List of regular temperaments

Main article: Regular temperament

Rank-2

2.3.5.x families

Rank-2 Temperaments

Form	Family	Name	Generator	Ploidacot	Usual Scale Type	ETs	Description	Subgroup	Commas	Accuracy (Vector)
7	Syntonic	Meantone	692-697c	monocot	softer diatonic, m-chromatic	7, 12	Common historical temperament for 5-limit diatonic harmony.	2.3.5	81/80	4 Medium
		Septimal Meantone	695-697c	monocot	softer diatonic, m-chromatic	19, 31	Canonical extension of the above to 2...7.	2.3.5.7	81/80, 225/224	4 Medium
		Flattone	692-694c	monocot	softer diatonic, m-chromatic	19, 26	Less accurate extension, more melodic intuition, easily extends to higher limits. 7-form version of Meantone.	2.3.5.7	525/512, 81/80	6 Low
12		Injera	92-96c	diploid monocot	thalassic	12, 26	Adds a 600c tritone representing 7/5 to meantone.	2.3.5.7	81/80, 50/49	5 Medium-low
7	Porcupine	Porcupine	161-166c	omega-tricot	onyx, pine	15, 22	Moderate-accuracy 2.3.5.11 temperament with a ~160c generator and a heptatonic MOS.	2.3.5.11	250/243, 100/99	5 Medium-low
		Septimal Porcupine	161-163c	omega-tricot	onyx, pine	15, 22	Extension of the above to the full 11-limit.	2.3.5.7.11	250/243, 100/99, 64/63	5 Medium-low
	Interclassical	Interclassical, Dicot	670-680c, 720-730c	dicot	mosh, dicoid	7, 10	5-limit exotemperament equating 5/4 and 6/5 to the same interval.	2.3.5	25/24	7 Very low
	Tetracot	Tetracot	175-180c	tetracot	archeotonic, 7L6s	34, 41	Interprets (3/2)^(1/4) as 10/9.	2.3.5.11	100/99, 243/242	2 High (2.3.5), Medium (extensions)
12	Diminished	Diminished	685-700c	tetraploid monocot	tetrawood, 4L 8s	12, 16	Sets 6/5 to 300 cents; a step up from 600 cents is 3/2.	2.3.5	648/625	5 Medium-low
		Dimisept	685-700c	tetraploid monocot	tetrawood, 4L 8s	12, 16	Exotempered extension of the above that sets 7/6 to 300 cents.	2.3.5.7	36/35, 50/49	7 Very low
	Augmented	Augmented	705-715c	triploid monocot	triwood, tcherepnin	12, 15	Sets 5/4 to 400 cents, a step down from 800c is 3/2 and 2 steps up is 7/4.	2.3.5.7	128/125	6 Low
	Schismic	Schismic	701-702c	monocot	harder diatonic, p-chromatic	41, 53	5-limit interpretation of Pythagorean tuning, best tuned when the fifth is flattened by a fraction of a cent.	2.3.5	schisma	1 Very high
		Garibaldi	702-703c	monocot	harder diatonic, p-chromatic	41, 53	7-limit interpretation of Pythagorean tuning. It is most accurate when the fifth is tuned slightly sharp.	2.3.5.7	schisma, 225/224	3 Medium-high
	Misty	Misty	701-708c	triploid monocot		12, 51	5/4 is 4 times the difference between 3/2 and 800c.	2.3.5	misty comma	3 Medium-high
	Diaschismic	Diaschismic	100-111c	diploid monocot	jaric, 10L 2s	12, 34	Temperament characterized by a perfect semioctave and a sharpened fifth or semitone generator. Two generators down reaches 5/4.	2.3.5.17	diaschisma, 136/135	4 Medium
		Septimal Diaschismic	103-104c	diploid monocot	jaric, 10L 2s	12, 34	Rather complex 7-limit extension of the above.	2.3.5.7.17	diaschisma, 126/125, 136/135	4 Medium
10		Pajara	109-111c	diploid monocot	jaric, 10L 2s	12, 22	Jubilic archytas diaschismic temperament. Contains jubilic chord structure and is strongly associated with 22edo.	2.3.5.7.17	diaschisma, 50/49, 136/135	5 Medium-low
3	Magic	Magic	378-382c	alpha-pentacot	mosh, sephiroid	19, 22	Stacks five flattened major thirds to form a perfect twelfth. 5/4-generated analog of Meantone.	2.3.5	magisma	4 Medium
	Wurschmidt	Wurschmidt	386-389c	beta-octacot	-	31, 34	Eight 5/4s stack to 3/2 and three 25/24s stack to two 16/15s. 5/4-generated analog of Schismic. Bad for MOSes.	2.3.5.11.23	576/575, 12167/12150	3 Medium-high
8	Father	Father	720-800c	monocot	antipentic	3, 5	Extremely inaccurate exotemperament which equates 5/4 with 4/3.	2.3.5	16/15	8 Extremely low
4	Kleismic	Kleismic, Cata	317c	alpha-hexacot	smitonic, 4L7s, 4L11s	19, 34	A highly accurate temperament equating a stack of six slightly sharp 6/5's to one 3/1 and three 6/5's to one 26/15.	2.3.5.13	kleisma, 325/324	2 High
10	Negri	Negri	124-128c	omega-tetracot		10, 19	Generator is a sharp minor second of 16/15 which stacks 3 times to 5/4, and can be seen as a counterpart of Porcupine.	2.3.5	16875/16384	5 Medium-low
		Semibuzzard	124-128c		taric	10, 28	Weak Jubilismic or Buzzard extension of Negri allowing intervals of 7 to be reached with a 600-cent offset.	2.3.5.7.11	16875/16384, 50/49, 243/242	6 Low
		Negrisept	124-128c			10, 19	Semaphore extension of negri.	2.3.5.7	16875/16384, 49/48	7 Very low

2.3.7.x families

Form	Family	Name	Generator	Ploidacot	Usual Scale Type	ETs	Description	Subgroup	Commas	Accuracy
5	Archy	Archy	709-720c	monocot	soft pentic, harder diatonic, p-chromatic	5, 22	2.3.7 counterpart of Meantone, which sharpens the fifth.	2.3.7	64/63	5 Medium-low
		Superpyth	709-711c	monocot	soft pentic, harder diatonic, p-chromatic	22, 27	Extension of the above to 2...7, favoring flatter tunings.	2.3.5.7	64/63, 245/243	5 Medium-low
	Gamelic	Slendric, Wonder	231-234c	tricot	1L 4s, machinoid, 5L 6s	5, 31	Splits the fifth in 3 parts, each of which is 8/7. Little relation to actual Slendro tuning.	2.3.7	gamelisma	3 Medium-high
		Mothra	231c	tricot	1L 4s, machinoid, 5L 6s	26, 31	Meantone extension of the above.	2.3.5.7	81/80, gamelisma	4 Medium
		Rodan	234c	tricot	1L 4s, machinoid, 5L 6s	41, 46	More accurate extension of the above.	2.3.5.7	245/243, gamelisma	4 Medium
		Miracle	117c	hexacot	antisinatonic, 10L 1s	31, 41	Generated by a 15/14~16/15 semitone, two of which reach a slendric 8/7.	2.3.5.7.11	225/224, 243/242, gamelisma	3 Medium-high
		Valentine	78c	enneacot	15L 1s, Carlos Alpha	15, 16	Scale with small steps strongly associated with Carlos Alpha.	2.3.5.7	126/125, gamelisma	3 Medium-high
	Buzzard	Buzzard	474-478c	alpha-tetracot		53, 58	Sharpens the 21/16 so that four of them stacks to the 3/1.	2.3.5.7.13	buzzardsma	4 Medium
	Interseptimal	Interseptimal, Semaphore	240-250c	alpha-dicot	4L 1s, semiquartal	5, 19	Equipentatonic, inaccurate 7-limit temperament.	2.3.7	49/48	6 Low
13	Squares	Squares	424-426c	beta-tetracot	3L 5s, 3L 8s, 3L 11s	14, 17	No-fives temperament generated by a flattened 9/7 equated with 14/11.	2.3.7.11	99/98, 243/242	4 Medium

2.3.x families

Form	Family	Name	Generator	Ploidacot	Usual Scale Type	ETs	Description	Subgroup	Commas	Accuracy
7	Rastmatic	Rastmatic	345-355c	dicot	mosh, dicoid	7, 10	Maps 11/9 and its fifth complement to a perfect neutral third.	2.3.11	243/242	3 Medium-high
		Mohajira	347-350c	dicot	mosh, dicoid	24, 31	Meantone extension of the above. Can optionally be extended to set 7/4 equal to the semiflat minor seventh, or via a strong meantone extension.	2.3.5.11	243/242, 81/80	5 Medium-low
	Intratridecimal	Intratridecimal	350-360c	dicot	mosh, dicoid	27, 10	Maps 16/13 and its fifth complement to a perfect neutral third.	2.3.13	512/507	4 Medium
		(To be named)	355-360c	dicot	mosh, dicoid	27, 10	Archy extension of the above.	2.3.7.13	512/507, 64/63	5 Medium-low

2.3.5.7.x families

Form	Family	Name	Generator	Ploidacot	Usual Scale Type	ETs	Description	Commas	Subgroup	Accuracy
7	Amity	Amity	338-340c	gamma-pentacot	7L 18s, 7L 25s	46, 53	Sets the spacing of the thirds to 7/6-#-6/5-#-#-5/4-#-9/7; mostly appears as a structural element of EDOs rather than an independent structure.	4375/4374, 5120/5103	2.3.5.7	2 High
12	Compton	Compton	385c	dodecaploid acot	dodecawood	12, 60	Acts as a closed circle of 12 fifths (see 12edo), but with 5/4 flattened by a diesis from 400c, and 7/4 flattened by twice that amount from 1000c.	pythagorean comma	2.3.5.7	3 Medium-high
4	Doublewide	Doublewide	325c			22, 48	Sets 6/5 and 7/6 the same distance from the 300c period, so that four ~25c generators stack to the semitone separating 3/2 from 600c.	50/49, 875/864	2.3.5.7	5 Medium-low
	Myna	Myna	309-311c	beta-decacot	-	27, 31	Sets 25/24 equal to twice 36/35.	126/125, 1728/1715	2.3.5.7	3 Medium-high
9	Orwell	Orwell	270-273c	alpha-heptacot	gramitonic	22, 31	Generator is a sharpened 7/6. Interval chain finds 7/6, 11/8, 8/5, 15/8, 11/10, 9/7, 3/2.	99/98, 121/120, 176/175	2.3.5.7.11	3 Medium-high
	Ennealimmal	Ennealimmal	44-53c	enneaploid dicot	enneawood	27, 45	Divides the octave into nine equal parts representing 27/25 and half of 7/6.	2401/2400, 4375/4374	2.3.5.7	1 Very high
8	Nusecond	Nusecond	154-155c		onyx, pine	31, 70	Generator is a neutral second, but places primes at high complexity, preferring ratios between them.	126/125, 2430/2401	2.3.5.7.11	4 Medium

No-threes families

Form	Family	Name	Generator	Ploidacot	Usual Scale Type	ETs	Description	Commas	Subgroup	Error
7	Mabilic	Mabilic	668-680c	alpha-triseph[a]	antidiatonic, armotonic, 9L 7s	7, 9	Basic antidiatonic temperament with no 3.	mabilisma	2.5.7	4 Medium
		Trismegistus	672-675c	alpha-triseph	antidiatonic, armotonic, 9L 7s	16, 25	High-accuracy but high complexity extension of prime 3.	gamelisma, magisma	2.3.5.7	4 Medium
		Semabila	668-672c	alpha-triseph	antidiatonic, armotonic, 9L 7s	9, 25	Combination of Mabilic and Semaphore.	49/48, 28672/28125	2.3.5.7	6 Low
		Mavila	675-680c	monocot	antidiatonic, armotonic, 7L 9s	7, 9	Exotemperament serving as an antidiatonic analog of meantone.	36/35, 135/128	2.3.5.7	7 Very low
11	Orgonismic	Orgone, Orgonic	320-325c	trimech[b]	4L7s	15, 26	A high-accuracy rank-2 temperament generated by a tempered 77/64.	65536/65219	2.7.11	3 Medium-high
		Superkleismic	320-325c	trimech	4L7s	15, 26	The main (albeit less accurate) extension of orgone to the full 11-limit.	100/99, 245/242, 385/384	2...11	4 Medium
6	Hemimean	Didacus	192-196c	diseph	1L 5s, 6L 1s	6, 25	Every other step of septimal meantone.	3136/3125	2.5.7	2 High

Non-octave families

Rank-2 Temperaments

Form	Family	Name	Generator	Ploidacot	Usual Scale Type	ETs	Description	Commas	Subgroup	Accuracy
b13	Sensamagic	Sensamagic	435-440c	monogem[c]	lambda	b4, b9[d]	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	3.5.7	3 Medium-high
8		Sensi	440-445c	beta-heptacot	3L 2s, checkertonic	19, 27	Very sharp extension of Sensamagic, which finds the octave at 125/63.	91/90, 126/125, 169/168	2.3.5.7.13	4 Medium

[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.

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 / Aberschismic	5120/5103	2.3.5.7	41, 46, 53	81/80 and 64/63 are equated. Sometimes used in aberrismic theory to interpret ternary scales as 2.3.5.7, and associated with argent tuning.	~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

See also

• Survey of efficient temperaments by subgroup (Xen Wiki)