List of pitch intervals

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File:Meantone comparison.png
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.
File:Music intervals frequency ratio equal tempered pythagorean comparison.svg
Comparison of two sets of musical intervals. The equal-tempered intervals are black; the Pythagorean intervals are green.

Below is a list of intervals expressible in terms of a prime limit (see Terminology), completed by a choice of intervals in various equal subdivisions of the octave or of other intervals. For commonly encountered harmonic or melodic intervals between pairs of notes in contemporary Western music theory, without consideration of the way in which they are tuned, see Interval (music) § Main intervals.

Terminology

  • 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

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 Audio file "Unison on C.mid" not found Unison,[3] monophony,[4] perfect prime,[3] tonic,[5] or fundamental 1, 12 3 M
0.03
65537 : 65536 65537 : 216 Audio file "Jot on C.mid" not found Sixty-five-thousand-five-hundred-thirty-seventh harmonic 65537 S
0.40
 C7♯− 4375 : 4374 54×7 : 2×37 Audio file "Ragisma on C.mid" not found Ragisma[3][6] 7 S
0.72
 E7777triple flat+ 2401 : 2400 74 : 25×3×52 Audio file "Breedsma on C.mid" not found Breedsma[3][6] 7 S
1.00
21/1200 21/1200 Audio file "Cent on C.mid" not found Cent[7] 1200
1.20
21/1000 21/1000 Audio file "Millioctave on C.mid" not found Millioctave 1000
1.95
B♯++ 32805 : 32768 38×5 : 215 Audio file "Schisma on C.mid" not found Schisma[3][5] 5
1.96
3:2÷(27/12) 3 : 219/12 Grad, Werckmeister[8]
3.99
101/1000 21/1000×51/1000 Audio file "Savart on C.mid" not found Savart or eptaméride 301.03
7.71
B7 upside-down♯ 225 : 224 32×52 : 25×7 Audio file "Septimal kleisma on C.mid" not found Septimal kleisma,[3][6] marvel comma 7 S
8.11
Bdouble sharp− 15625 : 15552 56 : 26×35 Audio file "Kleisma on C.mid" not found Kleisma or semicomma majeur[3][6] 5
10.06
Adouble sharpdouble sharp++ 2109375 : 2097152 33×57 : 221 Audio file "Semicomma on C.mid" not found Semicomma,[3][6] Fokker's comma[3] 5
10.85
C43U 160 : 159 25×5 : 3×53 Audio file "Johnston U53 on C.mid" not found Difference between 5:3 & 53:32 53 S
11.98
 C29 145 : 144 5×29 : 24×32 Audio file "Johnston 29 on C.mid" not found Difference between 29:16 & 9:5 29 S
12.50
21/96 21/96 Audio file "Sixteenth-tone on C.mid" not found Sixteenth tone 96
13.07
 B7 upside-down7 upside-down7 upside-down− 1728 : 1715 26×33 : 5×73 Audio file "Orwell comma on C.mid" not found Orwell comma[3][9] 7
13.47
 C43 129 : 128 3×43 : 27 Audio file "129th harmonic on C.mid" not found Hundred-twenty-ninth harmonic 43 S
13.79
Ddouble flat7 126 : 125 2×32×7 : 53 Audio file "Septimal semicomma on C.mid" not found Small septimal semicomma,[6] small septimal comma,[3] starling comma 7 S
14.37
C♭↑↑− 121 : 120 112 : 23×3×5 Audio file "Undecimal neutral second comma on C.mid" not found Undecimal seconds comma[3] 11 S
16.67
C↑[lower-alpha 1] 21/72 21/72 Audio file "1 step in 72-et on C.mid" not found 1 step in 72 equal temperament 72
18.13
C19U 96 : 95 25×3 : 5×19 Audio file "Johnston U19 on C.mid" not found Difference between 19:16 & 6:5 19 S
19.55
Ddouble flat--[2] 2048 : 2025 211 : 34×52 Audio file "Diaschisma on C.mid" not found Diaschisma,[3][6] minor comma 5
21.51
C+[2] 81 : 80 34 : 24×5 Audio file "Syntonic comma on C.mid" not found 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 Audio file "Holdrian comma on C.mid" not found Holdrian comma, Holder's comma, 1 step in 53 equal temperament 53
23.46
B♯+++ 531441 : 524288 312 : 219 Audio file "Pythagorean comma on C.mid" not found Pythagorean comma,[3][5][6][10][11] ditonic comma[3][6] 3
25.00
21/48 21/48 Audio file "Eighth-tone on C.mid" not found Eighth tone 48
26.84
C13 65 : 64 5×13 : 26 Audio file "Sixty-fifth harmonic on C.mid" not found Sixty-fifth harmonic,[5] 13th-partial chroma[3] 13 S
27.26
C7 upside-down− 64 : 63 26 : 32×7 Audio file "Septimal comma on C.mid" not found Septimal comma,[3][6][11] Archytas' comma,[3] 63rd subharmonic 7 S
29.27
 21/41 21/41 Audio file "1 step in 41-et on C.mid" not found 1 step in 41 equal temperament 41
31.19
D7♭↓ 56 : 55 23×7 : 5×11 Audio file "Ptolemy's enharmonic on C.mid" not found Undecimal diesis,[3] Ptolemy's enharmonic:[5] difference between (11 : 8) and (7 : 5) tritone 11 S
33.33
 CFile:Half up arrow.png/D♭File:Half down arrow.pngFile:Half down arrow.png[lower-alpha 1] 21/36 21/36 Audio file "Sixth-tone on C.mid" not found Sixth tone 36, 72
34.28
C17 51 : 50 3×17 : 2×52 Audio file "Johnston 17 on C.mid" not found Difference between 17:16 & 25:24 17 S
34.98
B7 upside-down7 upside-down♯- 50 : 49 2×52 : 72 Audio file "Septimal sixth-tone on C.mid" not found Septimal sixth tone or jubilisma, Erlich's decatonic comma or tritonic diesis[3][6] 7 S
35.70
D77♭ 49 : 48 72 : 24×3 Audio file "Septimal diesis on C.mid" not found Septimal diesis, slendro diesis or septimal 1/6-tone[3] 7 S
38.05
C23 46 : 45 2×23 : 32×5 Audio file "Johnston 23 on C.mid" not found Inferior quarter tone,[5] difference between 23:16 & 45:32 23 S
38.71
21/31 21/31 Audio file "1 step in 31-et on C.mid" not found 1 step in 31 equal temperament or Normal Diesis 31
38.91
C↓♯+ 45 : 44 32×5 : 4×11 Audio file "Undecimal diesis on C.mid" not found Undecimal diesis or undecimal fifth tone 11 S
40.00
21/30 21/30 Audio file "Fifth-tone on C.mid" not found Fifth tone 30
41.06
Ddouble flat− 128 : 125 27 : 53 Audio file "5-limit limma on C.mid" not found Enharmonic diesis or 5-limit limma, minor diesis,[6] diminished second,[5][6] minor diesis or diesis,[3] 125th subharmonic 5
41.72
D41U7♭ 42 : 41 2×3×7 : 41 Audio file "Lesser 41-limit fifth tone on C.mid" not found Lesser 41-limit fifth tone 41 S
42.75
C41 41 : 40 41 : 23×5 Audio file "Greater 41-limit fifth tone on C.mid" not found Greater 41-limit fifth tone 41 S
43.83
C13 upside down♯ 40 : 39 23×5 : 3×13 Audio file "Tridecimal fifth tone on C.mid" not found Tridecimal fifth tone 13 S
44.97
C19U13 39 : 38 3×13 : 2×19 Audio file "Novendecimal fifth tone on C.mid" not found Superior quarter-tone,[5] novendecimal fifth tone 19 S
46.17
D37U19double flat- 38 : 37 2×19 : 37 Audio file "Lesser 37-limit quarter tone on C.mid" not found Lesser 37-limit quarter tone 37 S
47.43
C37♯ 37 : 36 37 : 22×32 Audio file "Greater 37-limit quarter tone on C.mid" not found Greater 37-limit quarter tone 37 S
48.77
C7 upside-down 36 : 35 22×32 : 5×7 Audio file "Septimal quarter tone on C.mid" not found Septimal quarter tone, septimal diesis,[3][6] septimal chroma,[2] superior quarter tone[5] 7 S
49.98
246 : 239 3×41 : 239 Audio file "Just quarter tone on C.mid" not found Just quarter tone[11] 239
50.00
Chalf sharp/Dthree quarter flat 21/24 21/24 Audio file "Quarter tone on C.mid" not found Equal-tempered quarter tone 24
50.18
D17 upside down7♭ 35 : 34 5×7 : 2×17 Audio file "Lesser septendecimal quarter tone on C.mid" not found ET quarter-tone approximation,[5] lesser 17-limit quarter tone 17 S
50.72
B7 upside-down♯++ 59049 : 57344 310 : 213×7 Audio file "Harrison's comma on C.mid" not found Harrison's comma (10 P5s – 1 H7)[3] 7
51.68
C17↓♯ 34 : 33 2×17 : 3×11 Audio file "Greater septendecimal quarter tone on C.mid" not found Greater 17-limit quarter tone 17 S
53.27
C↑ 33 : 32 3×11 : 25 Audio file "Thirty-third harmonic on C.mid" not found Thirty-third harmonic,[5] undecimal comma, undecimal quarter tone 11 S
54.96
D31U♭- 32 : 31 25 : 31 Audio file "Thirty-first subharmonic on C.mid" not found Inferior quarter-tone,[5] thirty-first subharmonic 31 S
56.55
B2323♯+ 529 : 512 232 : 29 Audio file "Five-hundred-twenty-ninth harmonic on C.mid" not found Five-hundred-twenty-ninth harmonic 23
56.77
C31 31 : 30 31 : 2×3×5 Audio file "Johnston 31 on C.mid" not found Greater quarter-tone,[5] difference between 31:16 & 15:8 31 S
58.69
C29U♯ 30 : 29 2×3×5 : 29 Audio file "Lesser 29-limit quarter tone on C.mid" not found Lesser 29-limit quarter tone 29 S
60.75
C297 upside-down 29 : 28 29 : 22×7 Audio file "Greater 29-limit quarter tone on C.mid" not found Greater 29-limit quarter tone 29 S
62.96
D7♭- 28 : 27 22×7 : 33 Audio file "Septimal minor second on C.mid" not found Septimal minor second, small minor second, inferior quarter tone[5] 7 S
63.81
(3 : 2)1/11 31/11 : 21/11 Audio file "Beta scale step on C.mid" not found Beta scale step 18.75
65.34
C13 upside down♯+ 27 : 26 33 : 2×13 Audio file "Chromatic diesis on C.mid" not found Chromatic diesis,[12] tridecimal comma[3] 13 S
66.34
D197♭ 133 : 128 7×19 : 27 Audio file "Hundred-thirty-third harmonic on C.mid" not found One-hundred-thirty-third harmonic 19
66.67
CFile:Sims flagged arrow down.svg↑/C♯File:Half down arrow.png[lower-alpha 1] 21/18 21/18 Audio file "Third-tone on C.mid" not found Third tone 18, 36, 72
67.90
D13double flat- 26 : 25 2×13 : 52 Audio file "Tridecimal third tone on C.mid" not found Tridecimal third tone, third tone[5] 13 S
70.67
C♯[2] 25 : 24 52 : 23×3 Audio file "Just chromatic semitone on C.mid" not found 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
D23U♭- 24 : 23 23×3 : 23 Audio file "Lesser 23-limit semitone on C.mid" not found Lesser 23-limit semitone 23 S
75.00
21/16 23/48 Audio file "1 step in 16-et on C.mid" not found 1 step in 16 equal temperament, 3 steps in 48 16, 48
76.96
C23↓♯+ 23 : 22 23 : 2×11 Audio file "Greater 23-limit semitone on C.mid" not found Greater 23-limit semitone 23 S
78.00
(3 : 2)1/9 31/9 : 21/9 Audio file "Alpha scale step on C.mid" not found Alpha scale step 15.39
79.31
67 : 64 67 : 26 Audio file "Sixty-seventh harmonic on C.mid" not found Sixty-seventh harmonic[5] 67
80.54
C↑7 upside-down- 22 : 21 2×11 : 3×7 Audio file "Undecimal two-fifth tone on C.mid" not found Hard semitone,[5] two-fifth tone small semitone 11 S
84.47
D7♭ 21 : 20 3×7 : 22×5 Audio file "Septimal chromatic semitone on C.mid" not found Septimal chromatic semitone, minor semitone[3] 7 S
88.80
C19U♯ 20 : 19 22×5 : 19 Audio file "Novendecimal augmented unison on C.mid" not found Novendecimal augmented unison 19 S
90.22
D♭−−[2] 256 : 243 28 : 35 Audio file "Pythagorean minor semitone on C.mid" not found Pythagorean minor second or limma,[3][6][11] Pythagorean diatonic semitone, Low Semitone[14] 3
92.18
C♯+[2] 135 : 128 33×5 : 27 Audio file "Greater chromatic semitone on C.mid" not found 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
D19♭- 19 : 18 19 : 2×9 Novendecimal minor secondAudio file "Novendecimal minor second on C.mid" not found 19 S
97.36
D↓↓ 128 : 121 27 : 112 Audio file "121st subharmonic on C.mid" not found 121st subharmonic,[5][6] undecimal minor second 11
98.95
D17 upside down♭ 18 : 17 2×32 : 17 Audio file "Just minor semitone on C.mid" not found Just minor semitone, Arabic lute index finger[3] 17 S
100.00
C♯/D♭ 21/12 21/12 Audio file "Minor second on C.mid" not found Equal-tempered minor second or semitone 12 M
104.96
C17♯[2] 17 : 16 17 : 24 Audio file "Just major semitone on C.mid" not found 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 Audio file "Studie II interval on C.mid" not found Studie II interval (compound just major third, 5:1, divided into 25 equal parts) 25
111.73
D♭-[2] 16 : 15 24 : 3×5 Audio file "Just diatonic semitone on C.mid" not found 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 Audio file "Pythagorean apotome on C.mid" not found 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 Audio file "Secor on C.mid" not found Secor 10.28
119.44
C7 upside-down♯ 15 : 14 3×5 : 2×7 Audio file "Septimal diatonic semitone on C.mid" not found Septimal diatonic semitone, major diatonic semitone,[3] Cowell semitone[5] 7 S
125.00
25/48 25/48 Audio file "5 steps in 48-et on C.mid" not found 5 steps in 48 equal temperament 48
128.30
D13 upside down7 14 : 13 2×7 : 13 Audio file "Lesser tridecimal two-third tone on C.mid" not found Lesser tridecimal 2/3-tone[17] 13 S
130.23
C23♯+ 69 : 64 3×23 : 26 Audio file "Sixty-ninth harmonic on C.mid" not found Sixty-ninth harmonic[5] 23
133.24
D♭ 27 : 25 33 : 52 Audio file "Semitone Maximus on C.mid" not found 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♯File:Half up arrow.png/D♭File:Half up arrow.png[lower-alpha 1] 21/9 22/18 Audio file "Two-third tone on C.mid" not found Two-third tone 9, 18, 36, 72
138.57
D13♭- 13 : 12 13 : 22×3 Audio file "Greater tridecimal two-third tone on C.mid" not found Greater tridecimal 2/3-tone,[17] Three-quarter tone[5] 13 S
150.00
Cthree quarter sharp/Dhalf flat 23/24 21/8 Audio file "Neutral second on C.mid" not found Equal-tempered neutral second 8, 24
150.64
D↓[2] 12 : 11 22×3 : 11 Audio file "Lesser undecimal neutral second on C.mid" not found 3⁄4 tone or Undecimal neutral second,[3][5] trumpet three-quarter tone,[11] middle finger [between frets][14] 11 S
155.14
D7 35 : 32 5×7 : 25 Audio file "Thirty-fifth harmonic on C.mid" not found Thirty-fifth harmonic[5] 7
160.90
D−− 800 : 729 25×52 : 36 Audio file "Grave whole tone on C.mid" not found Grave whole tone,[3] neutral second, grave major second[citation needed] 5
165.00
D↑♭−[2] 11 : 10 11 : 2×5 Audio file "Greater undecimal neutral second on C.mid" not found Greater undecimal minor/major/neutral second, 4/5-tone[6] or Ptolemy's second[3] 11 S
171.43
21/7 21/7 Audio file "1 step in 7-et on C.mid" not found 1 step in 7 equal temperament 7
175.00
27/48 27/48 Audio file "7 steps in 48-et on C.mid" not found 7 steps in 48 equal temperament 48
179.70
71 : 64 71 : 26 Audio file "Seventy-first harmonic on C.mid" not found Seventy-first harmonic[5] 71
180.45
Edouble flat−−− 65536 : 59049 216 : 310 Audio file "Pythagorean diminished third.mid" not found Pythagorean diminished third,[3][6] Pythagorean minor tone 3
182.40
D−[2] 10 : 9 2×5 : 32 Audio file "Minor tone on C.mid" not found 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 Audio file "Major second on C.mid" not found Equal-tempered major second 6, 12 M
203.91
D[2] 9 : 8 32 : 23 Audio file "Major tone on C.mid" not found 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
D29 145 : 128 5×29 : 27 Audio file "Hundred-forty-fifth harmonic on C.mid" not found Hundred-forty-fifth harmonic 29
223.46
Edouble flat−[2] 256 : 225 28 : 32×52 Audio file "Just diminished third on C.mid" not found Just diminished third,[16] 225th subharmonic 5
225.00
23/16 29/48 Audio file "3 steps in 16-et on C.mid" not found 9 steps in 48 equal temperament 16, 48
227.79
73 : 64 73 : 26 Audio file "Seventy-third harmonic on C.mid" not found Seventy-third harmonic[5] 73
231.17
D7 upside-down−[2] 8 : 7 23 : 7 Audio file "Septimal major second on C.mid" not found Septimal major second,[4] septimal whole tone[3][5] 7 S
240.00
21/5 21/5 Audio file "1 step in 5-et on C.mid" not found 1 step in 5 equal temperament 5
247.74
D13 upside down♯ 15 : 13 3×5 : 13 Audio file "Tridecimal five-quarter tone on C.mid" not found Tridecimal 5⁄4 tone[3] 13
250.00
Dhalf sharp/Ethree quarter flat 25/24 25/24 Audio file "Five quarter tones on C.mid" not found 5 steps in 24 equal temperament 24
251.34
D37♯ 37 : 32 37 : 25 Audio file "Thirty-seventh harmonic on C.mid" not found Thirty-seventh harmonic[5] 37
253.08
D♯− 125 : 108 53 : 22×33 Audio file "Semi-augmented whole tone on C.mid" not found Semi-augmented whole tone,[3] semi-augmented second[citation needed] 5
262.37
E↓♭ 64 : 55 26 : 5×11 Audio file "55th subharmonic on C.mid" not found 55th subharmonic[5][6] 11
266.87
E7♭[2] 7 : 6 7 : 2×3 Audio file "Septimal minor third on C.mid" not found Septimal minor third[3][4][11] or Sub minor third[14] 7 S
268.80
D2313 299 : 256 13×23 : 28 Audio file "Two-hundred-ninety-ninth harmonic on C.mid" not found Two-hundred-ninety-ninth harmonic 23
274.58
D♯[2] 75 : 64 3×52 : 26 Audio file "Just augmented second on C.mid" not found Just augmented second,[16] Augmented tone,[14] augmented second[5][13] 5
275.00
211/48 211/48 Audio file "11 steps in 48-et on C.mid" not found 11 steps in 48 equal temperament 48
289.21
E13↓♭ 13 : 11 13 : 11 Audio file "Tridecimal minor third on C.mid" not found Tridecimal minor third[3] 13
294.13
E♭−[2] 32 : 27 25 : 33 Audio file "Pythagorean minor third on C.mid" not found Pythagorean minor third[3][5][6][14][16] semiditone, or 27th subharmonic 3
297.51
E19♭[2] 19 : 16 19 : 24 Audio file "19th harmonic on C.mid" not found 19th harmonic,[3] 19-limit minor third, overtone minor third[5] 19
300.00
D♯/E♭ 23/12 21/4 Audio file "Minor third on C.mid" not found Equal-tempered minor third 4, 12 M
301.85
D7 upside-down♯- 25 : 21[5] 52 : 3×7 Audio file "Second septimal minor third on C.mid" not found 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 Audio file "Quarter-comma meantone minor third on C.mid" not found Quarter-comma meantone minor third M
311.98
(3 : 2)4/9 34/9 : 24/9 Audio file "Alpha scale minor third on C.mid" not found Alpha scale minor third 3.85
315.64
E♭[2] 6 : 5 2×3 : 5 Audio file "Just minor third on C.mid" not found 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 Audio file "Pythagorean augmented second on C.mid" not found Pythagorean augmented second[3][6] 3
320.14
E7♭↑ 77 : 64 7×11 : 26 Audio file "Seventy-seventh harmonic on C.mid" not found Seventy-seventh harmonic[5] 11
325.00
213/48 213/48 Audio file "13 steps in 48-et on C.mid" not found 13 steps in 48 equal temperament 48
336.13
D177 upside-down♯- 17 : 14 17 : 2×7 Audio file "Superminor third on C.mid" not found Superminor third[18] 17
337.15
E♭+ 243 : 200 35 : 23×52 Audio file "Acute minor third on C.mid" not found Acute minor third[3] 5
342.48
E13♭ 39 : 32 3×13 : 25 Audio file "Thirty-ninth harmonic on C.mid" not found Thirty-ninth harmonic[5] 13
342.86
22/7 22/7 Audio file "2 steps in 7-et on C.mid" not found 2 steps in 7 equal temperament 7
342.91
E7 upside-down♭- 128 : 105 27 : 3×5×7 Audio file "105th subharmonic on C.mid" not found 105th subharmonic,[5] septimal neutral third[6] 7
347.41
E↑♭−[2] 11 : 9 11 : 32 Audio file "Undecimal neutral third on C.mid" not found Undecimal neutral third[3][5] 11
350.00
Dthree quarter sharp/Ehalf flat 27/24 27/24 Audio file "Neutral third on C.mid" not found Equal-tempered neutral third 24
354.55
E↓+ 27 : 22 33 : 2×11 Audio file "Zalzal's wosta on C.mid" not found Zalzal's wosta[6] 12:11 X 9:8[14] 11
359.47
E13 upside down[2] 16 : 13 24 : 13 Audio file "Tridecimal neutral third on C.mid" not found Tridecimal neutral third[3] 13
364.54
79 : 64 79 : 26 Audio file "Seventy-ninth harmonic on C.mid" not found Seventy-ninth harmonic[5] 79
364.81
E− 100 : 81 22×52 : 34 Audio file "Grave major third on C.mid" not found Grave major third[3] 5
375.00
25/16 215/48 Audio file "5 steps in 16-et on C.mid" not found 15 steps in 48 equal temperament 16, 48
384.36
F♭−− 8192 : 6561 213 : 38 Audio file "Pythagorean diminished fourth on C.mid" not found Pythagorean diminished fourth,[3][6] Pythagorean 'schismatic' third[5] 3
386.31
E[2] 5 : 4 5 : 22 Audio file "Just major third on C.mid" not found Just major third,[3][4][5][11][16] major third,[14] quarter-comma meantone major third 5 M S
397.10
E237+ 161 : 128 7×23 : 27 Audio file "One-hundred-sixty-first harmonic on C.mid" not found One-hundred-sixty-first harmonic 23
400.00
E 24/12 21/3 Audio file "Major third on C.mid" not found Equal-tempered major third 3, 12 M
402.47
E1917 323 : 256 17×19 : 28 Audio file "323rd harmonic on C.mid" not found Three-hundred-twenty-third harmonic 19
407.82
E+[2] 81 : 64 34 : 26 Audio file "Pythagorean major third on C.mid" not found Pythagorean major third,[3][5][6][14][16] ditone 3
417.51
F7↓+[2] 14 : 11 2×7 : 11 Audio file "Undecimal major third on C.mid" not found Undecimal diminished fourth or major third[3] 11
425.00
217/48 217/48 Audio file "17 steps in 48-et on C.mid" not found 17 steps in 48 equal temperament 48
427.37
F♭[2] 32 : 25 25 : 52 Audio file "Just diminished fourth on C.mid" not found Just diminished fourth,[16] diminished fourth,[5][13] 25th subharmonic 5
429.06
E41 41 : 32 41 : 25 Audio file "Forty-first harmonic on C.mid" not found Forty-first harmonic[5] 41
435.08
E7 upside-down[2] 9 : 7 32 : 7 Audio file "Septimal major third on C.mid" not found Septimal major third,[3][5] Bohlen-Pierce third,[3] Super major Third[14] 7
444.77
F↓ 128 : 99 27 : 9×11 Audio file "99th subharmonic on C.mid" not found 99th subharmonic[5][6] 11
450.00
Ehalf sharp/Fhalf flat 29/24 29/24 Audio file "Nine quarter tones on C.mid" not found 9 steps in 24 equal temperament 24
450.05
83 : 64 83 : 26 Audio file "Eighty-third harmonic on C.mid" not found Eighty-third harmonic[5] 83
454.21
F♭13 13 : 10 13 : 2×5 Audio file "Tridecimal major third on C.mid" not found Tridecimal major third or diminished fourth 13
456.99
E♯[2] 125 : 96 53 : 25×3 Audio file "Just augmented third on C.mid" not found Just augmented third, augmented third[5] 5
462.35
E7 upside-down7 upside-down- 64 : 49 26 : 72 Audio file "49th subharmonic on C.mid" not found 49th subharmonic[5][6] 7
470.78
F7+[2] 21 : 16 3×7 : 24 Audio file "Twenty-first harmonic on C.mid" not found Twenty-first harmonic, narrow fourth,[3] septimal fourth,[5] wide augmented third,[citation needed] H7 on G 7
475.00
219/48 219/48 Audio file "19 steps in 48-et on C.mid" not found 19 steps in 48 equal temperament 48
478.49
E♯+ 675 : 512 33×52 : 29 Audio file "Wide augmented third on C.mid" not found Six-hundred-seventy-fifth harmonic, wide augmented third[3] 5
480.00
22/5 22/5 Audio file "2 steps in 5-et on C.mid" not found 2 steps in 5 equal temperament 5
491.27
E17♯ 85 : 64 5×17 : 26 Audio file "Eighty-fifth harmonic on C.mid" not found Eighty-fifth harmonic[5] 17
498.04
F[2] 4 : 3 22 : 3 Audio file "Just perfect fourth on C.mid" not found Perfect fourth,[3][5][16] Pythagorean perfect fourth, Just perfect fourth or diatessaron[4] 3 S
500.00
F 25/12 25/12 Audio file "Perfect fourth on C.mid" not found Equal-tempered perfect fourth 12 M
501.42
F19+ 171 : 128 32×19 : 27 Audio file "Hundred-seventy-first harmonic on C.mid" not found One-hundred-seventy-first harmonic 19
510.51
(3 : 2)8/11 38/11 : 28/11 Audio file "Beta scale perfect fourth on C.mid" not found Beta scale perfect fourth 18.75
511.52
F43 43 : 32 43 : 25 Audio file "Forty-third harmonic on C.mid" not found Forty-third harmonic[5] 43
514.29
23/7 23/7 Audio file "3 steps in 7-et on C.mid" not found 3 steps in 7 equal temperament 7
519.55
F+[2] 27 : 20 33 : 22×5 Audio file "Wolf fourth on C.mid" not found 5-limit wolf fourth, acute fourth,[3] imperfect fourth[16] 5
521.51
E♯+++ 177147 : 131072 311 : 217 Audio file "Pythagorean augmented third on C.mid" not found Pythagorean augmented third[3][6] (F+ (pitch)) 3
525.00
27/16 221/48 Audio file "7 steps in 16-et on C.mid" not found 21 steps in 48 equal temperament 16, 48
531.53
F29+ 87 : 64 3×29 : 26 Audio file "Eighty-seventh harmonic on C.mid" not found Eighty-seventh harmonic[5] 29
536.95
F↓♯+ 15 : 11 3×5 : 11 Audio file "Undecimal augmented fourth on C.mid" not found Undecimal augmented fourth[3] 11
550.00
Fhalf sharp/Gthree quarter flat 211/24 211/24 Audio file "Eleven quarter tones on C.mid" not found 11 steps in 24 equal temperament 24
551.32
F↑[2] 11 : 8 11 : 23 Audio file "Eleventh harmonic on C.mid" not found eleventh harmonic,[5] undecimal tritone,[5] lesser undecimal tritone, undecimal semi-augmented fourth[3] 11
563.38
F13 upside down♯+ 18 : 13 2×9 : 13 Audio file "Tridecimal narrow tritone on C.mid" not found Tridecimal augmented fourth[3] 13
568.72
F♯[2] 25 : 18 52 : 2×32 Audio file "Classic augmented fourth on C.mid" not found Just augmented fourth[3][5] 5
570.88
89 : 64 89 : 26 Audio file "Eighty-ninth harmonic on C.mid" not found Eighty-ninth harmonic[5] 89
575.00
223/48 223/48 Audio file "23 steps in 48-et on C.mid" not found 23 steps in 48 equal temperament 48
582.51
G7♭[2] 7 : 5 7 : 5 Audio file "Lesser septimal tritone on C.mid" not found 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 Audio file "Diminished fifth tritone on C.mid" not found Pythagorean diminished fifth,[3][6] low Pythagorean tritone[5] 3
590.22
F♯+[2] 45 : 32 32×5 : 25 Audio file "Just augmented fourth on C.mid" not found 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
G1919♭ 361 : 256 192 : 28 Audio file "Three-hundred-sixty-first harmonic on C.mid" not found Three-hundred-sixty-first harmonic 19
600.00
F♯/G♭ 26/12 21/2=√2 Audio file "Tritone on C.mid" not found Equal-tempered tritone 2, 12 M
609.35
G137♭ 91 : 64 7×13 : 26 Audio file "Ninety-first harmonic on C.mid" not found Ninety-first harmonic[5] 13
609.78
G♭−[2] 64 : 45 26 : 32×5 Audio file "Just tritone on C.mid" not found 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 Audio file "Pythagorean augmented fourth on C.mid" not found Pythagorean tritone,[3][6] Pythagorean augmented fourth, high Pythagorean tritone[5] 3
617.49
F♯7 upside-down[2] 10 : 7 2×5 : 7 Audio file "Greater septimal tritone on C.mid" not found Greater septimal tritone, septimal tritone,[4][5] Euler's tritone[3] 7
625.00
225/48 225/48 Audio file "25 steps in 48-et on C.mid" not found 25 steps in 48 equal temperament 48
628.27
F23♯+ 23 : 16 23 : 24 Audio file "Twenty-third harmonic on C.mid" not found Twenty-third harmonic,[5] classic diminished fifth[citation needed] 23
631.28
G♭[2] 36 : 25 22×32 : 52 Audio file "Just diminished fifth on C.mid" not found Just diminished fifth[5] 5
646.99
F31♯+ 93 : 64 3×31 : 26 Audio file "Ninety-third harmonic on C.mid" not found Ninety-third harmonic[5] 31
648.68
G↓[2] 16 : 11 24 : 11 Audio file "Eleventh harmonic inverse on C.mid" not found ` undecimal semi-diminished fifth[3] 11
650.00
Fthree quarter sharp/Ghalf flat 213/24 213/24 Audio file "Thirteen quarter tones on C.mid" not found 13 steps in 24 equal temperament 24
665.51
G43U 47 : 32 47 : 25 Audio file "Forty-seventh harmonic on C.mid" not found Forty-seventh harmonic[5] 47
675.00
29/16 227/48 Audio file "9 steps in 16-et on C.mid" not found 27 steps in 48 equal temperament 16, 48
678.49
Adouble flat−−− 262144 : 177147 218 : 311 Audio file "Pythagorean diminished sixth on C.mid" not found Pythagorean diminished sixth[3][6] 3
680.45
G− 40 : 27 23×5 : 33 Audio file "Wolf fifth on C.mid" not found 5-limit wolf fifth,[5] or diminished sixth, grave fifth,[3][6][11] imperfect fifth,[16] 5
683.83
G19 95 : 64 5×19 : 26 Audio file "Ninety-fifth harmonic on C.mid" not found Ninety-fifth harmonic[5] 19
684.82
E232323double sharp++ 12167 : 8192 233 : 213 Audio file "12167th harmonic on C.mid" not found 12167th harmonic 23
685.71
24/7 : 1 Audio file "4 steps in 7-et on C.mid" not found 4 steps in 7 equal temperament
691.20
3:2÷(81:80)1/2 2×51/2 : 3 Audio file "Half-comma meantone perfect fifth on C.mid" not found Half-comma meantone perfect fifth M
694.79
3:2÷(81:80)1/3 21/3×51/3 : 31/3 Audio file "Third-comma meantone perfect fifth on C.mid" not found 1⁄3-comma meantone perfect fifth M
695.81
3:2÷(81:80)2/7 21/7×52/7 : 31/7 Audio file "Two seventh-comma meantone perfect fifth on C.mid" not found 2⁄7-comma meantone perfect fifth M
696.58
3:2÷(81:80)1/4 51/4 Audio file "Quarter-comma meantone perfect fifth on C.mid" not found Quarter-comma meantone perfect fifth M
697.65
3:2÷(81:80)1/5 31/5×51/5 : 21/5 Audio file "Fifth-comma meantone perfect fifth on C.mid" not found 1⁄5-comma meantone perfect fifth M
698.37
3:2÷(81:80)1/6 31/3×51/6 : 21/3 Audio file "Sixth-comma meantone perfect fifth on C.mid" not found 1⁄6-comma meantone perfect fifth M
700.00
G 27/12 27/12 Audio file "Perfect fifth on C.mid" not found Equal-tempered perfect fifth 12 M
701.89
231/53 231/53 Audio file "53-TET perfect fifth on C.mid" not found 53-TET perfect fifth 53
701.96
G[2] 3 : 2 3 : 2 Audio file "Just perfect fifth on C.mid" not found 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 Audio file "41-TET perfect fifth on C.mid" not found 41-TET perfect fifth 41
703.45
217/29 217/29 Audio file "29-TET perfect fifth on C.mid" not found 29-TET perfect fifth 29
719.90
97 : 64 97 : 26 Audio file "Ninety-seventh harmonic on C.mid" not found Ninety-seventh harmonic[5] 97
720.00
23/5 : 1 Audio file "3 steps in 5-et on C.mid" not found 3 steps in 5 equal temperament 5
721.51
Adouble flat− 1024 : 675 210 : 33×52 Audio file "Narrow diminished sixth on C.mid" not found Narrow diminished sixth[3] 5
725.00
229/48 229/48 Audio file "29 steps in 48-et on C.mid" not found 29 steps in 48 equal temperament 48
729.22
G7 upside-down- 32 : 21 24 : 3×7 Audio file "21st subharmonic on C.mid" not found 21st subharmonic,[5][6] septimal diminished sixth 7
733.23
F2317double sharp+ 391 : 256 17×23 : 28 Audio file "Three-hundred-ninety-first harmonic on C.mid" not found Three-hundred-ninety-first harmonic 23
737.65
A77♭+ 49 : 32 7×7 : 25 Audio file "Forty-ninth harmonic on C.mid" not found Forty-ninth harmonic[5] 7
743.01
Adouble flat 192 : 125 26×3 : 53 Audio file "Classic diminished sixth on C.mid" not found Classic diminished sixth[3] 5
750.00
Ghalf sharp/Athree quarter flat 215/24 215/24 Audio file "Subminor sixth on C.mid" not found 15 steps in 24 equal temperament 24
755.23
G↑ 99 : 64 32×11 : 26 Audio file "Ninety-ninth harmonic on C.mid" not found Ninety-ninth harmonic[5] 11
764.92
A7♭[2] 14 : 9 2×7 : 32 Audio file "Septimal minor sixth on C.mid" not found Septimal minor sixth[3][5] 7
772.63
G♯ 25 : 16 52 : 24 Audio file "Just augmented fifth on C.mid" not found Just augmented fifth[5][16] 5
775.00
231/48 231/48 Audio file "31 steps in 48-et on C.mid" not found 31 steps in 48 equal temperament 48
781.79
π : 2 Audio file "Wallis product (pi) on C.mid" not found Wallis product
782.49
G7 upside-down↑-[2] 11 : 7 11 : 7 Audio file "Undecimal minor sixth on C.mid" not found Undecimal minor sixth,[5] undecimal augmented fifth,[3] Fibonacci numbers 11
789.85
101 : 64 101 : 26 Audio file "Hundred-first harmonic on C.mid" not found Hundred-first harmonic[5] 101
792.18
A♭−[2] 128 : 81 27 : 34 Audio file "Pythagorean minor sixth on C.mid" not found Pythagorean minor sixth,[3][5][6] 81st subharmonic 3
798.40
A297♭+ 203 : 128 7×29 : 27 Audio file "Two-hundred-third harmonic on C.mid" not found Two-hundred-third harmonic 29
800.00
G♯/A♭ 28/12 22/3 Audio file "Minor sixth on C.mid" not found Equal-tempered minor sixth 3, 12 M
806.91
G17♯ 51 : 32 3×17 : 25 Audio file "Fifty-first harmonic on C.mid" not found Fifty-first harmonic[5] 17
813.69
A♭[2] 8 : 5 23 : 5 Audio file "Just minor sixth on C.mid" not found Just minor sixth[3][4][11][16] 5
815.64
G♯++ 6561 : 4096 38 : 212 Audio file "Pythagorean augmented fifth on C.mid" not found Pythagorean augmented fifth,[3][6] Pythagorean 'schismatic' sixth[5] 3
823.80
103 : 64 103 : 26 Audio file "Hundred-third harmonic on C.mid" not found Hundred-third harmonic[5] 103
825.00
211/16 233/48 Audio file "11 steps in 16-et on C.mid" not found 33 steps in 48 equal temperament 16, 48
832.18
G23♯+ 207 : 128 32×23 : 27 Audio file "Two-hundred-seventh harmonic on C.mid" not found Two-hundred-seventh harmonic 23
833.09
(51/2+1)/2 φ : 1 Audio file "Golden ratio on C.mid" not found Golden ratio (833 cents scale)
835.19
A♭+ 81 : 50 34 : 2×52 Audio file "Acute minor sixth on C.mid" not found Acute minor sixth[3] 5
840.53
A13♭[2] 13 : 8 13 : 23 Audio file "Tridecimal neutral sixth on C.mid" not found Tridecimal neutral sixth,[3] overtone sixth,[5] thirteenth harmonic 13
848.83
A19♭↑ 209 : 128 11×19 : 27 Audio file "Two-hundred-ninth harmonic on C.mid" not found Two-hundred-ninth harmonic 19
850.00
Gthree quarter sharp/Ahalf flat 217/24 217/24 Audio file "Neutral sixth on C.mid" not found Equal-tempered neutral sixth 24
852.59
A↓+[2] 18 : 11 2×32 : 11 Audio file "Undecimal neutral sixth on C.mid" not found Undecimal neutral sixth,[3][5] Zalzal's neutral sixth 11
857.09
A7+ 105 : 64 3×5×7 : 26 Audio file "Hundred-fifth harmonic on C.mid" not found Hundred-fifth harmonic[5] 7
857.14
25/7 25/7 Audio file "5 steps in 7-et on C.mid" not found 5 steps in 7 equal temperament 7
862.85
A− 400 : 243 24×52 : 35 Audio file "Grave major sixth on C.mid" not found Grave major sixth[3] 5
873.50
A43U 53 : 32 53 : 25 Audio file "Fifty-third harmonic on C.mid" not found Fifty-third harmonic[5] 53
875.00
235/48 235/48 Audio file "35 steps in 48-et on C.mid" not found 35 steps in 48 equal temperament 48
879.86
A↓7 upside-down 128 : 77 27 : 7×11 Audio file "77th subharmonic on C.mid" not found 77th subharmonic[5][6] 11
882.40
Bdouble flat−−− 32768 : 19683 215 : 39 Audio file "Pythagorean diminished seventh on C.mid" not found Pythagorean diminished seventh[3][6] 3
884.36
A[2] 5 : 3 5 : 3 Audio file "Just major sixth on C.mid" not found Just major sixth,[3][4][5][11][16] Bohlen-Pierce sixth,[3] 1⁄3-comma meantone major sixth 5 M
889.76
107 : 64 107 : 26 Audio file "Hundred-seventh harmonic on C.mid" not found Hundred-seventh harmonic[5] 107
892.54
B191919double flat 6859 : 4096 193 : 212 Audio file "6859th harmonic on C.mid" not found 6859th harmonic 19
900.00
A 29/12 23/4 Audio file "Dim seventh on C.mid" not found Equal-tempered major sixth 4, 12 M
902.49
A19U 32 : 19 25 : 19 Audio file "19th subharmonic on C.mid" not found 19th subharmonic[5][6] 19
905.87
A+[2] 27 : 16 33 : 24 Audio file "Pythagorean major sixth on C.mid" not found Pythagorean major sixth[3][5][11][16] 3
921.82
109 : 64 109 : 26 Audio file "Hundred-ninth harmonic on C.mid" not found Hundred-ninth harmonic[5] 109
925.00
237/48 237/48 Audio file "37 steps in 48-et on C.mid" not found 37 steps in 48 equal temperament 48
925.42
Bdouble flat−[2] 128 : 75 27 : 3×52 Audio file "Just diminished seventh on C.mid" not found Just diminished seventh,[16] diminished seventh,[5][13] 75th subharmonic 5
925.79
A2319+ 437 : 256 19×23 : 28 Audio file "Four-hundred-thirty-seventh harmonic on C.mid" not found Four-hundred-thirty-seventh harmonic 23
933.13
A7 upside-down[2] 12 : 7 22×3 : 7 Audio file "Septimal major sixth on C.mid" not found Septimal major sixth[3][4][5] 7
937.63
A↑ 55 : 32 5×11 : 25 Audio file "Fifty-fifth harmonic on C.mid" not found Fifty-fifth harmonic[5][20] 11
950.00
Ahalf sharp/Bthree quarter flat 219/24 219/24 Audio file "Subminor seventh on C.mid" not found 19 steps in 24 equal temperament 24
953.30
A37♯+ 111 : 64 3×37 : 26 Audio file "Hundred-eleventh harmonic on C.mid" not found Hundred-eleventh harmonic[5] 37
955.03
A♯[2] 125 : 72 53 : 23×32 Audio file "Just augmented sixth on C.mid" not found Just augmented sixth[5] 5
957.21
(3 : 2)15/11 315/11 : 215/11 Audio file "Beta scale 15 steps on C.mid" not found 15 steps in Beta scale 18.75
960.00
24/5 24/5 Audio file "12 steps in 15TET on C.mid" not found 4 steps in 5 equal temperament 5
968.83
B7♭[2] 7 : 4 7 : 22 Audio file "Harmonic seventh on C.mid" not found Septimal minor seventh,[4][5][11] harmonic seventh,[3][11] augmented sixth[citation needed] 7
975.00
213/16 239/48 Audio file "13 steps in 16-et on C.mid" not found 39 steps in 48 equal temperament 16, 48
976.54
A♯+[2] 225 : 128 32×52 : 27 Audio file "Two-hundred-twenty-fith harmonic on C.mid" not found Just augmented sixth[16] 5
984.21
113 : 64 113 : 26 Audio file "Hundred-thirteenth harmonic on C.mid" not found Hundred-thirteenth harmonic[5] 113
996.09
 B♭−[2] 16 : 9 24 : 32 Audio file "Lesser just minor seventh on C.mid" not found Pythagorean minor seventh,[3] Small just minor seventh,[4] lesser minor seventh,[16] just minor seventh,[11] Pythagorean small minor seventh[5] 3
999.47
B19♭ 57 : 32 3×19 : 25 Audio file "Fifty-seventh harmonic on C.mid" not found Fifty-seventh harmonic[5] 19
1000.00
 A♯/B♭ 210/12 25/6 Audio file "Minor seventh on C.mid" not found Equal-tempered minor seventh 6, 12 M
1014.59
A23♯+ 115 : 64 5×23 : 26 Audio file "Hundred-fifteenth harmonic on C.mid" not found Hundred-fifteenth harmonic[5] 23
1017.60
 B♭[2] 9 : 5 32 : 5 Audio file "Greater just minor seventh on C.mid" not found Greater just minor seventh,[16] large just minor seventh,[4][5] Bohlen-Pierce seventh[3] 5
1019.55
A♯+++ 59049 : 32768 310 : 215 Audio file "Pythagorean augmented sixth on C.mid" not found Pythagorean augmented sixth[3][6] 3
1025.00
241/48 241/48 Audio file "41 steps in 48-et on C.mid" not found 41 steps in 48 equal temperament 48
1028.57
26/7 26/7 Audio file "6 steps in 7-et on C.mid" not found 6 steps in 7 equal temperament 7
1029.58
B29♭ 29 : 16 29 : 24 Audio file "Twenty-ninth harmonic on C.mid" not found Twenty-ninth harmonic,[5] minor seventh[citation needed] 29
1035.00
 B↓[2] 20 : 11 22×5 : 11 Audio file "Lesser undecimal neutral seventh on C.mid" not found Lesser undecimal neutral seventh, large minor seventh[3] 11
1039.10
B♭+ 729 : 400 36 : 24×52 Audio file "Acute minor seventh on C.mid" not found Acute minor seventh[3] 5
1044.44
B13♭ 117 : 64 32×13 : 26 Audio file "Hundred-seventeenth harmonic on C.mid" not found Hundred-seventeenth harmonic[5] 13
1044.86
B7 upside-down♭- 64 : 35 26 : 5×7 Audio file "Septimal neutral seventh on C.mid" not found 35th subharmonic,[5] septimal neutral seventh[6] 7
1049.36
 B↑♭−[2] 11 : 6 11 : 2×3 Audio file "Undecimal neutral seventh on C.mid" not found 21⁄4-tone or Undecimal neutral seventh,[3] undecimal 'median' seventh[5] 11
1050.00
Athree quarter sharp/Bhalf flat 221/24 27/8 Audio file "Neutral seventh on C.mid" not found Equal-tempered neutral seventh 8, 24
1059.17
59 : 32 59 : 25 Audio file "Fifty-ninth harmonic on C.mid" not found Fifty-ninth harmonic[5] 59
1066.76
B− 50 : 27 2×52 : 33 Audio file "Grave major seventh on C.mid" not found Grave major seventh[3] 5
1071.70
B137 upside-down♭- 13 : 7 13 : 7 Audio file "Tridecimal neutral seventh on C.mid" not found Tridecimal neutral seventh[21] 13
1073.78
B717 119 : 64 7×17 : 26 Audio file "Hundred-nineteenth harmonic on C.mid" not found Hundred-nineteenth harmonic[5] 17
1075.00
243/48 243/48 Audio file "43 steps in 48-et on C.mid" not found 43 steps in 48 equal temperament 48
1086.31
C′♭−− 4096 : 2187 212 : 37 Audio file "Pythagorean diminished octave on C.mid" not found Pythagorean diminished octave[3][6] 3
1088.27
B[2] 15 : 8 3×5 : 23 Audio file "Just major seventh on C.mid" not found Just major seventh,[3][5][11][16] small just major seventh,[4] 1⁄6-comma meantone major seventh 5
1095.04
C17 upside down♭ 32 : 17 25 : 17 Audio file "17th subharmonic on C.mid" not found 17th subharmonic[5][6] 17
1100.00
B 211/12 211/12 Audio file "Major seventh on C.mid" not found Equal-tempered major seventh 12 M
1102.64
B↑↑♭- 121 : 64 112 : 26 Audio file "Hundred-twenty-first harmonic on C.mid" not found Hundred-twenty-first harmonic[5] 11
1107.82
C′♭− 256 : 135 28 : 33×5 Audio file "Octave minus major chroma on C.mid" not found Octave − major chroma,[3] 135th subharmonic, narrow diminished octave[citation needed] 5
1109.78
B+[2] 243 : 128 35 : 27 Audio file "Pythagorean major seventh on C.mid" not found Pythagorean major seventh[3][5][6][11] 3
1116.88
61 : 32 61 : 25 Audio file "Sixty-first harmonic on C.mid" not found Sixty-first harmonic[5] 61
1125.00
215/16 245/48 Audio file "15 steps in 16-et on C.mid" not found 45 steps in 48 equal temperament 16, 48
1129.33
C′♭[2] 48 : 25 24×3 : 52 Audio file "Classic diminished octave on C.mid" not found Classic diminished octave,[3][6] large just major seventh[4] 5
1131.02
B41 123 : 64 3×41 : 26 Audio file "Hundred-twenty-third harmonic on C.mid" not found Hundred-twenty-third harmonic[5] 41
1137.04
B7 upside-down 27 : 14 33 : 2×7 Audio file "Septimal major seventh on C.mid" not found Septimal major seventh[5] 7
1138.04
C1913♭ 247 : 128 13×19 : 27 Audio file "Two-hundred-forty-seventh harmonic on C.mid" not found Two-hundred-forty-seventh harmonic 19
1145.04
B31 31 : 16 31 : 24 Audio file "Thirty-first harmonic on C.mid" not found Thirty-first harmonic,[5] augmented seventh[citation needed] 31
1146.73
C↓ 64 : 33 26 : 3×11 Audio file "33rd subharmonic on C.mid" not found 33rd subharmonic[6] 11
1150.00
Bhalf sharp/Chalf flat 223/24 223/24 Audio file "Supermajor seventh on C.mid" not found 23 steps in 24 equal temperament 24
1151.23
C7 35 : 18 5×7 : 2×32 Audio file "Septimal supermajor seventh on C.mid" not found Septimal supermajor seventh, septimal quarter tone inverted 7
1158.94
B♯[2] 125 : 64 53 : 26 Audio file "Just augmented seventh on C.mid" not found Just augmented seventh,[5] 125th harmonic 5
1172.74
C7+ 63 : 32 32×7 : 25 Audio file "Sixty-third harmonic on C.mid" not found Sixty-third harmonic[5] 7
1175.00
247/48 247/48 Audio file "47 steps in 48-et on C.mid" not found 47 steps in 48 equal temperament 48
1178.49
C′− 160 : 81 25×5 : 34 Audio file "Octave minus syntonic comma on C.mid" not found Octave − syntonic comma,[3] semi-diminished octave[citation needed] 5
1179.59
B23↑ 253 : 128 11×23 : 27 Audio file "Two-hundred-fifty-third harmonic on C.mid" not found Two-hundred-fifty-third harmonic[5] 23
1186.42
127 : 64 127 : 26 Audio file "Hundred-twenty-seventh harmonic on C.mid" not found Hundred-twenty-seventh harmonic[5] 127
1200.00
C′ 2 : 1 2 : 1 Audio file "Perfect octave on C.mid" not found Octave[3][11] or diapason[4] 1, 12 3 M S

See also

Notes

  1. ↑ 1.0 1.1 1.2 1.3 Maneri-Sims notation

References

  1. ↑ 1.0 1.1 Fox, Christopher (2003). "Microtones and Microtonalities", Contemporary Music Review, v. 22, pt. 1–2. (Abingdon, Oxfordshire, UK: Routledge): p. 13.
  2. ↑ 2.00 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 2.20 2.21 2.22 2.23 2.24 2.25 2.26 2.27 2.28 2.29 2.30 2.31 2.32 2.33 2.34 2.35 2.36 2.37 2.38 2.39 2.40 2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.49 2.50 2.51 2.52 2.53 2.54 2.55 2.56 2.57 2.58 2.59 2.60 Fonville, John. 1991. "Ben Johnston's Extended Just Intonation: A Guide for Interpreters". Perspectives of New Music 29, no. 2 (Summer): 106–137.
  3. ↑ 3.000 3.001 3.002 3.003 3.004 3.005 3.006 3.007 3.008 3.009 3.010 3.011 3.012 3.013 3.014 3.015 3.016 3.017 3.018 3.019 3.020 3.021 3.022 3.023 3.024 3.025 3.026 3.027 3.028 3.029 3.030 3.031 3.032 3.033 3.034 3.035 3.036 3.037 3.038 3.039 3.040 3.041 3.042 3.043 3.044 3.045 3.046 3.047 3.048 3.049 3.050 3.051 3.052 3.053 3.054 3.055 3.056 3.057 3.058 3.059 3.060 3.061 3.062 3.063 3.064 3.065 3.066 3.067 3.068 3.069 3.070 3.071 3.072 3.073 3.074 3.075 3.076 3.077 3.078 3.079 3.080 3.081 3.082 3.083 3.084 3.085 3.086 3.087 3.088 3.089 3.090 3.091 3.092 3.093 3.094 3.095 3.096 3.097 3.098 3.099 3.100 3.101 3.102 3.103 3.104 3.105 3.106 3.107 3.108 3.109 3.110 3.111 3.112 "List of intervals", Huygens-Fokker Foundation. The Foundation uses "classic" to indicate "just" or leaves off any adjective, as in "major sixth".
  4. ↑ 4.00 4.01 4.02 4.03 4.04 4.05 4.06 4.07 4.08 4.09 4.10 4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18 4.19 4.20 4.21 4.22 4.23 Partch, Harry (1979). Genesis of a Music. pp. 68–69. ISBN 978-0-306-80106-8.
  5. ↑ 5.000 5.001 5.002 5.003 5.004 5.005 5.006 5.007 5.008 5.009 5.010 5.011 5.012 5.013 5.014 5.015 5.016 5.017 5.018 5.019 5.020 5.021 5.022 5.023 5.024 5.025 5.026 5.027 5.028 5.029 5.030 5.031 5.032 5.033 5.034 5.035 5.036 5.037 5.038 5.039 5.040 5.041 5.042 5.043 5.044 5.045 5.046 5.047 5.048 5.049 5.050 5.051 5.052 5.053 5.054 5.055 5.056 5.057 5.058 5.059 5.060 5.061 5.062 5.063 5.064 5.065 5.066 5.067 5.068 5.069 5.070 5.071 5.072 5.073 5.074 5.075 5.076 5.077 5.078 5.079 5.080 5.081 5.082 5.083 5.084 5.085 5.086 5.087 5.088 5.089 5.090 5.091 5.092 5.093 5.094 5.095 5.096 5.097 5.098 5.099 5.100 5.101 5.102 5.103 5.104 5.105 5.106 5.107 5.108 5.109 5.110 5.111 5.112 5.113 5.114 5.115 5.116 5.117 5.118 5.119 5.120 5.121 5.122 5.123 5.124 5.125 5.126 5.127 5.128 5.129 "Anatomy of an Octave", Kyle Gann (1998). Gann leaves off "just" but includes "5-limit". He uses "median" for "neutral".
  6. ↑ 6.00 6.01 6.02 6.03 6.04 6.05 6.06 6.07 6.08 6.09 6.10 6.11 6.12 6.13 6.14 6.15 6.16 6.17 6.18 6.19 6.20 6.21 6.22 6.23 6.24 6.25 6.26 6.27 6.28 6.29 6.30 6.31 6.32 6.33 6.34 6.35 6.36 6.37 6.38 6.39 6.40 6.41 6.42 6.43 6.44 6.45 6.46 6.47 6.48 6.49 6.50 Haluška, Ján (2003). The Mathematical Theory of Tone Systems, pp. 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". Proceedings of the Royal Society of London. 37 (232–234): 368–385. doi:10.1098/rspl.1884.0041. JSTOR 114325. S2CID 122407786.
  8. ↑ "Logarithmic Interval Measures", Huygens-Fokker Foundation. Accessed 2015-06-06.
  9. ↑ "Orwell Temperaments", Xenharmony.org.
  10. ↑ 10.0 10.1 Partch 1979, p. 70
  11. ↑ 11.00 11.01 11.02 11.03 11.04 11.05 11.06 11.07 11.08 11.09 11.10 11.11 11.12 11.13 11.14 11.15 11.16 11.17 11.18 11.19 11.20 11.21 11.22 11.23 11.24 11.25 11.26 11.27 Alexander John Ellis (March 1885). On the musical scales of various nations, p. 488. Journal of the Society of Arts, vol. XXXII, no. 1688
  12. ↑ William Smythe Babcock Mathews (1895). Pronouncing Dictionary and Condensed Encyclopedia of Musical Terms, p. 13. ISBN 1-112-44188-3.
  13. ↑ 13.0 13.1 13.2 13.3 13.4 13.5 Anger, Joseph Humfrey (1912). A Treatise on Harmony, with Exercises, Volume 3, pp. xiv–xv. W. Tyrrell.
  14. ↑ 14.00 14.01 14.02 14.03 14.04 14.05 14.06 14.07 14.08 14.09 14.10 14.11 14.12 14.13 14.14 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. [ISBN unspecified]
  15. ↑ A. R. Meuss (2004). Intervals, Scales, Tones and the Concert Pitch C. Temple Lodge Publishing. p. 15. ISBN 1902636465.
  16. ↑ 16.00 16.01 16.02 16.03 16.04 16.05 16.06 16.07 16.08 16.09 16.10 16.11 16.12 16.13 16.14 16.15 16.16 16.17 16.18 16.19 16.20 16.21 16.22 16.23 16.24 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".
  17. ↑ 17.0 17.1 "13th-harmonic", 31et.com.
  18. ↑ Brabner, John H. F. (1884). The National Encyclopaedia, vol. 13, p. 182. London. [ISBN unspecified]
  19. ↑ Sabat, Marc and von Schweinitz, Wolfgang (2004). "The Extended Helmholtz-Ellis JI Pitch Notation" [PDF], NewMusicBox. Accessed: 15 March 2014.
  20. ↑ Hermann L. F. von Helmholtz (2007). On the Sensations of Tone, p. 456. ISBN 978-1-60206-639-7.
  21. ↑ "Gallery of Just Intervals", Xenharmonic Wiki.

External links

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