467edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|467}} == Theory == 467et is consistent to thr 9-odd-limit. Using the patent val, it tempers out 4375/4374, 1640558367/1638400000, 52509..." |
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== Theory == | == Theory == | ||
467edo is [[consistent]] to the [[9-odd-limit]] with [[harmonic]]s [[3/1|3]], [[5/1|5]], and [[7/1|7]] all tuned flat. Using the [[patent val]], the equal temperament [[tempering out|tempers out]] [[4375/4374]], [[2100875/2097152]], 5250987/5242880, and {{monzo| -16 4 9 -4 }} in the 7-limit. | |||
In the 11-limit, the 467e [[val]] scores much better than the [[patent val]]. The 467e val tempers out 1375/1372, 24057/24010, 35937/35840, and 41503/41472, and in the 13-limit, [[625/624]], [[729/728]], [[1716/1715]], and [[2200/2197]]. The patent val tempers out [[540/539]], [[6250/6237]], 12005/11979, and 14700/14641, and in the 13-limit, 625/624, 729/728, and [[2080/2079]]. | |||
It [[support]]s [[mitonic]] and [[counterkleismic]]. | |||
=== 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|-740 467}} | | {{monzo| -740 467 }} | ||
|{{ | | {{mapping| 467 740 }} | ||
| 0.1439 | | 0.1439 | ||
| 0.1439 | | 0.1439 | ||
| 5.38 | | 5.38 | ||
|- | |- | ||
|2.3.5 | | 2.3.5 | ||
|{{monzo|-36 11 8}}, {{monzo|-16 35 -17}} | | {{monzo| -36 11 8 }}, {{monzo| -16 35 -17 }} | ||
|{{ | | {{mapping| 467 740 1084 }} | ||
| 0.2215 | | 0.2215 | ||
| 0.1608 | | 0.1608 | ||
| 6.02 | | 6.02 | ||
|- | |- | ||
|2.3.5.7 | | 2.3.5.7 | ||
|4375/4374, 2100875/2097152, | | 4375/4374, 2100875/2097152, {{monzo| -16 4 9 -4 }} | ||
|{{ | | {{mapping| 467 740 1084 1311 }} | ||
| 0.1741 | | 0.1741 | ||
| 0.1617 | | 0.1617 | ||
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! Temperaments | ! Temperaments | ||
|- | |- | ||
|1 | | 1 | ||
|71\467 | | 71\467 | ||
|182.441 | | 182.441 | ||
|10/9 | | 10/9 | ||
| | | [[Mitonic]] | ||
|- | |- | ||
|1 | | 1 | ||
|123\467 | | 123\467 | ||
|316.060 | | 316.060 | ||
|6/5 | | 6/5 | ||
|[[Counterhanson]] | | [[Counterhanson]] | ||
|} | |} | ||
<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 | ||