List of regular temperaments

Main article: Regular temperament

Rank-2

Rank-2 Temperaments

Form	Family	Name	Subgroup	Ploidacot	ETs	Usual Scale Type	Description	Commas	Generator size
7	Syntonic	Meantone	2.3.5	monocot	7, 12	softer diatonic, m-chromatic	Common historical temperament for 5-limit diatonic harmony.	81/80	692-697c
		Septimal Meantone	2.3.5.7	monocot	19, 31	softer diatonic, m-chromatic	Natural extension of the above to 2...7.	81/80, 225/224	695-697c
		Flattone	2.3.5.7	monocot	19, 26	softer diatonic, m-chromatic	Less accurate extension, more melodic intuition, easily extends to higher limits. 7-form version of Meantone.	525/512, 81/80	692-694c
	Mabilic	Mabilic	2.5.7	alpha-triseph[a]	7, 9	antidiatonic, armotonic, 9L 7s	Basic antidiatonic temperament with no 3.	mabilisma	668-680c
		Trismegistus	2.3.5.7	alpha-triseph	16, 25	antidiatonic, armotonic, 9L 7s	High-accuracy but high complexity extension of prime 3.	gamelisma, magisma	672-675c
		Semabila	2.3.5.7	alpha-triseph	9, 25	antidiatonic, armotonic, 9L 7s	Combination of Mabilic and Semaphore.	49/48, 28672/28125	668-672c
		Mavila	2.3.5.7	monocot	7, 9	antidiatonic, armotonic, 7L 9s	Exotemperament serving as an antidiatonic analog of meantone.	36/35, 135/128	675-680c
	Porcupine	Porcupine	2.3.5.11	omega-tricot	15, 22	onyx, pine	Moderate-accuracy 2.3.5.11 temperament with a ~160c generator and a heptatonic MOS.	250/243, 100/99	161-166c
		Septimal Porcupine	2.3.5.7.11	omega-tricot	15, 22	onyx, pine	Extension of the above to the full 11-limit.	250/243, 100/99, 64/63	161-163c
	Interclassical	Interclassical, Dicot	2.3.5	dicot	7, 10	mosh, dicoid	5-limit exotemperament equating 5/4 and 6/5 to the same interval.	25/24	670-680c, 720-730c
	Rastmic	Rastmic	2.3.11	dicot	7, 10	mosh, dicoid	Maps 11/9 and its fifth complement to a perfect neutral third.	243/242	345-355c
		Mohajira	2.3.5.11	dicot	24, 31	mosh, dicoid	Meantone extension of the above.	243/242, 81/80	347-350c
	Tetracot [rename]	Tetracot [rename]	2.3.5.11	tetracot	34, 41	archeotonic, 7L6s	Interprets (3/2)^(1/4) as 10/9.	100/99, 243/242	175-180c
5	Archy	Archy	2.3.7	monocot	5, 22	soft pentic, harder diatonic, p-chromatic	2.3.7 counterpart of Meantone, which sharpens the fifth.	64/63	709-720c
		Superpyth	2.3.5.7	monocot	22, 27	soft pentic, harder diatonic, p-chromatic	Extension of the above to 2...7, favoring flatter tunings.	64/63, 245/243	709-711c
	Gamelic	Slendric, Wonder	2.3.7	tricot	5, 31	1L 4s, machinoid, 5L 6s	Splits the fifth in 3 parts, each of which is 8/7. Little relation to actual Slendro tuning. Contains a pentatonic similar to porcupine's heptatonic.	gamelisma	231-234c
		Mothra	2.3.5.7	tricot	26, 31	1L 4s, machinoid, 5L 6s	Meantone extension of the above.	81/80, gamelisma	231c
		Rodan	2.3.5.7	tricot	41, 46	1L 4s, machinoid, 5L 6s	More accurate extension of the above.	245/243, gamelisma	234c
		Miracle	2.3.5.7.11	hexacot	31, 41	antisinatonic, 10L 1s	Generated by a 15/14~16/15 semitone, two of which reach a slendric 8/7.	225/224, 243/242, gamelisma	117c
		Valentine	2.3.5.7	enneacot	15, 16	15L 1s, Carlos Alpha	Scale with small steps strongly associated with Carlos Alpha.	126/125, gamelisma	78c
	Buzzard	Buzzard	2.3.5.7.13	alpha-tetracot	53, 58
	Interseptimal	Interseptimal, Semaphore	2.3.7	alpha-dicot	5, 19	4L 1s, semiquartal	Equipentatonic, inaccurate 7-limit temperament.	49/48	240-250c
12	Schismic	Schismic	2.3.5	monocot	41, 53	harder diatonic, p-chromatic	5-limit interpretation of Pythagorean tuning, best tuned when the fifth is flattened by a fraction of a cent.	schisma	701-702c
		Garibaldi	2.3.5.7	monocot	41, 53	harder diatonic, p-chromatic	7-limit interpretation of Pythagorean tuning. Despite being an extension of the above, it is most accurate when the fifth is tuned slightly sharp.	schisma, 225/224	702-703c
	Diaschismic	Diaschismic	2.3.5.17	diploid monocot	12, 34	jaric, 10L 2s	Temperament characterized by a perfect semioctave and a sharpened fifth or semitone generator. Two generators down reaches 5/4.	diaschisma	100-111c
		Septimal Diaschismic	2.3.5.7.17	diploid monocot	12, 34	jaric, 10L 2s	Rather complex 7-limit extension of the above.	diaschisma, 126/125	103-104c
10		Pajara	2.3.5.7.17	diploid monocot	12, 22	jaric, 10L 2s	Jubilic archytas diaschismic temperament. Contains jubilic chord structure and is strongly associated with 22edo.	diaschisma, 50/49	109-111c
11	Orgonismic	Orgone, Orgonic	2.7.11	trimech[b]	15, 26	4L7s	A high-accuracy rank-2 temperament generated by a tempered 77/64.	65536/65219	320-325c
3	Magic	Magic	2.3.5	alpha-pentacot	19, 22	mosh, sephiroid	Stacks five flattened major thirds to form a perfect twelfth.	magisma	378-382c
	Wurschmidt	Wurschmidt	2.3.5.11.23	beta-octacot	31, 34	-	Eight 5/4s stack to 3/2. Due to the sharp tuning of 5/4, MOS scales become quite awkward, however three 25/24s stack to two 16/15s. 2.5.3 analogue of schismic.	576/575, 12167/12150	386-389c
6	Hemithirds	Didacus	2.5.7.11	diseph	25, 31	archeotonic, 6L7s	Has a "meantone" generator (tempered 28/25); essentially a restriction of Septimal Meantone to 2.9.5.7.	3136/3125, 176/175	192c
b13	Sensamagic	Sensamagic	3.5.7	monogem[c]	b4, b9[d]	lambda	Basic tritave temperament that stacks 9/7 twice to reach 5/3. Generates the lambda (4L5s⟨3/1⟩) MOS scale, or can be used with octaves as Sensamagic.2.	245/243	435-440c
8		Sensi	2.3.5.7.13	beta-heptacot	19, 27	3L 2s, checkertonic	Very sharp extension of Sensamagic, which finds the octave at 125/63.	91/90, 126/125, 169/168	440-445c
		Hedgehog	2.3.5.7	diploid alpha-tricot	14c[e], 22	ekic	Porcupine extension of Sensamagic, which finds the octave at 49/25 (and consequently maps 7/5 to the semioctave).	50/49, 245/243	~435c
	Father	Father	2.3	monocot	3, 5	antipentic	Extremely inaccurate exotemperament which equates 5/4 with 4/3.	16/15	720-800c
4	Kleismic	Kleismic, Cata	2.3.5.13	alpha-hexacot	19, 34	smitonic, 4L7s, 4L11s	A highly accurate 5-limit temperament equating a stack of six slightly sharp 6/5's to one 3/1.	325/324, 625/624	317c
9	Orwell	Orwell	2.3.5.7.11	alpha-heptacot	22, 31
10	Negri	Negri	2.3.5.13	omega-tetracot	10, 19

[a] seph = divisions of 5/4

[b] mech = divisions of 7/4

[c] gem = divisions of 7/3 in a perfect twelfth (tritave) equivalent context

[d] A "b" prefixed to an equal temperament indicates the equal division of 3/1.

[e] A "c" suffixed to an equal temperament indicates that the second-best mapping of prime 5 is used.

Rank-3

Name	Commas	Subgroup	ETs	Description	Generators
Marvel	225/224, 385/384	2.3.5.7.11	19, 22, 31	16/15 and 15/14 are equated, or equivalently 32/25 and 9/7 are equated.	~3/2, ~81/80
Hemifamity / Argentismic	5120/5103	2.3.5.7	41, 46, 53	81/80 and 64/63 are equated. Sometimes used in aberrismic theory.	~3/2, ~81/80
Parapyth(ic)	352/351, 896/891	2.3.7.11.13	41, 46, 63	Based on Margo Schulter's regular tuning construct called "parapyth".	~3/2, ~28/27