541edo: Difference between revisions
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== Theory == | == Theory == | ||
541et is only consistent to the [[5-odd-limit]] and the [[harmonic]] 3 is about halfway between its steps. It has a reasonable approximation to the 2.9.5.7 | 541et is only [[consistent]] to the [[5-odd-limit]] and the [[harmonic]] [[3/1|3]] is about halfway between its steps. It has a reasonable approximation to the 2.9.5.7.13 [[subgroup]]. | ||
=== Odd harmonics === | === Odd harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
541edo is the 100th [[prime | 541edo is the 100th [[prime edo]]. [[1082edo]], which doubles it, gives a good correction to the harmonic 3. | ||
== 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|Comma List]] | ! rowspan="2" | [[Comma list|Comma List]] | ||
! rowspan="2" |[[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" |Optimal<br>8ve Stretch (¢) | ! rowspan="2" | Optimal<br>8ve Stretch (¢) | ||
! colspan="2" |Tuning Error | ! colspan="2" | Tuning Error | ||
|- | |- | ||
![[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
![[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
|- | |- | ||
|2.9 | | 2.9 | ||
|{{monzo|1715 -541}} | | {{monzo| 1715 -541 }} | ||
|{{mapping|541 1715}} | | {{mapping| 541 1715 }} | ||
| -0.0247 | | -0.0247 | ||
| 0.0247 | | 0.0247 | ||
| 1.11 | | 1.11 | ||
|- | |- | ||
|2.9.5 | | 2.9.5 | ||
|{{monzo|-20 -12 25}}, {{monzo|63 -25 7}} | | {{monzo| -20 -12 25 }}, {{monzo| 63 -25 7 }} | ||
|{{mapping|541 1715 1256}} | | {{mapping| 541 1715 1256 }} | ||
| +0.0355 | | +0.0355 | ||
| 0.0874 | | 0.0874 | ||
| 3.94 | | 3.94 | ||
|- | |- | ||
|2.9.5.7 | | 2.9.5.7 | ||
| | | 40500000/40353607, 43046721/43025920, 95703125/95551488 | ||
|{{mapping|541 1715 1256 1519}} | | {{mapping| 541 1715 1256 1519 }} | ||
| -0.0171 | | -0.0171 | ||
| 0.1184 | | 0.1184 | ||
| 5.34 | | 5.34 | ||
|- | |- | ||
|2.9.5.7 | | 2.9.5.7.13 | ||
| 4096/4095, 10985/10976, 2734375/2729376, 11390625/11361532 | |||
| {{mapping| 541 1715 1256 1519 2002 }} | |||
| -0.0211 | |||
| 0.1062 | |||
| 4.79 | |||
| | |||
|{{mapping|541 1715 1256 1519 | |||
| -0. | |||
| 0. | |||
| | |||
|} | |} | ||