354edo

← 353edo

354edo

355edo →

Prime factorization	2 × 3 × 59
Step size	3.38983 ¢
Fifth	207\354 (701.695 ¢) (→ 69\118)
Semitones (A1:m2)	33:27 (111.9 ¢ : 91.53 ¢)
Consistency limit	9
Distinct consistency limit	9

The 354 equal divisions of the octave (354edo), or the 354(-tone) equal temperament (354tet, 354et) when viewed from a regular temperament perspective, is the equal division of the octave into 354 parts of about 3.39 cents each.

Theory

354edo is enfactored in the 5-limit, with the same tuning as 118edo, defined by tempering out the schisma and the parakleisma. In the 7-limit, it tempers out 118098/117649 (stearnsma), 250047/250000 (landscape), and 703125/702464 (meter); in the 11-limit, 540/539, and 4000/3993; in the 13-limit, 729/728, 1575/1573, 1716/1715, 2080/2079, 4096/4095, and 4225/4224. It provides the optimal patent val for stearnscape.

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3.5.7	32805/32768, 118098/117649, 250047/250000	[⟨354 561 822 994]]	-0.0319	0.1432	4.23
2.3.5.7.11	540/539, 4000/3993, 32805/32768, 137781/137500	[⟨354 561 822 994 1225]]	-0.0963	0.1817	5.36
2.3.5.7.11.13	540/539, 729/728, 1575/1573, 4096/4095, 31250/31213	[⟨354 561 822 994 1225 1310]]	-0.0871	0.1671	4.93
2.3.5.7.11.13.17	540/539, 729/728, 936/935, 1156/1155, 1575/1573, 4096/4095	[⟨354 561 822 994 1225 1310 1447]]	-0.0791	0.1559	4.60
2.3.5.7.11.13.17.19	540/539, 729/728, 936/935, 969/968, 1156/1155, 1445/1444, 1521/1520	[⟨354 561 822 994 1225 1310 1447 1504]]	-0.0926	0.1509	4.43

Rank-2 temperaments

Note: 5-limit temperaments supported by 118et are not included.

Table of rank-2 temperaments by generator

Periods per octave	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
2	128\354 (49\354)	433.90 (166.10)	9/7 (11/10)	Pogo
3	147\354 (29\354)	498.31 (98.31)	4/3 (200/189)	Term / terminator
6	64\354 (5\354)	216.95 (16.95)	567/500 (245/243)	Stearnscape
6	147\354 (29\354)	498.31 (98.31)	4/3 (200/189)	Semiterm