List of musical intervals

From Wikipedia, the free encyclopedia

Equal-tempered refers to 12-tone equal temperament (easy to follow when you look at the cents: 100,200,300, 400, etc.)
Harmonic means an overtone of the harmonic series (an integer multiple of the root), transposed to fit within the octave
Pythagorean means 3-limit; 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
Septimal means a ratio of numbers with prime factors no higher than seven
Similarly, undecimal a ratio of numbers with prime factors no higher than eleven and so on with tridecimal (13), septendecimal (17)...

Cents	Ratio	Name(s)
0.00	1:1	Unison
0.40	4375:4374	Ragisma
0.72	2401:2400	Breedsma
1.00	2^1/1200:1	Cent
1.20	2 ^1/1000:1	Millioctave
1.95	32805:32768	Schisma
3.99	1 + (1/100) log₁₀2:1	Savart
7.71	225:224	Septimal kleisma or marvel comma
8.11	15625:15552	Kleisma
13.79	126:125	Septimal semicomma or starling comma
19.55	2048:2025	Diaschisma or minor comma
21.51	81:80	Syntonic comma, major comma, komma, or comma of Didymus
22.64	2^1/53:1	Arabian comma or Holder's comma
23.46	3¹²:2¹⁹	Pythagorean comma
27.26	64:63	Septimal comma or comma of Archytas
34.98	50:49	Septimal sixth-tone or jubilisma
35.70	49:48	Septimal diesis or slendro diesis
41.06	128:125	Enharmonic (5-limit) Diesis or Limma
48.77	36:35	Septimal quarter tone
50.00	2^1/24:1	Equal-tempered quarter tone
70.67	25:24	Just chromatic semitone, lesser chromatic semitone, minor semitone, or chromatic diesis
84.47	21:20	Septimal chromatic semitone
90.22	256:243	Pythagorean limma or Pythagorean minor semitone
92.18	135:128	Greater chromatic semitone, chromatic semitone, semitone medius
100.00	2^1/12:1	Equal-tempered minor second
111.73	16:15	Just diatonic semitone, major semitone, or limma
113.69	2187:2048	Pytharorean apotome or major semitone
119.44	15:14	Septimal diatonic semitone
133.24	27:25	Minor second or semitone Maximus
150.64	12:11	Lesser undecimal neutral second
165.00	11:10	Greater undecimal neutral second
182.40	10:9	Just minor tone
200.00	2^1/6:1	Equal-tempered major second
203.91	9:8	Just major tone or tonus
231.17	8:7	Septimal major second
266.87	7:6	Septimal minor third or subminor third
294.13	32:27	Pythagorean minor third
300.00	2^1/4:1	Equal-tempered minor third
315.64	6:5	Just minor third or semiditonus
347.41	11:9	Undecimal neutral third
386.31	5:4	Just major third or ditonus
400.00	2^1/3:1	Equal-tempered major third
407.82	81:64	Pythagorean major third or ditone
417.51	14:11	Undecimal major third
435.08	9:7	Septimal major third or supermajor third
498.04	4:3	Just perfect fourth or diatessaron
500.00	2^5/12:1	Equal-tempered perfect fourth
519.55	27:20	5-limit wolf fourth
551.32	11:8	Eleventh harmonic
582.51	7:5	Lesser septimal tritone
600.00	2^1/2:1	Equal-tempered tritone
617.49	10:7	Greater septimal tritone
648.68	16:11	Inversion of eleventh harmonic
680.45	40:27	5-limit wolf fifth
700.00	2^7/12:1	Equal-tempered perfect fifth
701.96	3:2	Just perfect fifth or diapente
764.92	14:9	Septimal minor sixth
782.49	11:7	Undecimal minor sixth
792.18	128:81	Pythagorean minor sixth
800.00	2^2/3:1	Equal-tempered minor sixth
813.69	8:5	Just minor sixth
852.59	18:11	Undecimal neutral sixth
884.36	5:3	Just major sixth
900.00	2^3/4:1	Equal-tempered major sixth
905.87	27:16	Pythagorean major sixth
933.13	12:7	Septimal major sixth
968.83	7:4	Septimal minor seventh, harmonic seventh
996.09	16:9	Lesser just minor seventh
1000.00	2^5/6:1	Equal-tempered minor seventh
1017.60	9:5	Greater just minor seventh
1035.00	20:11	Lesser undecimal neutral seventh
1049.36	11:6	Greater undecimal neutral seventh
1088.27	15:8	Just major seventh
1100.00	2^11/12:1	Equal-tempered major seventh
1109.78	243:128	Pythagorean major 7th
1200.00	2:1	Octave or diapason
1901.96	3:1	Tritave or just perfect twelfth
2400.00	4:1	Fifteenth or two octaves