List of musical intervals

Some terminology used in 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).
• Since the table is sortable, you can also sort the table by frequency ratio, by cents or alphabetically.

List

List of musical intervals

Cents	Freq. Ratio	Factors	Interval Name	E	Q	2	3	5	7	11	13	U
0.00	1 : 1	1 : 1	playUnison	E	Q	2	3	5	7	11	13
0.40	4375 : 4374	54·7 : 2·37	playRagisma						7	11	13
0.72	2401 : 2400	74 : 25·3·52	playBreedsma						7	11	13
1.00	21/1200 : 1		playCent									U
1.20	2 1/1000 : 1		playMillioctave									U
1.95	32805 : 32768	38·5 : 215	playSchisma					5	7	11	13
3.99	101/1000 : 1		playSavart or eptaméride									U
7.71	225 : 224	32·52 : 25·7	playSeptimal kleisma or marvel comma						7	11	13
8.11	15625 : 15552	56 : 26·35	playKleisma					5	7	11	13
13.07	1728:1715	26·33 : 5·73	playOrwell comma[1][2]						7	11	13
13.79	126 : 125	2·32·7 : 53	playSeptimal semicomma or starling comma						7	11	13
14.37	121 : 120	112 : 23·3·5	playUndecimal neutral seconds comma							11	13
16.67	21/72 : 1		play1 step in 72 equal temperament									U
19.55	2048 : 2025	211 : 34·52	playDiaschisma or minor comma					5	7	11	13
21.51	81 : 80	34 : 24·5	playSyntonic comma, major comma, komma, or comma of Didymus					5	7	11	13
22.64	21/53 : 1		playHoldrian comma, Holder's comma, or Arabian comma									U
23.46	312 : 219	312 : 219	playPythagorean comma				3	5	7	11	13
27.26	64 : 63	26 : 32·7	playSeptimal comma or comma of Archytas						7	11	13
29.27	21/41 : 1		play1 step in 41 equal temperament									U
31.19	56 : 55	23·7 : 5·11	playPtolemy's enharmonic: difference between (11 : 8) and (7 : 5) tritone							11	13
34.98	50 : 49	2·52 : 72	playSeptimal sixth-tone or jubilisma						7	11	13
35.70	49 : 48	72 : 24·3	playSeptimal diesis or slendro diesis						7	11	13
38.71	21/31 : 1		play1 step in 31 equal temperament									U
41.06	128 : 125	27 : 53	playEnharmonic (5-limit) Diesis or Limma					5	7	11	13
48.77	36 : 35	22·32 : 5·7	playSeptimal quarter tone						7	11	13
50.00	21/24 : 1		playEqual-tempered quarter tone		Q							U
70.67	25 : 24	52 : 23·3	playJust chromatic semitone, lesser chromatic semitone, minor semitone, or chromatic diesis					5	7	11	13
84.47	21 : 20	3·7 : 22·5	playSeptimal chromatic semitone						7	11	13
90.22	256 : 243	28 : 35	playPythagorean diatonic semitone or Pythagorean limma				3	5	7	11	13
92.18	135 : 128	33·5 : 27	playGreater chromatic semitone, chromatic semitone, semitone medius					5	7	11	13
100.00	21/12 : 1		playEqual-tempered minor second or semitone	E	Q							U
111.73	16 : 15	24 : 3·5	playJust diatonic semitone, major semitone, or limma					5	7	11	13
113.69	2187 : 2048	37 : 211	playPythagorean chromatic semitone or Pythagorean apotome				3	5	7	11	13
116.70	181/19 : 51/19		playSecor									U
119.44	15 : 14	3·5 : 2·7	playSeptimal diatonic semitone						7	11	13
133.24	27 : 25	33 : 52	playMinor second or semitone Maximus					5	7	11	13
150.00	23/24 : 1		playEqual-tempered neutral second		Q
150.64	12 : 11	22·3 : 11	playLesser undecimal neutral second							11	13
165.00	11 : 10	11 : 2·5	playGreater undecimal neutral second							11	13
171.43	21/7 : 1		play1 step in 7 equal temperament									U
180.45	65536 : 59049	216 : 310	playPythagorean diminished third, Pythagorean minor tone				3	5	7	11	13
182.40	10 : 9	2·5 : 32	playJust minor tone					5	7	11	13
200.00	22/12 : 1		playEqual-tempered major second	E	Q
203.91	9 : 8	32 : 23	playJust major tone, Pythagorean major second or tonus				3	5	7	11	13
231.17	8 : 7	23 : 7	playSeptimal major second						7	11	13
240.00	21/5 : 1		play1 step in 5 equal temperament									U
266.87	7 : 6	7 : 2·3	playSeptimal minor third or subminor third						7	11	13
294.13	32 : 27	25 : 33	playPythagorean minor third or semiditone				3	5	7	11	13
300.00	23/12 : 1		playEqual-tempered minor third	E	Q
315.64	6 : 5	2·3 : 5	playJust minor third					5	7	11	13
342.86	22/7 : 1		play2 steps in 7 equal temperament
347.41	11 : 9	11 : 32	playUndecimal neutral third							11	13
350.00	27/24 : 1		playEqual-tempered neutral third		Q
359.47	16 : 13	24 : 13	playTridecimal neutral third								13
386.31	5 : 4	5 : 22	playJust major third					5	7	11	13
400.00	24/12 : 1		playEqual-tempered major third	E	Q
407.82	81 : 64	34 : 26	playPythagorean major third or ditone				3	5	7	11	13
417.51	14 : 11	2·7 : 11	playUndecimal major third							11	13
435.08	9 : 7	32 : 7	playSeptimal major third or supermajor third						7	11	13
480.00	22/5 : 1		play2 steps in 5 equal temperament
498.04	4 : 3	22 : 3	playJust perfect fourth, Pythagorean perfect fourth or diatessaron				3	5	7	11	13
500.00	25/12 : 1		playEqual-tempered perfect fourth	E	Q
514.29	23/7 : 1		play3 steps in 7 equal temperament
519.55	27 : 20	33 : 22·5	play5-limit wolf fourth					5	7	11	13
551.32	11 : 8	11 : 23	playlesser undecimal tritone							11	13
582.51	7 : 5	7 : 5	playLesser septimal tritone						7	11	13
600.00	26/12 : 1		playEqual-tempered tritone	E	Q
617.49	10 : 7	2·5 : 7	playGreater septimal tritone						7	11	13
648.68	16 : 11	24 : 11	playInversion of eleventh harmonic							11	13
680.45	40 : 27	23·5 : 33	play5-limit wolf fifth or diminished sixth					5	7	11	13
700.00	27/12 : 1		playEqual-tempered perfect fifth	E	Q
701.96	3 : 2	3 : 2	playJust perfect fifth, Pythagorean perfect fifth or diapente				3	5	7	11	13
764.92	14 : 9	2·7 : 32	playseptimal minor sixth						7	11	13
782.49	11 : 7	11 : 7	playUndecimal minor sixth							11	13
792.18	128 : 81	27 : 34	playPythagorean minor sixth				3	5	7	11	13
800.00	28/12 : 1		playEqual-tempered minor sixth	E	Q
813.69	8 : 5	23 : 5	playJust minor sixth					5	7	11	13
840.53	13 : 8	13 : 23	playTridecimal neutral sixth, overtone sixth, 13th harmonic								13
850.00	217/24 : 1		playEqual-tempered neutral sixth		Q
852.59	18 : 11	2·32 : 11	playUndecimal neutral sixth							11	13
857.14	25/7 : 1		play5 steps in 7 equal temperament
884.36	5 : 3	5 : 3	playJust major sixth					5	7	11	13
900.00	29/12 : 1		playEqual-tempered major sixth	E	Q
905.87	27 : 16	33 : 24	playPythagorean major sixth				3	5	7	11	13
933.13	12 : 7	22·3 : 7	playSeptimal major sixth						7	11	13
960.00	24/5 : 1		play4 steps in 5 equal temperament
968.83	7 : 4	7 : 22	playSeptimal minor seventh or harmonic seventh						7	11	13
996.09	16 : 9	24 : 32	playLesser just minor seventh or Pythagorean minor seventh				3	5	7	11	13
1000.00	210/12 : 1		playEqual-tempered minor seventh	E	Q
1017.60	9 : 5	32 : 5	playGreater just minor seventh					5	7	11	13
1028.57	26/7 : 1		play6 steps in 7 equal temperament
1035.00	20 : 11	22·5 : 11	playLesser undecimal neutral seventh							11	13
1049.36	11 : 6	11 : 2·3	playGreater undecimal neutral seventh							11	13
1050.00	221/24 : 1		playEqual-tempered neutral seventh		Q
1088.27	15 : 8	3·5 : 23	playJust major seventh					5	7	11	13
1100.00	211/12 : 1		playEqual-tempered major seventh	E	Q
1109.78	243 : 128	35 : 27	playPythagorean major seventh				3	5	7	11	13
1200.00	2 : 1	2 : 1	playOctave or diapason	E	Q	2	3	5	7	11	13
1901.96	3 : 1	3 : 1	playTritave or just perfect twelfth				3	5	7	11	13
2400.00	4 : 1	22 : 1	playFifteenth or two octaves	E	Q	2	3	5	7	11	13

Comparison between equal-tempered (black) and Pythagorean (blue) intervals showing the relationship between frequency ratio and the intervals' values, in cents. Note that one octave equals 1200 cents.

See also

• List of meantone intervals

References

External links

• List of interval names in English (Archived copy)
• Xenharmonic.com septimal comma list (Archived copy)
• A great number of musical intervals