354edo: Difference between revisions
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Cmloegcmluin (talk | contribs) I've asked for the clutter of pages of different forms for the words defactor and enfactor to be deleted, so now pages that linked to them need to be updated to use the remaining working link |
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== Theory == | == 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 comma|landscape]]), and 703125/702464 ([[meter comma|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]]. | 354edo is [[enfactoring|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 comma|landscape]]), and 703125/702464 ([[meter comma|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 harmonics === | ||
Revision as of 22:46, 13 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
| 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 |