475edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|475}} == Theory == 475et is only consistent to the 5-odd-limit. It can be considered for the 2.3.5.11.13.19.23 subgroup, tempering out 23..." |
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== Theory == | == Theory == | ||
475edo is only [[consistent]] to the [[5-odd-limit]]. The equal temperament [[tempering out|tempers out]] {{monzo| -14 -19 19 }} ([[enneadeca]]) and {{monzo| 47 -15 -10 }} (quintosec comma) in the 5-limit. In the 7-limit, the 475d [[val]] [[support]]s [[enneadecal]] and the [[patent val]] supports [[cotoneum]]. | |||
It can be considered for the 2.3.5.11.13.19.23 [[subgroup]], tempering out [[2376/2375]], [[3250/3249]], 11132/11115, 11979/11960, 14300/14283 and 42757/42750. | |||
=== Prime harmonics === | === Prime harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
475 factors into 5<sup>2</sup> × 19, | Since 475 factors into 5<sup>2</sup> × 19, 475edo has subset edos {{EDOs| 5, 19, 25, and 95 }}. [[950edo]], which doubles it, gives a good correction to the harmonic 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|753 -475}} | | {{monzo| 753 -475 }} | ||
|{{mapping|475 753}} | | {{mapping| 475 753 }} | ||
| -0.1138 | | -0.1138 | ||
| 0.1138 | | 0.1138 | ||
| 4.50 | | 4.50 | ||
|- | |- | ||
|2.3.5 | | 2.3.5 | ||
|{{monzo|-14 -19 19}}, {{monzo|47 -15 -10}} | | {{monzo| -14 -19 19 }}, {{monzo| 47 -15 -10 }} | ||
|{{mapping|475 753 1103}} | | {{mapping| 475 753 1103 }} | ||
| -0.1064 | | -0.1064 | ||
| 0.0935 | | 0.0935 | ||
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! Temperaments | ! Temperaments | ||
|- | |- | ||
|1 | | 1 | ||
|157\475 | | 157\475 | ||
|396.63 | | 396.63 | ||
|98304/78125 | | 98304/78125 | ||
|[[Squarschmidt]] | | [[Squarschmidt]] | ||
|- | |- | ||
|5 | | 5 | ||
|329\475<br>(44\475) | | 329\475<br>(44\475) | ||
|831.16<br>(111.16) | | 831.16<br>(111.16) | ||
| | | 160/99<br>(16/15) | ||
|[[ | | [[Quintosec]] | ||
|- | |- | ||
|19 | | 19 | ||
|197\475<br>(3\475) | | 197\475<br>(3\475) | ||
|497.68<br>(7.58) | | 497.68<br>(7.58) | ||
|4/3<br>(225/224) | | 4/3<br>(225/224) | ||
|[[Enneadecal]] | | [[Enneadecal]] (475d) | ||
|} | |} | ||
<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 | ||