680edo: Difference between revisions
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 680 factors into primes as {{nowrap| 2<sup>3</sup> × 5 × 17 }}, 680edo has subset edos {{EDOs| 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, and 340 }}. | Since 680 factors into primes as {{nowrap| 2<sup>3</sup> × 5 × 17 }}, 680edo has subset edos {{EDOs| 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, and 340 }}. | ||
== 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 | |||
| {{Monzo| 47 -15 -10 }}, {{monzo| -5 -32 24 }} | |||
| {{Mapping| 680 1078 1579 }} | |||
| -0.1062 | |||
| 0.1061 | |||
| 6.01 | |||
|- | |||
| 2.3.5.7 | |||
| 2401/2400, 67108864/66976875, {{monzo| 8 -20 9 1 }} | |||
| {{Mapping| 680 1078 1579 1909 }} | |||
| -0.0795 | |||
| 0.1029 | |||
| 5.83 | |||
|} | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |||
|- | |||
! Periods<br>per 8ve | |||
! Generator* | |||
! Cents* | |||
! Associated<br>ratio* | |||
! Temperaments | |||
|- | |||
| 5 | |||
| 63\612 | |||
| 111.18 | |||
| 16/15 | |||
| [[Quintosec]] (680) | |||
|- | |||
| 10 | |||
| 5\612 | |||
| 8.82 | |||
| 225/224 | |||
| [[Decoid]] (680) | |||
|} | |||
<nowiki/>* In [[normal forms #Minimal-generator form|minimal-generator form]] | |||