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1277edo: Difference between revisions

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Created page with "{{Infobox ET}} {{EDO intro|1277}} == Theory == 1277edo is consistent to the 11-odd-limit. The equal temperament tempers out 4375/4374, 52734375/..."
 
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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|1277}}
{{ED intro}}


== Theory ==
== Theory ==
1277edo is [[consistent]] to the [[11-odd-limit]]. The equal temperament [[tempering out|tempers out]] [[4375/4374]], 52734375/52706752 and {{monzo|51 -13 -1 -10}} in the 7-limit; 4375/4374, 759375/758912, 151263/151250 and 2097152/2096325 in the 11-limit. It [[support]]s [[nanismic]], [[nanic]], [[ragismic]], [[bragi]], [[revopentic]], [[revopent]], [[sasaquinbizo-atriyo]], [[starscape]], [[nommismic]], [[technologismic]], [[supermajor]] and [[monzismic]].
1277edo is [[consistent]] to the [[11-odd-limit]]. The equal temperament [[tempering out|tempers out]] [[4375/4374]], 52734375/52706752, 645700815/645657712 ([[starscape comma]]) and {{monzo| 51 -13 -1 -10 }} ([[technologisma]]) in the 7-limit; 151263/151250, 759375/758912, and 2097152/2096325 in the 11-limit. It [[support]]s [[monzismic]], [[supermajor]], [[revopent]], as well as the rank-3 temperament [[bragi]].


=== Prime harmonics ===
=== Prime harmonics ===
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=== Subsets and supersets ===
=== Subsets and supersets ===
1277edo is the 206th [[prime EDO]].
1277edo is the 206th [[prime edo]]. [[2554edo]], which divides the edostep in two, is the smallest edo [[distinctly consistent]] through the [[41-odd-limit]], and provides correction for harmonics 11 through 41.


== 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" |[[Mapping]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|-
|2.3
! rowspan="2" | [[Subgroup]]
|{{monzo|2024 -1277}}
! rowspan="2" | [[Comma list]]
|{{mapping|1277 2024}}
! rowspan="2" | [[Mapping]]
| -0.0009
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo| 2024 -1277 }}
| {{mapping| 1277 2024 }}
| −0.0009
| 0.0009
| 0.0009
| 0.10
| 0.10
|-
|-
|2.3.5
| 2.3.5
|{{monzo|54 -37 2}}, {{monzo|-67 -9 35}}
| {{monzo| 54 -37 2 }}, {{monzo| -67 -9 35 }}
|{{mapping|1277 2024 2965}}
| {{mapping| 1277 2024 2965 }}
| +0.0132
| +0.0132
| 0.0199
| 0.0199
| 2.12
| 2.12
|-
|-
|2.3.5.7
| 2.3.5.7
|4375/4374, 52734375/52706752, {{monzo|51 -13 -1 -10}}
| 4375/4374, 52734375/52706752, {{monzo| 51 -13 -1 -10 }}
|{{mapping|1277 2024 2965 3585}}
| {{mapping| 1277 2024 2965 3585 }}
| +0.0093
| +0.0093
| 0.0186
| 0.0186
| 1.98
| 1.98
|-
|-
|2.3.5.7.11
| 2.3.5.7.11
|4375/4374, 759375/758912, 151263/151250, 2097152/2096325
| 4375/4374, 151263/151250, 759375/758912, 2097152/2096325
|{{mapping|1277 2024 2965 3585 4418}}
| {{mapping| 1277 2024 2965 3585 4418 }}
| -0.0092
| −0.0092
| 0.0405
| 0.0405
| 4.31
| 4.31
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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
|-
! Periods<br />per 8ve
! Generator*
! Generator*
! Cents*
! Cents*
! Associated<br>Ratio*
! Associated<br />ratio*
! Temperaments
! Temperaments
|-
|-
|1
| 1
|265\1277
| 265\1277
|249.021
| 249.021
|{{monzo|-27 11 3 1}}
| {{monzo| -27 11 3 1 }}
|[[Monzismic]]
| [[Monzismic]]
|-
|-
|1
| 1
|380\1277
| 380\1277
|357.087
| 357.087
|768/625
| 768/625
|[[Dodifo]]
| [[Dodifo]]
|-
|-
|1
| 1
|463\1277
| 463\1277
|435.082
| 435.082
|9/7
| 9/7
|[[Supermajor]]
| [[Supermajor]]
|}
|}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
== Music ==
; [[Francium]]
* "mututhery" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/6EUbC14BVFJ20b1C4cCOFe Spotify] | [https://francium223.bandcamp.com/track/mututhery Bandcamp] | [https://www.youtube.com/watch?v=0j7yaypCOts YouTube] – in Monzismic[19], 1277edo tuning
* "Makeup Is Soothing." from ''Random Sentences'' (2025) – [https://open.spotify.com/track/6SJHf64ENaPnzQKlnO315x Spotify] | [https://francium223.bandcamp.com/track/makeup-is-soothing Bandcamp] | [https://www.youtube.com/watch?v=zw1oavPPnqU YouTube] – in Aunusic, 1277edo tuning


<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
[[Category:Listen]]
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