467edo

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467edo

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Prime factorization	467 (prime)
Step size	2.56959 ¢
Fifth	273\467 (701.499 ¢)
Semitones (A1:m2)	43:36 (110.5 ¢ : 92.51 ¢)
Consistency limit	9
Distinct consistency limit	9

Theory

467et is consistent to thr 9-odd-limit. Using the patent val, it tempers out 4375/4374, 1640558367/1638400000, 5250987/5242880 and 2100875/2097152 in the 7-limit; 25165824/25109315, 1019215872/1019046875, 2097152/2096325, 26214400/26198073, 104162436/103984375, 166698/166375, 12005/11979, 151263/151250, 117649/117612, 514714375/514434888, 226492416/226474325, 104857600/104825259, 472392/471625, 540/539, 6250/6237, 1953125/1948617, 825000/823543, 85937500/85766121, 47265625/47258883 and 9453125/9437184 in the 11-limit. It supports counterkleismic and minos.

Odd harmonics

Approximation of odd harmonics in 467edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.46	-0.87	-0.09	-0.91	+1.14	-0.27	+1.24	+0.40	+0.56	-0.55	+1.28
	Relative (%)	-17.7	-34.0	-3.5	-35.5	+44.5	-10.5	+48.2	+15.5	+21.8	-21.2	+49.7
Steps (reduced)		740 (273)	1084 (150)	1311 (377)	1480 (79)	1616 (215)	1728 (327)	1825 (424)	1909 (41)	1984 (116)	2051 (183)	2113 (245)

Subsets and supersets

467edo is the 91st prime edo.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[-740 467⟩	⟨467 740]	0.1439	0.1439	5.38
2.3.5	[-36 11 8⟩, [-16 35 -17⟩	⟨467 740 1084]	0.2215	0.1608	6.02
2.3.5.7	4375/4374, 2100875/2097152, 5250987/5242880	⟨467 740 1084 1311]	0.1741	0.1617	6.05

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated Ratio*	Temperaments
1	71\467	182.441	10/9	Minortone / Mitonic
1	123\467	316.060	6/5	Counterhanson

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