List of pitch intervals

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Below is a list of intervals exprimable 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.

Comparison between tunings: Pythagorean, equal-tempered, 1/4-comma meantone, and others. For each, the common origin is arbitrarily chosen as C. The degrees are arranged in the order or the cycle of fifths; as in each of these tunings except just intonation all fifths are of the same size, the tunings appear as straight lines, the slope indicating the relative tempering with respect to Pythagorean, which has pure fifths (3:2, 702 cents). The Pythagorean Ab (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 Ab 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 Ab and G#, is much larger than in Pythagorean, and with the flat degree higher than the sharp one.

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 factorized into 2·5 (and 9 in 3·3). There exists another type of limit, the odd limit, a concept used by Harry Partch (bigger of odd numbers obtained after dividing numerator and denominator by highest possible powers of 2), but it is not used here. The term "limit" was devised by Partch.[1]
  • By definition, every interval in a given limit can also be part of a limit of higher order. For instance, a 3-limit unit can also be part of a 5-limit tuning and so on. By sorting the limit columns in the table below, all intervals of a given limit can be brought together (sort backwards by clicking the button twice).
  • Pythagorean tuning means 3-limit intonation—a ratio of numbers with prime factors no higher than three.
  • Just intonation means 5-limit intonation—a ratio of numbers with prime factors no higher than five.
  • Septimal, undecimal, tridecimal, and septendecimal mean, respectively, 7, 11, 13, and 17-limit intonation.
  • Meantone refers to meantone temperament, where the whole tone is the mean of the major third. In general, a meantone is constructed in the same way as Pythagorean tuning, as a stack of fifths: the tone is reached after two fifths, the major third after four, so that as all fifths are the same, the tone is the mean of the third. In a meantone temperament, each fifth is narrowed ("tempered") by the same small amount. The most common of meantone temperaments is the quarter-comma meantone, in which each fifth is tempered by 1/4 of the syntonic comma, so that after four steps the major third (as C-G-D-A-E) is a full syntonic comma lower than the Pythagorean one. The extremes of the meantone systems encountered in historical practice are the Pythagorean tuning, where the whole tone corresponds to 9:8, i.e (3:2)2/2, the mean of the major third (3:2)4/4, and the fifth (3:2) is not tempered; and the 1/3-comma meantone, where the fifth is tempered to the extent that three ascending fifths produce a pure minor third.(See Meantone temperaments). The music program Logic Pro uses also 1/2-comma meantone temperament.
  • Equal-tempered refers to X-tone equal temperament with intervals corresponding to X divisions per octave.
  • Tempered intervals however cannot be expressed in terms of prime limits and, unless exceptions, are not found in the table below.
  • The table can also be sorted by frequency ratio, by cents, or alphabetically.

List[edit]

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 About this sound play Unison,[3] monophony,[4] perfect prime,[3] tonic,[5] or fundamental 1, 12 3 M
0.40
C7- 4375 : 4374 54·7 : 2·37 About this sound play Ragisma[3][6] 7 S
0.72
E7777triple flat+ 2401 : 2400 74 : 25·3·52 About this sound play Breedsma[3][6] 7 S
1.00
21/1200 21/1200 About this sound play Cent 1200
1.20
21/1000 21/1000 About this sound play Millioctave 1000
1.95
B++ 32805 : 32768 38·5 : 215 About this sound play Schisma[3][5] 5
3.99
101/1000 21/1000·51/1000 About this sound play Savart or eptaméride 301.03
7.71
B7 upside-down 225 : 224 32·52 : 25·7 About this sound play Septimal kleisma,[3][6] marvel comma 7 S
8.11
Bdouble sharp- 15625 : 15552 56 : 26·35 About this sound play Kleisma or semicomma majeur[3][6] 5
10.06
Adouble sharpdouble sharp++ 2109375 : 2097152 33·57 : 221 About this sound play Semicomma,[3][6] Fokker's comma[3] 5
11.98
C29 145 : 144 5·29 : 24·32 About this sound play Difference between 29:16 & 9:5 29 S
12.50
21/96 21/96 About this sound play Sixteenth tone 96
13.07
B7 upside-down7 upside-down7 upside-down- 1728 : 1715 26·33 : 5·73 About this sound play Orwell comma[3][7] 7
13.79
Ddouble flat7 upside-down 126 : 125 2·32·7 : 53 About this sound play Small septimal semicomma,[6] small septimal comma,[3] starling comma 7 S
14.37
C- 121 : 120 112 : 23·3·5 About this sound play Undecimal seconds comma[3] 11 S
16.67
C[a] 21/72 21/72 About this sound play 1 step in 72 equal temperament 72
18.13
C19U 96 : 95 25·3 : 5·19 About this sound play Difference between 19:16 & 6:5 19 S
19.55
Ddouble flat--[2] 2048 : 2025 211 : 34·52 About this sound play Diaschisma,[3][6] minor comma 5
21.51
C+[2] 81 : 80 34 : 24·5 About this sound play Syntonic comma,[3][5][6] major comma, komma, chromatic diesis, or comma of Didymus[3][6][8][9] 5 S
22.64
21/53 21/53 About this sound play Holdrian comma, Holder's comma, 1 step in 53 equal temperament 53
23.46
B+++ 531441 : 524288 312 : 219 About this sound play Pythagorean comma,[3][5][6][8][9] ditonic comma[3][6] 3
25.00
21/48 21/48 About this sound play Eighth tone 48
26.84
C13 65 : 64 5·13 : 26 About this sound play Sixty-fifth harmonic,[5] 13th-partial chroma[3] 13 S
27.26
C7 upside-down- 64 : 63 26 : 32·7 About this sound play Septimal comma,[3][6][9] Archytas' comma[3] 7 S
29.27
21/41 21/41 About this sound play 1 step in 41 equal temperament 41
31.19
D7 56 : 55 23·7 : 5·11 About this sound play Ptolemy's enharmonic:[5] difference between (11 : 8) and (7 : 5) tritone 11 S
33.33
CHalf up arrow.png/DHalf down arrow.pngHalf down arrow.png[a] 21/36 21/36 About this sound play Sixth tone 36, 72
34.28
C17 51 : 50 3·17 : 2·52 About this sound play Difference between 17:16 & 25:24 17 S
34.98
B7 upside-down7 upside-down- 50 : 49 2·52 : 72 About this sound play Septimal sixth tone or jubilisma, Erlich's decatonic comma or tritonic diesis[3][6] 7 S
35.70
D77 49 : 48 72 : 24·3 About this sound play Septimal diesis, slendro diesis or septimal 1/6-tone[3] 7 S
38.05
C23 46 : 45 2·23 : 32·5 About this sound play Inferior quarter tone,[5] difference between 23:16 & 45:32 23 S
38.71
21/31 21/31 About this sound play 1 step in 31 equal temperament 31
38.91
C+ 45 : 44 32·5 : 4·11 About this sound play Undecimal diesis or undecimal fifth tone 11 S
40.00
21/30 21/30 About this sound play Fifth tone 30
41.06
Ddouble flat- 128 : 125 27 : 53 About this sound play Enharmonic diesis or 5-limit limma, minor diesis,[6] diminished second,[5][6] minor diesis or diesis[3] 5
41.72
D41U7 42 : 41 2·3·7 : 41 About this sound play Lesser 41-limit fifth tone 41 S
42.75
C41 41 : 40 41 : 23·5 About this sound play Greater 41-limit fifth tone 41 S
43.83
C13 upside down 40 : 39 23·5 : 3·13 About this sound play Tridecimal fifth tone 13 S
44.97
C19U13 39 : 38 3·13 : 2·19 About this sound play Superior quarter-tone,[5] novendecimal fifth tone 19 S
46.17
D37U19double flat- 38 : 37 2·19 : 37 About this sound play Lesser 37-limit quarter tone 37 S
47.43
C37 37 : 36 37 : 22·32 About this sound play Greater 37-limit quarter tone 37 S
48.77
C7 upside-down 36 : 35 22·32 : 5·7 About this sound play Septimal quarter tone, septimal diesis,[3][6] septimal comma,[2] superior quarter tone[5] 7 S
50.00
Chalf sharp/Dthree quarter flat 21/24 21/24 About this sound play Equal-tempered quarter tone 24
50.18
D17 upside down7 35 : 34 5·7 : 2·17 About this sound play ET quarter-tone approximation,[5] lesser 17-limit quarter tone 17 S
50.72
B7 upside-down++ 59049 : 57344 310 : 213·7 About this sound play Harrison's comma (9 P5s - 1 H7)[3] 24 7
51.68
C17 34 : 33 2·17 : 3·11 About this sound play Greater 17-limit quarter tone 17 S
53.27
C 33 : 32 3·11 : 25 About this sound play Thirty-third harmonic,[5] undecimal comma, undecimal quarter tone 11 S
54.96
D31U- 32 : 31 25 : 31 About this sound play Inferior quarter-tone,[5] thirty-first subharmonic 31 S
56.77
C31 31 : 30 31 : 2·3·5 About this sound play Inferior quarter-tone,[5] difference between 31:16 & 15:8 31 S
58.69
C29U 30 : 29 2·3·5 : 29 About this sound play Lesser 29-limit quarter tone 29 S
60.75
C297 upside-down 29 : 28 29 : 22·7 About this sound play Greater 29-limit quarter tone 29 S
62.96
C7- 28 : 27 22·7 : 33 About this sound play Septimal minor second, small minor second, inferior quarter tone[5] 7 S
63.81
(3 : 2)1/11 31/11 : 21/11 About this sound play Beta scale step 18.75
65.34
C13 upside down+ 27 : 26 33 : 2·13 About this sound play Chromatic diesis,[10] tridecimal comma[3] 13 S
66.67
CCheck down arrow.png/CHalf down arrow.png[a] 21/18 21/18 About this sound play Third tone 18, 36, 72
67.90
D13double flat- 26 : 25 2·13 : 52 About this sound play Tridecimal third tone, third tone[5] 13 S
70.67
C[2] 25 : 24 52 : 23·3 About this sound play Just chromatic semitone or minor chroma,[3] lesser chromatic semitone, small (just) semitone[9] or minor second,[4] minor chromatic semitone,[11] or minor semitone,[5] 2/7-comma meantone chromatic semitone 5 S
73.68
D23U- 24 : 23 23·3 : 23 About this sound play Lesser 23-limit semitone 23 S
76.96
C23+ 23 : 22 23 : 2·11 About this sound play Greater 23-limit semitone 23 S
78.00
(3 : 2)1/9 31/9 : 21/9 About this sound play Alpha scale step 15.39
79.31
67 : 64 67 : 26 About this sound play Sixty-seventh harmonic[5] 67
80.54
C7 upside-down- 22 : 21 2·11 : 3·7 About this sound play Hard semitone,[5] two-fifth tone small semitone 11 S
84.47
D7 21 : 20 3·7 : 22·5 About this sound play Septimal chromatic semitone, minor semitone[3] 7 S
88.80
C19U 20 : 19 22·5 : 19 About this sound play Novendecimal augmented unison 19 S
90.22
D--[2] 256 : 243 28 : 35 About this sound play Pythagorean minor second or limma,[3][6][9] Pythagorean diatonic semitone, Low Semitone[12] 3
92.18
C+[2] 135 : 128 33·5 : 27 About this sound play Greater chromatic semitone, chromatic semitone, semitone medius, major chroma or major limma,[3] small limma,[9] major chromatic semitone,[11] limma ascendant[5] 5
93.60
D19- 19 : 18 19 : 2·9 Novendecimal minor secondAbout this sound play 19 S
98.95
D17 upside down 18 : 17 2·32 : 17 About this sound play Just minor semitone, Arabic lute index finger[3] 17 S
100.00
C/D 21/12 21/12 About this sound play Equal-tempered minor second or semitone 12 M
104.96
C17[2] 17 : 16 17 : 24 About this sound play Minor diatonic semitone, just major semitone, overtone semitone,[5] 17th harmonic,[3] limma[citation needed] 17 S
111.73
D-[2] 16 : 15 24 : 3·5 About this sound play Just minor second,[13] just diatonic semitone, large just semitone or major second,[4] major semitone,[5] limma, minor diatonic semitone,[3] diatonic second[14] semitone,[12] diatonic semitone,[9] 1/6-comma meantone minor second 5 S
113.69
C++ 2187 : 2048 37 : 211 About this sound play apotome[3][9] 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 About this sound play Secor 10.28
119.44
C7 upside-down 15 : 14 3·5 : 2·7 About this sound play Septimal diatonic semitone, major diatonic semitone,[3] Cowell semitone[5] 7 S
128.30
D13 upside down7 14 : 13 2·7 : 13 About this sound play Lesser tridecimal 2/3-tone[15] 13 S
130.23
C23+ 69 : 64 3·23 : 26 About this sound play Sixty-ninth harmonic[5] 23
133.24
D 27 : 25 33 : 52 About this sound play Semitone maximus, minor second, large limma or Bohlen-Pierce small semitone,[3] high semitone,[12] alternate Renaissance half-step,[5] large limma, acute minor second[citation needed] 5
133.33
CHalf up arrow.png/DHalf up arrow.png[a] 21/9 22/18 About this sound play Two-third tone 9, 18, 36, 72
138.57
D13- 13 : 12 13 : 22·3 About this sound play Greater tridecimal 2/3-tone,[15] Three-quarter tone[5] 13 S
150.00
Cthree quarter sharp/Dhalf flat 23/24 21/8 About this sound play Equal-tempered neutral second 8, 24
150.64
D↓[2] 12 : 11 22·3 : 11 About this sound play 3/4-tone or Undecimal neutral second,[3][5] trumpet three-quarter tone[9] 11 S
155.14
D7 35 : 32 5·7 : 25 About this sound play Thirty-fifth harmonic[5] 7
160.90
D-- 800 : 729 25·52 : 36 About this sound play Grave whole tone,[3] neutral second, grave major second[citation needed] 5
165.00
D-[2] 11 : 10 11 : 2·5 About this sound play Greater undecimal minor/major/neutral second, 4/5-tone or Ptolemy's second[3] 11 S
171.43
21/7 21/7 About this sound play 1 step in 7 equal temperament 7
179.70
71 : 64 71 : 26 About this sound play Seventy-first harmonic[5] 71
180.45
Edouble flat--- 65536 : 59049 216 : 310 About this sound play Pythagorean diminished third,[3][6] Pythagorean minor tone 3
182.40
D-[2] 10 : 9 2·5 : 32 About this sound play Small just whole tone or major second,[4] minor whole tone,[3][5] lesser whole tone,[14] minor tone,[12] minor second,[9] half-comma meantone major second 5 S
200.00
D 22/12 21/6 About this sound play Equal-tempered major second 6, 12 M
203.91
D[2] 9 : 8 32 : 23 About this sound play Pythagorean major second, Large just whole tone or major second[9] (sesquioctavan),[4] tonus, major whole tone,[3][5] greater whole tone,[14] major tone[12] 3 S
223.46
Edouble flat-[2] 256 : 225 28 : 32·52 About this sound play Just diminished third[14] 5
227.79
73 : 64 73 : 26 About this sound play Seventy-third harmonic[5] 73
231.17
D7 upside-down-[2] 8 : 7 23 : 7 About this sound play Septimal major second,[4] septimal whole tone[3][5] 7 S
240.00
21/5 21/5 About this sound play 1 step in 5 equal temperament 5
251.34
D37 37 : 32 37 : 25 About this sound play Thirty-seventh harmonic[5] 37
253.08
D- 125 : 108 53 : 22·33 About this sound play Semi-augmented whole tone,[3] semi-augmented second[citation needed] 5
266.87
E7[2] 7 : 6 7 : 2·3 About this sound play Septimal minor third[3][4][9] or Sub minor third[12] 7 S
274.58
D[2] 75 : 64 3·52 : 26 About this sound play Just augmented second,[14] Augmented tone,[12] augmented second[5][11] 5
294.13
E-[2] 32 : 27 25 : 33 About this sound play Pythagorean minor third[3][5][6][12][14] or semiditone 3
297.51
E19[2] 19 : 16 19 : 24 About this sound play 19th harmonic,[3] 19-limit minor third, overtone minor third,[5] Pythagorean minor third[citation needed] 19
300.00
D/E 23/12 21/4 About this sound play Equal-tempered minor third 4, 12 M
310.26
6:5÷(81:80)1/4 22 : 53/4 About this sound play Quarter-comma meantone minor third M
311.98
(3 : 2)4/9 34/9 : 24/9 About this sound play Alpha scale minor third 3.85
315.64
E[2] 6 : 5 2·3 : 5 About this sound play Just minor third,[3][4][5][9][14] minor third,[12] 1/3-comma meantone minor third 5 M S
317.60
D++ 19683 : 16384 39 : 214 About this sound play Pythagorean augmented second[3][6] 3
320.14
E7 77 : 64 7·11 : 26 About this sound play Seventy-seventh harmonic[5] 11
337.15
E+ 243 : 200 35 : 23·52 About this sound play Acute minor third[3] 5
342.48
E13 39 : 32 3·13 : 25 About this sound play Thirty-ninth harmonic[5] 13
342.86
22/7 22/7 About this sound play 2 steps in 7 equal temperament 7
347.41
E-[2] 11 : 9 11 : 32 About this sound play Undecimal neutral third[3] 11
350.00
Dthree quarter sharp/Ehalf flat 27/24 27/24 About this sound play Equal-tempered neutral third 24
359.47
E13 upside down[2] 16 : 13 24 : 13 About this sound play Tridecimal neutral third[3] 13
364.54
79 : 64 79 : 26 About this sound play Seventy-ninth harmonic[5] 79
364.81
E- 100 : 81 22·52 : 34 About this sound play Grave major third[3] 5
384.36
F-- 8192 : 6561 213 : 38 About this sound play Pythagorean diminished fourth,[3][6] Pythagorean 'schismatic' third[5] 3
386.31
E[2] 5 : 4 5 : 22 About this sound play Just major third,[3][4][5][9][14] major third,[12] quarter-comma meantone major third 5 M S
400.00
E 24/12 21/3 About this sound play Equal-tempered major third 3, 12 M
407.82
E+[2] 81 : 64 34 : 26 About this sound play Pythagorean major third,[3][5][6][12][14] ditone 3
417.51
F7+[2] 14 : 11 2·7 : 11 About this sound play Undecimal diminished fourth or major third[3] 11
427.37
F[2] 32 : 25 25 : 52 About this sound play Just diminished fourth,[14] diminished fourth[5][11] 5
429.06
E41 41 : 32 41 : 25 About this sound play Forty-first harmonic[5] 41
435.08
E7 upside-down[2] 9 : 7 32 : 7 About this sound play Septimal major third,[3][5] Bohlen-Pierce third,[3] Super major Third[12] 7
450.05
83 : 64 83 : 26 About this sound play Eighty-third harmonic[5] 83
454.21
F13 13 : 10 13 : 2·5 About this sound play Tridecimal major third or diminished fourth 13
456.99
E[2] 125 : 96 53 : 25·3 About this sound play Just augmented third, augmented third[5] 5
470.78
F7+[2] 21 : 16 3·7 : 24 About this sound play About this sound play Twenty-first harmonic, narrow fourth,[3] septimal fourth,[5] wide augmented third[citation needed] 7
478.49
E+ 675 : 512 33·52 : 29 About this sound play Wide augmented third[3] 5
480.00
22/5 22/5 About this sound play 2 steps in 5 equal temperament 5
491.27
E17 85 : 64 5·17 : 26 About this sound play Eighty-fifth harmonic[5] 17
498.04
F[2] 4 : 3 22 : 3 About this sound play Perfect fourth,[3][5][14] Pythagorean perfect fourth, Just perfect fourth or diatessaron[4] 3 S
500.00
F 25/12 25/12 About this sound play Equal-tempered perfect fourth 12 M
510.51
(3 : 2)8/11 38/11 : 28/11 About this sound play Beta scale perfect fourth 18.75
511.52
43 : 32 43 : 25 About this sound play Forty-third harmonic[5] 43
514.29
23/7 23/7 About this sound play 3 steps in 7 equal temperament 7
519.55
F+[2] 27 : 20 33 : 22·5 About this sound play 5-limit wolf fourth, acute fourth,[3] imperfect fourth[14] 5
521.51
E+++ 177147 : 131072 311 : 217 About this sound play Pythagorean augmented third[3][6] (F+ (pitch)) 3
531.53
F29+ 87 : 64 3·29 : 26 About this sound play Eighty-seventh harmonic[5] 29
551.32
F[2] 11 : 8 11 : 23 About this sound play eleventh harmonic,[5] undecimal tritone,[5] lesser undecimal tritone, undecimal semi-augmented fourth[3] 11
568.72
F[2] 25 : 18 52 : 2·32 About this sound play Just augmented fourth[3][5] 5
570.88
89 : 64 89 : 26 About this sound play Eighty-ninth harmonic[5] 89
582.51
G7[2] 7 : 5 7 : 5 About this sound play Lesser septimal tritone, septimal tritone[3][4][5] Huygens' tritone or Bohlen-Pierce fourth,[3] septimal fifth,[9] septimal diminished fifth[16] 7
588.27
G-- 1024 : 729 210 : 36 About this sound play Pythagorean diminished fifth,[3][6] low Pythagorean tritone[5] 3
590.22
F+[2] 45 : 32 32·5 : 25 About this sound play Just augmented fourth, just tritone,[4][9] tritone,[6] diatonic tritone,[3] 'augmented' or 'false' fourth,[14] high 5-limit tritone,[5] 1/6-comma meantone augmented fourth 5
600.00
F/G 26/12 21/2=√2 About this sound play Equal-tempered tritone 2, 12 M
609.35
G137 91 : 64 7·13 : 26 About this sound play Ninety-first harmonic[5] 13
609.78
G-[2] 64 : 45 26 : 32·5 About this sound play Just tritone,[4] 2nd tritone,[6] 'false' fifth,[14] diminished fifth,[11] low 5-limit tritone[5] 5
611.73
F#++ 729 : 512 36 : 29 About this sound play Pythagorean tritone,[3][6] Pythagorean augmented fourth, high Pythagorean tritone[5] 3
617.49
F7 upside-down[2] 10 : 7 2·5 : 7 About this sound play Greater septimal tritone, septimal tritone,[4][5] Euler's tritone[3] 7
628.27
F23+ 23 : 16 23 : 24 About this sound play Twenty-third harmonic,[5] classic diminished fifth[citation needed] 23
631.28
G[2] 36 : 25 22·32 : 52 About this sound play Just diminished fifth[5] 5
646.99
F31+ 93 : 64 3·31 : 26 About this sound play Ninety-third harmonic[5] 31
648.68
G↓[2] 16 : 11 24 : 11 About this sound play Inversion of eleventh harmonic, undecimal semi-diminished fifth[3] 11
665.51
47 : 32 47 : 25 About this sound play Forty-seventh harmonic[5] 47
678.49
Adouble flat--- 262144 : 177147 218 : 311 About this sound play Pythagorean diminished sixth[3][6] 3
680.45
G- 40 : 27 23·5 : 33 About this sound play 5-limit wolf fifth,[5] or diminished sixth, grave fifth,[3][6][9] imperfect fifth,[14] 5
683.83
G19 95 : 64 5·19 : 26 About this sound play Ninety-fifth harmonic[5] 19
691.20
3:2÷(81:80)1/2 2·51/2 : 3 About this sound play Half-comma meantone perfect fifth M
694.79
3:2÷(81:80)1/3 21/3·51/3 : 31/3 About this sound play 1/3-comma meantone perfect fifth M
695.81
3:2÷(81:80)2/7 21/7·52/7 : 31/7 About this sound play 2/7-comma meantone perfect fifth M
696.58
3:2÷(81:80)1/4 51/4 About this sound play Quarter-comma meantone perfect fifth M
697.65
3:2÷(81:80)1/5 31/5·51/5 : 21/5 About this sound play 1/5-comma meantone perfect fifth M
698.37
3:2÷(81:80)1/6 31/3·51/6 : 21/3 About this sound play 1/6-comma meantone perfect fifth M
700.00
G 27/12 27/12 About this sound play Equal-tempered perfect fifth 12 M
701.89
231/53 231/53 About this sound play 53-TET perfect fifth 53
701.96
G[2] 3 : 2 3 : 2 About this sound play Perfect fifth,[3][5][14] Pythagorean perfect fifth, Just perfect fifth or diapente,[4] fifth,[12] Just fifth[9] 3 S
702.44
224/41 224/41 About this sound play 41-TET perfect fifth 41
703.45
217/29 217/29 About this sound play 29-TET perfect fifth 29
719.90
97 : 64 97 : 26 About this sound play Ninety-seventh harmonic[5] 97
721.51
Adouble flat- 1024 : 675 210 : 33·52 About this sound play Narrow diminished sixth[3] 5
737.65
A77+ 49 : 32 7·7 : 25 About this sound play Forty-ninth harmonic[5] 7
743.01
Adouble flat 192 : 125 26·3 : 53 About this sound play Classic diminished sixth[3] 5
755.23
G 99 : 64 32·11 : 26 About this sound play Ninety-ninth harmonic[5] 11
764.92
A7[2] 14 : 9 2·7 : 32 About this sound play Septimal minor sixth[3][5] 7
772.63
G 25 : 16 52 : 24 About this sound play Just augmented fifth[5][14] 5
782.49
G-[2] 11 : 7 11 : 7 About this sound play Undecimal minor sixth,[5] undecimal augmented fifth,[3] pi 11
789.85
101 : 64 101 : 26 About this sound play Hundred-first harmonic[5] 101
792.18
A-[2] 128 : 81 27 : 34 About this sound play Pythagorean minor sixth[3][5][6] 3
800.00
G/A 28/12 22/3 About this sound play Equal-tempered minor sixth 3, 12 M
806.91
G17 51 : 32 3·17 : 25 About this sound play Fifty-first harmonic[5] 17
813.69
A[2] 8 : 5 23 : 5 About this sound play Just minor sixth[3][4][9][14] 5
815.64
G++ 6561 : 4096 38 : 212 About this sound play Pythagorean augmented fifth,[3][6] Pythagorean 'schismatic' sixth[5] 3
823.80
103 : 64 103 : 26 About this sound play Hundred-third harmonic[5] 103
833.09
51/2+1 : 2 About this sound play Golden ratio (833 cents scale)
833.11
233 : 144 233 : 24·32 About this sound play Golden ratio approximation (833 cents scale) 233
835.19
A+ 81 : 50 34 : 2·52 About this sound play Acute minor sixth[3] 5
840.53
A13[2] 13 : 8 13 : 23 About this sound play Tridecimal neutral sixth,[3] overtone sixth,[5] thirteenth harmonic 13
850.00
Gthree quarter sharp/Ahalf flat 217/24 217/24 About this sound play Equal-tempered neutral sixth 24
852.59
A↓[2] 18 : 11 2·32 : 11 About this sound play Undecimal neutral sixth,[3][5] Zalzal's neutral sixth 11
857.10
A7+ 105 : 64 3·5·7 : 26 About this sound play Hundred-fifth harmonic[5] 7
857.14
25/7 25/7 About this sound play 5 steps in 7 equal temperament 7
862.85
A- 400 : 243 24·52 : 35 About this sound play Grave major sixth[3] 5
873.51
53 : 32 53 : 25 About this sound play Fifty-third harmonic[5] 53
882.40
Bdouble flat--- 32768 : 19683 215 : 39 About this sound play Pythagorean diminished seventh[3][6] 3
884.36
A[2] 5 : 3 5 : 3 About this sound play Just major sixth,[3][4][5][9][14] Bohlen-Pierce sixth,[3] 1/3-comma meantone major sixth 5 M
889.76
107 : 64 107 : 26 About this sound play Hundred-seventh harmonic[5] 107
900.00
A 29/12 23/4 About this sound play Equal-tempered major sixth 4, 12 M
905.87
A+[2] 27 : 16 33 : 24 About this sound play Pythagorean major sixth[3][5][9][14] 3
921.82
109 : 64 109 : 26 About this sound play Hundred-ninth harmonic[5] 109
925.42
Bdouble flat-[2] 128 : 75 27 : 3·52 About this sound play Just diminished seventh,[14] diminished seventh[5][11] 5
933.13
A7 upside-down[2] 12 : 7 22·3 : 7 About this sound play Septimal major sixth[3][4][5] 7
937.63
A 55 : 32 5·11 : 25 About this sound play Fifty-fifth harmonic[5] 11
953.30
A37+ 111 : 64 3·37 : 26 About this sound play Hundred-eleventh harmonic[5] 37
955.03
A[2] 125 : 72 53 : 23·32 About this sound play Just augmented sixth[5] 5
957.21
(3 : 2)15/11 315/11 : 215/11 About this sound play 15 steps in Beta scale 18.75
960.00
24/5 24/5 About this sound play 4 steps in 5 equal temperament 5
968.83
B7[2] 7 : 4 7 : 22 About this sound play Septimal minor seventh,[4][5][9] harmonic seventh,[3][9] augmented sixth[citation needed] 7
976.54
A+[2] 225 : 128 32·52 : 27 About this sound play Just augmented sixth[14] 5
984.22
113 : 64 113 : 26 About this sound play Hundred-thirteenth harmonic[5] 113
996.09
B-[2] 16 : 9 24 : 32 About this sound play Pythagorean minor seventh,[3] Small just minor seventh,[4] lesser minor seventh,[14] just minor seventh,[9] Pythagorean small minor seventh[5] 3
999.47
B19 57 : 32 3·19 : 25 About this sound play Fifty-seventh harmonic[5] 19
1000.00
A/B 210/12 25/6 About this sound play Equal-tempered minor seventh 6, 12 M
1014.59
A23+ 115 : 64 5·23 : 26 About this sound play Hundred-fifteenth harmonic[5] 23
1017.60
B[2] 9 : 5 32 : 5 About this sound play Greater just minor seventh,[14] large just minor seventh,[4][5] Bohlen-Pierce seventh[3] 5
1019.55
A+++ 59049 : 32768 310 : 215 About this sound play Pythagorean augmented sixth[3][6] 3
1028.57
26/7 26/7 About this sound play 6 steps in 7 equal temperament 7
1029.58
B29 29 : 16 29 : 24 About this sound play Twenty-ninth harmonic,[5] minor seventh[citation needed] 29
1035.00
B↓[2] 20 : 11 22·5 : 11 About this sound play Lesser undecimal neutral seventh, large minor seventh[3] 11
1039.10
B+ 729 : 400 36 : 24·52 About this sound play Acute minor seventh[3] 5
1044.44
A13 117 : 64 32·13 : 26 About this sound play Hundred-seventeenth harmonic[5] 13
1049.36
B-[2] 11 : 6 11 : 2·3 About this sound play 21/4-tone or Undecimal neutral seventh,[3] undecimal 'median' seventh[5] 11
1050.00
Athree quarter sharp/Bhalf flat 221/24 27/8 About this sound play Equal-tempered neutral seventh 8, 24
1059.17
59 : 32 59 : 25 About this sound play Fifty-ninth harmonic[5] 59
1066.76
B- 50 : 27 2·52 : 33 About this sound play Grave major seventh[3] 5
1073.78
B717 119 : 64 7·17 : 26 About this sound play Hundred-nineteenth harmonic[5] 17
1086.31
C-- 4096 : 2187 212 : 37 About this sound play Pythagorean diminished octave[3][6] 3
1088.27
B[2] 15 : 8 3·5 : 23 About this sound play Just major seventh,[3][5][9][14] small just major seventh,[4] 1/6-comma meantone major seventh 5
1100.00
B 211/12 211/12 About this sound play Equal-tempered major seventh 12 M
1102.64
B- 121 : 64 112 : 26 About this sound play Hundred-twenty-first harmonic[5] 11
1107.82
C'- 256 : 135 28 : 33·5 About this sound play Octave − major chroma,[3] narrow diminished octave[citation needed] 5
1109.78
B+[2] 243 : 128 35 : 27 About this sound play Pythagorean major seventh[3][5][6][9] 3
1116.89
61 : 32 61 : 25 About this sound play Sixty-first harmonic[5] 61
1129.33
C'[2] 48 : 25 24·3 : 52 About this sound play Classic diminished octave,[3][6] large just major seventh[4] 5
1131.02
B41 123 : 64 3·41 : 26 About this sound play Hundred-twenty-third harmonic[5] 41
1137.04
B7 upside-down 27 : 14 33 : 2·7 About this sound play Septimal major seventh[5] 7
1145.04
B31 31 : 16 31 : 24 About this sound play Thirty-first harmonic,[5] augmented seventh[citation needed] 31
1151.23
C7 35 : 18 5·7 : 2·32 About this sound play Septimal supermajor seventh, septimal quarter tone inverted 7
1158.94
B[2] 125 : 64 53 : 26 About this sound play Just augmented seventh,[5] 125th harmonic 5
1172.74
C7+ 63 : 32 32·7 : 25 About this sound play Sixty-third harmonic[5] 7
1178.49
C'- 160 : 81 25·5 : 34 About this sound play Octave − syntonic comma,[3] semi-diminished octave[citation needed] 5
1186.42
127 : 64 127 : 26 About this sound play Hundred-twenty-seventh harmonic[5] 127
1200.00
C' 2 : 1 2 : 1 About this sound play Octave[3][9] or diapason[4] 1, 12 3 M S
1223.46
B+++ 531441 : 262144 312 : 218 About this sound play Pythagorean augmented seventh[3][6] 3
1525.86
21/2+1 About this sound play Silver ratio
1901.96
G' 3 : 1 3 : 1 About this sound play Tritave or just perfect twelfth 3
2400.00
C" 4 : 1 22 : 1 About this sound play Fifteenth or two octaves 1, 12 3 M
3986.31
E''' 10 : 1 5·2 : 1 About this sound play Decade, compound just major third 5 M

See also[edit]

Notes[edit]

  1. ^ a b c d Maneri-Sims notation

References[edit]

  1. ^ a b Fox, Christopher (2003). "Microtones and Microtonalities", Contemporary Music Review, v. 22, pt. 1-2. (Abingdon, Oxfordshire, UK: Routledge): p.13.
  2. ^ a b c d e f g h i j k l m n o p q r s t u v w x y z aa ab ac ad ae af ag ah ai aj ak al am an ao ap aq ar as at au av aw ax ay az ba bb bc bd be bf bg bh bi Fonville, John. 1991. "Ben Johnston's Extended Just Intonation: A Guide for Interpreters". Perspectives of New Music 29, no. 2 (Summer): 106–37.
  3. ^ a b c d e f g h i j k l m n o p q r s t u v w x y z aa ab ac ad ae af ag ah ai aj ak al am an ao ap aq ar as at au av aw ax ay az ba bb bc bd be bf bg bh bi bj bk bl bm bn bo bp bq br bs bt bu bv bw bx by bz ca cb cc cd ce cf cg ch ci cj ck cl cm cn co cp cq cr cs ct cu cv cw cx cy cz da db dc dd "List of intervals", Huygens-Fokker Foundation. The Foundation uses "classic" to indicate "just" or leaves off any adjective, as in "major sixth".
  4. ^ a b c d e f g h i j k l m n o p q r s t u v w x Partch, Harry (1979). Genesis of a Music, p.68-69. ISBN 978-0-306-80106-8.
  5. ^ a b c d e f g h i j k l m n o p q r s t u v w x y z aa ab ac ad ae af ag ah ai aj ak al am an ao ap aq ar as at au av aw ax ay az ba bb bc bd be bf bg bh bi bj bk bl bm bn bo bp bq br bs bt bu bv bw bx by bz ca cb cc cd ce cf cg ch ci cj ck cl cm cn co cp cq cr cs ct cu cv cw cx cy cz da db dc dd de df dg dh di dj dk dl dm "Anatomy of an Octave", KyleGann.com. Gann leaves off "just" but includes "5-limit".
  6. ^ a b c d e f g h i j k l m n o p q r s t u v w x y z aa ab ac ad ae af ag ah ai aj ak al Haluška, Ján (2003). The Mathematical Theory of Tone Systems, p.xxv-xxix. ISBN 978-0-8247-4714-5.
  7. ^ "Orwell Temperaments", Xenharmony.org.
  8. ^ a b Partch (1979), p.70.
  9. ^ a b c d e f g h i j k l m n o p q r s t u v w x y z aa Alexander John Ellis (1885). On the musical scales of various nations, p.488. s.n.
  10. ^ William Smythe Babcock Mathews (1895). Pronouncing dictionary and condensed encyclopedia of musical terms, p.13. ISBN 1-112-44188-3.
  11. ^ a b c d e f Anger, Joseph Humfrey (1912). A treatise on harmony, with exercises, Volume 3, p.xiv-xv. W. Tyrrell.
  12. ^ a b c d e f g h i j k l m 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.
  13. ^ A. R. Meuss (2004). Intervals, Scales, Tones and the Concert Pitch C. Temple Lodge Publishing. p. 15. ISBN 1902636465. 
  14. ^ a b c d e f g h i j k l m n o p q r s t u v w x y 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".
  15. ^ a b "13th-harmonic", 31et.com.
  16. ^ Sabat, Marc and von Schweinitz, Wolfgang (2004). "The Extended Helmholtz-Ellis JI Pitch Notation" [PDF], NewMusicBox.org. Accessed: 04:12, 15 March 2014 (UTC).

External links[edit]