1171edo: Difference between revisions
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{{Infobox ET}} | |||
{{ED intro}} | |||
== Theory == | |||
1171edo is a very strong 5-limit division, being the first one past [[612edo|612]] with a lower 5-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]]. It has a 5-limit [[comma basis]] consisting of the [[monzisma]], {{monzo| 54 -37 2 }} and whoosh, {{monzo| 37 25 -33 }}. While not a strong higher-limit system, it is [[consistency|distinctly consistent]] through the [[27-odd-limit]], and is very strong on the 2.3.5.11 [[subgroup]]. | |||
=== Prime harmonics === | |||
{{Harmonics in equal|1171}} | |||
=== Subsets and supersets === | |||
1171edo is the 193rd [[prime edo]]. [[2342edo]] which doubles it, corrects its [[harmonic]] [[7/1|7]] to a near-just quality. | |||
== Regular temperament properties == | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |||
|- | |||
! Periods<br />per 8ve | |||
! Generator* | |||
! Cents* | |||
! Associated<br />ratio* | |||
! Temperaments | |||
|- | |||
| 1 | |||
| 129\1171 | |||
| 132.195 | |||
| {{Monzo| -38 5 13 }} | |||
| [[Astro]] | |||
|- | |||
| 1 | |||
| 243\1171 | |||
| 249.018 | |||
| {{Monzo| -26 18 -1 }} | |||
| [[Monzismic]] | |||
|- | |||
| 1 | |||
| 315\1171 | |||
| 322.801 | |||
| {{Monzo| -6 23 -13 }} | |||
| [[Senior]] | |||
|- | |||
| 1 | |||
| 335\1171 | |||
| 343.296 | |||
| 8000/6561 | |||
| [[Raider]] | |||
|- | |||
| 1 | |||
| 547\1171 | |||
| 560.547 | |||
| 864/625 | |||
| [[Whoosh]] | |||
|} | |||
<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 | |||
== Music == | |||
; [[Francium]] | |||
* "Right On Friendly Lovers" from ''Naughty Girl Era'' (2024) – [https://open.spotify.com/track/208kkCqXksQWhT0zdxFXYm Spotify] | [https://francium223.bandcamp.com/track/right-on-friendly-lovers Bandcamp] | [https://www.youtube.com/watch?v=_qqisIAkVRc YouTube] − in Friesachic, 1171edo tuning | |||
* "Apply to a Print" from ''I Want To'' (2025) – [https://open.spotify.com/track/5botrdPX1YdFmk2mP6kbOr Spotify] | [https://francium223.bandcamp.com/track/apply-to-a-print Bandcamp] | [https://www.youtube.com/watch?v=ui-ORXPgqaE YouTube] – in Viljevic, 1171edo tuning | |||