270edo: Difference between revisions
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{{Harmonics in equal|270|prec=3}} | {{Harmonics in equal|270|prec=3}} | ||
=== | === Subsets and supersets === | ||
270 is a very composite number. The prime factorization is: 270 = 2 × 3<sup>3</sup> × 5, with divisors 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90 and 135. | 270 is a very composite number. The prime factorization is: 270 = 2 × 3<sup>3</sup> × 5, with divisors 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90 and 135. This means that 270edo can be conceptualised as the superset of, for example, [[10edo]] and [[27edo]], which are both interesting and somewhat peculiar in their own right. | ||
This means that 270edo can be conceptualised as the superset | |||
[[540edo]], which divides the edostep in two, provides good correction for the 17th and 23rd harmonics. | [[540edo]], which divides the edostep in two, provides good correction for the 17th and 23rd harmonics. | ||
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== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
! rowspan="2" | Subgroup | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" | [[Comma list]] | ! rowspan="2" | [[Comma list|Comma List]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br>8ve | ! rowspan="2" | Optimal<br>8ve Stretch (¢) | ||
! colspan="2" | Tuning | ! colspan="2" | Tuning Error | ||
|- | |- | ||
! [[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
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|+Table of rank-2 temperaments by generator | |+Table of rank-2 temperaments by generator | ||
! Periods<br>per 8ve | ! Periods<br>per 8ve | ||
! Generator<br>( | ! Generator<br>(Reduced) | ||
! Cents<br>( | ! Cents<br>(Reduced) | ||
! Associated<br> | ! Associated<br>Ratio | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
|1 | | 1 | ||
|1\270 | | 1\270 | ||
|4.44 | | 4.44 | ||
|385/384 | | 385/384 | ||
|[[ | | [[Keenanose]] | ||
|- | |- | ||
| 1 | | 1 | ||
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| [[Newt]] | | [[Newt]] | ||
|- | |- | ||
|1 | | 1 | ||
|97\270 | | 97\270 | ||
|431.11 | | 431.11 | ||
|77/60 | | 77/60 | ||
|[[Lockerbie]] | | [[Lockerbie]] | ||
|- | |- | ||
| 1 | | 1 | ||
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| [[Trinealimmal]] | | [[Trinealimmal]] | ||
|} | |} | ||