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757edo: Difference between revisions

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Created page with "{{Infobox ET}} {{EDO intro|757}} == Theory == 757edo is consistent to the 7-odd-limit, tempering out 4375/4374, 67108864/66976875 and 282475249/281250000. Usi..."
 
m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"
 
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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|757}}
{{ED intro}}


== Theory ==
== Theory ==
757edo is [[consistent]] to the [[7-odd-limit]], [[tempering out]] [[4375/4374]], 67108864/66976875 and 282475249/281250000. Using the [[patent val]], it tempers out [[5632/5625]], 4375/4374, [[160083/160000]] and 5764801/5749920 in the [[11-limit]].
757edo is [[consistent]] to the [[7-odd-limit]]. As an equal temperament, it [[tempering out|tempers out]] [[4375/4374]], 67108864/66976875 and 282475249/281250000. Using the [[patent val]], it tempers out [[5632/5625]], [[160083/160000]] and 5764801/5749920 in the [[11-limit]].


=== Prime harmonics ===
=== Prime 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" |[[Comma list|Comma List]]
! rowspan="2" | [[Subgroup]]
! rowspan="2" |[[Mapping]]
! rowspan="2" | [[Comma list]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! rowspan="2" | [[Mapping]]
! colspan="2" |Tuning Error
! rowspan="2" | Optimal<br />8ve stretch (¢)
|-
! colspan="2" | Tuning error
![[TE error|Absolute]] (¢)
|-
![[TE simple badness|Relative]] (%)
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
|-
| 2.3
| 2.3
| {{monzo|1200 -757}}
| {{monzo| 1200 -757 }}
| {{mapping|757 1200}}
| {{mapping| 757 1200 }}
| -0.0917
| −0.0917
| 0.0917
| 0.0917
| 5.78
| 5.78
|-
|-
| 2.3.5
| 2.3.5
| {{monzo|24 -21 4}}, {{monzo|78 5 -37}}
| {{monzo| 24 -21 4 }}, {{monzo| 78 5 -37 }}
| {{mapping|757 1200 1758}}
| {{mapping| 757 1200 1758 }}
| -0.1295
| −0.1295
| 0.0920
| 0.0920
| 5.80
| 5.80
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| 2.3.5.7
| 2.3.5.7
| 4375/4374, 67108864/66976875, 282475249/281250000
| 4375/4374, 67108864/66976875, 282475249/281250000
| {{mapping|757 1200 1758 2125}}
| {{mapping| 757 1200 1758 2125 }}
| -0.0735
| −0.0735
| 0.1256
| 0.1256
| 7.92
| 7.92
|-
|-
| 2.3.5.7.11
| 2.3.5.7.11
| 5632/5625, 4375/4374, 160083/160000, 5764801/5749920
| 4375/4374, 5632/5625, 160083/160000, 5764801/5749920
| {{mapping|757 1200 1758 2125 2619}}
| {{mapping| 757 1200 1758 2125 2619 }}
| -0.0780
| −0.0780
| 0.1127
| 0.1127
| 7.11
| 7.11
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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
|-
! Periods<br />per 8ve
! Generator*
! Generator*
! Cents*
! Cents*
! Associated<br>Ratio*
! Associated<br />ratio*
! Temperaments
! Temperaments
|-
|-
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| [[Vulture]]
| [[Vulture]]
|}
|}
<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if 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
== Music ==
; [[Francium]]
* "developeed" from ''wiloliquy'' (2025) – [https://open.spotify.com/track/1RaOpdvBzCxAED154qb5UT Spotify] | [https://francium223.bandcamp.com/track/developeed Bandcamp] | [https://www.youtube.com/watch?v=rskZavKFwv4 YouTube] – in Vulture, 757edo tuning
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