200edo: Difference between revisions
→Theory: changed titles |
Added regular temperament properties |
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=== Subsets and supersets === | === Subsets and supersets === | ||
200's divisors are: {{EDOs| 2, 4, 5, 8, 10, 20, 25, 40, 50, 100 }}. It factorizes as 5<sup>2</sup> × 2<sup>3</sup>. | 200's divisors are: {{EDOs| 2, 4, 5, 8, 10, 20, 25, 40, 50, 100 }}. It factorizes as 5<sup>2</sup> × 2<sup>3</sup>. | ||
==Regular temperament properties== | |||
{| class="wikitable center-4 center-5 center-6" | |||
! rowspan="2" |[[Subgroup]] | |||
! 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 | |||
|{{monzo|317 -200}} | |||
|{{val|200 317}} | |||
| -0.0142 | |||
| 0.0142 | |||
| 0.24 | |||
|- | |||
|2.3.5 | |||
|32805/32768, {{monzo|2 -32 21}} | |||
|{{val|200 317 464}} | |||
| +0.3226 | |||
| 0.4767 | |||
| 7.95 | |||
|- | |||
|2.3.5.7 | |||
|1029/1024, 10976/10935, 32805/32768 | |||
|{{val|200 317 464 561}} | |||
| +0.4937 | |||
| 0.5082 | |||
| 8.47 | |||
|} | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
|+Table of rank-2 temperaments by generator | |||
! Periods<br>per 8ve | |||
! Generator<br>(reduced) | |||
! Cents<br>(reduced) | |||
! Associated<br>ratio | |||
! Temperaments | |||
|- | |||
|1 | |||
|23\200 | |||
|138.00 | |||
|625/576 | |||
|[[Quartemka]] | |||
|- | |||
|1 | |||
|39\200 | |||
|234.00 | |||
|9375/8192 | |||
|[[Guiron]] | |||
|- | |||
|1 | |||
|83\200 | |||
|498.00 | |||
|4/3 | |||
|[[Helmholtz]] | |||
|} | |||
== Scales == | == Scales == | ||