List of pitch intervals

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Below is a list of musical intervals. Some terminology used in the list:

  • In music, the prime limit (henceforth referred to simply as the limit) is a number measuring the harmony of an interval. The lower the number, the more consonant the interval is considered to be. It is defined as the largest prime number occurring in the factorizations of the numerator and denominator of the frequency ratio. The limit of the just perfect fourth (4 : 3) is 3, but the just minor tone (10 : 9) has a limit of 5, because 9 can be factorized into 3×3, and 10 into 2×5. There exists another type of limit, the odd limit, which differs slightly from the prime limit, but is not used here.
  • Equal-tempered refers to 12-tone equal temperament with intervals corresponding to 100 cent multiples (e.g., 100, 200, 300, etc.).
  • Pythagorean means 3-limit just intonation—a ratio of numbers with prime factors no higher than three.
  • Just means 5-limit just intonation—a ratio of numbers with prime factors no higher than five.
  • Similarly, septimal, undecimal, tridecimal, and septendecimal mean, respectively, 7, 11, 13, and 17-limit just intonation.
  • By definition every tone in a 3-limit unit can also be part of a 5-limit tuning and so on. By sorting the limit column all tones of that limit can be brought together (tip: sort backwards by clicking the button twice).
  • Meantone refers to meantone temperament, the most common of which is quarter-comma meantone. In general, a meantone is constructed the same way as Pythagorean tuning, as a stack of perfect fifths, but in a meantone, each fifth is narrowed by the same small amount (a portion of the syntonic comma such as 1/4).
  • Since the table is sortable, you can also sort the table by frequency ratio, by cents or alphabetically.

Contents

List [edit]

Code Legend
E 12-tone equal temperament.
Q 24-tone equal temperament, or Arab tone system.
T Other equal temperament.
2 2-limit tones (only fundamental and octaves).
2 3 3-limit just intonation, or Pythagorean.
2 3 5 5-limit (not 3-limit) just intonation, or just.
2 3 5 7 7-limit (not 5-limit) just intonation, or septimal.
2 3 5 7 11 11-limit (not 7-limit) just intonation, or undecimal.
2 3 5 7 11 13 13-limit (not 11-limit) just intonation, or tridecimal.
2 3 5 7 11 13 17 17-limit (not 13-limit) just intonation, or septendecimal.
2 3 5 7 11 13 17 19 19-limit (not 17-limit) just intonation, or novendecimal.
J Other (higher limit) just intonation.
M Meantone temperament.
U A unit of measurement.
S Superparticular number.
List of musical intervals
Cents Note (from C) Freq. Ratio Factors Interval Name E Q 2 3 5 7 11 13 17 19 M U S
0.00
 C[1] 1 : 1 1 : 1 About this sound playUnison[2] or monophony,[3] perfect prime[2] E Q 2 3 5 7 11 13 17 19 M
0.04
 101/100,000,000 : 1 About this sound playJot U
0.40
 101/10,000 : 1 About this sound playDecaméride U
0.40
 4375 : 4374 54·7 : 2·37 About this sound playRagisma[2][4] 7 11 13 17 19 S
0.72
 2401 : 2400 74 : 25·3·52 About this sound playBreedsma[2][4] 7 11 13 17 19 S
1.00
 21/1200 : 1 About this sound playCent U
1.20
 21/1000 : 1 About this sound playMillioctave U
1.95
 B♯++[a] 32805 : 32768 38·5 : 215 About this sound playSchisma[2] 5 7 11 13 17 19
2.00
 101/2000 : 1 About this sound playDemi-heptaméride U
2.00
 21/600 : 1 About this sound playCentitone, Iring, two cents U
3.99
 101/1000 : 1 About this sound playSavart or eptaméride U
7.71
 225 : 224 32·52 : 25·7 About this sound playSeptimal kleisma,[2][4] marvel comma 7 11 13 17 19 S
8.11
 15625 : 15552 56 : 26·35 About this sound playKleisma or semicomma majeur[2][4] 5 7 11 13 17 19
10.06
 2109375 : 2097152 33·57 : 221 About this sound playSemicomma,[2][4] Fokker's comma[2] 5 7 11 13 17 19
12.50
 21/96 : 1 About this sound play16th-tone, 1 step in 96 equal temperament U
13.07
 1728:1715 26·33 : 5·73 About this sound playOrwell comma[2][5] 7 11 13 17 19
13.79
 Ddouble flat7 upside-down[a] 126 : 125 2·32·7 : 53 About this sound playSmall septimal semicomma,[4] small septimal comma,[2] starling comma 7 11 13 17 19 S
14.37
 121 : 120 112 : 23·3·5 About this sound playUndecimal seconds comma[2] 11 13 17 19 S
16.67
 C↑[b] 21/72 : 1 About this sound play12th-tone, 1 step in 72 equal temperament, one morion U
18.18
 21/66 : 1 About this sound play11th-tone, 1 step in 66 equal temperament U
19.55
 Ddouble flat--[1] 2048 : 2025 211 : 34·52 About this sound playDiaschisma,[2][4] minor comma 5 7 11 13 17 19
20.00
 21/60 : 1 About this sound play10th-tone, 1 step in 60 equal temperament U
21.51
 C+[1] 81 : 80 34 : 24·5 About this sound playSyntonic comma,[2][4] major comma, komma, chromatic diesis, or comma of Didymus[2][4][6][7] 5 7 11 13 17 19 S
22.22
 21/54 : 1 About this sound play9th-tone, 1 step in 54 equal temperament U
22.64
 21/53 : 1 About this sound playHoldrian comma, Holder's comma, 1 step in 53 equal temperament U
23.46
 B♯+++[a] 531441 : 524288 312 : 219 About this sound playPythagorean comma,[2][4][6][7] ditonic comma[2][4] 3 5 7 11 13 17 19
25.00
 21/48 : 1 About this sound play8th-tone, 1 step in 48 equal temperament U
27.26
 64 : 63 26 : 32·7 About this sound playSeptimal comma,[2][4][7] Archytas' comma[2] 7 11 13 17 19 S
27.90
 107/1000 : 1 About this sound playMéride U
28.57
 21/42 : 1 About this sound play7th-tone, 1 step in 42 equal temperament U
29.27
 21/41 : 1 About this sound play1 step in 41 equal temperament U
31.19
 56 : 55 23·7 : 5·11 About this sound playPtolemy's enharmonic:[8] difference between (11 : 8) and (7 : 5) tritone 11 13 17 19 S
33.33
 CHalf up arrow.png[b] 21/36 : 1 About this sound play6th-tone, 1 step in 36 equal temperament U
34.98
 50 : 49 2·52 : 72 About this sound playSeptimal sixth-tone or jubilisma, Erlich's decatonic comma or tritonic diesis[2][4] 7 11 13 17 19 S
35.70
 D77♭[a] 49 : 48 72 : 24·3 About this sound playSeptimal diesis, slendro diesis or septimal 1/6-tone[2] 7 11 13 17 19 S
38.71
 21/31 : 1 About this sound play1 step in 31 equal temperament U
40.00
 21/30 : 1 About this sound play5th-tone, 1 step in 30 equal temperament U
41.06
 Ddouble flat-[a] 128 : 125 27 : 53 About this sound playEnharmonic diesis or 5-limit limma, minor diesis or diminished second,[4] minor diesis or diesis,[2] three inverted decades 5 7 11 13 17 19
48.77
 C7 upside-down[a] 36 : 35 22·32 : 5·7 About this sound playSeptimal quarter tone, septimal diesis,[2][4] septimal comma[1] 7 11 13 17 19 S
50.00
 Chalf sharp/Dthree quarter flat 21/24 : 1 About this sound playEqual-tempered quarter tone Q U
52.17
 21/23 : 1 About this sound play1 step in 23 equal temperament U
53.27
 C↑[a] 33 : 32 3·11 : 25 About this sound play33rd harmonic 11 13 17 19 S
54.55
 21/22 : 1 About this sound play1 step in 22 equal temperament U
57.14
 21/21 : 1 About this sound play1 step in 21 equal temperament U
60.00
 21/20 : 1 About this sound play1 step in 20 equal temperament U
62.96
 28 : 27 22·7 : 33 About this sound playSeptimal third-tone 7 11 13 17 19 S
63.16
 C♯[9] 21/19 : 1 About this sound play1 step in 19 equal temperament U
63.81
 (3 : 2)1/11 : 1 About this sound playBeta scale step U
65.34
 27 : 26 33 : 2·13 About this sound playChromatic diesis,[10] tridecimal comma[2] 13 17 19 U S
66.67
 21/18 : 1 About this sound play3rd-tone, 1 step in 18 equal temperament U
70.59
 D♭[11] 21/17 : 1 About this sound play1 step in 17 equal temperament U
70.67
 C♯[1] 25 : 24 52 : 23·3 About this sound playJust chromatic semitone or minor chroma,[2] lesser chromatic semitone, small (just) semitone[7] or minor second,[3] minor chromatic semitone,[12] or minor semitone 5 7 11 13 17 19 S
75.00
 21/16 : 1 About this sound play1 step in 16 equal temperament U
78.00
 (3 : 2)1/9 : 1 About this sound playAlpha scale step U
80.00
 C↑[9] 21/15 : 1 About this sound play1 step in 15 equal temperament U
84.47
 D7♭[a] 21 : 20 3·7 : 22·5 About this sound playSeptimal chromatic semitone, minor semitone[2] 7 11 13 17 19 S
85.71
 21/14 : 1 About this sound play1 step in 14 equal temperament U
90.22
 D♭--[1] 256 : 243 28 : 35 About this sound playPythagorean minor second or limma,[2][4][7] Pythagorean diatonic semitone, Low Semitone[13] 3 5 7 11 13 17 19
92.18
 C♯+[1] 135 : 128 33·5 : 27 About this sound playGreater chromatic semitone, chromatic semitone, semitone medius, major chroma or major limmma,[2] small limma,[7] major chromatic semitone,[12] 135th harmonic 5 7 11 13 17 19
92.31
 21/13 : 1 About this sound play1 step in 13 equal temperament U
98.95
 18 : 17 2·32 : 17 About this sound playJust minor semitone, Arabic lute index finger[2] 17 19 S
100.00
 C♯/D♭ 21/12 : 1 About this sound playEqual-tempered minor second or semitone E Q U
104.96
 C17♯[1] 17 : 16 17 : 24 About this sound playJust major semitone, overtone semitone, 17th harmonic[2] 17 19 S
109.09
 21/11 : 1 About this sound play1 step in 11 equal temperament U
111.73
 D♭-[1] 16 : 15 24 : 3·5 About this sound playJust diatonic semitone, large just semitone or major second,[3] major semitone, limma, minor diatonic semitone,[2] diatonic second[14] semitone,[13] diatonic semitone[7] 5 7 11 13 17 19 S
113.69
 C♯++[a] 2187 : 2048 37 : 211 About this sound playapotome[2][7] or Pythagorean major semitone,[4] Pythagorean augmented unison, Pythagorean chromatic semitone, or Pythagorean apotome 3 5 7 11 13 17 19
116.72
 181/19 : 51/19 About this sound playSecor U
119.44
 C7 upside-down♯[a] 15 : 14 3·5 : 2·7 About this sound playSeptimal diatonic semitone, major diatonic semitone[2] 7 11 13 17 19 S
120.00
 21/10 : 1 About this sound play1 step in 10 equal temperament U
133.24
 D♭[a] 27 : 25 33 : 52 About this sound playMinor second, semitone Maximus, large limma or Bohlen-Pierce small semitone,[2] high semitone[13] 5 7 11 13 17 19
133.33
 21/9 : 1 About this sound play1 step in 9 equal temperament U
150.00
 Cthree quarter sharp/Dhalf flat 23/24 : 1 About this sound playEqual-tempered neutral second Q
150.64
 D↓[1] 12 : 11 22·3 : 11 About this sound play3/4-tone or Undecimal neutral second,[2] trumpet three-quarter tone[7] 11 13 17 19 S
165.00
 D↑♭-[1] 11 : 10 11 : 2·5 About this sound playGreater undecimal neutral second, 4/5-tone or Ptolemy's second[2] 11 13 17 19 S
171.43
 21/7 : 1 About this sound play1 step in 7 equal temperament U
180.45
 Edouble flat---[a] 65536 : 59049 216 : 310 About this sound playPythagorean diminished third,[2][4] Pythagorean minor tone 3 5 7 11 13 17 19
182.40
 D-[1] 10 : 9 2·5 : 32 About this sound playSmall just whole tone or major second,[3] minor whole tone,[2] lesser whole tone,[14] minor tone,[13] minor second[7] 5 7 11 13 17 19 S
200.00
 D 22/12 : 1 About this sound playEqual-tempered major second E Q
203.91
 D[1] 9 : 8 32 : 23 About this sound playPythagorean major second, Large just whole tone or major second[7] (sesquioctavan),[3] tonus, major whole tone,[2] greater whole tone,[14] major tone,[13] 9th harmonic 3 5 7 11 13 17 19 S
223.46
 Edouble flat-[1] 256 : 225 28 : 32·52 About this sound playJust diminished third[14] 5 7 11 13 17 19
231.17
 D7 upside-down-[1] 8 : 7 23 : 7 About this sound playSeptimal major second,[3] septimal whole tone[2] 7 11 13 17 19 S
240.00
 21/5 : 1 About this sound play1 step in 5 equal temperament U
266.87
 E7♭[1] 7 : 6 7 : 2·3 About this sound playSeptimal minor third[2][3][7] or Sub minor Third[13] 7 11 13 17 19 S
274.58
 D♯[1] 75 : 64 3·52 : 26 About this sound playJust augmented second,[14] Augmented Tone,[13] augmented second,[12] 75th harmonic 5 7 11 13 17 19
294.13
 E♭-[1] 32 : 27 25 : 33 About this sound playPythagorean minor third[2][4][13][14] or semiditone 3 5 7 11 13 17 19
297.51
 E19♭[1] 19 : 16 19 : 24 About this sound play19th harmonic,[2] 19-limit minor third 19
300.00
 D♯/E♭ 23/12 : 1 About this sound playEqual-tempered minor third E Q
310.26
 6:5÷(81:80)1/4 About this sound playQuarter-comma meantone minor third M
311.98
 (3 : 2)4/9 : 1 About this sound playAlpha scale minor third
315.64
 E♭[1] 6 : 5 2·3 : 5 About this sound playJust minor third,[2][3][7][14] minor third[13] 5 7 11 13 17 19 S
317.60
 D♯++[a] 19683 : 16384 39 : 214 About this sound playPythagorean augmented second[2][4] 3 5 7 11 13 17 19
342.86
 22/7 : 1 About this sound play2 steps in 7 equal temperament
347.41
 E↑♭-[1] 11 : 9 11 : 32 About this sound playUndecimal neutral third[2] 11 13 17 19
350.00
 Dthree quarter sharp/Ehalf flat 27/24 : 1 About this sound playEqual-tempered neutral third Q
359.47
 E↓13 upside down[1] 16 : 13 24 : 13 About this sound playTridecimal neutral third[2] 13 17 19
384.36
 F♭--[a] 8192 : 6561 213 : 38 About this sound playPythagorean diminished fourth[2][4] 3 5 7 11 13 17 19
386.31
 E[1] 5 : 4 5 : 22 About this sound playJust major third,[2][3][7][14] major third,[13] 5th harmonic, one decade 5 7 11 13 17 19 M S
400.00
 E 24/12 : 1 About this sound playEqual-tempered major third E Q
407.82
 E+[1] 81 : 64 34 : 26 About this sound playPythagorean major third,[2][4][13][14] ditone, 81st harmonic 3 5 7 11 13 17 19
417.51
 F7↓+[1] 14 : 11 2·7 : 11 About this sound playUndecimal diminished fourth or major third[2] 11 13 17 19
427.37
 F♭[1] 32 : 25 25 : 52 About this sound playJust diminished fourth,[14] diminished fourth,[12] two inverted decades 5 7 11 13 17 19
435.08
 E7 upside-down[1] 9 : 7 32 : 7 About this sound playSeptimal major third or Bohlen-Pierce third,[2] Super major Third[13] 7 11 13 17 19
456.99
 E♯[1] 125 : 96 53 : 25·3 About this sound playJust augmented third 5 7 11 13 17 19
470.78
 F7+[1] 21 : 16 3·7 : 24 About this sound play About this sound play21st harmonic, narrow fourth[2] 7 11 13 17 19
480.00
 22/5 : 1 About this sound play2 steps in 5 equal temperament
498.04
 F[1] 4 : 3 22 : 3 About this sound playPerfect fourth,[2][14] Pythagorean perfect fourth, Just perfect fourth or diatessaron[3] 3 5 7 11 13 17 19 S
500.00
 F 25/12 : 1 About this sound playEqual-tempered perfect fourth E Q
510.51
 (3 : 2)8/11 : 1 About this sound playBeta scale perfect fourth
514.29
 23/7 : 1 About this sound play3 steps in 7 equal temperament
519.55
 F+[1] 27 : 20 33 : 22·5 About this sound play5-limit wolf fourth, acute fourth,[2] imperfect fourth[14] 5 7 11 13 17 19
521.51
 E♯+++[a] 177147 : 131072 311 : 217 About this sound playPythagorean augmented third[2][4] (F+ (pitch)) 3 5 7 11 13 17 19
551.32
 F↑[1] 11 : 8 11 : 23 About this sound play11th harmonic, lesser undecimal tritone, undecimal semi-augmented fourth[2] 11 13 17 19
568.72
 F♯[1] 25 : 18 52 : 2·32 About this sound playJust augmented fourth[2] 5 7 11 13 17 19
582.51
 G7♭[1] 7 : 5 About this sound playLesser septimal tritone, septimal tritone[2][3] Huygens' tritone or Bohlen-Pierce fourth,[2] septimal fifth[7] 7 11 13 17 19
588.27
 G♭--[a] 1024 : 729 210 : 36 About this sound playPythagorean diminished fifth[2][4] 3 5 7 11 13 17 19
590.22
 F♯+[1] 45 : 32 32·5 : 25 About this sound playJust augmented fourth, just tritone,[3][7] tritone,[4] diatonic tritone,[2] 'augmented' or 'false' fourth,[14] 45th harmonic 5 7 11 13 17 19
600.00
 F♯/G♭ 26/12 : 1 = \scriptstyle \sqrt{2} About this sound playEqual-tempered tritone E Q
609.78
 G♭-[1] 64 : 45 26 : 32·5 About this sound playJust tritone,[3] 2nd tritone,[4] 'false' fifth,[14] diminished fifth[12] 5 7 11 13 17 19
611.73
 F#++[a] 729 : 512 36 : 29 About this sound playPythagorean tritone,[2][4] Pythagorean augmented fourth 3 5 7 11 13 17 19
617.49
 F♯7 upside-down[1] 10 : 7 2·5 : 7 About this sound playGreater septimal tritone, septimal tritone,[3] Euler's tritone[2] 7 11 13 17 19
628.27
 23 : 16 23 : 24 About this sound play23rd harmonic
631.28
 G♭[1] 36 : 25 22·32 : 52 About this sound playJust diminished fifth 5 7 11 13 17 19
648.68
 G↓[1] 16 : 11 24 : 11 About this sound playInversion of 11th harmonic, undecimal semi-diminished fifth[2] 11 13 17 19
678.49
 Adouble flat---[a] 262144 : 177147 218 : 311 About this sound playPythagorean diminished sixth[2][4] 3 5 7 11 13 17 19
680.45
 G-[a] 40 : 27 23·5 : 33 About this sound play5-limit wolf fifth or diminished sixth, grave fifth,[2][4][7] imperfect fifth,[14] 5 7 11 13 17 19
696.58
 3:2÷(81:80)1/4 About this sound playQuarter-comma meantone perfect fifth M
700.00
 G 27/12 : 1 About this sound playEqual-tempered perfect fifth E Q
701.96
 G[1] 3 : 2 3 : 2 About this sound playPerfect fifth,[2][14] Pythagorean perfect fifth, Just perfect fifth or diapente,[3] fifth,[13] Just fifth,[7] 3rd harmonic 3 5 7 11 13 17 19 S
764.92
 A7♭[1] 14 : 9 2·7 : 32 About this sound playSeptimal minor sixth[2] 7 11 13 17 19
772.63
 G♯[a] 25 : 16 52 : 24 About this sound playJust augmented fifth,[14] 25th harmonic, two decades 5 7 11 13 17 19
782.49
 G↑-[1] 11 : 7 11 : 7 About this sound playUndecimal minor sixth, undecimal augmented fifth[2] 11 13 17 19
792.18
 A♭-[1] 128 : 81 27 : 34 About this sound playPythagorean minor sixth[2][4] 3 5 7 11 13 17 19
800.00
 G♯/A♭ 28/12 : 1 About this sound playEqual-tempered minor sixth E Q
813.69
 A♭[1] 8 : 5 23 : 5 About this sound playJust minor sixth,[2][3][7][14] one inverted decade 5 7 11 13 17 19
815.64
 G♯++[a] 6561 : 4096 38 : 212 About this sound playPythagorean augmented fifth[2][4] 3 5 7 11 13 17 19
833.09
 \varphi ≈233 : 144 233 : 24·32 About this sound playGolden ratio
840.53
 A13♭[1] 13 : 8 13 : 23 About this sound playTridecimal neutral sixth,[2] overtone sixth, 13th harmonic 13 17 19
850.00
 Gthree quarter sharp/Ahalf flat 217/24 : 1 About this sound playEqual-tempered neutral sixth Q
852.59
 A↓[1] 18 : 11 2·32 : 11 About this sound playUndecimal neutral sixth,[2] Zalzal's neutral sixth 11 13 17 19
857.14
 25/7 : 1 About this sound play5 steps in 7 equal temperament
882.40
 Bdouble flat---[a] 32768 : 19683 215 : 39 About this sound playPythagorean diminished seventh[2][4] 3 5 7 11 13 17 19
884.36
 A[1] 5 : 3 5 : 3 About this sound playJust major sixth,[2][3][7][14] Bohlen-Pierce sixth[2] 5 7 11 13 17 19
900.00
 A 29/12 : 1 About this sound playEqual-tempered major sixth E Q
905.87
 A+[1] 27 : 16 33 : 24 About this sound playPythagorean major sixth,[2][7][14] 27th harmonic 3 5 7 11 13 17 19
925.42
 Bdouble flat-[1] 128 : 75 27 : 3·52 About this sound playJust diminished seventh,[14] diminished seventh[12] 5 7 11 13 17 19
933.13
 A7 upside-down[1] 12 : 7 22·3 : 7 About this sound playSeptimal major sixth[2][3] 7 11 13 17 19
955.03
 A♯[1] 125 : 72 53 : 23·32 About this sound playJust augmented sixth 5 7 11 13 17 19
957.21
 (3 : 2)15/11 : 1 About this sound play15 steps in Beta scale
960.00
 24/5 : 1 About this sound play4 steps in 5 equal temperament
968.83
 B7♭[1] 7 : 4 7 : 22 About this sound playSeptimal minor seventh,[3][7] harmonic seventh,[2][7] 7th harmonic 7 11 13 17 19
976.54
 A♯+[1] 225 : 128 32·52 : 27 About this sound playJust augmented sixth,[14] 225th harmonic 5 7 11 13 17 19
996.09
 B♭-[1] 16 : 9 24 : 32 About this sound playPythagorean minor seventh,[2] Small just minor seventh,[3] lesser minor seventh,[14] just minor seventh[7] 3 5 7 11 13 17 19
1000.00
 A♯/B♭ 210/12 : 1 About this sound playEqual-tempered minor seventh E Q
1017.60
 B♭[1] 9 : 5 32 : 5 About this sound playGreater just minor seventh,[14] large just minor seventh,[3] Bohlen-Pierce seventh[2] 5 7 11 13 17 19
1019.55
 A♯+++[a] 59049 : 32768 310 : 215 About this sound playPythagorean augmented sixth[2][4] 3 5 7 11 13 17 19
1028.57
 26/7 : 1 About this sound play6 steps in 7 equal temperament
1029.58
 29 : 16 29 : 24 About this sound play29th harmonic
1035.00
 B↓[1] 20 : 11 22·5 : 11 About this sound playLesser undecimal neutral seventh, large minor seventh[2] 11 13 17 19
1049.36
 B↑♭-[1] 11 : 6 11 : 2·3 About this sound play21/4-tone or Undecimal neutral seventh[2] 11 13 17 19
1050.00
 Athree quarter sharp/Bhalf flat 221/24 : 1 About this sound playEqual-tempered neutral seventh Q
1086.31
 C♭--[a] 4096 : 2187 212 : 37 About this sound playPythagorean diminished octave[2][4] 3 5 7 11 13 17 19
1088.27
 B[1] 15 : 8 3·5 : 23 About this sound playJust major seventh,[2][7][14] small just major seventh,[3] 15th harmonic 5 7 11 13 17 19
1100.00
 B 211/12 : 1 About this sound playEqual-tempered major seventh E Q
1109.78
 B+[1] 243 : 128 35 : 27 About this sound playPythagorean major seventh,[2][4][7] 243 harmonic 3 5 7 11 13 17 19
1129.33
 C♭[1] 48 : 25 24·3 : 52 About this sound playClassic diminished octave,[2][4] large just major seventh[3] 5 7 11 13 17 19
1158.94
 B♯[1] 125 : 64 53 : 26 About this sound playJust augmented seventh, 125th harmonic, three decades 5 7 11 13 17 19
1200.00
 C' 2 : 1 2 : 1 About this sound playOctave,[2][7] or diapason,[3] 2nd harmonic E Q 2 3 5 7 11 13 17 19 M U S
1223.46
 B♯+++[a] 531441 : 262144 312 : 218 About this sound playPythagorean augmented seventh[2][4] 3 5 7 11 13 17 19
1901.96
 G' 3 : 1 3 : 1 About this sound playTritave or just perfect twelfth 3 5 7 11 13 17 19 U
2400.00
 C" 4 : 1 22 : 1 About this sound playFifteenth or two octaves E Q 2 3 5 7 11 13 17 19 M
3986.31
 E 10 : 1 52 : 1 About this sound playDecade 5 7 11 13 17 19 M

See also [edit]

Note [edit]

  1. ^ 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 Ben Johnston's notation.
  2. ^ a b Maneri-Sims notation.

References [edit]

  1. ^ 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.
  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 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 "List of intervals", Huygens-Fokker Foundation. The Foundation uses "classic" to indicate "just" or leaves off any adjective, as in "major sixth".
  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 Partch, Harry (1979). Genesis of a Music, p.68-69. ISBN 978-0-306-80106-8.
  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 y z aa ab ac ad ae af ag ah ai aj ak Haluška, Ján (2003). The Mathematical Theory of Tone Systems, p.xxv-xxix. ISBN 978-0-8247-4714-5.
  5. ^ "Orwell Temperaments", Xenharmony.org.
  6. ^ a b Partch (1979), p.70.
  7. ^ 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.
  8. ^ "Anatomy of an Octave", KyleGann.com.
  9. ^ a b Myles Leigh Skinner (2007). Toward a Quarter-tone Syntax: Analyses of Selected Works by Blackwood, Haba, Ives, and Wyschnegradsky, p.52. ISBN 9780542998478.
  10. ^ William Smythe Babcock Mathews (1895). Pronouncing dictionary and condensed encyclopedia of musical terms, p.13. ISBN 1-112-44188-3.
  11. ^ Blackwood, Easley (Summer, 1991). "Modes and Chord Progressions in Equal Tunings", p.175, Perspectives of New Music, Vol. 29, No. 2, pp. 166-200.
  12. ^ a b c d e f Anger, Joseph Humfrey (1912). A treatise on harmony, with exercises, Volume 3, p.xiv-xv. W. Tyrrell.
  13. ^ a b c d e f g h i j k l m Hermann Ludwig F. von Helmholtz (Alexander John Ellis, trans.) (1875). On the sensations of tone as a physiological basis for the theory of music, p.644. ISBN .
  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".

External links [edit]
List of musical intervals by name or by ratio
Intervals (list by name & list by ratio)
Numbers in brackets are the number of semitones in the interval.
Fractional semitones are approximate.
Twelve-semitone
(Western)
Perfect
Other systems
Other intervals
Groups
Measurement
Others
Measurement
Monochord.jpg
Just intonation
Temperaments
Irregular
Traditional
non-Western
Non-octave
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