# List of pitch intervals

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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.

## Contents

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

• 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 14 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 13-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 12-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

ColumnLegend
TETX-tone equal temperament (12-tet, etc.).
Limit3-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.
MMeantone temperament or tuning.
SSuperparticular ratio (no separate color code).
List of musical intervals
CentsNote (from C)Freq. ratioPrime factorsInterval nameTETLimitMS
0.00C [2] 1 : 11 : 1 Unison, [3] monophony, [4] perfect prime, [3] tonic, [5] or fundamental 1, 123M
0.03 65537 : 6553665537 : 216Sixty-five-thousand-five-hundred-thirty-seventh harmonic 65537S
0.40C 4375 : 437454×7 : 2×377S
0.72E +2401 : 240074 : 25×3×527S
1.00 21/120021/12001200
1.20 21/100021/10001000
1.95 B++32805 : 3276838×5 : 2155
1.96 3:2÷(27/12)3 : 219/12 Grad, Werckmeister [8]
3.99 101/100021/1000×51/1000 Savart or eptaméride301.03
7.71 B 225 : 22432×52 : 25×7 Septimal kleisma, [3] [6] marvel comma7S
8.11 B 15625 : 1555256 : 26×35 Kleisma or semicomma majeur [3] [6] 5
10.06 A ++2109375 : 209715233×57 : 221 Semicomma, [3] [6] Fokker's comma [3] 5
10.85 C 160 : 15925×5 : 3×53Difference between 5:3 & 53:3253S
11.98C 145 : 1445×29 : 24×32Difference between 29:16 & 9:529S
12.50 21/9621/9696
13.07B 1728 : 171526×33 : 5×737
13.47C 129 : 1283×43 : 27Hundred-twenty-ninth harmonic43S
13.79 D 126 : 1252×32×7 : 53Small septimal semicomma, [6] small septimal comma, [3] starling comma7S
14.37 C121 : 120112 : 23×3×5Undecimal seconds comma [3] 11S
16.67 C [lower-alpha 1] 21/7221/721 step in 72 equal temperament 72
18.13 C 96 : 9525×3 : 5×19Difference between 19:16 & 6:519S
19.55 D -- [2] 2048 : 2025211 : 34×52 Diaschisma, [3] [6] minor comma5
21.51 C+ [2] 81 : 8034 : 24×5 Syntonic comma, [3] [5] [6] major comma, komma, chromatic diesis, or comma of Didymus [3] [6] [10] [11] 5S
22.64 21/5321/53 Holdrian comma, Holder's comma, 1 step in 53 equal temperament 53
23.46 B+++531441 : 524288312 : 219 Pythagorean comma, [3] [5] [6] [10] [11] ditonic comma [3] [6] 3
25.00 21/4821/4848
26.84 C 65 : 645×13 : 26Sixty-fifth harmonic, [5] 13th-partial chroma [3] 13S
27.26 C 64 : 6326 : 32×7 Septimal comma, [3] [6] [11] Archytas' comma, [3] 63rd subharmonic7S
29.2721/4121/411 step in 41 equal temperament 41
31.19 D 56 : 5523×7 : 5×11 Undecimal diesis, [3] Ptolemy's enharmonic: [5] difference between (11 : 8) and (7 : 5) tritone11S
33.33C /D [lower-alpha 1] 21/3621/3636, 72
34.28 C 51 : 503×17 : 2×52Difference between 17:16 & 25:2417S
34.98 B -50 : 492×52 : 72 Septimal sixth tone or jubilisma, Erlich's decatonic comma or tritonic diesis [3] [6] 7S
35.70 D 49 : 4872 : 24×3 Septimal diesis, slendro diesis or septimal 1/6-tone [3] 7S
38.05 C 46 : 452×23 : 32×5Inferior quarter tone, [5] difference between 23:16 & 45:3223S
38.71 21/3121/311 step in 31 equal temperament 31
38.91 C+45 : 4432×5 : 4×11 Undecimal diesis or undecimal fifth tone 11S
40.00 21/3021/3030
41.06 D 128 : 12527 : 53 Enharmonic diesis or 5-limit limma, minor diesis, [6] diminished second, [5] [6] minor diesis or diesis, [3] 125th subharmonic5
41.72 D 42 : 412×3×7 : 41Lesser 41-limit fifth tone41S
42.75 C 41 : 4041 : 23×5Greater 41-limit fifth tone41S
43.83 C 40 : 3923×5 : 3×13Tridecimal fifth tone13S
44.97 C 39 : 383×13 : 2×19Superior quarter-tone, [5] novendecimal fifth tone19S
46.17 D -38 : 372×19 : 37Lesser 37-limit quarter tone37S
47.43 C 37 : 3637 : 22×32Greater 37-limit quarter tone37S
48.77 C 36 : 3522×32 : 5×7 Septimal quarter tone, septimal diesis, [3] [6] septimal chroma, [2] superior quarter tone [5] 7S
49.98 246 : 2393×41 : 239Just quarter tone [11] 239
50.00 C /D 21/2421/24Equal-tempered quarter tone 24
50.18 D 35 : 345×7 : 2×17ET quarter-tone approximation, [5] lesser 17-limit quarter tone17S
50.72 B ++59049 : 57344310 : 213×7Harrison's comma (10 P5s - 1 H7) [3] 7
51.68 C 34 : 332×17 : 3×11Greater 17-limit quarter tone17S
53.27 C33 : 323×11 : 25Thirty-third harmonic, [5] undecimal comma, undecimal quarter tone11S
54.96 D -32 : 3125 : 31Inferior quarter-tone, [5] thirty-first subharmonic31S
56.55 B +529 : 512232 : 29Five-hundred-twenty-ninth harmonic23
56.77 C 31 : 3031 : 2×3×5Greater quarter-tone, [5] difference between 31:16 & 15:831S
58.69 C 30 : 292×3×5 : 29Lesser 29-limit quarter tone29S
60.75 C 29 : 2829 : 22×7Greater 29-limit quarter tone29S
62.96 D -28 : 2722×7 : 33Septimal minor second, small minor second, inferior quarter tone [5] 7S
63.81 (3 : 2)1/1131/11 : 21/11 Beta scale step18.75
65.34 C +27 : 2633 : 2×13 Chromatic diesis, [12] tridecimal comma [3] 13S
66.34 D 133 : 1287×19 : 27One-hundred-thirty-third harmonic19
66.67 C /C [lower-alpha 1] 21/1821/1818, 36, 72
67.90 D -26 : 252×13 : 52Tridecimal third tone, third tone [5] 13S
70.67 C [2] 25 : 2452 : 23×3 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] 27-comma meantone chromatic semitone, augmented unison5S
73.68 D -24 : 2323×3 : 23Lesser 23-limit semitone23S
75.00 21/1623/481 step in 16 equal temperament, 3 steps in 4816, 48
76.96 C +23 : 2223 : 2×11Greater 23-limit semitone23S
78.00 (3 : 2)1/931/9 : 21/9 Alpha scale step15.39
79.31 67 : 6467 : 26Sixty-seventh harmonic [5] 67
80.54 C -22 : 212×11 : 3×7Hard semitone, [5] two-fifth tone small semitone11S
84.47 D 21 : 203×7 : 22×5 Septimal chromatic semitone, minor semitone [3] 7S
88.80 C 20 : 1922×5 : 19Novendecimal augmented unison19S
90.22 D−− [2] 256 : 24328 : 35Pythagorean minor second or limma, [3] [6] [11] Pythagorean diatonic semitone, Low Semitone [14] 3
92.18 C+ [2] 135 : 12833×5 : 27Greater 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 : 1819 : 2×9Novendecimal minor second19S
97.36 D↓↓128 : 12127 : 112121st subharmonic, [5] [6] undecimal minor second11
98.95 D 18 : 172×32 : 17Just minor semitone, Arabic lute index finger [3] 17S
100.00 C/D21/1221/12Equal-tempered minor second or semitone 12M
104.96 C [2] 17 : 1617 : 24 Minor diatonic semitone, just major semitone, overtone semitone, [5] 17th harmonic, [3] limma[ citation needed ]17S
111.45 255(5 : 1)1/25 Studie II interval (compound just major third, 5:1, divided into 25 equal parts)25
111.73 D- [2] 16 : 1524 : 3×5 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] 16-comma meantone minor second5S
113.69 C++2187 : 204837 : 211Apotome [3] [11] or Pythagorean major semitone, [6] Pythagorean augmented unison, Pythagorean chromatic semitone, or Pythagorean apotome 3
116.72 (18 : 5)1/1921/19×32/19 : 51/1910.28
119.44 C 15 : 143×5 : 2×7 Septimal diatonic semitone, major diatonic semitone, [3] Cowell semitone [5] 7S
125.00 25/4825/485 steps in 48 equal temperament48
128.30 D 14 : 132×7 : 13Lesser tridecimal 2/3-tone [17] 13S
130.23 C +69 : 643×23 : 26Sixty-ninth harmonic [5] 23
133.24 D27 : 2533 : 52 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 [lower-alpha 1] 21/922/189, 18, 36, 72
138.57 D -13 : 1213 : 22×3Greater tridecimal 2/3-tone, [17] Three-quarter tone [5] 13S
150.00 C /D 23/2421/8Equal-tempered neutral second 8, 24
150.64 D↓ [2] 12 : 1122×3 : 1134 tone or Undecimal neutral second, [3] [5] trumpet three-quarter tone, [11] middle finger [between frets] [14] 11S
155.14 D 35 : 325×7 : 25Thirty-fifth harmonic [5] 7
160.90 D−−800 : 72925×52 : 36Grave whole tone, [3] neutral second, grave major second[ citation needed ]5
165.00 D [2] 11 : 1011 : 2×5Greater undecimal minor/major/neutral second, 4/5-tone [6] or Ptolemy's second [3] 11S
171.43 21/721/71 step in 7 equal temperament 7
175.00 27/4827/487 steps in 48 equal temperament48
179.70 71 : 6471 : 26Seventy-first harmonic [5] 71
180.45 E −−−65536 : 59049216 : 310Pythagorean diminished third, [3] [6] Pythagorean minor tone3
182.40 D- [2] 10 : 92×5 : 32 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 second5S
200.00 D22/1221/6Equal-tempered major second 6, 12M
203.91 D [2] 9 : 832 : 23Pythagorean 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] 3S
215.89 D 145 : 1285×29 : 27Hundred-forty-fifth harmonic29
223.46 E [2] 256 : 22528 : 32×52Just diminished third, [16] 225th subharmonic5
225.00 23/1629/489 steps in 48 equal temperament16, 48
227.79 73 : 6473 : 26Seventy-third harmonic [5] 73
231.17 D [2] 8 : 723 : 7 Septimal major second, [4] septimal whole tone [3] [5] 7S
240.00 21/521/51 step in 5 equal temperament 5
247.74 D 15 : 133×5 : 13Tridecimal 54 tone [3] 13
250.00 D /E 25/2425/245 steps in 24 equal temperament24
251.34 D 37 : 3237 : 25Thirty-seventh harmonic [5] 37
253.08 D125 : 10853 : 22×33Semi-augmented whole tone, [3] semi-augmented second[ citation needed ]5
262.37 E↓64 : 5526 : 5×1155th subharmonic [5] [6] 11
268.80 D 299 : 25613×23 : 28Two-hundred-ninety-ninth harmonic23
266.87 E [2] 7 : 67 : 2×3 Septimal minor third [3] [4] [11] or Sub minor third [14] 7S
274.58 D [2] 75 : 643×52 : 26Just augmented second, [16] Augmented tone, [14] augmented second [5] [13] 5
275.00 211/48211/4811 steps in 48 equal temperament48
289.21 E 13 : 1113 : 11Tridecimal minor third [3] 13
294.13 E [2] 32 : 2725 : 33 Pythagorean minor third [3] [5] [6] [14] [16] semiditone, or 27th subharmonic3
297.51 E [2] 19 : 1619 : 2419th harmonic, [3] 19-limit minor third, overtone minor third [5] 19
300.00 D/E23/1221/4Equal-tempered minor third 4, 12M
301.85 D -25 : 21 [5] 52 : 3×7Quasi-equal-tempered minor third, 2nd 7-limit minor third, Bohlen-Pierce second [3] [6] 7
310.26 6:5÷(81:80)1/422 : 53/4Quarter-comma meantone minor thirdM
311.98 (3 : 2)4/934/9 : 24/93.85
315.64 E [2] 6 : 52×3 : 5 Just minor third, [3] [4] [5] [11] [16] minor third, [14] 13-comma meantone minor third5MS
317.60 D++19683 : 1638439 : 214Pythagorean augmented second [3] [6] 3
320.14 E 77 : 647×11 : 26Seventy-seventh harmonic [5] 11
325.00 213/48213/4813 steps in 48 equal temperament48
336.13 D -17 : 1417 : 2×7Superminor third [18] 17
337.15 E+243 : 20035 : 23×52Acute minor third [3] 5
342.48 E 39 : 323×13 : 25Thirty-ninth harmonic [5] 13
342.86 22/722/72 steps in 7 equal temperament 7
342.91 E -128 : 10527 : 3×5×7105th subharmonic, [5] septimal neutral third [6] 7
347.41 E [2] 11 : 911 : 32Undecimal neutral third [3] [5] 11
350.00 D /E 27/2427/24Equal-tempered neutral third 24
354.55 E+27 : 2233 : 2×11Zalzal's wosta [6] 12:11 X 9:8 [14] 11
359.47 E [2] 16 : 1324 : 13Tridecimal neutral third [3] 13
364.54 79 : 6479 : 26Seventy-ninth harmonic [5] 79
364.81 E−100 : 8122×52 : 34Grave major third [3] 5
375.00 25/16215/4815 steps in 48 equal temperament16, 48
384.36 F−−8192 : 6561213 : 38Pythagorean diminished fourth, [3] [6] Pythagorean 'schismatic' third [5] 3
386.31 E [2] 5 : 45 : 22 Just major third, [3] [4] [5] [11] [16] major third, [14] quarter-comma meantone major third5MS
397.10 E +161 : 1287×23 : 27One-hundred-sixty-first harmonic23
400.00 E24/1221/3Equal-tempered major third 3, 12M
402.47 E 323 : 25617×19 : 28Three-hundred-twenty-third harmonic19
407.82 E+ [2] 81 : 6434 : 26Pythagorean major third, [3] [5] [6] [14] [16] ditone 3
417.51 F + [2] 14 : 112×7 : 11Undecimal diminished fourth or major third [3] 11
425.00 217/48217/4817 steps in 48 equal temperament48
427.37 F [2] 32 : 2525 : 52Just diminished fourth, [16] diminished fourth, [5] [13] 25th subharmonic5
429.06 E 41 : 3241 : 25Forty-first harmonic [5] 41
435.08 E [2] 9 : 732 : 7 Septimal major third, [3] [5] Bohlen-Pierce third, [3] Super major Third [14] 7
444.77 F↓128 : 9927 : 9×1199th subharmonic [5] [6] 11
450.00 E /F 29/2429/249 steps in 24 equal temperament24
450.05 83 : 6483 : 26Eighty-third harmonic [5] 83
454.21 F 13 : 1013 : 2×5Tridecimal major third or diminished fourth13
456.99 E [2] 125 : 9653 : 25×3Just augmented third, augmented third [5] 5
462.35 E -64 : 4926 : 7249th subharmonic [5] [6] 7
470.78 F + [2] 21 : 163×7 : 24Twenty-first harmonic, narrow fourth, [3] septimal fourth, [5] wide augmented third,[ citation needed ] H7 on G7
475.00 219/48219/4819 steps in 48 equal temperament48
478.49 E+675 : 51233×52 : 29Six-hundred-seventy-fifth harmonic, wide augmented third [3] 5
480.00 22/522/52 steps in 5 equal temperament 5
491.27 E 85 : 645×17 : 26Eighty-fifth harmonic [5] 17
498.04 F [2] 4 : 322 : 3Perfect fourth, [3] [5] [16] Pythagorean perfect fourth, Just perfect fourth or diatessaron [4] 3S
500.00 F25/1225/12Equal-tempered perfect fourth 12M
501.42 F +171 : 12832×19 : 27One-hundred-seventy-first harmonic19
510.51 (3 : 2)8/1138/11 : 28/1118.75
511.52 F 43 : 3243 : 25Forty-third harmonic [5] 43
514.29 23/723/73 steps in 7 equal temperament 7
519.55 F+ [2] 27 : 2033 : 22×55-limit wolf fourth, acute fourth, [3] imperfect fourth [16] 5
521.51 E+++177147 : 131072311 : 217Pythagorean augmented third [3] [6] (F+ (pitch))3
525.00 27/16221/4821 steps in 48 equal temperament16, 48
531.53 F +87 : 643×29 : 26Eighty-seventh harmonic [5] 29
536.95 F+15 : 113×5 : 11Undecimal augmented fourth [3] 11
550.00 F /G 211/24211/2411 steps in 24 equal temperament24
551.32 F [2] 11 : 811 : 23 eleventh harmonic, [5] undecimal tritone, [5] lesser undecimal tritone, undecimal semi-augmented fourth [3] 11
563.38 F +18 : 132×9 : 13Tridecimal augmented fourth [3] 13
568.72 F [2] 25 : 1852 : 2×32Just augmented fourth [3] [5] 5
570.88 89 : 6489 : 26Eighty-ninth harmonic [5] 89
575.00 223/48223/4823 steps in 48 equal temperament48
582.51 G [2] 7 : 57 : 5Lesser 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 : 729210 : 36Pythagorean diminished fifth, [3] [6] low Pythagorean tritone [5] 3
590.22 F+ [2] 45 : 3232×5 : 25Just augmented fourth, just tritone, [4] [11] tritone, [6] diatonic tritone, [3] 'augmented' or 'false' fourth, [16] high 5-limit tritone, [5] 16-comma meantone augmented fourth5
595.03 G 361 : 256192 : 28Three-hundred-sixty-first harmonic19
600.00 F/G 26/12 21/2=2Equal-tempered tritone 2, 12M
609.35 G 91 : 647×13 : 26Ninety-first harmonic [5] 13
609.78 G [2] 64 : 4526 : 32×5Just tritone, [4] 2nd tritone, [6] 'false' fifth, [16] diminished fifth, [13] low 5-limit tritone, [5] 45th subharmonic5
611.73 F++729 : 51236 : 29Pythagorean tritone, [3] [6] Pythagorean augmented fourth, high Pythagorean tritone [5] 3
617.49 F [2] 10 : 72×5 : 7Greater septimal tritone, septimal tritone, [4] [5] Euler's tritone [3] 7
625.00 225/48225/4825 steps in 48 equal temperament48
628.27 F +23 : 1623 : 24Twenty-third harmonic, [5] classic diminished fifth[ citation needed ]23
631.28 G [2] 36 : 2522×32 : 525
646.99 F +93 : 643×31 : 26Ninety-third harmonic [5] 31
648.68 G↓ [2] 16 : 1124 : 11` undecimal semi-diminished fifth [3] 11
650.00 F /G 213/24213/2413 steps in 24 equal temperament24
665.51 G 47 : 3247 : 25Forty-seventh harmonic [5] 47
675.00 29/16227/4827 steps in 48 equal temperament16, 48
678.49 A −−−262144 : 177147218 : 311Pythagorean diminished sixth [3] [6] 3
680.45 G−40 : 2723×5 : 335-limit wolf fifth, [5] or diminished sixth, grave fifth, [3] [6] [11] imperfect fifth, [16] 5
683.83 G 95 : 645×19 : 26Ninety-fifth harmonic [5] 19
684.82 E ++12167 : 8192233 : 21312167th harmonic23
685.71 24/7 : 14 steps in 7 equal temperament
691.20 3:2÷(81:80)1/22×51/2 : 3Half-comma meantone perfect fifthM
694.79 3:2÷(81:80)1/321/3×51/3 : 31/313-comma meantone perfect fifthM
695.81 3:2÷(81:80)2/721/7×52/7 : 31/727-comma meantone perfect fifthM
696.58 3:2÷(81:80)1/451/4Quarter-comma meantone perfect fifthM
697.65 3:2÷(81:80)1/531/5×51/5 : 21/515-comma meantone perfect fifthM
698.37 3:2÷(81:80)1/631/3×51/6 : 21/316-comma meantone perfect fifthM
700.00 G27/1227/12Equal-tempered perfect fifth 12M
701.89 231/53231/5353
701.96 G [2] 3 : 23 : 2 Perfect fifth, [3] [5] [16] Pythagorean perfect fifth, Just perfect fifth or diapente, [4] fifth, [14] Just fifth [11] 3S
702.44 224/41224/4141
703.45 217/29217/2929
719.90 97 : 6497 : 26Ninety-seventh harmonic [5] 97
720.00 23/5 : 13 steps in 5 equal temperament5
721.51 A 1024 : 675210 : 33×52Narrow diminished sixth [3] 5
725.00 229/48229/4829 steps in 48 equal temperament48
729.22 G -32 : 2124 : 3×721st subharmonic, [5] [6] septimal diminished sixth 7
733.23 F +391 : 25617×23 : 28Three-hundred-ninety-first harmonic23
737.65 A +49 : 327×7 : 25Forty-ninth harmonic [5] 7
743.01 A 192 : 12526×3 : 53Classic diminished sixth [3] 5
750.00 G /A 215/24215/2415 steps in 24 equal temperament24
755.23 G99 : 6432×11 : 26Ninety-ninth harmonic [5] 11
764.92 A [2] 14 : 92×7 : 327
772.63 G25 : 1652 : 24
775.00 231/48231/4831 steps in 48 equal temperament48
781.79 π  : 2
782.49 G - [2] 11 : 711 : 7 Undecimal minor sixth, [5] undecimal augmented fifth, [3] Fibonacci numbers 11
789.85 101 : 64101 : 26Hundred-first harmonic [5] 101
792.18 A [2] 128 : 8127 : 34Pythagorean minor sixth, [3] [5] [6] 81st subharmonic3
798.40 A +203 : 1287×29 : 27Two-hundred-third harmonic29
800.00 G/A28/1222/3Equal-tempered minor sixth 3, 12M
806.91 G 51 : 323×17 : 25Fifty-first harmonic [5] 17
813.69 A [2] 8 : 523 : 55
815.64 G++6561 : 409638 : 212Pythagorean augmented fifth, [3] [6] Pythagorean 'schismatic' sixth [5] 3
823.80 103 : 64103 : 26Hundred-third harmonic [5] 103
825.00 211/16233/4833 steps in 48 equal temperament16, 48
832.18 G +207 : 12832×23 : 27Two-hundred-seventh harmonic23
833.09 51/2+1 : 2 : 1
833.11 233 : 144233 : 24×32 Golden ratio approximation (833 cents scale) 233
835.19 A+81 : 5034 : 2×52Acute minor sixth [3] 5
840.53 A [2] 13 : 813 : 23Tridecimal neutral sixth, [3] overtone sixth, [5] thirteenth harmonic 13
848.83 A 209 : 12811×19 : 27Two-hundred-ninth harmonic19
850.00 G /A 217/24217/24Equal-tempered neutral sixth 24
852.59 A↓+ [2] 18 : 112×32 : 11Undecimal neutral sixth, [3] [5] Zalzal's neutral sixth11
857.09 A +105 : 643×5×7 : 26Hundred-fifth harmonic [5] 7
857.14 25/725/75 steps in 7 equal temperament 7
862.85 A−400 : 24324×52 : 35Grave major sixth [3] 5
873.50 A 53 : 3253 : 25Fifty-third harmonic [5] 53
875.00 235/48235/4835 steps in 48 equal temperament48
879.86 A↓ 128 : 7727 : 7×1177th subharmonic [5] [6] 11
882.40 B −−−32768 : 19683215 : 39Pythagorean diminished seventh [3] [6] 3
884.36 A [2] 5 : 35 : 3Just major sixth, [3] [4] [5] [11] [16] Bohlen-Pierce sixth, [3] 13-comma meantone major sixth5M
889.76 107 : 64107 : 26Hundred-seventh harmonic [5] 107
892.54 B 6859 : 4096193 : 2126859th harmonic19
900.00 A29/1223/4Equal-tempered major sixth 4, 12M
902.49 A 32 : 1925 : 1919
905.87 A+ [2] 27 : 1633 : 24Pythagorean major sixth [3] [5] [11] [16] 3
921.82 109 : 64109 : 26Hundred-ninth harmonic [5] 109
925.00 237/48237/4837 steps in 48 equal temperament48
925.42 B [2] 128 : 7527 : 3×52Just diminished seventh, [16] diminished seventh, [5] [13] 75th subharmonic5
925.79 A +437 : 25619×23 : 28Four-hundred-thirty-seventh harmonic23
933.13 A [2] 12 : 722×3 : 77
937.63 A55 : 325×11 : 25Fifty-fifth harmonic [5] [20] 11
950.00 A /B 219/24219/24