List of pitch intervals

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 Pythagorean tuning (blue), equal-tempered (black), 1/4-comma meantone (red) and 1-3-comma meantone (green). For each, the common origin is arbitrarily chosen as C. The degrees are arranged in the order or the cycle of fiths; as in each of these tunings 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

• The prime limit, a concept introduced by Harry Partch,^[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 (bigger of odd numbers obtained after dividing numerator and denominator by highest possible powers of 2), but it is not used here.
• 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

List of musical intervals

Cents	Note (from C)	Freq. ratio	Prime Factors	Interval name	TET	3	5	7	11	13	17	19	H	M	S
0.00	C[2]	1 : 1	1 : 1	playUnison,[3] monophony,[4] perfect prime,[3] tonic,[5] or fundamental	1, 12	3	5	7	11	13	17	19	H	M
0.40	C♯-	4375 : 4374	54·7 : 2·37	playRagisma[3][6]				7	11	13	17	19	H		S
0.72	E+	2401 : 2400	74 : 25·3·52	playBreedsma[3][6]				7	11	13	17	19	H		S
1.00		21/1200	21/1200	playCent	1200
1.20		21/1000	21/1000	playMillioctave	1000
1.95	B♯++	32805 : 32768	38·5 : 215	playSchisma[3][5]			5	7	11	13	17	19	H
3.99		101/1000	21/1000·51/1000	playSavart or eptaméride	301.03
7.71	B♯	225 : 224	32·52 : 25·7	playSeptimal kleisma,[3][6] marvel comma				7	11	13	17	19	H		S
8.11	B-	15625 : 15552	56 : 26·35	playKleisma or semicomma majeur[3][6]			5	7	11	13	17	19	H
10.06	A++	2109375 : 2097152	33·57 : 221	playSemicomma,[3][6] Fokker's comma[3]			5	7	11	13	17	19	H
11.98	C29	145 : 144	5·29 : 24·32	playDifference between 29:16 & 9:5									H
12.50		21/96	21/96	playSixteenth-tone	96
13.07	B-	1728 : 1715	26·33 : 5·73	playOrwell comma[3][7]				7	11	13	17	19	H
13.79	D	126 : 125	2·32·7 : 53	playSmall septimal semicomma,[6] small septimal comma,[3] starling comma				7	11	13	17	19	H		S
14.37	C♭↑↑-	121 : 120	112 : 23·3·5	playUndecimal seconds comma[3]					11	13	17	19	H		S
16.67		21/72	21/72	play1 step in 72 equal temperament	72
18.13	C	96 : 95	25·3 : 5·19	playDifference between 19:16 & 6:5								19	H
19.55	D--[2]	2048 : 2025	211 : 34·52	playDiaschisma,[3][6] minor comma			5	7	11	13	17	19	H
21.51	C+[2]	81 : 80	34 : 24·5	playSyntonic comma,[3][5][6] major comma, komma, chromatic diesis, or comma of Didymus[3][6][8][9]			5	7	11	13	17	19	H		S
22.64		21/53	21/53	playHoldrian comma, Holder's comma, 1 step in 53 equal temperament	53
23.46	B♯+++	531441 : 524288	312 : 219	playPythagorean comma,[3][5][6][8][9] ditonic comma[3][6]		3	5	7	11	13	17	19	H
25.00		21/48	21/48	playEighth-tone	48
26.84	C	65 : 64	5·13 : 26	playSixty-fifth harmonic,[5] 13th-partial chroma[3]						13	17	19	H		S
27.26	C-	64 : 63	26 : 32·7	playSeptimal comma,[3][6][9] Archytas' comma[3]				7	11	13	17	19	H		S
29.27		21/41	21/41	play1 step in 41 equal temperament	41
31.19	D♭↓	56 : 55	23·7 : 5·11	playPtolemy's enharmonic:[5] difference between (11 : 8) and (7 : 5) tritone					11	13	17	19	H		S
33.33		21/36	21/36	playSixth-tone	36
34.28	C	51 : 50	3·17 : 2·52	playDifference between 17:16 & 25:24							17	19	H		S
34.98	B♯-	50 : 49	2·52 : 72	playSeptimal sixth-tone or jubilisma, Erlich's decatonic comma or tritonic diesis[3][6]				7	11	13	17	19	H		S
35.70	D♭	49 : 48	72 : 24·3	playSeptimal diesis, slendro diesis or septimal 1/6-tone[3]				7	11	13	17	19	H		S
38.05	C23	46 : 45	2·23 : 32·5	playDifference between 23:16 & 45:32									H
38.71		21/31	21/31	play1 step in 31 equal temperament	31
40.00		21/30	21/30	playFifth-tone	30
41.06	D-	128 : 125	27 : 53	playEnharmonic diesis or 5-limit limma, minor diesis,[6] diminished second,[5][6] minor diesis or diesis[3]			5	7	11	13	17	19	H
48.77	C	36 : 35	22·32 : 5·7	playSeptimal quarter tone, septimal diesis,[3][6] septimal comma,[2] superior quarter-tone[5]				7	11	13	17	19	H		S
50.00	C/D	21/24	21/24	playEqual-tempered quarter tone	24
53.27	C↑	33 : 32	3·11 : 25	playThirty-third harmonic,[5] undecimal comma, undecimal quarter-tone					11	13	17	19	H		S
56.77	C31	31 : 30	31 : 2·3·5	playDifference between 31:16 & 15:8									H
62.96	C♯-	28 : 27	22·7 : 33	playSeptimal minor second, small minor second, inferior quarter-tone[5]				7	11	13	17	19	H		S
63.81		(3 : 2)1/11	31/11 : 21/11	playBeta scale step	18.75
65.34	C♯+	27 : 26	33 : 2·13	playChromatic diesis,[10] tridecimal comma[3]						13	17	19	H		S
66.67		21/18	21/18	playThird-tone	18
70.67	C♯[2]	25 : 24	52 : 23·3	playJust 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	7	11	13	17	19	H		S
78.00		(3 : 2)1/9	31/9 : 21/9	playAlpha scale step	15.39
79.31		67 : 64	67 : 26	playSixty-seventh harmonic[5]									H
84.47	D♭	21 : 20	3·7 : 22·5	playSeptimal chromatic semitone, minor semitone[3]				7	11	13	17	19	H		S
90.22	D♭--[2]	256 : 243	28 : 35	playPythagorean minor second or limma,[3][6][9] Pythagorean diatonic semitone, Low Semitone[12]		3	5	7	11	13	17	19	H
92.18	C♯+[2]	135 : 128	33·5 : 27	playGreater chromatic semitone, chromatic semitone, semitone medius, major chroma or major limma,[3] small limma,[9] major chromatic semitone,[11] limma ascendant[5]			5	7	11	13	17	19	H
98.95	D♭	18 : 17	2·32 : 17	playJust minor semitone, Arabic lute index finger[3]							17	19	H		S
100.00	C♯/D♭	21/12	21/12	playEqual-tempered minor second or semitone	12									M
104.96	C♯[2]	17 : 16	17 : 24	playMinor diatonic semitone, just major semitone, overtone semitone,[5] 17th harmonic,[3] limma							17	19	H		S
111.73	D♭-[2]	16 : 15	24 : 3·5	playJust 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	7	11	13	17	19	H		S
113.69	C♯++	2187 : 2048	37 : 211	playapotome[3][9] or Pythagorean major semitone,[6] Pythagorean augmented unison, Pythagorean chromatic semitone, or Pythagorean apotome		3	5	7	11	13	17	19	H
116.72		(18 : 5)1/19	21/19·32/19 : 51/19	playSecor	10.28
119.44	C♯	15 : 14	3·5 : 2·7	playSeptimal diatonic semitone, major diatonic semitone[3]				7	11	13	17	19	H		S
130.23	C23♯+	69 : 64	3·23 : 26	playSixty-ninth harmonic[5]									H
133.24	D♭	27 : 25	33 : 52	playSemitone maximus, minor second, large limma or Bohlen-Pierce small semitone,[3] high semitone,[12] alternate Renaissance half-step,[5] large limma, acute minor second			5	7	11	13	17	19	H
150.00	C/D	23/24	21/8	playEqual-tempered neutral second	8, 24
150.64	D↓[2]	12 : 11	22·3 : 11	play3/4-tone or Undecimal neutral second,[3][5] trumpet three-quarter tone[9]					11	13	17	19	H		S
155.14	D	35 : 32	5·7 : 25	playThirty-fifth harmonic[5]				7	11	13	17	19	H
160.90	D--	800 : 729	25·52 : 36	playGrave whole tone,[3] neutral second, grave major second			5	7	11	13	17	19	H
165.00	D↑♭-[2]	11 : 10	11 : 2·5	playGreater undecimal minor/major/neutral second, 4/5-tone or Ptolemy's second[3]					11	13	17	19	H		S
171.43		21/7	21/7	play1 step in 7 equal temperament	7
179.70		71 : 64	71 : 26	playSeventy-first harmonic[5]									H
180.45	E---	65536 : 59049	216 : 310	playPythagorean diminished third,[3][6] Pythagorean minor tone		3	5	7	11	13	17	19	H
182.40	D-[2]	10 : 9	2·5 : 32	playSmall 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	7	11	13	17	19	H		S
200.00	D	22/12	21/6	playEqual-tempered major second	6, 12									M
203.91	D[2]	9 : 8	32 : 23	playPythagorean 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	5	7	11	13	17	19	H		S
223.46	E-[2]	256 : 225	28 : 32·52	playJust diminished third[14]			5	7	11	13	17	19	H
227.79		73 : 64	73 : 26	playSeventy-third harmonic[5]									H
231.17	D-[2]	8 : 7	23 : 7	playSeptimal major second,[4] septimal whole tone[3][5]				7	11	13	17	19	H		S
240.00		21/5	21/5	play1 step in 5 equal temperament	5
251.34		37 : 32	37 : 25	playThirty-seventh harmonic[5]									H
253.08	D♯-	125 : 108	53 : 22·33	playSemi-augmented whole tone,[3] semi-augmented second			5	7	11	13	17	19	H
266.87	E♭[2]	7 : 6	7 : 2·3	playSeptimal minor third[3][4][9] or Sub minor Third[12]				7	11	13	17	19	H		S
274.58	D♯[2]	75 : 64	3·52 : 26	playJust augmented second,[14] Augmented Tone,[12] augmented second[5][11]			5	7	11	13	17	19	H
294.13	E♭-[2]	32 : 27	25 : 33	playPythagorean minor third[3][5][6][12][14] or semiditone		3	5	7	11	13	17	19	H
297.51	E♭[2]	19 : 16	19 : 24	play19th harmonic,[3] 19-limit minor third, overtone minor third,[5] Pythagorean minor third								19	H
300.00	D♯/E♭	23/12	21/4	playEqual-tempered minor third	4, 12									M
310.26		6:5÷(81:80)1/4	22 : 53/4	playQuarter-comma meantone minor third										M
311.98		(3 : 2)4/9	34/9 : 24/9	playAlpha scale minor third	3.85
315.64	E♭[2]	6 : 5	2·3 : 5	playJust minor third,[3][4][5][9][14] minor third,[12] 1/3-comma meantone minor third			5	7	11	13	17	19	H	M	S
317.60	D♯++	19683 : 16384	39 : 214	playPythagorean augmented second[3][6]		3	5	7	11	13	17	19	H
320.14		77 : 64	7·11 : 26	playSeventy-seventh harmonic[5]					11	13	17	19	H
337.15	E♭+	243 : 200	35 : 23·52	playAcute minor third[3]			5	7	11	13	17	19	H
342.48	E♭	39 : 32	3·13 : 25	playThirty-ninth harmonic[5]						13	17	19	H
342.86		22/7	22/7	play2 steps in 7 equal temperament	7
347.41	E↑♭-[2]	11 : 9	11 : 32	playUndecimal neutral third[3]					11	13	17	19	H
350.00	D/E	27/24	27/24	playEqual-tempered neutral third	24
359.47	E[2]	16 : 13	24 : 13	playTridecimal neutral third[3]						13	17	19	H
364.54		79 : 64	79 : 26	playSeventy-ninth harmonic[5]									H
364.81	E-	100 : 81	22·52 : 34	playGrave major third[3]			5	7	11	13	17	19	H
384.36	F♭--	8192 : 6561	213 : 38	playPythagorean diminished fourth,[3][6] Pythagorean 'schismatic' third[5]		3	5	7	11	13	17	19	H
386.31	E[2]	5 : 4	5 : 22	playJust major third,[3][4][5][9][14] major third,[12] quarter-comma meantone major third			5	7	11	13	17	19	H	M	S
400.00	E	24/12	21/3	playEqual-tempered major third	3, 12									M
407.82	E+[2]	81 : 64	34 : 26	playPythagorean major third,[3][5][6][12][14] ditone		3	5	7	11	13	17	19	H
417.51	F↓+[2]	14 : 11	2·7 : 11	playUndecimal diminished fourth or major third[3]					11	13	17	19	H
427.37	F♭[2]	32 : 25	25 : 52	playJust diminished fourth,[14] diminished fourth[5][11]			5	7	11	13	17	19	H
429.06		41 : 32	41 : 25	playForty-first harmonic[5]									H
435.08	E[2]	9 : 7	32 : 7	playSeptimal major third,[3][5] Bohlen-Pierce third,[3] Super major Third[12]				7	11	13	17	19	H
450.05		83 : 64	83 : 26	playEighty-third harmonic[5]									H
454.21	F♭	13 : 10	13 : 2·5	playTridecimal major third or diminished fourth						13	17	19	H
456.99	E♯[2]	125 : 96	53 : 25·3	playJust augmented third, augmented third[5]			5	7	11	13	17	19	H
470.78	F+[2]	21 : 16	3·7 : 24	play  playTwenty-first harmonic, narrow fourth,[3] septimal fourth,[5] wide augmented third				7	11	13	17	19	H
478.49	E♯+	675 : 512	33·52 : 29	playWide augmented third[3]			5	7	11	13	17	19	H
480.00		22/5	22/5	play2 steps in 5 equal temperament	5
491.27	E♯	85 : 64	5·17 : 26	playEighty-fifth harmonic[5]							17	19	H
498.04	F[2]	4 : 3	22 : 3	playPerfect fourth,[3][5][14] Pythagorean perfect fourth, Just perfect fourth or diatessaron[4]		3	5	7	11	13	17	19	H		S
500.00	F	25/12	25/12	playEqual-tempered perfect fourth	12									M
510.51		(3 : 2)8/11	38/11 : 28/11	playBeta scale perfect fourth	18.75
511.52		43 : 32	43 : 25	playForty-third harmonic[5]									H
514.29		23/7	23/7	play3 steps in 7 equal temperament	7
519.55	F+[2]	27 : 20	33 : 22·5	play5-limit wolf fourth, acute fourth,[3] imperfect fourth[14]			5	7	11	13	17	19	H
521.51	E♯+++	177147 : 131072	311 : 217	playPythagorean augmented third[3][6] (F+ (pitch))		3	5	7	11	13	17	19	H
531.53	F29+	87 : 64	3·29 : 26	playEighty-seventh harmonic[5]									H
551.32	F↑[2]	11 : 8	11 : 23	playeleventh harmonic,[5] undecimal tritone,[5] lesser undecimal tritone, undecimal semi-augmented fourth[3]					11	13	17	19	H
568.72	F♯[2]	25 : 18	52 : 2·32	playJust augmented fourth[3][5]			5	7	11	13	17	19	H
570.88		89 : 64	89 : 26	playEighty-ninth harmonic[5]									H
582.51	G♭[2]	7 : 5	7 : 5	playLesser septimal tritone, septimal tritone[3][4][5] Huygens' tritone or Bohlen-Pierce fourth,[3] septimal fifth,[9] septimal diminished fifth[15]				7	11	13	17	19	H
588.27	G♭--	1024 : 729	210 : 36	playPythagorean diminished fifth,[3][6] low Pythagorean tritone[5]		3	5	7	11	13	17	19	H
590.22	F♯+[2]	45 : 32	32·5 : 25	playJust 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	7	11	13	17	19	H
600.00	F♯/G♭	26/12	21/2	playEqual-tempered tritone	2, 12									M
609.35	G♭	91 : 64	7·13 : 26	playNinety-first harmonic[5]						13	17	19	H
609.78	G♭-[2]	64 : 45	26 : 32·5	playJust tritone,[4] 2nd tritone,[6] 'false' fifth,[14] diminished fifth,[11] low 5-limit tritone[5]			5	7	11	13	17	19	H
611.73	F#++	729 : 512	36 : 29	playPythagorean tritone,[3][6] Pythagorean augmented fourth, high Pythagorean tritone[5]		3	5	7	11	13	17	19	H
617.49	F♯[2]	10 : 7	2·5 : 7	playGreater septimal tritone, septimal tritone,[4][5] Euler's tritone[3]				7	11	13	17	19	H
628.27	F23♯+	23 : 16	23 : 24	playTwenty-third harmonic,[5] classic diminished fifth									H
631.28	G♭[2]	36 : 25	22·32 : 52	playJust diminished fifth[5]			5	7	11	13	17	19	H
646.99	F31♯+	93 : 64	3·31 : 26	playNinety-third harmonic[5]									H
648.68	G↓[2]	16 : 11	24 : 11	playInversion of eleventh harmonic, undecimal semi-diminished fifth[3]					11	13	17	19	H
665.51		47 : 32	47 : 25	playForty-seventh harmonic[5]									H
678.49	A---	262144 : 177147	218 : 311	playPythagorean diminished sixth[3][6]		3	5	7	11	13	17	19	H
680.45	G-	40 : 27	23·5 : 33	play5-limit wolf fifth,[5] or diminished sixth, grave fifth,[3][6][9] imperfect fifth,[14]			5	7	11	13	17	19	H
683.83	G	95 : 64	5·19 : 26	playNinety-fifth harmonic[5]								19	H
691.20		3:2÷(81:80)1/2	2·51/2 : 3	playHalf-comma meantone perfect fifth										M
694.79		3:2÷(81:80)1/3	21/3·51/3 : 31/3	play1/3-comma meantone perfect fifth										M
695.81		3:2÷(81:80)2/7	21/7·52/7 : 31/7	play2/7-comma meantone perfect fifth										M
696.58		3:2÷(81:80)1/4	51/4	playQuarter-comma meantone perfect fifth										M
697.65		3:2÷(81:80)1/5	31/5·51/5 : 21/5	play1/5-comma meantone perfect fifth										M
698.37		3:2÷(81:80)1/6	31/3·51/6 : 21/3	play1/6-comma meantone perfect fifth										M
700.00	G	27/12	27/12	playEqual-tempered perfect fifth	12									M
701.89		231/53	231/53	play53-TET perfect fifth	53
701.96	G[2]	3 : 2	3 : 2	playPerfect fifth,[3][5][14] Pythagorean perfect fifth, Just perfect fifth or diapente,[4] fifth,[12] Just fifth[9]		3	5	7	11	13	17	19	H		S
702.44		224/41	224/41	play41-TET perfect fifth	41
703.45		217/29	217/29	play29-TET perfect fifth	29
719.90		97 : 64	97 : 26	playNinety-seventh harmonic[5]									H
721.51	A-	1024 : 675	210 : 33·52	playNarrow diminished sixth[3]			5	7	11	13	17	19	H
737.65	A♭+	49 : 32	7·7 : 25	playForty-ninth harmonic[5]				7	11	13	17	19	H
743.01	A	192 : 125	26·3 : 53	playClassic diminished sixth[3]			5	7	11	13	17	19	H
755.23		99 : 64	32·11 : 26	playNinety-ninth harmonic[5]					11	13	17	19	H
764.92	A♭[2]	14 : 9	2·7 : 32	playSeptimal minor sixth[3][5]				7	11	13	17	19	H
772.63	G♯	25 : 16	52 : 24	playJust augmented fifth[5][14]			5	7	11	13	17	19	H
782.49	G↑-[2]	11 : 7	11 : 7	playUndecimal minor sixth,[5] undecimal augmented fifth,[3] pi					11	13	17	19	H
789.85		101 : 64	101 : 26	playHundred-first harmonic[5]									H
792.18	A♭-[2]	128 : 81	27 : 34	playPythagorean minor sixth[3][5][6]		3	5	7	11	13	17	19	H
800.00	G♯/A♭	28/12	22/3	playEqual-tempered minor sixth	3, 12									M
806.91	G♯	51 : 32	3·17 : 25	playFifty-first harmonic[5]							17	19	H
813.69	A♭[2]	8 : 5	23 : 5	playJust minor sixth[3][4][9][14]			5	7	11	13	17	19	H
815.64	G♯++	6561 : 4096	38 : 212	playPythagorean augmented fifth,[3][6] Pythagorean 'schismatic' sixth[5]		3	5	7	11	13	17	19	H
823.80		103 : 64	103 : 26	playHundred-third harmonic[5]									H
833.09		51/2+1 : 2		playGolden ratio (833 cents scale)
833.11		233 : 144	233 : 24·32	playGolden ratio approximation (833 cents scale)									H
835.19	A♭+	81 : 50	34 : 2·52	playAcute minor sixth[3]			5	7	11	13	17	19	H
840.53	A♭[2]	13 : 8	13 : 23	playTridecimal neutral sixth,[3] overtone sixth,[5] thirteenth harmonic						13	17	19	H
850.00	G/A	217/24	217/24	playEqual-tempered neutral sixth	24
852.59	A↓[2]	18 : 11	2·32 : 11	playUndecimal neutral sixth,[3][5] Zalzal's neutral sixth					11	13	17	19	H
857.10	A+	105 : 64	3·5·7 : 26	playHundred-fifth harmonic[5]				7	11	13	17	19	H
857.14		25/7	25/7	play5 steps in 7 equal temperament	7
862.85	A-	400 : 243	24·52 : 35	playGrave major sixth[3]			5	7	11	13	17	19	H
873.51		53 : 32	53 : 25	playFifty-third harmonic[5]									H
882.40	B---	32768 : 19683	215 : 39	playPythagorean diminished seventh[3][6]		3	5	7	11	13	17	19	H
884.36	A[2]	5 : 3	5 : 3	playJust major sixth,[3][4][5][9][14] Bohlen-Pierce sixth,[3] 1/3-comma meantone major sixth			5	7	11	13	17	19	H	M
889.76		107 : 64	107 : 26	playHundred-seventh harmonic[5]									H
900.00	A	29/12	23/4	playEqual-tempered major sixth	4, 12									M
905.87	A+[2]	27 : 16	33 : 24	playPythagorean major sixth[3][5][9][14]		3	5	7	11	13	17	19	H
921.82		109 : 64	109 : 26	playHundred-ninth harmonic[5]									H
925.42	B-[2]	128 : 75	27 : 3·52	playJust diminished seventh,[14] diminished seventh[5][11]			5	7	11	13	17	19	H
933.13	A[2]	12 : 7	22·3 : 7	playSeptimal major sixth[3][4][5]				7	11	13	17	19	H
937.63	A↑	55 : 32	5·11 : 25	playFifty-fifth harmonic[5]					11	13	17	19	H
953.30		111 : 64	3·37 : 26	playHundred-eleventh harmonic[5]									H
955.03	A♯[2]	125 : 72	53 : 23·32	playJust augmented sixth[5]			5	7	11	13	17	19	H
957.21		(3 : 2)15/11	315/11 : 215/11	play15 steps in Beta scale	18.75
960.00		24/5	24/5	play4 steps in 5 equal temperament	5
968.83	B♭[2]	7 : 4	7 : 22	playSeptimal minor seventh,[4][5][9] harmonic seventh,[3][9] augmented sixth				7	11	13	17	19	H
976.54	A♯+[2]	225 : 128	32·52 : 27	playJust augmented sixth[14]			5	7	11	13	17	19	H
984.22		113 : 64	113 : 26	playHundred-thirteenth harmonic[5]									H
996.09	B♭-[2]	16 : 9	24 : 32	playPythagorean minor seventh,[3] Small just minor seventh,[4] lesser minor seventh,[14] just minor seventh,[9] Pythagorean small minor seventh[5]		3	5	7	11	13	17	19	H
999.47	B♭	57 : 32	3·19 : 25	playFifty-seventh harmonic[5]								19	H
1000.00	A♯/B♭	210/12	25/6	playEqual-tempered minor seventh	6, 12									M
1014.59	A23♯+	115 : 64	5·23 : 26	playHundred-fifteenth harmonic[5]									H
1017.60	B♭[2]	9 : 5	32 : 5	playGreater just minor seventh,[14] large just minor seventh,[4][5] Bohlen-Pierce seventh[3]			5	7	11	13	17	19	H
1019.55	A♯+++	59049 : 32768	310 : 215	playPythagorean augmented sixth[3][6]		3	5	7	11	13	17	19	H
1028.57		26/7	26/7	play6 steps in 7 equal temperament	7
1029.58	B29♭	29 : 16	29 : 24	playTwenty-ninth harmonic,[5] minor seventh									H
1035.00	B↓[2]	20 : 11	22·5 : 11	playLesser undecimal neutral seventh, large minor seventh[3]					11	13	17	19	H
1039.10	B♭+	729 : 400	36 : 24·52	playAcute minor seventh[3]			5	7	11	13	17	19	H
1044.44	A♭	117 : 64	32·13 : 26	playHundred-seventeenth harmonic[5]						13	17	19	H
1049.36	B↑♭-[2]	11 : 6	11 : 2·3	play21/4-tone or Undecimal neutral seventh,[3] undecimal 'median' seventh[5]					11	13	17	19	H
1050.00	A/B	221/24	27/8	playEqual-tempered neutral seventh	8, 24
1059.17		59 : 32	59 : 25	playFifty-ninth harmonic[5]									H
1066.76	B-	50 : 27	2·52 : 33	playGrave major seventh[3]			5	7	11	13	17	19	H
1073.78	B	119 : 64	7·17 : 26	playHundred-nineteenth harmonic[5]							17	19	H
1086.31	C♭--	4096 : 2187	212 : 37	playPythagorean diminished octave[3][6]		3	5	7	11	13	17	19	H
1088.27	B[2]	15 : 8	3·5 : 23	playJust major seventh,[3][5][9][14] small just major seventh,[4] 1/6-comma meantone major seventh			5	7	11	13	17	19	H
1100.00	B	211/12	211/12	playEqual-tempered major seventh	12									M
1102.64	B↑↑♭-	121 : 64	112 : 26	playHundred-twenty-first harmonic[5]					11	13	17	19	H
1107.82	C'♭-	256 : 135	28 : 33·5	playOctave − major chroma,[3] narrow diminished octave			5	7	11	13	17	19	H
1109.78	B+[2]	243 : 128	35 : 27	playPythagorean major seventh[3][5][6][9]		3	5	7	11	13	17	19	H
1116.89		61 : 32	61 : 25	playSixty-first harmonic[5]									H
1129.33	C'♭[2]	48 : 25	24·3 : 52	playClassic diminished octave,[3][6] large just major seventh[4]			5	7	11	13	17	19	H
1131.02		123 : 64	3·41 : 26	playHundred-twenty-third harmonic[5]									H
1137.04	B	27 : 14	33 : 2·7	playSeptimal major seventh[5]				7	11	13	17	19	H
1145.04	B31	31 : 16	31 : 24	playThirty-first harmonic,[5] augmented seventh									H
1158.94	B♯[2]	125 : 64	53 : 26	playJust augmented seventh,[5] 125th harmonic			5	7	11	13	17	19	H
1172.74	C+	63 : 32	32·7 : 25	playSixty-third harmonic[5]				7	11	13	17	19	H
1178.49	C'-	160 : 81	25·5 : 34	playOctave − syntonic comma,[3] semi-diminished octave			5	7	11	13	17	19	H
1186.42		127 : 64	127 : 26	playHundred-twenty-seventh harmonic[5]									H
1200.00	C'	2 : 1	2 : 1	playOctave[3][9] or diapason[4]	1, 12	3	5	7	11	13	17	19	H	M	S
1223.46	B♯+++	531441 : 262144	312 : 218	playPythagorean augmented seventh[3][6]		3	5	7	11	13	17	19	H
1525.86		21/2+1		playSilver ratio
1901.96	G'	3 : 1	3 : 1	playTritave or just perfect twelfth		3	5	7	11	13	17	19	H
2400.00	C"	4 : 1	22 : 1	playFifteenth or two octaves	1, 12	3	5	7	11	13	17	19	H	M
3986.31	E'''	10 : 1	5·2 : 1	playDecade, compound just major third			5	7	11	13	17	19	H	M

See also

• List of chord progressions
• List of meantone intervals
• List of musical scales and modes

References