354edo: Difference between revisions
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=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
Note: 5-limit temperaments supported by [[118edo|118et]] are not included. | |||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
|+Table of rank-2 temperaments by generator | |+Table of rank-2 temperaments by generator | ||
Revision as of 19:38, 30 January 2022
| ← 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
Script error: No such module "primes_in_edo".
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 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 |