List of pitch intervals

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

• 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.).
Limit2-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.
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 : 1Unison,[3] monophony,[4] perfect prime,[3] tonic,[5] or fundamental1, 122M
0.03 65537 : 6553665537 : 216Largest known Fermat prime, Sixty-five-thousand-five-hundred-thirty-seventh harmonic 65537S
0.40C4375 : 437454×7 : 2×377S
0.72E+2401 : 240074 : 25×3×527S
1.00 21/120021/12001200
1.20 21/100021/1000Millioctave1000
1.95 B++32805 : 3276838×5 : 2155
3.99 101/100021/1000×51/1000Savart or eptaméride301.03
7.71 B225 : 22432×52 : 25×7Septimal kleisma,[3][6] marvel comma7S
8.11 B15625 : 1555256 : 26×35Kleisma or semicomma majeur[3][6]5
10.06 A++2109375 : 209715233×57 : 221Semicomma,[3][6] Fokker's comma[3]5
10.85 C160 : 15925×5 : 3×53Difference between 5:3 & 53:3253S
11.98C145 : 1445×29 : 24×32Difference between 29:16 & 9:529S
12.50 21/9621/96Sixteenth tone96
13.07B1728 : 171526×33 : 5×737
13.47C129 : 1283×43 : 27Hundred-twenty-ninth harmonic43S
13.79 D126 : 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 temperament72
18.13 C96 : 9525×3 : 5×19Difference between 19:16 & 6:519S
19.55 D--[2]2048 : 2025211 : 34×52Diaschisma,[3][6] minor comma5
21.51 C+[2]81 : 8034 : 24×5Syntonic comma,[3][5][6] major comma, komma, chromatic diesis, or comma of Didymus[3][6][9][10]5S
22.64 21/5321/53Holdrian comma, Holder's comma, 1 step in 53 equal temperament53
23.46 B+++531441 : 524288312 : 219Pythagorean comma,[3][5][6][9][10] ditonic comma[3][6]3
25.00 21/4821/48Eighth tone48
26.84 C65 : 645×13 : 26Sixty-fifth harmonic,[5] 13th-partial chroma[3]13S
27.26 C64 : 6326 : 32×7Septimal comma,[3][6][10] Archytas' comma,[3] 63rd subharmonic7S
29.2721/4121/411 step in 41 equal temperament41
31.19 D56 : 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]21/3621/36Sixth tone36, 72
34.28 C51 : 503×17 : 2×52Difference between 17:16 & 25:2417S
34.98 B-50 : 492×52 : 72Septimal sixth tone or jubilisma, Erlich's decatonic comma or tritonic diesis[3][6]7S
35.70 D49 : 4872 : 24×3Septimal diesis, slendro diesis or septimal 1/6-tone[3]7S
38.05 C46 : 452×23 : 32×5Inferior quarter tone,[5] difference between 23:16 & 45:3223S
38.71 21/3121/311 step in 31 equal temperament31
38.91 C+45 : 4432×5 : 4×11Undecimal diesis or undecimal fifth tone 11S
40.00 21/3021/30Fifth tone30
41.06 D128 : 12527 : 53Enharmonic diesis or 5-limit limma, minor diesis,[6] diminished second,[5][6] minor diesis or diesis,[3] 125th subharmonic5
41.72 D42 : 412×3×7 : 41Lesser 41-limit fifth tone41S
42.75 C41 : 4041 : 23×5Greater 41-limit fifth tone41S
43.83 C40 : 3923×5 : 3×13Tridecimal fifth tone13S
44.97 C39 : 383×13 : 2×19Superior quarter-tone,[5] novendecimal fifth tone19S
46.17 D-38 : 372×19 : 37Lesser 37-limit quarter tone37S
47.43 C37 : 3637 : 22×32Greater 37-limit quarter tone37S
48.77 C36 : 3522×32 : 5×7Septimal quarter tone, septimal diesis,[3][6] septimal comma,[2] superior quarter tone[5]7S
49.98 246 : 2393×41 : 239Just quarter tone[10]239
50.00 C/D21/2421/24Equal-tempered quarter tone24
50.18 D35 : 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 C34 : 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
55.09 D35 : 325×7 : 25Thirty-fifth harmonic7
56.55 B+529 : 512232 : 29Five-hundred-twenty-ninth harmonic23
56.77 C31 : 3031 : 2×3×5Greater quarter-tone,[5] difference between 31:16 & 15:831S
58.69 C30 : 292×3×5 : 29Lesser 29-limit quarter tone29S
60.75 C29 : 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 : 21/11Beta scale step18.75
65.34 C+27 : 2633 : 2×13Chromatic diesis,[11] tridecimal comma[3]13S
66.34 D133 : 1287×19 : 27One-hundred-thirty-third harmonic19
66.67 C/C[lower-alpha 1]21/1821/18Third tone18, 36, 72
67.90 D-26 : 252×13 : 52Tridecimal third tone, third tone[5]13S
70.67 C[2]25 : 2452 : 23×3Just chromatic semitone or minor chroma,[3] lesser chromatic semitone, small (just) semitone[10] or minor second,[4] minor chromatic semitone,[12] 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 : 21/9Alpha 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 D21 : 203×7 : 22×5Septimal chromatic semitone, minor semitone[3]7S
88.80 C20 : 1922×5 : 19Novendecimal augmented unison19S
90.22 D−−[2]256 : 24328 : 35Pythagorean minor second or limma,[3][6][10] Pythagorean diatonic semitone, Low Semitone[13]3
92.18 C+[2]135 : 12833×5 : 27Greater chromatic semitone, chromatic semitone, semitone medius, major chroma or major limma,[3] small limma,[10] major chromatic semitone,[12] limma ascendant[5]5
93.60 D-19 : 1819 : 2×9Novendecimal minor second 19S
97.36 D↓↓128 : 12127 : 112121st subharmonic[5][6], undecimal minor second11
98.95 D18 : 172×32 : 17Just minor semitone, Arabic lute index finger[3]17S
100.00 C/D21/1221/12Equal-tempered minor second or semitone12M
104.96 C[2]17 : 1617 : 24Minor diatonic semitone, just major semitone, overtone semitone,[5] 17th harmonic,[3] limma17S
111.45 255(5 : 1)1/25Studie II interval (compound just major third, 5:1, divided into 25 equal parts)25
111.73 D-[2]16 : 1524 : 3×5Just minor second,[14] just diatonic semitone, large just semitone or major second,[4] major semitone,[5] limma, minor diatonic semitone,[3] diatonic second[15] semitone,[13] diatonic semitone,[10] 16-comma meantone minor second5S
113.69 C++2187 : 204837 : 211Apotome[3][10] or Pythagorean major semitone,[6] Pythagorean augmented unison, Pythagorean chromatic semitone, or Pythagorean apotome3
116.72 (18 : 5)1/1921/19×32/19 : 51/19Secor10.28
119.44 C15 : 143×5 : 2×7Septimal diatonic semitone, major diatonic semitone,[3] Cowell semitone[5]7S
125.00 25/4825/485 steps in 48 equal temperament48
128.30 D14 : 132×7 : 13Lesser tridecimal 2/3-tone[16]13S
130.23 C+69 : 643×23 : 26Sixty-ninth harmonic[5]23
133.24 D27 : 2533 : 52Semitone maximus, minor second, large limma or Bohlen-Pierce small semitone,[3] high semitone,[13] alternate Renaissance half-step,[5] large limma, acute minor second5
133.33 C/D[lower-alpha 1]21/922/18Two-third tone9, 18, 36, 72
138.57 D-13 : 1213 : 22×3Greater tridecimal 2/3-tone,[16] Three-quarter tone[5]13S
150.00 C/D23/2421/8Equal-tempered neutral second8, 24
150.64 D↓[2]12 : 1122×3 : 1134 tone or Undecimal neutral second,[3][5] trumpet three-quarter tone,[10] middle finger [between frets][13]11S
155.14 D35 : 325×7 : 25Thirty-fifth harmonic[5]7
160.90 D−−800 : 72925×52 : 36Grave whole tone,[3] neutral second, grave major second5
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 temperament7
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 : 32Small just whole tone or major second,[4] minor whole tone,[3][5] lesser whole tone,[15] minor tone,[13] minor second,[10] half-comma meantone major second5S
200.00 D22/1221/6Equal-tempered major second6, 12M
203.91 D[2]9 : 832 : 23Pythagorean major second, Large just whole tone or major second[10] (sesquioctavan),[4] tonus, major whole tone,[3][5] greater whole tone,[15] major tone[13]3S
215.89 D145 : 1285×29 : 27Hundred-forty-fifth harmonic29
223.46 E[2]256 : 22528 : 32×52Just diminished third,[15] 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 : 7Septimal major second,[4] septimal whole tone[3][5]7S
240.00 21/521/51 step in 5 equal temperament5
247.74 D15 : 133×5 : 13Tridecimal 54 tone[3]13
250.00 D/E25/2425/245 steps in 24 equal temperament24
251.34 D37 : 3237 : 25Thirty-seventh harmonic[5]37
253.08 D125 : 10853 : 22×33Semi-augmented whole tone,[3] semi-augmented second5
262.37 E↓64 : 5526 : 5×1155th subharmonic[5][6]11
268.80 D299 : 25613×23 : 28Two-hundred-ninety-ninth harmonic23
266.87 E[2]7 : 67 : 2×3Septimal minor third[3][4][10] or Sub minor third[13]7S
274.58 D[2]75 : 643×52 : 26Just augmented second,[15] Augmented tone,[13] augmented second[5][12]5
275.00 211/48211/4811 steps in 48 equal temperament48
289.21 E13 : 1113 : 11Tridecimal minor third[3]13S
294.13 E[2]32 : 2725 : 33Pythagorean minor third[3][5][6][13][15] 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 third4, 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 : 5Just minor third,[3][4][5][10][15] minor third,[13] 13-comma meantone minor third5MS
317.60 D++19683 : 1638439 : 214Pythagorean augmented second[3][6]3
320.14 E77 : 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[17]17
337.15 E+243 : 20035 : 23×52Acute minor third[3]5
342.48 E39 : 323×13 : 25Thirty-ninth harmonic[5]13
342.86 22/722/72 steps in 7 equal temperament7
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/E27/2427/24Equal-tempered neutral third24
354.55 E+27 : 2233 : 2×11Zalzal's wosta[6] 12:11 X 9:8[13]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 : 22Just major third,[3][4][5][10][15] major third,[13] quarter-comma meantone major third5MS
397.10 E+161 : 1287×23 : 27One-hundred-sixty-first harmonic23
400.00 E24/1221/3Equal-tempered major third3, 12M
402.47 E323 : 25617×19 : 28Three-hundred-twenty-third harmonic19
407.82 E+[2]81 : 6434 : 26Pythagorean major third,[3][5][6][13][15] ditone3
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,[15] diminished fourth,[5][12] 25th subharmonic5
429.06 E41 : 3241 : 25Forty-first harmonic[5]41
435.08 E[2]9 : 732 : 7Septimal major third,[3][5] Bohlen-Pierce third,[3] Super major Third[13]7
444.77 F↓128 : 9927 : 9×1199th subharmonic[5][6]11
450.00 E/F29/2429/249 steps in 24 equal temperament24
450.05 83 : 6483 : 26Eighty-third harmonic[5]83
454.21 F13 : 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, 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 temperament5
491.27 E85 : 645×17 : 26Eighty-fifth harmonic[5]17
498.04 F[2]4 : 322 : 3Perfect fourth,[3][5][15] Pythagorean perfect fourth, Just perfect fourth or diatessaron[4]3S
500.00 F25/1225/12Equal-tempered perfect fourth12M
501.42 F+171 : 12832×19 : 27One-hundred-seventy-first harmonic19
510.51 (3 : 2)8/1138/11 : 28/1118.75
511.52 F43 : 3243 : 25Forty-third harmonic[5]43
514.29 23/723/73 steps in 7 equal temperament7
519.55 F+[2]27 : 2033 : 22×55-limit wolf fourth, acute fourth,[3] imperfect fourth[15]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/G211/24211/2411 steps in 24 equal temperament24
551.32 F[2]11 : 811 : 23eleventh 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,[10] septimal diminished fifth[18]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][10] tritone,[6] diatonic tritone,[3] 'augmented' or 'false' fourth,[15] high 5-limit tritone,[5] 16-comma meantone augmented fourth5
595.03 G361 : 256192 : 28Three-hundred-sixty-first harmonic19
600.00 F/G26/1221/2=2Equal-tempered tritone2, 12M
609.35 G91 : 647×13 : 26Ninety-first harmonic[5]13
609.78 G[2]64 : 4526 : 32×5Just tritone,[4] 2nd tritone,[6] 'false' fifth,[15] diminished fifth,[12] 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 fifth23
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/G213/24213/2413 steps in 24 equal temperament24
665.51 G47 : 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][10] imperfect fifth,[15]5
683.83 G95 : 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 fifth12M
701.89 231/53231/5353
701.96 G[2]3 : 23 : 2Perfect fifth,[3][5][15] Pythagorean perfect fifth, Just perfect fifth or diapente,[4] fifth,[13] Just fifth[10]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 A1024 : 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 sixth7
733.23 F+391 : 25617×23 : 28Three-hundred-ninety-first harmonic23
737.65 A+49 : 327×7 : 25Forty-ninth harmonic[5]7
743.01 A192 : 12526×3 : 53Classic diminished sixth[3]5
750.00 G/A215/24215/2415 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 : 2Wallis product
782.49 G-[2]11 : 711 : 7Undecimal minor sixth,[5] undecimal augmented fifth,[3] Fibonacci numbers11
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 sixth3, 12M
806.91 G51 : 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 : 2φ : 1
833.11 233 : 144233 : 24×32Golden 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 harmonic13
848.83 A209 : 12811×19 : 27Two-hundred-ninth harmonic19
850.00 G/A217/24217/24Equal-tempered neutral sixth24
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 temperament7
862.85 A−400 : 24324×52 : 35Grave major sixth[3]5
873.50 A53 : 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][10][15] Bohlen-Pierce sixth,[3] 13-comma meantone major sixth5M
889.76 107 : 64107 : 26Hundred-seventh harmonic[5]107
892.54 B6859 : 4096193 : 2126859th harmonic19
900.00 A29/1223/4Equal-tempered major sixth4, 12M
902.49 A32 : 1925 : 1919
905.87 A+[2]27 : 1633 : 24Pythagorean major sixth[3][5][10][15]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,[15] diminished seventh,[5][12] 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][19]11
950.00 A/B219/24219/2419 steps in 24 equal temperament24
953.30 A+111 : 643×37 : 26Hundred-eleventh harmonic[5]37
955.03 A[2]125 : 7253 : 23×325
957.21 (3 : 2)15/11315/11 : 215/1115 steps in Beta scale18.75
960.00 24/524/54 steps in 5 equal temperament5
968.83 B[2]7 : 47 : 22Septimal minor seventh,[4][5][10] harmonic seventh,[3][10] augmented sixth7
975.00 213/16239/4839 steps in 48 equal temperament16, 48
976.54 A+[2]225 : 12832×52 : 275
984.21 113 : 64113 : 26Hundred-thirteenth harmonic[5]113
996.09B[2]16 : 924 : 32Pythagorean minor seventh,[3] Small just minor seventh,[4] lesser minor seventh,[15] just minor seventh,[10] Pythagorean small minor seventh[5]3
999.47 B57 : 323×19 : 25Fifty-seventh harmonic[5]19
1000.00A/B210/1225/6Equal-tempered minor seventh6, 12M
1014.59 A+115 : 645×23 : 26Hundred-fifteenth harmonic[5]23
1017.60B[2]9 : 532 : 5Greater just minor seventh,[15] large just minor seventh,[4][5] Bohlen-Pierce seventh[3]5
1019.55 A+++59049 : 32768310 : 215Pythagorean augmented sixth[3][6]3
1025.00 241/48241/4841 steps in 48 equal temperament48
1028.57 26/726/76 steps in 7 equal temperament7
1029.58 B29 : 1629 : 24Twenty-ninth harmonic,[5] minor seventh29
1035.00B↓[2]20 : 1122×5 : 11Lesser undecimal neutral seventh, large minor seventh[3]11
1039.10 B+729 : 40036 : 24×52Acute minor seventh[3]5
1044.44 B117 : 6432×13 : 26Hundred-seventeenth harmonic[5]13
1044.86 B-64 : 3526 : 5×735th subharmonic,[5] septimal neutral seventh[6]7
1049.36B[2]11 : 611 : 2×3214-tone or Undecimal neutral seventh,[3] undecimal 'median' seventh[5]11
1050.00 A/B221/2427/8Equal-tempered neutral seventh8, 24
1059.17 59 : 3259 : 25Fifty-ninth harmonic[5]59
1066.76 B−50 : 272×52 : 33Grave major seventh[3]5
1071.70 B-13 : 713 : 7Tridecimal neutral seventh[20]13
1073.78 B119 : 647×17 : 26Hundred-nineteenth harmonic[5]17
1075.00 243/48243/4843 steps in 48 equal temperament48
1086.31 C′−−4096 : 2187212 : 37Pythagorean diminished octave[3][6]3
1088.27 B[2]15 : 83×5 : 23Just major seventh,[3][5][10][15] small just major seventh,[4] 16-comma meantone major seventh5
1095.04 C32 : 1725 : 1717th subharmonic[5][6]17
1100.00 B211/12211/12Equal-tempered major seventh12M
1102.64 B-121 : 64112 : 26Hundred-twenty-first harmonic[5]11
1107.82 C′256 : 13528 : 33×5Octave − major chroma,[3] 135th subharmonic, narrow diminished octave5
1109.78 B+[2]243 : 12835 : 27Pythagorean major seventh[3][5][6][10]3
1116.88 61 : 3261 : 25Sixty-first harmonic[5]61
1125.00 215/16245/4845 steps in 48 equal temperament16, 48
1129.33 C′[2]48 : 2524×3 : 52Classic diminished octave,[3][6] large just major seventh[4]5
1131.02 B123 : 643×41 : 26Hundred-twenty-third harmonic[5]41
1137.04 B27 : 1433 : 2×7Septimal major seventh[5]7
1138.04 C247 : 12813×19 : 27Two-hundred-forty-seventh harmonic19
1145.04 B31 : 1631 : 24Thirty-first harmonic,[5] augmented seventh31
1146.73 C↓64 : 3326 : 3×1133rd subharmonic[6]11
1150.00 B/C223/24223/2423 steps in 24 equal temperament24
1151.23 C35 : 185×7 : 2×32Septimal supermajor seventh, septimal quarter tone inverted 7
1158.94 B[2]125 : 6453 : 26Just augmented seventh,[5] 125th harmonic5
1172.74 C+63 : 3232×7 : 25Sixty-third harmonic[5]7
1175.00 247/48247/4847 steps in 48 equal temperament48
1178.49 C′−160 : 8125×5 : 34Octave − syntonic comma,[3] semi-diminished octave5
1179.59 B253 : 12811×23 : 27Two-hundred-fifty-third harmonic[5]23
1186.42 127 : 64127 : 26Hundred-twenty-seventh harmonic[5]127
1200.00 C′2 : 12 : 1Octave[3][10] or diapason[4]1, 122MS
1223.46 B+++531441 : 262144312 : 218Pythagorean augmented seventh[3][6]3
1525.86 21/2+1Silver ratio
1901.96 G′3 : 13 : 1Tritave or just perfect twelfth3
2400.00 C″4 : 122 : 1Fifteenth or two octaves1, 122M
3986.31 E‴10 : 15×2 : 1Decade, compound just major third5M

Notes

1. Maneri-Sims notation

References

1. Fox, Christopher (2003). "Microtones and Microtonalities", Contemporary Music Review, v. 22, pt. 1-2. (Abingdon, Oxfordshire, UK: Routledge): p.13.
2. Fonville, John. 1991. "Ben Johnston's Extended Just Intonation: A Guide for Interpreters". Perspectives of New Music 29, no. 2 (Summer): 106–37.
3. "List of intervals", Huygens-Fokker Foundation. The Foundation uses "classic" to indicate "just" or leaves off any adjective, as in "major sixth".
4. Partch, Harry (1979). Genesis of a Music, p.68-69. ISBN 978-0-306-80106-8.
5. "Anatomy of an Octave", KyleGann.com. Gann leaves off "just" but includes "5-limit". He uses "median" for "neutral".
6. Haluška, Ján (2003). The Mathematical Theory of Tone Systems, p.xxv-xxix. ISBN 978-0-8247-4714-5.
7. Ellis, Alexander J.; Hipkins, Alfred J. (1884), "Tonometrical Observations on Some Existing Non-Harmonic Musical Scales" (PDF), Proceedings of the Royal Society of London, 37 (232–234): 368–385, doi:10.1098/rspl.1884.0041, JSTOR 114325.
8. "Orwell Temperaments", Xenharmony.org.
9. Partch (1979), p.70.
10. Alexander John Ellis (1885). On the musical scales of various nations, p.488. s.n.
11. William Smythe Babcock Mathews (1895). Pronouncing dictionary and condensed encyclopedia of musical terms, p.13. ISBN 1-112-44188-3.
12. Anger, Joseph Humfrey (1912). A treatise on harmony, with exercises, Volume 3, p.xiv-xv. W. Tyrrell.
13. Hermann Ludwig F. von Helmholtz (Alexander John Ellis, trans.) (1875). "Additions by the translator", On the sensations of tone as a physiological basis for the theory of music, p.644. No ISBN specified.
14. A. R. Meuss (2004). Intervals, Scales, Tones and the Concert Pitch C. Temple Lodge Publishing. p. 15. ISBN 1902636465.
15. Paul, Oscar (1885). A manual of harmony for use in music-schools and seminaries and for self-instruction, p.165. Theodore Baker, trans. G. Schirmer. Paul uses "natural" for "just".
16. "13th-harmonic", 31et.com.
17. Brabner, John H. F. (1884). The National Encyclopaedia, Vol.13, p.182. London. [ISBN unspecified]
18. Sabat, Marc and von Schweinitz, Wolfgang (2004). "The Extended Helmholtz-Ellis JI Pitch Notation" [PDF], NewMusicBox.org. Accessed: 04:12, 15 March 2014 (UTC).
19. Hermann L. F Von Helmholtz (2007). On the Sensations of Tone, p.456. ISBN 978-1-60206-639-7.
20. "Gallery of Just Intervals", Xenharmonic.wikispaces.com.
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