2023edo: Difference between revisions

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-{{EDO intro|2023}}
+{{Infobox ET}}
+{{ED intro}}
 == Theory ==
+edo is [[Enfactoring|enfactored]] in the 5-limit, with the same mapping as [[289edo]]. As such it maps the period to [[25/24]], which means [[septendecima]] is also tempered out. In the 17-limit on the [[patent val]], it is a tuning for the [[leaves]] temperament.
+If we impose a stricter harmonic approach, and require all errors to be below 25%, the subgroup consisting of first 7 such harmonics for 2023edo is 2.13.17.23.47.61.71.
+In the 2023e val, it supports the altierran rank-3 temperament tempering out the [[schisma]] and the [[quartisma]].
+=== Prime harmonics ===
 {{Harmonics in equal|2023}}
-First 7 primes with less than 1 standard deviation error in 2023edo are: 2, 13, 17, 23, 47, 61, 71.
-In the 2023e val, it supports the altierran rank-3 temperament tempering out the [[schisma]] and the [[quartisma]].
+=== Subsets and supersets ===
+Since 2023 factors as {{factorization|2023}}, 2023edo has subset edos {{EDOs| 7, 17, 119, and 289 }}.
+== Regular temperament properties ==
+=== Rank-2 temperaments ===
+Note: 5-limit temperaments supported by 289edo are not included.
+{| 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
+|-
+| 17
+| 144\2023<br />(25\2023)
+| 85.417<br />(14.829)
+| 1024/975<br />(8192/8125)
+| [[Leaves]]
+|}
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
-The divisors of 2023 are {{EDOs|1, 7, 17, 119, 289}}. It factors as 7 * 17<sup>2</sup>.
+== Music ==
+; [[Eliora]]
+* [https://www.youtube.com/watch?v=8K2RYO_oCnM ''Bagatelle in 11/8♭ Leaves''] (2023)
-[[Category:Quartismic]]
+[[Category:Listen]]