361edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|361}} == Theory == 361et is consistent to the 9-odd-limit, tempering out 43046721/43025920, 2460375/2458624, 703125/702464, 48828125/48..." |
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== Theory == | == Theory == | ||
361et is consistent to the [[9-odd-limit]], tempering out [[ | 361et is [[consistent]] to the [[9-odd-limit]] with flat tunings of [[harmonic]]s [[3/1|3]], [[5/1|5]], and [[7/1|7]]. The equal temperament [[tempering out|tempers out]] [[4375/4374]], [[703125/702464]], 2460375/2458624, [[43046721/43025920]], and 48828125/48771072 in the 7-limit. It [[support]]s the 5-limit [[submajor]] temperament. | ||
=== Odd harmonics === | === Odd 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|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]] (%) | ||
|- | |- | ||
|2.3 | | 2.3 | ||
|{{monzo|-572 361}} | | {{monzo| -572 361 }} | ||
|{{mapping|361 572}} | | {{mapping| 361 572 }} | ||
| 0.1798 | | 0.1798 | ||
| 0.1798 | | 0.1798 | ||
| 5.41 | | 5.41 | ||
|- | |- | ||
|2.3.5 | | 2.3.5 | ||
|{{monzo|-36 11 8}}, {{monzo|-14 -19 19}} | | {{monzo| -36 11 8 }}, {{monzo| -14 -19 19 }} | ||
|{{mapping|361 572 838}} | | {{mapping| 361 572 838 }} | ||
| 0.2230 | | 0.2230 | ||
| 0.1590 | | 0.1590 | ||
| 4.78 | | 4.78 | ||
|- | |- | ||
|2.3.5.7 | | 2.3.5.7 | ||
|4375/4374, 2460375/2458624 | | 4375/4374, 823543/819200, 2460375/2458624 | ||
|{{mapping|361 572 838 1013}} | | {{mapping| 361 572 838 1013 }} | ||
| 0.3020 | | 0.3020 | ||
| 0.1941 | | 0.1941 | ||
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! Temperaments | ! Temperaments | ||
|- | |- | ||
|1 | | 1 | ||
|166\361 | | 166\361 | ||
|551.80 | | 551.80 | ||
|48/35 | | 48/35 | ||
|[[Emka]] | | [[Emka]] | ||
|- | |- | ||
|19 | | 19 | ||
|150\361<br>(2\361) | | 150\361<br>(2\361) | ||
|498.61<br>(6.65) | | 498.61<br>(6.65) | ||
|4/3<br>(225/224) | | 4/3<br>(225/224) | ||
|[[Enneadecal]] | | [[Enneadecal]] | ||
|} | |} | ||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | <nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | ||