389edo: Difference between revisions
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== Theory == | == Theory == | ||
{{Primes in edo|389|columns= | {{Primes in edo|389|columns=8}} | ||
The best | |||
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 === | === 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. | 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 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. | |||
== Regular temperament properties == | |||
{| class="wikitable center-4 center-5 center-6" | |||
! rowspan="2" |Subgroup | |||
! rowspan="2" |[[Comma list]] | |||
! rowspan="2" |[[Mapping]] | |||
! rowspan="2" |Optimal | |||
8ve stretch (¢) | |||
! colspan="2" |Tuning error | |||
|- | |||
![[TE error|Absolute]] (¢) | |||
![[TE simple badness|Relative]] (%) | |||
|- | |||
|2.3.5 | |||
|{{monzo|20 -17 3}}, {{monzo|-39 -12 25}} | |||
|[{{val|389 617 903}}] | |||
| -0.19 | |||
|0.500 | |||
|16.2 | |||
|- | |||
|2.3.5 | |||
|2109375/2097152, {{monzo|-7, 44, -27}} | |||
|[{{val|389 616 903}}] | |||
|0.46 | |||
|0.451 | |||
|14.6 | |||
|- | |||
|2.5.7 | |||
|2100875/2097152, {{monzo|0, 52, -43}} | |||
|[{{val|389 903 1092}}] | |||
|0.12 | |||
|0.131 | |||
|4.2 | |||
|} | |||
== Scales == | == Scales == | ||