601edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|601}} == Theory == 601edo is only consistent to the 3-odd-limit and the error of the harmonic 3 is very large. It can be used i..." |
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== Theory == | == Theory == | ||
601edo is | 601edo is in[[consistent]] to the [[5-odd-limit]] and both [[harmonic]]s [[3/1|3]] and [[5/1|5]] are about halfway between its steps. It can be used in the 2.9.15.7.11.13.19 [[subgroup]], [[tempering out]] [[41503/41472]], 104272/104247, [[10648/10647]], 388962/388531 and 10097379/10092544. | ||
=== Odd harmonics === | === Odd harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
601edo is the 110th [[prime | 601edo is the 110th [[prime edo]]. [[1202edo]], which doubles it, gives a good correction to the harmonics 3 and 5. | ||
== 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|-1905 601}} | | {{monzo| -1905 601 }} | ||
|{{mapping|601 1905}} | | {{mapping| 601 1905 }} | ||
| 0.0393 | | 0.0393 | ||
| 0.0393 | | 0.0393 | ||
| 1.97 | | 1.97 | ||
|- | |- | ||
|2.9.5 | | 2.9.5 | ||
|32805/32768, {{monzo|-105 -65 134}} | | 32805/32768, {{monzo| -105 -65 134 }} | ||
|{{mapping|601 1905 1395}} | | {{mapping| 601 1905 1395 }} | ||
| 0.1635 | | 0.1635 | ||
| 0.1785 | | 0.1785 | ||
| 8.94 | | 8.94 | ||
|- | |- | ||
|2.9.5.7 | | 2.9.5.7 | ||
|32805/32768, 68359375/68024448, {{monzo|-16 -5 -2 13}} | | 32805/32768, 68359375/68024448, {{monzo| -16 -5 -2 13 }} | ||
|{{mapping|601 1905 1395 1687}} | | {{mapping| 601 1905 1395 1687 }} | ||
| 0.1618 | | 0.1618 | ||
| 0.1546 | | 0.1546 | ||
| 7.74 | | 7.74 | ||
|- | |- | ||
|2.9.5.7.11 | | 2.9.5.7.11 | ||
|6250/6237, 41503/41472, 32805/32768, 3294225/3294172 | | 6250/6237, 41503/41472, 32805/32768, 3294225/3294172 | ||
|{{mapping|601 1905 1395 1687 2079}} | | {{mapping| 601 1905 1395 1687 2079 }} | ||
| 0.1431 | | 0.1431 | ||
| 0.1432 | | 0.1432 | ||
| 7.17 | | 7.17 | ||
|- | |- | ||
|2.9.5.7.11.13 | | 2.9.5.7.11.13 | ||
|1575/1573, 6250/6237, 41503/41472, 32805/32768, 2200/2197 | | 1575/1573, 6250/6237, 41503/41472, 32805/32768, 2200/2197 | ||
|{{mapping|601 1905 1395 1687 2079 2224}} | | {{mapping| 601 1905 1395 1687 2079 2224 }} | ||
| 0.1160 | | 0.1160 | ||
| 0.1441 | | 0.1441 | ||
| 7.22 | | 7.22 | ||
|} | |} | ||