144edo

← 143edo

144edo

145edo →

Prime factorization	24 × 32
Step size	8.33333 ¢
Fifth	84\144 (700 ¢) (→ 7\12)
Semitones (A1:m2)	12:12 (100 ¢ : 100 ¢)
Consistency limit	11
Distinct consistency limit	11

Theory

144edo is closely related to 72edo, but the patent vals differ on the mapping for 13 and 17. It is enfactored in the 11-limit, tempering out 225/224, 243/242, 385/384, 441/440, and 4000/3993. Using the patent val, it tempers out 847/845, 1188/1183, 1701/1690, 1875/1859, and 4225/4224 in the 13-limit.

Although the patent val comes out on top accuracy in the 13-limit, in the 17-limit 144 falls behind to 144g. The 144g val tempers out 170/169, 289/288, 375/374, 561/560, 595/594. It supports semihemisecordite, the 62 & 82f temperament. The patent val tempers out 273/272, 715/714, 833/832, 875/867, 891/884, and 1275/1274. It supports hemisecordite, the 41 & 103 temperament, though 103edo is better suited for this purpose. In the 19-limit the patent val tempers out 210/209, 325/323, 343/342, 363/361, 400/399, 513/512, and 665/663.

Besides all these, the 144eff val supports hemimiracle, the 41 & 103e temperament. 144ee supports oracle, the 31 & 113e temperament. 144cf supports necromanteion, the 31 & 113cf temperament.

Prime harmonics

Approximation of odd harmonics in 144edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-1.96	-2.98	-2.16	-3.91	-1.32	+1.14	+3.40	+3.38	+2.49	-4.11	-3.27
	Relative (%)	-23.5	-35.8	-25.9	-46.9	-15.8	+13.7	+40.8	+40.5	+29.8	-49.4	-39.3
Steps (reduced)		228 (84)	334 (46)	404 (116)	456 (24)	498 (66)	533 (101)	563 (131)	589 (13)	612 (36)	632 (56)	651 (75)

Subsets and supersets

144edo is the square of world-dominant 12edo. One step of it is called farab.

Since 144 factors into 2⁴ × 3², 144edo has subset edos 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, and 72.

Approximation to φ

144edo is the 12th Fibonacci edo. As a consequence of being a Fibonacci edo, it can produce extremely precise approximation of the logarithmic golden ratio at 89 steps. In addition, it also excellently represents the acoustic golden ratio by 100 steps.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3.5.7.11.13	225/224, 243/242, 385/384, 847/845, 1875/1859	[⟨144 228 334 404 498 533]]	+0.560	0.595	7.13
2.3.5.7.11.13.17	170/169, 225/224, 243/242, 289/288, 375/374, 385/384	[⟨144 228 334 404 498 533 588]] (144g)	+0.653	0.596	7.15
2.3.5.7.11.13.17	225/224, 243/242, 273/272, 325/324, 847/845, 875/867	[⟨144 228 334 404 498 533 589]] (144)	+0.362	0.734	8.80

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator (Reduced)	Cents (Reduced)	Associated Ratio	Temperament
1	7\144	58.33	27/26	Hemisecordite (144)
2	7\144	58.33	27/26	Semihemisecordite (144g)

Music

Amano Hideya

• Like an endless uphill (2022)