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457edo: Difference between revisions

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Created page with "{{Infobox ET}} {{EDO intro|457}} == Theory == 457et tempers out 283115520/282475249, 1220703125/1219784832, 26873856/26796875, 65625/65536 and 200120949/200000000 in the 7..."
 
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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|457}}
{{ED intro}}
 
== Theory ==
== Theory ==
457et tempers out 283115520/282475249, 1220703125/1219784832, 26873856/26796875, [[65625/65536]] and 200120949/200000000 in the 7-limit; 95703125/95664294, 100663296/100656875, 161280/161051, 29296875/29218112, 166698/166375, 1953125/1951488, 151263/151250, 2359296/2358125, [[540/539]], 5767168/5764801, 825000/823543, [[8019/8000]], 160083/160000, 16808715/16777216, 539055/537824, 244515348/244140625, 67110351/67108864 and 43923/43904 in the 11-limit.
457edo is [[consistent]] to the [[7-odd-limit]], but the error of [[harmonic]] [[3/1|3]] is quite large. As an equal temperament, it [[tempering out|tempers out]] [[19683/19600]] and [[65625/65536]] in the [[7-limit]]; [[540/539]], [[8019/8000]], and 43923/43904 in the [[11-limit]].
===Odd harmonics===
 
=== Odd harmonics ===
{{Harmonics in equal|457}}
{{Harmonics in equal|457}}
===Subsets and supersets===
 
457edo is the 88th [[prime edo]].  
=== Subsets and supersets ===
==Regular temperament properties==
457edo is the 88th [[prime edo]].
 
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" |[[Subgroup]]
! rowspan="2" |[[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|-
|2.3
! rowspan="2" | [[Subgroup]]
|{{monzo|-724 457}}
! rowspan="2" | [[Comma list]]
|{{val|457 724}}
! rowspan="2" | [[Mapping]]
| 0.2716
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo| -724 457 }}
| {{mapping| 457 724 }}
| +0.2716
| 0.2716
| 0.2716
| 10.34
| 10.34
|-
|-
|2.3.5
| 2.3.5
|{{monzo|-36 11 8}}, {{monzo|-5 31 -19}}
| {{monzo| -36 11 8 }}, {{monzo| -5 31 -19 }}
|{{val|457 724 1061}}
| {{mapping| 457 724 1061 }}
| 0.2267
| +0.2267
| 0.2307
| 0.2307
| 8.79
| 8.79
|-
|-
|2.3.5.7
| 2.3.5.7
|19683/19600, 65625/65536, 7381125/7340032
| 19683/19600, 65625/65536, 7381125/7340032
|{{val|457 724 1061 1283}}
| {{mapping| 457 724 1061 1283 }}
| 0.1609
| +0.1609
| 0.2300
| 0.2300
| 8.76
| 8.76
|-
|-
|2.3.5.7.11
| 2.3.5.7.11
|540/539, 8019/8000, 19683/19600, 43923/43904
| 540/539, 8019/8000, 19683/19600, 43923/43904
|{{val|457 724 1061 1283 1581}}
| {{mapping| 457 724 1061 1283 1581 }}
| 0.1227
| +0.1227
| 0.2194
| 0.2194
| 8.36
| 8.36
|-
|-
|2.3.5.7.11.13
| 2.3.5.7.11.13
|540/539, 1716/1715, 4225/4224, 41067/40960, 43940/43923
| 540/539, 1716/1715, 4225/4224, 41067/40960, 43940/43923
|{{val|457 724 1061 1283 1581 1691}}
| {{mapping| 457 724 1061 1283 1581 1691 }}
| 0.1142
| +0.1142
| 0.2012
| 0.2012
| 7.66
| 7.66
|-
|-
|2.3.5.7.11.13.17
| 2.3.5.7.11.13.17
|936/935, 1089/1088, 1275/1274, 1575/1573, 2601/2600, 4225/4224
| 936/935, 1089/1088, 1275/1274, 1575/1573, 2601/2600, 4225/4224
|{{val|457 724 1061 1283 1581 1691 1868}}
| {{mapping| 457 724 1061 1283 1581 1691 1868 }}
| 0.0952
| +0.0952
| 0.1920
| 0.1920
| 7.31
| 7.31
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=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
! Periods<br>per 8ve
|-
! Generator<br>(reduced)
! Periods<br />per 8ve
! Cents<br>(reduced)
! Generator*
! Associated<br>ratio
! Cents*
! Associated<br />ratio*
! Temperaments
! Temperaments
|-
|-
|1
| 1
|10\457
| 10\457
|26.258
| 26.258
|49/48
| 49/48
|[[Sfourth]]
| [[Sfourth]]
|-
|-
|1
| 1
|136\457
| 136\457
|357.11
| 357.11
|49/40
| 49/40
|[[Dodifo]]
| [[Dodifo]]
|-
|-
|1
| 1
|213\457
| 213\457
|559.30
| 559.30
|864/625
| 864/625
|[[Tritriple]]
| [[Tritriple]]
|}
|}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
== Music ==
; [[Francium]]
* "Less and Less" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/5w3K1Q6VhCkUPMXmuh5pVt Spotify] | [https://francium223.bandcamp.com/track/less-and-less Bandcamp] | [https://www.youtube.com/watch?v=y4MGhHE20b4 YouTube]
* "Porcelain Stoneware" from ''Scoop'' (2024) – [https://open.spotify.com/track/055lRdMBKr37MU8HQqlvus Spotify] | [https://francium223.bandcamp.com/track/porcelain-stoneware Bandcamp] | [https://www.youtube.com/watch?v=bzycN6PYMQQ YouTube]
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/457edo"