497edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|497}} == Theory == 497et only is consistent to the 5-limit. Using the patent val, it tempers out 67108864/66976875, 48828125/48771072, 2100875/20..." |
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== Theory == | == Theory == | ||
497et only is consistent to the 5-limit. Using the patent val, | 497et only is [[consistent]] to the [[5-odd-limit]]. Using the [[patent val]], the equal temperament [[tempering out|tempers out]] [[2100875/2097152]], 48828125/48771072, 67108864/66976875, and 200120949/200000000 in the 7-limit; [[5632/5625]], 42875/42768, 43923/43904, [[131072/130977]], 151263/151250, 160083/160000, and 391314/390625 in the 11-limit. | ||
=== Odd harmonics === | === Odd harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
497 factors into 7 × 41, with [[7edo]] and [[41edo]] as its subset edos. [[1491edo]], which triples it, gives a good correction to | 497 factors into 7 × 41, with [[7edo]] and [[41edo]] as its subset edos. [[1491edo]], which triples it, gives a good correction to harmonics 3 and 7. | ||
== 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|788 -497}} | | {{monzo| 788 -497 }} | ||
|{{mapping|497 788}} | | {{mapping| 497 788 }} | ||
| -0.2084 | | -0.2084 | ||
| 0.2084 | | 0.2084 | ||
| 8.63 | | 8.63 | ||
|- | |- | ||
|2.3.5 | | 2.3.5 | ||
|{{monzo|38 -2 -15}}, {{ | | {{monzo| 38 -2 -15 }}, {{monzo| 12 -31 16 }} | ||
|{{mapping|497 788 1154}} | | {{mapping| 497 788 1154 }} | ||
| -0.1396 | | -0.1396 | ||
| 0.1961 | | 0.1961 | ||
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|+Table of rank-2 temperaments by generator | |+Table of rank-2 temperaments by generator | ||
! Periods<br>per 8ve | ! Periods<br>per 8ve | ||
! Generator | ! Generator* | ||
! Cents | ! Cents* | ||
! Associated<br>Ratio* | ! Associated<br>Ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
|1 | | 1 | ||
|80\497 | | 80\497 | ||
|193.16 | | 193.16 | ||
|262144/234375 | | 262144/234375 | ||
|[[Luna]] | | [[Luna]] | ||
|} | |} | ||
<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 | ||