354edo

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← 353edo354edo355edo →
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.

Prime harmonics

Approximation of prime intervals in 354 EDO
Prime number 2 3 5 7 11 13 17 19
Error absolute (¢) +0.00 -0.26 +0.13 +0.67 +1.22 +0.15 +0.13 +0.79
relative (%) +0 -8 +4 +20 +36 +4 +4 +23
Steps (reduced) 354 (0) 561 (207) 822 (114) 994 (286) 1225 (163) 1310 (248) 1447 (31) 1504 (88)

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
118 167\354
(2\354)
566.101
(6.78)
165/119
(?)
Oganesson