List of pitch intervals

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.

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.

Comparison of two sets of musical intervals. The equal-tempered intervals are black; the Pythagorean intervals are green.

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	playⓘ Unison,[3] monophony,[4] perfect prime,[3] tonic,[5] or fundamental	1, 12	3	M
0.03		65537 : 65536	65537 : 216	playⓘ Sixty-five-thousand-five-hundred-thirty-seventh harmonic		65537		S
0.40	C♯−	4375 : 4374	54×7 : 2×37	playⓘ Ragisma[3][6]		7		S
0.72	E+	2401 : 2400	74 : 25×3×52	playⓘ Breedsma[3][6]		7		S
1.00		21/1200	21/1200	playⓘ Cent[7]	1200
1.20		21/1000	21/1000	playⓘ Millioctave	1000
1.95	B♯++	32805 : 32768	38×5 : 215	playⓘ Schisma[3][5]		5
1.96		3:2÷(27/12)	3 : 219/12	Grad, Werckmeister[8]
3.99		101/1000	21/1000×51/1000	playⓘ Savart or eptaméride	301.03
7.71	B♯	225 : 224	32×52 : 25×7	playⓘ Septimal kleisma,[3][6] marvel comma		7		S
8.11	B−	15625 : 15552	56 : 26×35	playⓘ Kleisma or semicomma majeur[3][6]		5
10.06	A++	2109375 : 2097152	33×57 : 221	playⓘ Semicomma,[3][6] Fokker's comma[3]		5
10.85	C	160 : 159	25×5 : 3×53	playⓘ Difference between 5:3 & 53:32		53		S
11.98	C	145 : 144	5×29 : 24×32	playⓘ Difference between 29:16 & 9:5		29		S
12.50		21/96	21/96	playⓘ Sixteenth tone	96
13.07	B−	1728 : 1715	26×33 : 5×73	playⓘ Orwell comma[3][9]		7
13.47	C	129 : 128	3×43 : 27	playⓘ Hundred-twenty-ninth harmonic		43		S
13.79	D	126 : 125	2×32×7 : 53	playⓘ Small septimal semicomma,[6] small septimal comma,[3] starling comma		7		S
14.37	C♭↑↑−	121 : 120	112 : 23×3×5	playⓘ Undecimal seconds comma[3]		11		S
16.67	C↑[a]	21/72	21/72	playⓘ 1 step in 72 equal temperament	72
18.13	C	96 : 95	25×3 : 5×19	playⓘ Difference between 19:16 & 6:5		19		S
19.55	D--[2]	2048 : 2025	211 : 34×52	playⓘ Diaschisma,[3][6] minor comma		5
21.51	C+[2]	81 : 80	34 : 24×5	playⓘ 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	playⓘ Holdrian comma, Holder's comma, 1 step in 53 equal temperament	53
23.46	B♯+++	531441 : 524288	312 : 219	playⓘ Pythagorean comma,[3][5][6][10][11] ditonic comma[3][6]		3
25.00		21/48	21/48	playⓘ Eighth tone	48
26.84	C	65 : 64	5×13 : 26	playⓘ Sixty-fifth harmonic,[5] 13th-partial chroma[3]		13		S
27.26	C−	64 : 63	26 : 32×7	playⓘ Septimal comma,[3][6][11] Archytas' comma,[3] 63rd subharmonic		7		S
29.27		21/41	21/41	playⓘ 1 step in 41 equal temperament	41
31.19	D♭↓	56 : 55	23×7 : 5×11	playⓘ Undecimal diesis,[3] Ptolemy's enharmonic:[5] difference between (11 : 8) and (7 : 5) tritone		11		S
33.33	C/D♭[a]	21/36	21/36	playⓘ Sixth tone	36, 72
34.28	C	51 : 50	3×17 : 2×52	playⓘ Difference between 17:16 & 25:24		17		S
34.98	B♯-	50 : 49	2×52 : 72	playⓘ Septimal sixth tone or jubilisma, Erlich's decatonic comma or tritonic diesis[3][6]		7		S
35.70	D♭	49 : 48	72 : 24×3	playⓘ Septimal diesis, slendro diesis or septimal 1/6-tone[3]		7		S
38.05	C	46 : 45	2×23 : 32×5	playⓘ Inferior quarter tone,[5] difference between 23:16 & 45:32		23		S
38.71		21/31	21/31	playⓘ 1 step in 31 equal temperament or Normal Diesis	31
38.91	C↓♯+	45 : 44	32×5 : 4×11	playⓘ Undecimal diesis or undecimal fifth tone		11		S
40.00		21/30	21/30	playⓘ Fifth tone	30
41.06	D−	128 : 125	27 : 53	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 : 23×5	playⓘ Greater 41-limit fifth tone		41		S
43.83	C♯	40 : 39	23×5 : 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 : 22×32	playⓘ Greater 37-limit quarter tone		37		S
48.77	C	36 : 35	22×32 : 5×7	playⓘ Septimal quarter tone, septimal diesis,[3][6] septimal chroma,[2] superior quarter tone[5]		7		S
49.98		246 : 239	3×41 : 239	playⓘ Just quarter tone[11]		239
50.00	C/D	21/24	21/24	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	310 : 213×7	playⓘ Harrison's comma (10 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 : 25	playⓘ Thirty-third harmonic,[5] undecimal comma, undecimal quarter tone		11		S
54.96	D♭-	32 : 31	25 : 31	playⓘ Inferior quarter-tone,[5] thirty-first subharmonic		31		S
56.55	B♯+	529 : 512	232 : 29	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 : 22×7	playⓘ Greater 29-limit quarter tone		29		S
62.96	D♭-	28 : 27	22×7 : 33	playⓘ Septimal minor second, small minor second, inferior quarter tone[5]		7		S
63.81		(3 : 2)1/11	31/11 : 21/11	playⓘ Beta scale step	18.75
65.34	C♯+	27 : 26	33 : 2×13	playⓘ Chromatic diesis,[12] tridecimal comma[3]		13		S
66.34	D♭	133 : 128	7×19 : 27	playⓘ One-hundred-thirty-third harmonic		19
66.67	C↑/C♯[a]	21/18	21/18	playⓘ Third tone	18, 36, 72
67.90	D-	26 : 25	2×13 : 52	playⓘ Tridecimal third tone, third tone[5]		13		S
70.67	C♯[2]	25 : 24	52 : 23×3	playⓘ 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	D♭-	24 : 23	23×3 : 23	playⓘ Lesser 23-limit semitone		23		S
75.00		21/16	23/48	playⓘ 1 step in 16 equal temperament, 3 steps in 48	16, 48
76.96	C↓♯+	23 : 22	23 : 2×11	playⓘ Greater 23-limit semitone		23		S
78.00		(3 : 2)1/9	31/9 : 21/9	playⓘ Alpha scale step	15.39
79.31		67 : 64	67 : 26	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 : 22×5	playⓘ Septimal chromatic semitone, minor semitone[3]		7		S
88.80	C♯	20 : 19	22×5 : 19	playⓘ Novendecimal augmented unison		19		S
90.22	D♭−−[2]	256 : 243	28 : 35	playⓘ Pythagorean minor second or limma,[3][6][11] Pythagorean diatonic semitone, Low Semitone[14]		3
92.18	C♯+[2]	135 : 128	33×5 : 27	playⓘ 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	D♭-	19 : 18	19 : 2×9	Novendecimal minor secondplayⓘ		19		S
97.36	D↓↓	128 : 121	27 : 112	playⓘ 121st subharmonic,[5][6] undecimal minor second		11
98.95	D♭	18 : 17	2×32 : 17	playⓘ Just minor semitone, Arabic lute index finger[3]		17		S
100.00	C♯/D♭	21/12	21/12	playⓘ Equal-tempered minor second or semitone	12		M
104.96	C♯[2]	17 : 16	17 : 24	playⓘ 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	playⓘ Studie II interval (compound just major third, 5:1, divided into 25 equal parts)	25
111.73	D♭-[2]	16 : 15	24 : 3×5	playⓘ 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	playⓘ 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	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
125.00		25/48	25/48	playⓘ 5 steps in 48 equal temperament	48
128.30	D	14 : 13	2×7 : 13	playⓘ Lesser tridecimal 2/3-tone[17]		13		S
130.23	C♯+	69 : 64	3×23 : 26	playⓘ Sixty-ninth harmonic[5]		23
133.24	D♭	27 : 25	33 : 52	playⓘ 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♯/D♭[a]	21/9	22/18	playⓘ Two-third tone	9, 18, 36, 72
138.57	D♭-	13 : 12	13 : 22×3	playⓘ Greater tridecimal 2/3-tone,[17] Three-quarter tone[5]		13		S
150.00	C/D	23/24	21/8	playⓘ Equal-tempered neutral second	8, 24
150.64	D↓[2]	12 : 11	22×3 : 11	playⓘ 3⁄4 tone or Undecimal neutral second,[3][5] trumpet three-quarter tone,[11] middle finger [between frets][14]		11		S
155.14	D	35 : 32	5×7 : 25	playⓘ Thirty-fifth harmonic[5]		7
160.90	D−−	800 : 729	25×52 : 36	playⓘ Grave whole tone,[3] neutral second, grave major second[citation needed]		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		21/7	21/7	playⓘ 1 step in 7 equal temperament	7
175.00		27/48	27/48	playⓘ 7 steps in 48 equal temperament	48
179.70		71 : 64	71 : 26	playⓘ Seventy-first harmonic[5]		71
180.45	E−−−	65536 : 59049	216 : 310	playⓘ Pythagorean diminished third,[3][6] Pythagorean minor tone		3
182.40	D−[2]	10 : 9	2×5 : 32	playⓘ 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	playⓘ Equal-tempered major second	6, 12		M
203.91	D[2]	9 : 8	32 : 23	playⓘ 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	D	145 : 128	5×29 : 27	playⓘ Hundred-forty-fifth harmonic		29
223.46	E−[2]	256 : 225	28 : 32×52	playⓘ Just diminished third,[16] 225th subharmonic		5
225.00		23/16	29/48	playⓘ 9 steps in 48 equal temperament	16, 48
227.79		73 : 64	73 : 26	playⓘ Seventy-third harmonic[5]		73
231.17	D−[2]	8 : 7	23 : 7	playⓘ Septimal major second,[4] septimal whole tone[3][5]		7		S
240.00		21/5	21/5	playⓘ 1 step in 5 equal temperament	5
247.74	D♯	15 : 13	3×5 : 13	playⓘ Tridecimal 5⁄4 tone[3]		13
250.00	D/E	25/24	25/24	playⓘ 5 steps in 24 equal temperament	24
251.34	D♯	37 : 32	37 : 25	playⓘ Thirty-seventh harmonic[5]		37
253.08	D♯−	125 : 108	53 : 22×33	playⓘ Semi-augmented whole tone,[3] semi-augmented second[citation needed]		5
262.37	E↓♭	64 : 55	26 : 5×11	playⓘ 55th subharmonic[5][6]		11
266.87	E♭[2]	7 : 6	7 : 2×3	playⓘ Septimal minor third[3][4][11] or Sub minor third[14]		7		S
268.80	D	299 : 256	13×23 : 28	playⓘ Two-hundred-ninety-ninth harmonic		23
274.58	D♯[2]	75 : 64	3×52 : 26	playⓘ Just augmented second,[16] Augmented tone,[14] augmented second[5][13]		5
275.00		211/48	211/48	playⓘ 11 steps in 48 equal temperament	48
289.21	E↓♭	13 : 11	13 : 11	playⓘ Tridecimal minor third[3]		13
294.13	E♭−[2]	32 : 27	25 : 33	playⓘ Pythagorean minor third[3][5][6][14][16] semiditone, or 27th subharmonic		3
297.51	E♭[2]	19 : 16	19 : 24	playⓘ 19th harmonic,[3] 19-limit minor third, overtone minor third[5]		19
300.00	D♯/E♭	23/12	21/4	playⓘ Equal-tempered minor third	4, 12		M
301.85	D♯-	25 : 21[5]	52 : 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	22 : 53/4	playⓘ Quarter-comma meantone minor third			M
311.98		(3 : 2)4/9	34/9 : 24/9	playⓘ Alpha scale minor third	3.85
315.64	E♭[2]	6 : 5	2×3 : 5	playⓘ 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	playⓘ Pythagorean augmented second[3][6]		3
320.14	E♭↑	77 : 64	7×11 : 26	playⓘ Seventy-seventh harmonic[5]		11
325.00		213/48	213/48	playⓘ 13 steps in 48 equal temperament	48
336.13	D♯-	17 : 14	17 : 2×7	playⓘ Superminor third[18]		17
337.15	E♭+	243 : 200	35 : 23×52	playⓘ Acute minor third[3]		5
342.48	E♭	39 : 32	3×13 : 25	playⓘ Thirty-ninth harmonic[5]		13
342.86		22/7	22/7	playⓘ 2 steps in 7 equal temperament	7
342.91	E♭-	128 : 105	27 : 3×5×7	playⓘ 105th subharmonic,[5] septimal neutral third[6]		7
347.41	E↑♭−[2]	11 : 9	11 : 32	playⓘ Undecimal neutral third[3][5]		11
350.00	D/E	27/24	27/24	playⓘ Equal-tempered neutral third	24
354.55	E↓+	27 : 22	33 : 2×11	playⓘ Zalzal's wosta[6] 12:11 X 9:8[14]		11
359.47	E[2]	16 : 13	24 : 13	playⓘ Tridecimal neutral third[3]		13
364.54		79 : 64	79 : 26	playⓘ Seventy-ninth harmonic[5]		79
364.81	E−	100 : 81	22×52 : 34	playⓘ Grave major third[3]		5
375.00		25/16	215/48	playⓘ 15 steps in 48 equal temperament	16, 48
384.36	F♭−−	8192 : 6561	213 : 38	playⓘ Pythagorean diminished fourth,[3][6] Pythagorean 'schismatic' third[5]		3
386.31	E[2]	5 : 4	5 : 22	playⓘ Just major third,[3][4][5][11][16] major third,[14] quarter-comma meantone major third		5	M	S
397.10	E+	161 : 128	7×23 : 27	playⓘ One-hundred-sixty-first harmonic		23
400.00	E	24/12	21/3	playⓘ Equal-tempered major third	3, 12		M
402.47	E	323 : 256	17×19 : 28	playⓘ Three-hundred-twenty-third harmonic		19
407.82	E+[2]	81 : 64	34 : 26	playⓘ Pythagorean major third,[3][5][6][14][16] ditone		3
417.51	F↓+[2]	14 : 11	2×7 : 11	playⓘ Undecimal diminished fourth or major third[3]		11
425.00		217/48	217/48	playⓘ 17 steps in 48 equal temperament	48
427.37	F♭[2]	32 : 25	25 : 52	playⓘ Just diminished fourth,[16] diminished fourth,[5][13] 25th subharmonic		5
429.06	E	41 : 32	41 : 25	playⓘ Forty-first harmonic[5]		41
435.08	E[2]	9 : 7	32 : 7	playⓘ Septimal major third,[3][5] Bohlen-Pierce third,[3] Super major Third[14]		7
444.77	F↓	128 : 99	27 : 9×11	playⓘ 99th subharmonic[5][6]		11
450.00	E/F	29/24	29/24	playⓘ 9 steps in 24 equal temperament	24
450.05		83 : 64	83 : 26	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	53 : 25×3	playⓘ Just augmented third, augmented third[5]		5
462.35	E-	64 : 49	26 : 72	playⓘ 49th subharmonic[5][6]		7
470.78	F+[2]	21 : 16	3×7 : 24	playⓘ Twenty-first harmonic, narrow fourth,[3] septimal fourth,[5] wide augmented third,[citation needed] H7 on G		7
475.00		219/48	219/48	playⓘ 19 steps in 48 equal temperament	48
478.49	E♯+	675 : 512	33×52 : 29	playⓘ Six-hundred-seventy-fifth harmonic, wide augmented third[3]		5
480.00		22/5	22/5	playⓘ 2 steps in 5 equal temperament	5
491.27	E♯	85 : 64	5×17 : 26	playⓘ Eighty-fifth harmonic[5]		17
498.04	F[2]	4 : 3	22 : 3	playⓘ Perfect fourth,[3][5][16] Pythagorean perfect fourth, Just perfect fourth or diatessaron[4]		3		S
500.00	F	25/12	25/12	playⓘ Equal-tempered perfect fourth	12		M
501.42	F+	171 : 128	32×19 : 27	playⓘ One-hundred-seventy-first harmonic		19
510.51		(3 : 2)8/11	38/11 : 28/11	playⓘ Beta scale perfect fourth	18.75
511.52	F	43 : 32	43 : 25	playⓘ Forty-third harmonic[5]		43
514.29		23/7	23/7	playⓘ 3 steps in 7 equal temperament	7
519.55	F+[2]	27 : 20	33 : 22×5	playⓘ 5-limit wolf fourth, acute fourth,[3] imperfect fourth[16]		5
521.51	E♯+++	177147 : 131072	311 : 217	playⓘ Pythagorean augmented third[3][6] (F+ (pitch))		3
525.00		27/16	221/48	playⓘ 21 steps in 48 equal temperament	16, 48
531.53	F+	87 : 64	3×29 : 26	playⓘ Eighty-seventh harmonic[5]		29
536.95	F↓♯+	15 : 11	3×5 : 11	playⓘ Undecimal augmented fourth[3]		11
550.00	F/G	211/24	211/24	playⓘ 11 steps in 24 equal temperament	24
551.32	F↑[2]	11 : 8	11 : 23	playⓘ eleventh harmonic,[5] undecimal tritone,[5] lesser undecimal tritone, undecimal semi-augmented fourth[3]		11
563.38	F♯+	18 : 13	2×9 : 13	playⓘ Tridecimal augmented fourth[3]		13
568.72	F♯[2]	25 : 18	52 : 2×32	playⓘ Just augmented fourth[3][5]		5
570.88		89 : 64	89 : 26	playⓘ Eighty-ninth harmonic[5]		89
575.00		223/48	223/48	playⓘ 23 steps in 48 equal temperament	48
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,[11] septimal diminished fifth[19]		7
588.27	G♭−−	1024 : 729	210 : 36	playⓘ Pythagorean diminished fifth,[3][6] low Pythagorean tritone[5]		3
590.22	F♯+[2]	45 : 32	32×5 : 25	playⓘ 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	G♭	361 : 256	192 : 28	playⓘ Three-hundred-sixty-first harmonic		19
600.00	F♯/G♭	26/12	21/2=√2	playⓘ Equal-tempered tritone	2, 12		M
609.35	G♭	91 : 64	7×13 : 26	playⓘ Ninety-first harmonic[5]		13
609.78	G♭−[2]	64 : 45	26 : 32×5	playⓘ 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	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
625.00		225/48	225/48	playⓘ 25 steps in 48 equal temperament	48
628.27	F♯+	23 : 16	23 : 24	playⓘ Twenty-third harmonic,[5] classic diminished fifth[citation needed]		23
631.28	G♭[2]	36 : 25	22×32 : 52	playⓘ Just diminished fifth[5]		5
646.99	F♯+	93 : 64	3×31 : 26	playⓘ Ninety-third harmonic[5]		31
648.68	G↓[2]	16 : 11	24 : 11	playⓘ ` undecimal semi-diminished fifth[3]		11
650.00	F/G	213/24	213/24	playⓘ 13 steps in 24 equal temperament	24
665.51	G	47 : 32	47 : 25	playⓘ Forty-seventh harmonic[5]		47
675.00		29/16	227/48	playⓘ 27 steps in 48 equal temperament	16, 48
678.49	A−−−	262144 : 177147	218 : 311	playⓘ Pythagorean diminished sixth[3][6]		3
680.45	G−	40 : 27	23×5 : 33	playⓘ 5-limit wolf fifth,[5] or diminished sixth, grave fifth,[3][6][11] imperfect fifth,[16]		5
683.83	G	95 : 64	5×19 : 26	playⓘ Ninety-fifth harmonic[5]		19
684.82	E++	12167 : 8192	233 : 213	playⓘ 12167th harmonic		23
685.71		24/7 : 1		playⓘ 4 steps in 7 equal temperament
691.20		3:2÷(81:80)1/2	2×51/2 : 3	playⓘ Half-comma meantone perfect fifth			M
694.79		3:2÷(81:80)1/3	21/3×51/3 : 31/3	playⓘ 1⁄3-comma meantone perfect fifth			M
695.81		3:2÷(81:80)2/7	21/7×52/7 : 31/7	playⓘ 2⁄7-comma meantone perfect fifth			M
696.58		3:2÷(81:80)1/4	51/4	playⓘ Quarter-comma meantone perfect fifth			M
697.65		3:2÷(81:80)1/5	31/5×51/5 : 21/5	playⓘ 1⁄5-comma meantone perfect fifth			M
698.37		3:2÷(81:80)1/6	31/3×51/6 : 21/3	playⓘ 1⁄6-comma meantone perfect fifth			M
700.00	G	27/12	27/12	playⓘ Equal-tempered perfect fifth	12		M
701.89		231/53	231/53	playⓘ 53-TET perfect fifth	53
701.96	G[2]	3 : 2	3 : 2	playⓘ 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	playⓘ 41-TET perfect fifth	41
703.45		217/29	217/29	playⓘ 29-TET perfect fifth	29
719.90		97 : 64	97 : 26	playⓘ Ninety-seventh harmonic[5]		97
720.00		23/5 : 1		playⓘ 3 steps in 5 equal temperament	5
721.51	A−	1024 : 675	210 : 33×52	playⓘ Narrow diminished sixth[3]		5
725.00		229/48	229/48	playⓘ 29 steps in 48 equal temperament	48
729.22	G-	32 : 21	24 : 3×7	playⓘ 21st subharmonic,[5][6] septimal diminished sixth		7
733.23	F+	391 : 256	17×23 : 28	playⓘ Three-hundred-ninety-first harmonic		23
737.65	A♭+	49 : 32	7×7 : 25	playⓘ Forty-ninth harmonic[5]		7
743.01	A	192 : 125	26×3 : 53	playⓘ Classic diminished sixth[3]		5
750.00	G/A	215/24	215/24	playⓘ 15 steps in 24 equal temperament	24
755.23	G↑	99 : 64	32×11 : 26	playⓘ Ninety-ninth harmonic[5]		11
764.92	A♭[2]	14 : 9	2×7 : 32	playⓘ Septimal minor sixth[3][5]		7
772.63	G♯	25 : 16	52 : 24	playⓘ Just augmented fifth[5][16]		5
775.00		231/48	231/48	playⓘ 31 steps in 48 equal temperament	48
781.79		π : 2		playⓘ Wallis product
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 : 26	playⓘ Hundred-first harmonic[5]		101
792.18	A♭−[2]	128 : 81	27 : 34	playⓘ Pythagorean minor sixth,[3][5][6] 81st subharmonic		3
798.40	A♭+	203 : 128	7×29 : 27	playⓘ Two-hundred-third harmonic		29
800.00	G♯/A♭	28/12	22/3	playⓘ Equal-tempered minor sixth	3, 12		M
806.91	G♯	51 : 32	3×17 : 25	playⓘ Fifty-first harmonic[5]		17
813.69	A♭[2]	8 : 5	23 : 5	playⓘ Just minor sixth[3][4][11][16]		5
815.64	G♯++	6561 : 4096	38 : 212	playⓘ Pythagorean augmented fifth,[3][6] Pythagorean 'schismatic' sixth[5]		3
823.80		103 : 64	103 : 26	playⓘ Hundred-third harmonic[5]		103
825.00		211/16	233/48	playⓘ 33 steps in 48 equal temperament	16, 48
832.18	G♯+	207 : 128	32×23 : 27	playⓘ Two-hundred-seventh harmonic		23
833.09		(51/2+1)/2	φ : 1	playⓘ Golden ratio (833 cents scale)
835.19	A♭+	81 : 50	34 : 2×52	playⓘ Acute minor sixth[3]		5
840.53	A♭[2]	13 : 8	13 : 23	playⓘ Tridecimal neutral sixth,[3] overtone sixth,[5] thirteenth harmonic		13
848.83	A♭↑	209 : 128	11×19 : 27	playⓘ Two-hundred-ninth harmonic		19
850.00	G/A	217/24	217/24	playⓘ Equal-tempered neutral sixth	24
852.59	A↓+[2]	18 : 11	2×32 : 11	playⓘ Undecimal neutral sixth,[3][5] Zalzal's neutral sixth		11
857.09	A+	105 : 64	3×5×7 : 26	playⓘ Hundred-fifth harmonic[5]		7
857.14		25/7	25/7	playⓘ 5 steps in 7 equal temperament	7
862.85	A−	400 : 243	24×52 : 35	playⓘ Grave major sixth[3]		5
873.50	A	53 : 32	53 : 25	playⓘ Fifty-third harmonic[5]		53
875.00		235/48	235/48	playⓘ 35 steps in 48 equal temperament	48
879.86	A↓	128 : 77	27 : 7×11	playⓘ 77th subharmonic[5][6]		11
882.40	B−−−	32768 : 19683	215 : 39	playⓘ Pythagorean diminished seventh[3][6]		3
884.36	A[2]	5 : 3	5 : 3	playⓘ 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	playⓘ Hundred-seventh harmonic[5]		107
892.54	B	6859 : 4096	193 : 212	playⓘ 6859th harmonic		19
900.00	A	29/12	23/4	playⓘ Equal-tempered major sixth	4, 12		M
902.49	A	32 : 19	25 : 19	playⓘ 19th subharmonic[5][6]		19
905.87	A+[2]	27 : 16	33 : 24	playⓘ Pythagorean major sixth[3][5][11][16]		3
921.82		109 : 64	109 : 26	playⓘ Hundred-ninth harmonic[5]		109
925.00		237/48	237/48	playⓘ 37 steps in 48 equal temperament	48
925.42	B−[2]	128 : 75	27 : 3×52	playⓘ Just diminished seventh,[16] diminished seventh,[5][13] 75th subharmonic		5
925.79	A+	437 : 256	19×23 : 28	playⓘ Four-hundred-thirty-seventh harmonic		23
933.13	A[2]	12 : 7	22×3 : 7	playⓘ Septimal major sixth[3][4][5]		7
937.63	A↑	55 : 32	5×11 : 25	playⓘ Fifty-fifth harmonic[5][20]		11
950.00	A/B	219/24	219/24	playⓘ 19 steps in 24 equal temperament	24
953.30	A♯+	111 : 64	3×37 : 26	playⓘ Hundred-eleventh harmonic[5]		37
955.03	A♯[2]	125 : 72	53 : 23×32	playⓘ Just augmented sixth[5]		5
957.21		(3 : 2)15/11	315/11 : 215/11	playⓘ 15 steps in Beta scale	18.75
960.00		24/5	24/5	playⓘ 4 steps in 5 equal temperament	5
968.83	B♭[2]	7 : 4	7 : 22	playⓘ Septimal minor seventh,[4][5][11] harmonic seventh,[3][11] augmented sixth[citation needed]		7
975.00		213/16	239/48	playⓘ 39 steps in 48 equal temperament	16, 48
976.54	A♯+[2]	225 : 128	32×52 : 27	playⓘ Just augmented sixth[16]		5
984.21		113 : 64	113 : 26	playⓘ Hundred-thirteenth harmonic[5]		113
996.09	B♭−[2]	16 : 9	24 : 32	playⓘ 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	B♭	57 : 32	3×19 : 25	playⓘ Fifty-seventh harmonic[5]		19
1000.00	A♯/B♭	210/12	25/6	playⓘ Equal-tempered minor seventh	6, 12		M
1014.59	A♯+	115 : 64	5×23 : 26	playⓘ Hundred-fifteenth harmonic[5]		23
1017.60	B♭[2]	9 : 5	32 : 5	playⓘ Greater just minor seventh,[16] large just minor seventh,[4][5] Bohlen-Pierce seventh[3]		5
1019.55	A♯+++	59049 : 32768	310 : 215	playⓘ Pythagorean augmented sixth[3][6]		3
1025.00		241/48	241/48	playⓘ 41 steps in 48 equal temperament	48
1028.57		26/7	26/7	playⓘ 6 steps in 7 equal temperament	7
1029.58	B♭	29 : 16	29 : 24	playⓘ Twenty-ninth harmonic,[5] minor seventh[citation needed]		29
1035.00	B↓[2]	20 : 11	22×5 : 11	playⓘ Lesser undecimal neutral seventh, large minor seventh[3]		11
1039.10	B♭+	729 : 400	36 : 24×52	playⓘ Acute minor seventh[3]		5
1044.44	B♭	117 : 64	32×13 : 26	playⓘ Hundred-seventeenth harmonic[5]		13
1044.86	B♭-	64 : 35	26 : 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	221/24	27/8	playⓘ Equal-tempered neutral seventh	8, 24
1059.17		59 : 32	59 : 25	playⓘ Fifty-ninth harmonic[5]		59
1066.76	B−	50 : 27	2×52 : 33	playⓘ Grave major seventh[3]		5
1071.70	B♭-	13 : 7	13 : 7	playⓘ Tridecimal neutral seventh[21]		13
1073.78	B	119 : 64	7×17 : 26	playⓘ Hundred-nineteenth harmonic[5]		17
1075.00		243/48	243/48	playⓘ 43 steps in 48 equal temperament	48
1086.31	C′♭−−	4096 : 2187	212 : 37	playⓘ Pythagorean diminished octave[3][6]		3
1088.27	B[2]	15 : 8	3×5 : 23	playⓘ Just major seventh,[3][5][11][16] small just major seventh,[4] 1⁄6-comma meantone major seventh		5
1095.04	C♭	32 : 17	25 : 17	playⓘ 17th subharmonic[5][6]		17
1100.00	B	211/12	211/12	playⓘ Equal-tempered major seventh	12		M
1102.64	B↑↑♭-	121 : 64	112 : 26	playⓘ Hundred-twenty-first harmonic[5]		11
1107.82	C′♭−	256 : 135	28 : 33×5	playⓘ Octave − major chroma,[3] 135th subharmonic, narrow diminished octave[citation needed]		5
1109.78	B+[2]	243 : 128	35 : 27	playⓘ Pythagorean major seventh[3][5][6][11]		3
1116.88		61 : 32	61 : 25	playⓘ Sixty-first harmonic[5]		61
1125.00		215/16	245/48	playⓘ 45 steps in 48 equal temperament	16, 48
1129.33	C′♭[2]	48 : 25	24×3 : 52	playⓘ Classic diminished octave,[3][6] large just major seventh[4]		5
1131.02	B	123 : 64	3×41 : 26	playⓘ Hundred-twenty-third harmonic[5]		41
1137.04	B	27 : 14	33 : 2×7	playⓘ Septimal major seventh[5]		7
1138.04	C♭	247 : 128	13×19 : 27	playⓘ Two-hundred-forty-seventh harmonic		19
1145.04	B	31 : 16	31 : 24	playⓘ Thirty-first harmonic,[5] augmented seventh[citation needed]		31
1146.73	C↓	64 : 33	26 : 3×11	playⓘ 33rd subharmonic[6]		11
1150.00	B/C	223/24	223/24	playⓘ 23 steps in 24 equal temperament	24
1151.23	C	35 : 18	5×7 : 2×32	playⓘ Septimal supermajor seventh, septimal quarter tone inverted		7
1158.94	B♯[2]	125 : 64	53 : 26	playⓘ Just augmented seventh,[5] 125th harmonic		5
1172.74	C+	63 : 32	32×7 : 25	playⓘ Sixty-third harmonic[5]		7
1175.00		247/48	247/48	playⓘ 47 steps in 48 equal temperament	48
1178.49	C′−	160 : 81	25×5 : 34	playⓘ Octave − syntonic comma,[3] semi-diminished octave[citation needed]		5
1179.59	B↑	253 : 128	11×23 : 27	playⓘ Two-hundred-fifty-third harmonic[5]		23
1186.42		127 : 64	127 : 26	playⓘ Hundred-twenty-seventh harmonic[5]		127
1200.00	C′	2 : 1	2 : 1	playⓘ Octave[3][11] or diapason[4]	1, 12	3	M	S

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): 106–137.
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. pp. 68–69. ISBN 978-0-306-80106-8.
5. "Anatomy of an Octave", Kyle Gann (1998). Gann leaves off "just" but includes "5-limit". He uses "median" for "neutral".
6. 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. Partch 1979, p. 70
11. 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. Anger, Joseph Humfrey (1912). A Treatise on Harmony, with Exercises, Volume 3, pp. xiv–xv. W. Tyrrell.
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. 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. "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

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