354edo
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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
| ← 353edo | 354edo | 355edo → |
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
| 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.
| Periods per 8ve |
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 |