389edo: Difference between revisions
m Categories |
|||
| Line 1: | Line 1: | ||
389edo | '''389edo''' divides the octave into parts of 3.0848c each. | ||
== Theory == | == Theory == | ||
| Line 58: | Line 58: | ||
|} | |} | ||
== Scales == | == Scales == | ||
* Solstice[69] | * Solstice[69] | ||
* SolsticeDay[94] | * SolsticeDay[94] | ||
| Line 64: | Line 63: | ||
== Links == | == Links == | ||
https://individual.utoronto.ca/kalendis/leap/index.htm#mod | https://individual.utoronto.ca/kalendis/leap/index.htm#mod | ||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | |||
Revision as of 21:44, 3 July 2022
389edo divides the octave into parts of 3.0848c each.
Theory
Script error: No such module "primes_in_edo".
389edo has two mappings for 3, which makes it a dual-fifth system. The best approach to this tuning is through a 2.5.7.11.17 subgroup.
Relation to a calendar reform
389edo represents the north solstice (summer in the northern hemisphere) leap year cycle 69/389 as devised by Sym454 inventor Irvin Bromberg. The outcome scale uses 327\389, or 62\389 as its generator. The solstice leap day scale with 94 notes uses 269\389 as a generator. Since this is a maximum evenness scale, temperament can be generated by simply merging the numerator and the denominator.
Solstice Leap Day (94 & 295)
295 seems to precede 389.
Subgroup: 2.5.7.11.17
POTE generator: 370.1796c
Comma list: 250000/248897, 2100875/2097152, 4096000/4092529
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal
8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3.5 | [20 -17 3⟩, [-39 -12 25⟩ | [⟨389 617 903]] | -0.19 | 0.500 | 16.2 |
| 2.3.5 | 2109375/2097152, [-7, 44, -27⟩ | [⟨389 616 903]] (389b) | 0.46 | 0.451 | 14.6 |
| 2.5.7 | 2100875/2097152, [0, 52, -43⟩ | [⟨389 903 1092]] | 0.12 | 0.131 | 4.2 |
| 2.5.7.11.17 | 6664/6655, 156250/155771, 180625/180224, 184960/184877 | [⟨389 903 1092 1346 1590]] | 0.03 | 0.177 | 5.7 |
Scales
- Solstice[69]
- SolsticeDay[94]