443edo

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443edo

444edo →

Prime factorization	443 (prime)
Step size	2.7088 ¢
Fifth	259\443 (701.58 ¢)
Semitones (A1:m2)	41:34 (111.1 ¢ : 92.1 ¢)
Consistency limit	3
Distinct consistency limit	3

Theory

443edo is inconsistent to the 5-odd-limit and the error of harmonic 5 is quite large. To start with, the patent val ⟨443 702 1029 1244 1533] as well as the 443cde val ⟨443 702 1028 1243 1532] are worth considering.

Using the patent val, the equal temperament tempers out 6144/6125, 32805/32768, and 67108864/66976875 in the 7-limit; 540/539, 5632/5625, 8019/8000, and 131072/130977 in the 11-limit. It supports hemischis, the 130 & 313 temperament.

Prime harmonics

Approximation of prime harmonics in 443edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	-0.37	+1.05	+0.93	+1.28	-0.80	+0.69	+0.46	+0.17	-0.23	+0.79
	Relative (%)	+0.0	-13.8	+38.6	+34.2	+47.2	-29.5	+25.4	+16.8	+6.2	-8.6	+29.1
Steps (reduced)		443 (0)	702 (259)	1029 (143)	1244 (358)	1533 (204)	1639 (310)	1811 (39)	1882 (110)	2004 (232)	2152 (380)	2195 (423)

Subsets and supersets

443edo is the 86th prime edo. 886edo, which doubles it, gives a good correction until the 11-limit.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[-702 443⟩	[⟨443 702]]	0.1183	0.1183	4.37

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated Ratio*	Temperaments
1	92\443	249.21	15/13	Hemischis (443)

* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct

Scales

• Hemischis19

Music

Francium

• "Confusion" from HemischisMatic EP (2023) – Spotify | Bandcamp | YouTube – hemischis in 443edo tuning