1106edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|1106}} | {{EDO intro|1106}} | ||
== Theory == | |||
1106edo is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak edo]]. It is strong as a 7-limit system; the only edos lower than it with a lower 7-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] being {{EDOs| 171, 270, 342, 441 and 612 }}. It is even stronger in the 11-limit; the only ones beating it out now being {{EDOs| 270, 342 and 612 }}. It is less strong in the 13 and 17 limits, but even so is distinctly [[consistent]] through the [[17-odd-limit]]. | 1106edo is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak edo]]. It is strong as a 7-limit system; the only edos lower than it with a lower 7-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] being {{EDOs| 171, 270, 342, 441 and 612 }}. It is even stronger in the 11-limit; the only ones beating it out now being {{EDOs| 270, 342 and 612 }}. It is less strong in the 13 and 17 limits, but even so is distinctly [[consistent]] through the [[17-odd-limit]]. | ||
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=== Divisors === | === Divisors === | ||
Since 1106 factors into 2 × 7 × 79, it has subset edos {{EDOs| 2, 7, 14, 79, 158, and 553 }}. | Since 1106 factors into 2 × 7 × 79, it has subset edos {{EDOs| 2, 7, 14, 79, 158, and 553 }}. | ||
== Regular temperament properties == | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
! Periods<br>per 8ve | |||
! Generator<br>(Reduced) | |||
! Cents<br>(Reduced) | |||
! Associated<br>Ratio | |||
! Temperaments | |||
|- | |||
| 1 | |||
| 213\1106 | |||
| 231.103 | |||
| 8/7 | |||
| [[Orga]] | |||
|- | |||
| 1 | |||
| 401\1106 | |||
| 435.081 | |||
| 9/7 | |||
| [[Supermajor]] | |||
|- | |||
| 2 | |||
| 401\1106 | |||
| 435.081 | |||
| 9/7 | |||
| [[Semisupermajor]] | |||
|- | |||
| 7 | |||
| 479\1106<br>(5\1106) | |||
| 519.711<br>(5.424) | |||
| 27/20<br>(325/324) | |||
| [[Brahmagupta]] | |||
|- | |||
| 79 | |||
| 459\1106<br>(11\1106) | |||
| 498.011<br>(11.935) | |||
| 4/3<br>(?) | |||
| [[Gold]] | |||
|} |