 G nbsp nbsp 361 256 192 28 play Three hundred sixty first harmonic 19 600 00 F G 26 12 21 2 2 play Equal tempered tritone 2 12 M 609 35 G nbsp nbsp 91 64 7 13 26 play Ninety first harmonic 5 13 609 78 G 2 64 45 26 32 5 play Just tritone 4 2nd tritone 6 false fifth 16 diminished fifth 13 low 5 limit tritone 5 45th subharmonic 5 611 73 F 729 512 36 29 play Pythagorean tritone 3 6 Pythagorean augmented fourth high Pythagorean tritone 5 3 617 49 F nbsp 2 10 7 2 5 7 play Greater septimal tritone septimal tritone 4 5 Euler s tritone 3 7 625 00 225 48 225 48 play 25 steps in 48 equal temperament 48 628 27 F nbsp 23 16 23 24 play Twenty third harmonic 5 classic diminished fifth citation needed 23 631 28 G 2 36 25 22 32 52 play Just diminished fifth 5 5 646 99 F nbsp 93 64 3 31 26 play Ninety third harmonic 5 31 648 68 G 2 16 11 24 11 play undecimal semi diminished fifth 3 11 650 00 F nbsp G nbsp 213 24 213 24 play 13 steps in 24 equal temperament 24 665 51 G nbsp 47 32 47 25 play Forty seventh harmonic 5 47 675 00 29 16 227 48 play 27 steps in 48 equal temperament 16 48 678 49 A nbsp 262144 177147 218 311 play Pythagorean diminished sixth 3 6 3 680 45 G 40 27 23 5 33 play 5 limit wolf fifth 5 or diminished sixth grave fifth 3 6 11 imperfect fifth 16 5 683 83 G nbsp 95 64 5 19 26 play Ninety fifth harmonic 5 19 684 82 E nbsp nbsp nbsp nbsp 12167 8192 233 213 play 12167th harmonic 23 685 71 24 7 1 play 4 steps in 7 equal temperament 691 20 3 2 81 80 1 2 2 51 2 3 play Half comma meantone perfect fifth M 694 79 3 2 81 80 1 3 21 3 51 3 31 3 play 1 3 comma meantone perfect fifth M 695 81 3 2 81 80 2 7 21 7 52 7 31 7 play 2 7 comma meantone perfect fifth M 696 58 3 2 81 80 1 4 51 4 play Quarter comma meantone perfect fifth M 697 65 3 2 81 80 1 5 31 5 51 5 21 5 play 1 5 comma meantone perfect fifth M 698 37 3 2 81 80 1 6 31 3 51 6 21 3 play 1 6 comma meantone perfect fifth M 700 00 G 27 12 27 12 play Equal tempered perfect fifth 12 M 701 89 231 53 231 53 play 53 TET perfect fifth 53 701 96 G 2 3 2 3 2 play Perfect fifth 3 5 16 Pythagorean perfect fifth Just perfect fifth or diapente 4 fifth 14 Just fifth 11 3 S 702 44 224 41 224 41 play 41 TET perfect fifth 41 703 45 217 29 217 29 play 29 TET perfect fifth 29 719 90 97 64 97 26 play Ninety seventh harmonic 5 97 720 00 23 5 1 play 3 steps in 5 equal temperament 5 721 51 A nbsp 1024 675 210 33 52 play Narrow diminished sixth 3 5 725 00 229 48 229 48 play 29 steps in 48 equal temperament 48 729 22 G nbsp 32 21 24 s, wikipedia, wiki, book, books, library,

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