328edo: Difference between revisions
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The '''328 equal divisions of the octave''' ('''328edo''') divides the octave into 328 [[equal]] parts of 3.659 [[cent]]s each. | The '''328 equal divisions of the octave''' ('''328edo'''), or the '''328(-tone) equal temperament''' ('''328tet''', '''328et''') when viewed from a [[regular temperament]] perspective, divides the octave into 328 [[equal]] parts of 3.659 [[cent]]s each. | ||
== Theory == | == Theory == | ||
| Line 8: | Line 8: | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Primes in edo|328}} | {{Primes in edo|328}} | ||
== Regular temperament properties == | |||
{| class="wikitable center-4 center-5 center-6" | |||
! rowspan="2" | Subgroup | |||
! rowspan="2" | [[Comma list]] | |||
! rowspan="2" | [[Mapping]] | |||
! rowspan="2" | Optimal<br>8ve stretch (¢) | |||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |||
| 2.3.5.7 | |||
| 2401/2400, 3136/3125, 589824/588245 | |||
| [{{val| 328 520 762 921 }}] | |||
| -0.298 | |||
| 0.229 | |||
| 6.27 | |||
|- | |||
| 2.3.5.7.11 | |||
| 2401/2400, 3136/3125, 9801/9800, 19712/19683 | |||
| [{{val| 328 520 762 921 1135 }}] | |||
| -0.303 | |||
| 0.205 | |||
| 5.61 | |||
|- | |||
| 2.3.5.7.11.13 | |||
| 676/675, 1001/1000, 1716/1715, 3136/3125, 10648/10647 | |||
| [{{val| 328 520 762 921 1135 1214 }}] | |||
| -0.295 | |||
| 0.188 | |||
| 5.15 | |||
|- | |||
| 2.3.5.7.11.13.17 | |||
| 676/675, 936/935, 1001/1000, 1156/1155, 1716/1715, 3136/3125 | |||
| [{{val| 328 520 762 921 1135 1214 1341 }}] | |||
| -0.293 | |||
| 0.174 | |||
| 4.77 | |||
|} | |||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||
[[Category:Hemiwürschmidt]] | [[Category:Hemiwürschmidt]] | ||
[[Category:Semiporwell]] | [[Category:Semiporwell]] | ||
Revision as of 16:44, 4 December 2021
The 328 equal divisions of the octave (328edo), or the 328(-tone) equal temperament (328tet, 328et) when viewed from a regular temperament perspective, divides the octave into 328 equal parts of 3.659 cents each.
Theory
328edo is enfactored in the 5-limit, with the same tuning as 164edo. It tempers out 2401/2400, 3136/3125, and 6144/6125 in the 7-limit, 9801/9800, 16384/16335 and 19712/19683 in the 11-limit, 676/675, 1001/1000, 1716/1715 and 2080/2079 in the 13-limit, 936/935, 1156/1155 and 2601/2600 in the 17-limit, so that it supports würschmidt and hemiwürschmidt, and provides the optimal patent val for 7-limit hemiwürschmidt, 11- and 13-limit semihemiwür, and 13-limit semiporwell.
328 factors into 23 × 41, with subset edos 2, 4, 8, 41, 82, and 164.
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 | 2401/2400, 3136/3125, 589824/588245 | [⟨328 520 762 921]] | -0.298 | 0.229 | 6.27 |
| 2.3.5.7.11 | 2401/2400, 3136/3125, 9801/9800, 19712/19683 | [⟨328 520 762 921 1135]] | -0.303 | 0.205 | 5.61 |
| 2.3.5.7.11.13 | 676/675, 1001/1000, 1716/1715, 3136/3125, 10648/10647 | [⟨328 520 762 921 1135 1214]] | -0.295 | 0.188 | 5.15 |
| 2.3.5.7.11.13.17 | 676/675, 936/935, 1001/1000, 1156/1155, 1716/1715, 3136/3125 | [⟨328 520 762 921 1135 1214 1341]] | -0.293 | 0.174 | 4.77 |