List of pitch intervals

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

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.

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

List

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	play Unison,[3] monophony,[4] perfect prime,[3] tonic,[5] or fundamental	1, 12	3	M
0.40	C♯-	4375 : 4374	5^4·7 : 2·3^7	play Ragisma[3][6]		7		S
0.72	E+	2401 : 2400	7^4 : 2^5·3·5^2	play Breedsma[3][6]		7		S
1.00		2^1/1200	2^1/1200	play Cent[7]	1200
1.20		2^1/1000	2^1/1000	play Millioctave	1000
1.95	B♯++	32805 : 32768	3^8·5 : 2^15	play Schisma[3][5]		5
3.99		10^1/1000	2^1/1000·5^1/1000	play Savart or eptaméride	301.03
7.71	B♯	225 : 224	3^2·5^2 : 2^5·7	play Septimal kleisma,[3][6] marvel comma		7		S
8.11	B-	15625 : 15552	5^6 : 2^6·3^5	play Kleisma or semicomma majeur[3][6]		5
10.06	A++	2109375 : 2097152	3^3·5^7 : 2^21	play Semicomma,[3][6] Fokker's comma[3]		5
11.98	C	145 : 144	5·29 : 2^4·3^2	play Difference between 29:16 & 9:5		29		S
12.50		2^1/96	2^1/96	play Sixteenth tone	96
13.07	B-	1728 : 1715	2^6·3^3 : 5·7^3	play Orwell comma[3][8]		7
13.47	C	129 : 128	3·43 : 2^7	play Hundred-twenty-ninth harmonic		43		S
13.79	D	126 : 125	2·3^2·7 : 5^3	play Small septimal semicomma,[6] small septimal comma,[3] starling comma		7		S
14.37	C♭↑↑-	121 : 120	11^2 : 2^3·3·5	play Undecimal seconds comma[3]		11		S
16.67	C↑[lower-alpha 1]	2^1/72	2^1/72	play 1 step in 72 equal temperament	72
18.13	C	96 : 95	2^5·3 : 5·19	play Difference between 19:16 & 6:5		19		S
19.55	D--[2]	2048 : 2025	2^11 : 3^4·5^2	play Diaschisma,[3][6] minor comma		5
21.51	C+[2]	81 : 80	3^4 : 2^4·5	play Syntonic comma,[3][5][6] major comma, komma, chromatic diesis, or comma of Didymus[3][6][9][10]		5		S
22.64		2^1/53	2^1/53	play Holdrian comma, Holder's comma, 1 step in 53 equal temperament	53
23.46	B♯+++	531441 : 524288	3^12 : 2^19	play Pythagorean comma,[3][5][6][9][10] ditonic comma[3][6]		3
25.00		2^1/48	2^1/48	play Eighth tone	48
26.84	C	65 : 64	5·13 : 2^6	play Sixty-fifth harmonic,[5] 13th-partial chroma[3]		13		S
27.26	C-	64 : 63	2^6 : 3^2·7	play Septimal comma,[3][6][10] Archytas' comma,[3] 63rd subharmonic		7		S
29.27		2^1/41	2^1/41	play 1 step in 41 equal temperament	41
31.19	D♭↓	56 : 55	2^3·7 : 5·11	play Ptolemy's enharmonic:[5] difference between (11 : 8) and (7 : 5) tritone		11		S
33.33	C/D♭[lower-alpha 1]	2^1/36	2^1/36	play Sixth tone	36, 72
34.28	C	51 : 50	3·17 : 2·5^2	play Difference between 17:16 & 25:24		17		S
34.98	B♯-	50 : 49	2·5^2 : 7^2	play Septimal sixth tone or jubilisma, Erlich's decatonic comma or tritonic diesis[3][6]		7		S
35.70	D♭	49 : 48	7^2 : 2^4·3	play Septimal diesis, slendro diesis or septimal 1/6-tone[3]		7		S
38.05	C	46 : 45	2·23 : 3^2·5	play Inferior quarter tone,[5] difference between 23:16 & 45:32		23		S
38.71		2^1/31	2^1/31	play 1 step in 31 equal temperament	31
38.91	C↓♯+	45 : 44	3^2·5 : 4·11	play Undecimal diesis or undecimal fifth tone		11		S
40.00		2^1/30	2^1/30	play Fifth tone	30
41.06	D-	128 : 125	2^7 : 5^3	play Enharmonic diesis or 5-limit limma, minor diesis,[6] diminished second,[5][6] minor diesis or diesis,[3] 125th subharmonic		5
41.72	D♭	42 : 41	2·3·7 : 41	play Lesser 41-limit fifth tone		41		S
42.75	C	41 : 40	41 : 2^3·5	play Greater 41-limit fifth tone		41		S
43.83	C♯	40 : 39	2^3·5 : 3·13	play Tridecimal fifth tone		13		S
44.97	C	39 : 38	3·13 : 2·19	play Superior quarter-tone,[5] novendecimal fifth tone		19		S
46.17	D-	38 : 37	2·19 : 37	play Lesser 37-limit quarter tone		37		S
47.43	C♯	37 : 36	37 : 2^2·3^2	play Greater 37-limit quarter tone		37		S
48.77	C	36 : 35	2^2·3^2 : 5·7	play Septimal quarter tone, septimal diesis,[3][6] septimal comma,[2] superior quarter tone[5]		7		S
49.98		246 : 239	3·41 : 239	play Just quarter tone[10]		239
50.00	C/D	2^1/24	2^1/24	play Equal-tempered quarter tone	24
50.18	D♭	35 : 34	5·7 : 2·17	play ET quarter-tone approximation,[5] lesser 17-limit quarter tone		17		S
50.72	B♯++	59049 : 57344	3^10 : 2^13·7	play Harrison's comma (9 P5s - 1 H7)[3]		7
51.68	C↓♯	34 : 33	2·17 : 3·11	play Greater 17-limit quarter tone		17		S
53.27	C↑	33 : 32	3·11 : 2^5	play Thirty-third harmonic,[5] undecimal comma, undecimal quarter tone		11		S
54.96	D♭-	32 : 31	2^5 : 31	play Inferior quarter-tone,[5] thirty-first subharmonic		31		S
56.55	B♯+	529 : 512	23^2 : 2^9	play Five-hundred-twenty-ninth harmonic		23
56.77	C	31 : 30	31 : 2·3·5	play Greater quarter-tone,[5] difference between 31:16 & 15:8		31		S
58.69	C♯	30 : 29	2·3·5 : 29	play Lesser 29-limit quarter tone		29		S
60.75	C	29 : 28	29 : 2^2·7	play Greater 29-limit quarter tone		29		S
62.96	D♭-	28 : 27	2^2·7 : 3^3	play Septimal minor second, small minor second, inferior quarter tone[5]		7		S
63.81		(3 : 2)^1/11	3^1/11 : 2^1/11	play Beta scale step	18.75
65.34	C♯+	27 : 26	3^3 : 2·13	play Chromatic diesis,[11] tridecimal comma[3]		13		S
66.67	C↑/C♯[lower-alpha 1]	2^1/18	2^1/18	play Third tone	18, 36, 72
67.90	D-	26 : 25	2·13 : 5^2	play Tridecimal third tone, third tone[5]		13		S
70.67	C♯[2]	25 : 24	5^2 : 2^3·3	play Just chromatic semitone or minor chroma,[3] lesser chromatic semitone, small (just) semitone[10] or minor second,[4] minor chromatic semitone,[12] or minor semitone,[5] 2/7-comma meantone chromatic semitone		5		S
73.68	D♭-	24 : 23	2^3·3 : 23	play Lesser 23-limit semitone		23		S
76.96	C↓♯+	23 : 22	23 : 2·11	play Greater 23-limit semitone		23		S
78.00		(3 : 2)^1/9	3^1/9 : 2^1/9	play Alpha scale step	15.39
79.31		67 : 64	67 : 2^6	play Sixty-seventh harmonic[5]		67
80.54	C↑-	22 : 21	2·11 : 3·7	play Hard semitone,[5] two-fifth tone small semitone		11		S
84.47	D♭	21 : 20	3·7 : 2^2·5	play Septimal chromatic semitone, minor semitone[3]		7		S
88.80	C♯	20 : 19	2^2·5 : 19	play Novendecimal augmented unison		19		S
90.22	D♭--[2]	256 : 243	2^8 : 3^5	play Pythagorean minor second or limma,[3][6][10] Pythagorean diatonic semitone, Low Semitone[13]		3
92.18	C♯+[2]	135 : 128	3^3·5 : 2^7	play Greater chromatic semitone, chromatic semitone, semitone medius, major chroma or major limma,[3] small limma,[10] major chromatic semitone,[12] limma ascendant[5]		5
93.60	D♭-	19 : 18	19 : 2·9	Novendecimal minor second play		19		S
97.36	D↓↓	128 : 121	2^7 : 11^11	play 121st subharmonic[5][6]		11
98.95	D♭	18 : 17	2·3^2 : 17	play Just minor semitone, Arabic lute index finger[3]		17		S
100.00	C♯/D♭	2^1/12	2^1/12	play Equal-tempered minor second or semitone	12		M
104.96	C♯[2]	17 : 16	17 : 2^4	play Minor diatonic semitone, just major semitone, overtone semitone,[5] 17th harmonic,[3] limma		17		S
111.73	D♭-[2]	16 : 15	2^4 : 3·5	play Just minor second,[14] just diatonic semitone, large just semitone or major second,[4] major semitone,[5] limma, minor diatonic semitone,[3] diatonic second[15] semitone,[13] diatonic semitone,[10] 1/6-comma meantone minor second		5		S
113.69	C♯++	2187 : 2048	3^7 : 2^11	play apotome[3][10] or Pythagorean major semitone,[6] Pythagorean augmented unison, Pythagorean chromatic semitone, or Pythagorean apotome		3
116.72		(18 : 5)^1/19	2^1/19·3^2/19 : 5^1/19	play Secor	10.28
119.44	C♯	15 : 14	3·5 : 2·7	play Septimal diatonic semitone, major diatonic semitone,[3] Cowell semitone[5]		7		S
128.30	D	14 : 13	2·7 : 13	play Lesser tridecimal 2/3-tone[16]		13		S
130.23	C♯+	69 : 64	3·23 : 2^6	play Sixty-ninth harmonic[5]		23
133.24	D♭	27 : 25	3^3 : 5^2	play Semitone maximus, minor second, large limma or Bohlen-Pierce small semitone,[3] high semitone,[13] alternate Renaissance half-step,[5] large limma, acute minor second		5
133.33	C♯/D♭[lower-alpha 1]	2^1/9	2^2/18	play Two-third tone	9, 18, 36, 72
138.57	D♭-	13 : 12	13 : 2^2·3	play Greater tridecimal 2/3-tone,[16] Three-quarter tone[5]		13		S
150.00	C/D	2^3/24	2^1/8	play Equal-tempered neutral second	8, 24
150.64	D↓[2]	12 : 11	2^2·3 : 11	play 3/4-tone or Undecimal neutral second,[3][5] trumpet three-quarter tone,[10] middle finger [between frets][13]		11		S
155.14	D	35 : 32	5·7 : 2^5	play Thirty-fifth harmonic[5]		7
160.90	D--	800 : 729	2^5·5^2 : 3^6	play Grave whole tone,[3] neutral second, grave major second		5
165.00	D↑♭-[2]	11 : 10	11 : 2·5	play Greater undecimal minor/major/neutral second, 4/5-tone[6] or Ptolemy's second[3]		11		S
171.43		2^1/7	2^1/7	play 1 step in 7 equal temperament	7
179.70		71 : 64	71 : 2^6	play Seventy-first harmonic[5]		71
180.45	E---	65536 : 59049	2^16 : 3^10	play Pythagorean diminished third,[3][6] Pythagorean minor tone		3
182.40	D-[2]	10 : 9	2·5 : 3^2	play Small just whole tone or major second,[4] minor whole tone,[3][5] lesser whole tone,[15] minor tone,[13] minor second,[10] half-comma meantone major second		5		S
200.00	D	2^2/12	2^1/6	play Equal-tempered major second	6, 12		M
203.91	D[2]	9 : 8	3^2 : 2^3	play Pythagorean major second, Large just whole tone or major second[10] (sesquioctavan),[4] tonus, major whole tone,[3][5] greater whole tone,[15] major tone[13]		3		S
223.46	E-[2]	256 : 225	2^8 : 3^2·5^2	play Just diminished third[15]		5
227.79		73 : 64	73 : 2^6	play Seventy-third harmonic[5]		73
231.17	D-[2]	8 : 7	2^3 : 7	play Septimal major second,[4] septimal whole tone[3][5]		7		S
240.00		2^1/5	2^1/5	play 1 step in 5 equal temperament	5
251.34	D♯	37 : 32	37 : 2^5	play Thirty-seventh harmonic[5]		37
253.08	D♯-	125 : 108	5^3 : 2^2·3^3	play Semi-augmented whole tone,[3] semi-augmented second		5
262.37	E↓♭	64 : 55	2^6 : 5·11	play 55th subharmonic[5][6]		11
268.80	D	299 : 256	13·23 : 2^8	play Two-hundred-ninety-ninth harmonic		23
266.87	E♭[2]	7 : 6	7 : 2·3	play Septimal minor third[3][4][10] or Sub minor third[13]		7		S
274.58	D♯[2]	75 : 64	3·5^2 : 2^6	play Just augmented second,[15] Augmented tone,[13] augmented second[5][12]		5
294.13	E♭-[2]	32 : 27	2^5 : 3^3	play Pythagorean minor third[3][5][6][13][15] semiditone, or 27th subharmonic		3
297.51	E♭[2]	19 : 16	19 : 2^4	play 19th harmonic,[3] 19-limit minor third, overtone minor third[5]		19
300.00	D♯/E♭	2^3/12	2^1/4	play Equal-tempered minor third	4, 12		M
301.85	D♯-	25 : 21[5]	5^2 : 3·7	play Quasi-equal-tempered minor third, 2nd 7-limit minor third, Bohlen-Pierce second[3][6]		7
310.26		6:5÷(81:80)^1/4	2^2 : 5^3/4	play Quarter-comma meantone minor third			M
311.98		(3 : 2)^4/9	3^4/9 : 2^4/9	play Alpha scale minor third	3.85
315.64	E♭[2]	6 : 5	2·3 : 5	play Just minor third,[3][4][5][10][15] minor third,[13] 1/3-comma meantone minor third		5	M	S
317.60	D♯++	19683 : 16384	3^9 : 2^14	play Pythagorean augmented second[3][6]		3
320.14	E♭↑	77 : 64	7·11 : 2^6	play Seventy-seventh harmonic[5]		11
336.13	D♯-	17 : 14	17 : 2·7	play Superminor third[17]		17
337.15	E♭+	243 : 200	3^5 : 2^3·5^2	play Acute minor third[3]		5
342.48	E♭	39 : 32	3·13 : 2^5	play Thirty-ninth harmonic[5]		13
342.86		2^2/7	2^2/7	play 2 steps in 7 equal temperament	7
342.91	E♭-	128 : 105	2^7 : 3·5·7	play 105th subharmonic,[5] septimal neutral third[6]		7
347.41	E↑♭-[2]	11 : 9	11 : 3^2	play Undecimal neutral third[3][5]		11
350.00	D/E	2^7/24	2^7/24	play Equal-tempered neutral third	24
359.47	E[2]	16 : 13	2^4 : 13	play Tridecimal neutral third[3]		13
364.54		79 : 64	79 : 2^6	play Seventy-ninth harmonic[5]		79
364.81	E-	100 : 81	2^2·5^2 : 3^4	play Grave major third[3]		5
384.36	F♭--	8192 : 6561	2^13 : 3^8	play Pythagorean diminished fourth,[3][6] Pythagorean 'schismatic' third[5]		3
386.31	E[2]	5 : 4	5 : 2^2	play Just major third,[3][4][5][10][15] major third,[13] quarter-comma meantone major third		5	M	S
397.10	E+	161 : 128	7·23 : 2^7	play One-hundred-sixty-first harmonic		23
400.00	E	2^4/12	2^1/3	play Equal-tempered major third	3, 12		M
407.82	E+[2]	81 : 64	3^4 : 2^6	play Pythagorean major third,[3][5][6][13][15] ditone		3
417.51	F↓+[2]	14 : 11	2·7 : 11	play Undecimal diminished fourth or major third[3]		11
427.37	F♭[2]	32 : 25	2^5 : 5^2	play Just diminished fourth,[15] diminished fourth,[5][12] 25th subharmonic		5
429.06	E	41 : 32	41 : 2^5	play Forty-first harmonic[5]		41
435.08	E[2]	9 : 7	3^2 : 7	play Septimal major third,[3][5] Bohlen-Pierce third,[3] Super major Third[13]		7
444.77	F↓	128 : 99	2^7 : 9·11	play 99th subharmonic[5][6]		11
450.05		83 : 64	83 : 2^6	play Eighty-third harmonic[5]		83
454.21	F♭	13 : 10	13 : 2·5	play Tridecimal major third or diminished fourth		13
456.99	E♯[2]	125 : 96	5^3 : 2^5·3	play Just augmented third, augmented third[5]		5
462.35	E-	64 : 49	2^6 : 7^2	play 49th subharmonic[5][6]		7
470.78	F+[2]	21 : 16	3·7 : 2^4	play Twenty-first harmonic, narrow fourth,[3] septimal fourth,[5] wide augmented third, H7 on G		7
478.49	E♯+	675 : 512	3^3·5^2 : 2^9	play Wide augmented third[3]		5
480.00		2^2/5	2^2/5	play 2 steps in 5 equal temperament	5
491.27	E♯	85 : 64	5·17 : 2^6	play Eighty-fifth harmonic[5]		17
498.04	F[2]	4 : 3	2^2 : 3	play Perfect fourth,[3][5][15] Pythagorean perfect fourth, Just perfect fourth or diatessaron[4]		3		S
500.00	F	2^5/12	2^5/12	play Equal-tempered perfect fourth	12		M
510.51		(3 : 2)^8/11	3^8/11 : 2^8/11	play Beta scale perfect fourth	18.75
511.52	F	43 : 32	43 : 2^5	play Forty-third harmonic[5]		43
514.29		2^3/7	2^3/7	play 3 steps in 7 equal temperament	7
519.55	F+[2]	27 : 20	3^3 : 2^2·5	play 5-limit wolf fourth, acute fourth,[3] imperfect fourth[15]		5
521.51	E♯+++	177147 : 131072	3^11 : 2^17	play Pythagorean augmented third[3][6] (F+ (pitch))		3
531.53	F+	87 : 64	3·29 : 2^6	play Eighty-seventh harmonic[5]		29
551.32	F↑[2]	11 : 8	11 : 2^3	play eleventh harmonic,[5] undecimal tritone,[5] lesser undecimal tritone, undecimal semi-augmented fourth[3]		11
568.72	F♯[2]	25 : 18	5^2 : 2·3^2	play Just augmented fourth[3][5]		5
570.88		89 : 64	89 : 2^6	play Eighty-ninth harmonic[5]		89
582.51	G♭[2]	7 : 5	7 : 5	play Lesser septimal tritone, septimal tritone[3][4][5] Huygens' tritone or Bohlen-Pierce fourth,[3] septimal fifth,[10] septimal diminished fifth[18]		7
588.27	G♭--	1024 : 729	2^10 : 3^6	play Pythagorean diminished fifth,[3][6] low Pythagorean tritone[5]		3
590.22	F♯+[2]	45 : 32	3^2·5 : 2^5	play Just augmented fourth, just tritone,[4][10] tritone,[6] diatonic tritone,[3] 'augmented' or 'false' fourth,[15] high 5-limit tritone,[5] 1/6-comma meantone augmented fourth		5
600.00	F♯/G♭	2^6/12	2^1/2=√2	play Equal-tempered tritone	2, 12		M
609.35	G♭	91 : 64	7·13 : 2^6	play Ninety-first harmonic[5]		13
609.78	G♭-[2]	64 : 45	2^6 : 3^2·5	play Just tritone,[4] 2nd tritone,[6] 'false' fifth,[15] diminished fifth,[12] low 5-limit tritone,[5] 45th subharmonic		5
611.73	F♯++	729 : 512	3^6 : 2^9	play Pythagorean tritone,[3][6] Pythagorean augmented fourth, high Pythagorean tritone[5]		3
617.49	F♯[2]	10 : 7	2·5 : 7	play Greater septimal tritone, septimal tritone,[4][5] Euler's tritone[3]		7
628.27	F♯+	23 : 16	23 : 2^4	play Twenty-third harmonic,[5] classic diminished fifth		23
631.28	G♭[2]	36 : 25	2^2·3^2 : 5^2	play Just diminished fifth[5]		5
646.99	F♯+	93 : 64	3·31 : 2^6	play Ninety-third harmonic[5]		31
648.68	G↓[2]	16 : 11	2^4 : 11	play ` undecimal semi-diminished fifth[3]		11
665.51		47 : 32	47 : 2^5	play Forty-seventh harmonic[5]		47
678.49	A---	262144 : 177147	2^18 : 3^11	play Pythagorean diminished sixth[3][6]		3
680.45	G-	40 : 27	2^3·5 : 3^3	play 5-limit wolf fifth,[5] or diminished sixth, grave fifth,[3][6][10] imperfect fifth,[15]		5
683.83	G	95 : 64	5·19 : 2^6	play Ninety-fifth harmonic[5]		19
684.82	E++	12167 : 8192	23^3 : 2^13	play 12167th harmonic		23
691.20		3:2÷(81:80)^1/2	2·5^1/2 : 3	play Half-comma meantone perfect fifth			M
694.79		3:2÷(81:80)^1/3	2^1/3·5^1/3 : 3^1/3	play 1/3-comma meantone perfect fifth			M
695.81		3:2÷(81:80)^2/7	2^1/7·5^2/7 : 3^1/7	play 2/7-comma meantone perfect fifth			M
696.58		3:2÷(81:80)^1/4	5^1/4	play Quarter-comma meantone perfect fifth			M
697.65		3:2÷(81:80)^1/5	3^1/5·5^1/5 : 2^1/5	play 1/5-comma meantone perfect fifth			M
698.37		3:2÷(81:80)^1/6	3^1/3·5^1/6 : 2^1/3	play 1/6-comma meantone perfect fifth			M
700.00	G	2^7/12	2^7/12	play Equal-tempered perfect fifth	12		M
701.89		2^31/53	2^31/53	play 53-TET perfect fifth	53
701.96	G[2]	3 : 2	3 : 2	play Perfect fifth,[3][5][15] Pythagorean perfect fifth, Just perfect fifth or diapente,[4] fifth,[13] Just fifth[10]		3		S
702.44		2^24/41	2^24/41	play 41-TET perfect fifth	41
703.45		2^17/29	2^17/29	play 29-TET perfect fifth	29
719.90		97 : 64	97 : 2^6	play Ninety-seventh harmonic[5]		97
721.51	A-	1024 : 675	2^10 : 3^3·5^2	play Narrow diminished sixth[3]		5
729.22	G-	32 : 21	2^4 : 3·7	play 21st subharmonic[5][6]		7
733.23	F+	391 : 256	17·23 : 2^8	play Three-hundred-ninety-first harmonic		23
737.65	A♭+	49 : 32	7·7 : 2^5	play Forty-ninth harmonic[5]		7
743.01	A	192 : 125	2^6·3 : 5^3	play Classic diminished sixth[3]		5
755.23	G↑	99 : 64	3^2·11 : 2^6	play Ninety-ninth harmonic[5]		11
764.92	A♭[2]	14 : 9	2·7 : 3^2	play Septimal minor sixth[3][5]		7
772.63	G♯	25 : 16	5^2 : 2^4	play Just augmented fifth[5][15]		5
782.49	G↑-[2]	11 : 7	11 : 7	play Undecimal minor sixth,[5] undecimal augmented fifth,[3] Fibonacci numbers		11
789.85		101 : 64	101 : 2^6	play Hundred-first harmonic[5]		101
792.18	A♭-[2]	128 : 81	2^7 : 3^4	play Pythagorean minor sixth,[3][5][6] 81st subharmonic		3
800.00	G♯/A♭	2^8/12	2^2/3	play Equal-tempered minor sixth	3, 12		M
806.91	G♯	51 : 32	3·17 : 2^5	play Fifty-first harmonic[5]		17
813.69	A♭[2]	8 : 5	2^3 : 5	play Just minor sixth[3][4][10][15]		5
815.64	G♯++	6561 : 4096	3^8 : 2^12	play Pythagorean augmented fifth,[3][6] Pythagorean 'schismatic' sixth[5]		3
823.80		103 : 64	103 : 2^6	play Hundred-third harmonic[5]		103
832.18	G♯+	207 : 128	3^2·23 : 2^7	play Two-hundred-seventh harmonic		23
833.09		5^1/2+1 : 2		play Golden ratio (833 cents scale)
833.11		233 : 144	233 : 2^4·3^2	play Golden ratio approximation (833 cents scale)		233
835.19	A♭+	81 : 50	3^4 : 2·5^2	play Acute minor sixth[3]		5
840.53	A♭[2]	13 : 8	13 : 2^3	play Tridecimal neutral sixth,[3] overtone sixth,[5] thirteenth harmonic		13
850.00	G/A	2^17/24	2^17/24	play Equal-tempered neutral sixth	24
852.59	A↓[2]	18 : 11	2·3^2 : 11	play Undecimal neutral sixth,[3][5] Zalzal's neutral sixth		11
857.10	A+	105 : 64	3·5·7 : 2^6	play Hundred-fifth harmonic[5]		7
857.14		2^5/7	2^5/7	play 5 steps in 7 equal temperament	7
862.85	A-	400 : 243	2^4·5^2 : 3^5	play Grave major sixth[3]		5
873.51		53 : 32	53 : 2^5	play Fifty-third harmonic[5]		53
879.86	A↓	128 : 77	2^7 : 7·11	play 77th subharmonic[5][6]		11
882.40	B---	32768 : 19683	2^15 : 3^9	play Pythagorean diminished seventh[3][6]		3
884.36	A[2]	5 : 3	5 : 3	play Just major sixth,[3][4][5][10][15] Bohlen-Pierce sixth,[3] 1/3-comma meantone major sixth		5	M
889.76		107 : 64	107 : 2^6	play Hundred-seventh harmonic[5]		107
900.00	A	2^9/12	2^3/4	play Equal-tempered major sixth	4, 12		M
902.49	A	32 : 19	2^5 : 19	play 19th subharmonic[5][6]		19
905.87	A+[2]	27 : 16	3^3 : 2^4	play Pythagorean major sixth[3][5][10][15]		3
921.82		109 : 64	109 : 2^6	play Hundred-ninth harmonic[5]		109
925.42	B-[2]	128 : 75	2^7 : 3·5^2	play Just diminished seventh,[15] diminished seventh,[5][12] 75th subharmonic		5
925.79	A+	437 : 256	19·23 : 2^8	play Four-hundred-thirty-seventh harmonic		23
933.13	A[2]	12 : 7	2^2·3 : 7	play Septimal major sixth[3][4][5]		7
937.63	A↑	55 : 32	5·11 : 2^5	play Fifty-fifth harmonic[5][19]		11
953.30	A♯+	111 : 64	3·37 : 2^6	play Hundred-eleventh harmonic[5]		37
955.03	A♯[2]	125 : 72	5^3 : 2^3·3^2	play Just augmented sixth[5]		5
957.21		(3 : 2)^15/11	3^15/11 : 2^15/11	play 15 steps in Beta scale	18.75
960.00		2^4/5	2^4/5	play 4 steps in 5 equal temperament	5
968.83	B♭[2]	7 : 4	7 : 2^2	play Septimal minor seventh,[4][5][10] harmonic seventh,[3][10] augmented sixth		7
976.54	A♯+[2]	225 : 128	3^2·5^2 : 2^7	play Just augmented sixth[15]		5
984.22		113 : 64	113 : 2^6	play Hundred-thirteenth harmonic[5]		113
996.09	B♭-[2]	16 : 9	2^4 : 3^2	play Pythagorean minor seventh,[3] Small just minor seventh,[4] lesser minor seventh,[15] just minor seventh,[10] Pythagorean small minor seventh[5]		3
999.47	B♭	57 : 32	3·19 : 2^5	play Fifty-seventh harmonic[5]		19
1000.00	A♯/B♭	2^10/12	2^5/6	play Equal-tempered minor seventh	6, 12		M
1014.59	A♯+	115 : 64	5·23 : 2^6	play Hundred-fifteenth harmonic[5]		23
1017.60	B♭[2]	9 : 5	3^2 : 5	play Greater just minor seventh,[15] large just minor seventh,[4][5] Bohlen-Pierce seventh[3]		5
1019.55	A♯+++	59049 : 32768	3^10 : 2^15	play Pythagorean augmented sixth[3][6]		3
1028.57		2^6/7	2^6/7	play 6 steps in 7 equal temperament	7
1029.58	B♭	29 : 16	29 : 2^4	play Twenty-ninth harmonic,[5] minor seventh		29
1035.00	B↓[2]	20 : 11	2^2·5 : 11	play Lesser undecimal neutral seventh, large minor seventh[3]		11
1039.10	B♭+	729 : 400	3^6 : 2^4·5^2	play Acute minor seventh[3]		5
1044.44	B♭	117 : 64	3^2·13 : 2^6	play Hundred-seventeenth harmonic[5]		13
1044.86	B♭-	64 : 35	2^6 : 5·7	play 35th subharmonic,[5] septimal neutral seventh[6]		7
1049.36	B↑♭-[2]	11 : 6	11 : 2·3	play 21/4-tone or Undecimal neutral seventh,[3] undecimal 'median' seventh[5]		11
1050.00	A/B	2^21/24	2^7/8	play Equal-tempered neutral seventh	8, 24
1059.17		59 : 32	59 : 2^5	play Fifty-ninth harmonic[5]		59
1066.76	B-	50 : 27	2·5^2 : 3^3	play Grave major seventh[3]		5
1073.78	B	119 : 64	7·17 : 2^6	play Hundred-nineteenth harmonic[5]		17
1086.31	C♭--	4096 : 2187	2^12 : 3^7	play Pythagorean diminished octave[3][6]		3
1088.27	B[2]	15 : 8	3·5 : 2^3	play Just major seventh,[3][5][10][15] small just major seventh,[4] 1/6-comma meantone major seventh		5
1095.04	C♭	32 : 17	2^5 : 17	play 17th subharmonic[5][6]		17
1100.00	B	2^11/12	2^11/12	play Equal-tempered major seventh	12		M
1102.64	B↑↑♭-	121 : 64	11^2 : 2^6	play Hundred-twenty-first harmonic[5]		11
1107.82	C'♭-	256 : 135	2^8 : 3^3·5	play Octave − major chroma,[3] narrow diminished octave		5
1109.78	B+[2]	243 : 128	3^5 : 2^7	play Pythagorean major seventh[3][5][6][10]		3
1116.89		61 : 32	61 : 2^5	play Sixty-first harmonic[5]		61
1129.33	C'♭[2]	48 : 25	2^4·3 : 5^2	play Classic diminished octave,[3][6] large just major seventh[4]		5
1131.02	B	123 : 64	3·41 : 2^6	play Hundred-twenty-third harmonic[5]		41
1137.04	B	27 : 14	3^3 : 2·7	play Septimal major seventh[5]		7
1145.04	B	31 : 16	31 : 2^4	play Thirty-first harmonic,[5] augmented seventh		31
1146.73	C↓	64 : 33	2^6 : 3·11	play 33rd subharmonic[6]		11
1151.23	C	35 : 18	5·7 : 2·3^2	play Septimal supermajor seventh, septimal quarter tone inverted		7
1158.94	B♯[2]	125 : 64	5^3 : 2^6	play Just augmented seventh,[5] 125th harmonic		5
1172.74	C+	63 : 32	3^2·7 : 2^5	play Sixty-third harmonic[5]		7
1178.49	C'-	160 : 81	2^5·5 : 3^4	play Octave − syntonic comma,[3] semi-diminished octave		5
1179.59	B↑	253 : 128	11·23 : 2^7	play Two-hundred-fifty-third harmonic[5]		23
1186.42		127 : 64	127 : 2^6	play Hundred-twenty-seventh harmonic[5]		127
1200.00	C'	2 : 1	2 : 1	play Octave[3][10] or diapason[4]	1, 12	3	M	S
1223.46	B♯+++	531441 : 262144	3^12 : 2^18	play Pythagorean augmented seventh[3][6]		3
1525.86		2^1/2+1		play Silver ratio
1901.96	G'	3 : 1	3 : 1	play Tritave or just perfect twelfth		3
2400.00	C"	4 : 1	2^2 : 1	play Fifteenth or two octaves	1, 12	3	M
3986.31	E'''	10 : 1	5·2 : 1	play Decade, compound just major third		5	M

See also

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

Notes

1. Maneri-Sims notation

References

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

External links

• "Names of seven-limit commas", XenHarmony.org. (Archived copy)
• "Anatomy of an Octave", KyleGann.com.
• "List of Overtones", Xenharmonic.Wikispaces.com.
• "All Known Musical Intervals" (by Dale Pond), Svpvril.com.