389edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ED intro}} | |||
== Theory == | == Theory == | ||
389edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1|3]] is about halfway between its steps, which makes it a [[dual-fifth system]]. Otherwise, it has a reasonable approximation to harmonics [[7/1|7]], [[9/1|9]], and [[17/1|17]], with optional additions of either [[5/1|5]] or [[11/1|11]] and [[15/1|15]], making it suitable for a 2.9.5.7.17 or 2.9.15.7.11.17 [[subgroup]] interpretation. | |||
=== Odd harmonics === | |||
=== | {{Harmonics in equal|389}} | ||
==== Solstice | === Subsets and supersets === | ||
389edo is the 77th [[prime edo]]. | |||
=== Miscelleneous properties === | |||
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 [[maximal evenness]] scale, temperament can be generated by simply merging the numerator and the denominator. | |||
==== Solstice leap day (94 & 295) ==== | |||
295 seems to precede 389. | 295 seems to precede 389. | ||
| Line 20: | Line 25: | ||
== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
|- | |- | ||
![[TE error|Absolute]] (¢) | ! rowspan="2" | [[Subgroup]] | ||
![[TE simple badness|Relative]] (%) | ! rowspan="2" | [[Comma list|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 | | 2.3.5 | ||
|{{monzo|20 -17 3}}, {{monzo|-39 -12 25}} | | {{monzo| 20 -17 3 }}, {{monzo| -39 -12 25 }} | ||
| | | {{mapping| 389 617 903 }} | ||
| | | −0.19 | ||
|0.500 | | 0.500 | ||
|16.2 | | 16.2 | ||
|- | |- | ||
|2.3.5 | | 2.3.5 | ||
|2109375/2097152, {{monzo|-7 | | 2109375/2097152, {{monzo|-7 44 -27 }} | ||
| | | {{mapping| 389 616 903 }} (389b) | ||
|0.46 | | +0.46 | ||
|0.451 | | 0.451 | ||
|14.6 | | 14.6 | ||
|- | |- | ||
|2.5.7 | | 2.5.7 | ||
|2100875/2097152, {{monzo|0 | | 2100875/2097152, {{monzo| 0 52 -43 }} | ||
| | | {{mapping| 389 903 1092 }} | ||
|0.12 | | +0.12 | ||
|0.131 | | 0.131 | ||
|4.2 | | 4.2 | ||
|- | |- | ||
|2.5.7.11.17 | | 2.5.7.11.17 | ||
|6664/6655, 156250/155771, 180625/180224, 184960/184877 | | 6664/6655, 156250/155771, 180625/180224, 184960/184877 | ||
| | | {{mapping| 389 903 1092 1346 1590 }} | ||
|0.03 | | +0.03 | ||
|0.177 | | 0.177 | ||
|5.7 | | 5.7 | ||
|} | |} | ||
== Scales == | == Scales == | ||
* Solstice[69] | * Solstice[69] | ||
* SolsticeDay[94] | * SolsticeDay[94] | ||