1277edo: Difference between revisions
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== Theory == | == Theory == | ||
1277edo is [[consistent]] to the [[11-odd-limit]]. | 1277edo is [[consistent]] to the [[11-odd-limit]]. As an equal temperament, it [[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 (temperament)|supermajor]], [[revopent]], as well as the rank-3 temperament [[bragi]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
| Line 17: | Line 17: | ||
! rowspan="2" | [[Comma list]] | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br | ! rowspan="2" | Optimal<br>8ve stretch (¢) | ||
! colspan="2" | Tuning error | ! colspan="2" | Tuning error | ||
|- | |- | ||
| Line 24: | Line 24: | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{ | | {{Monzo| 2024 -1277 }} | ||
| {{ | | {{Mapping| 1277 2024 }} | ||
| −0.0009 | | −0.0009 | ||
| 0.0009 | | 0.0009 | ||
| Line 31: | Line 31: | ||
|- | |- | ||
| 2.3.5 | | 2.3.5 | ||
| {{ | | {{Monzo| 54 -37 2 }}, {{monzo| -67 -9 35 }} | ||
| {{ | | {{Mapping| 1277 2024 2965 }} | ||
| +0.0132 | | +0.0132 | ||
| 0.0199 | | 0.0199 | ||
| Line 39: | Line 39: | ||
| 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 }} | ||
| +0.0093 | | +0.0093 | ||
| 0.0186 | | 0.0186 | ||
| Line 46: | Line 46: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 4375/4374, 151263/151250, 759375/758912, 2097152/2096325 | | 4375/4374, 151263/151250, 759375/758912, 2097152/2096325 | ||
| {{ | | {{Mapping| 1277 2024 2965 3585 4418 }} | ||
| −0.0092 | | −0.0092 | ||
| 0.0405 | | 0.0405 | ||
| Line 56: | Line 56: | ||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
|- | |- | ||
! Periods<br | ! Periods<br>per 8ve | ||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br | ! Associated<br>ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 65: | Line 65: | ||
| 265\1277 | | 265\1277 | ||
| 249.021 | | 249.021 | ||
| {{ | | {{Monzo| -27 11 3 1 }} | ||
| [[Monzismic]] | | [[Monzismic]] | ||
|- | |- | ||
| Line 78: | Line 78: | ||
| 435.082 | | 435.082 | ||
| 9/7 | | 9/7 | ||
| [[Supermajor]] | | [[Supermajor (temperament)|Supermajor]] | ||
|} | |} | ||
<nowiki />* [[Normal | <nowiki/>* [[Normal forms|Octave-reduced form]], reduced to the first half-octave, and [[Normal forms|minimal form]] in parentheses if distinct | ||
== Music == | == Music == | ||
; [[Francium]] | ; [[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 | * "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 | * "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 | ||
[[Category:Listen]] | [[Category:Listen]] | ||