109edo: Difference between revisions

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==Theory==

109edo [[tempering out|tempers out]] 20000/19683 in the [[5-limit]]; [[245/243]], 2401/2400 and 65625/65536 in the [[7-limit]]; [[385/384]], 1375/1372, and 4000/3993 in the [[11-limit]]. It provides the [[optimal patent val]] for 7-limit [[octacot]] temperament, and 11 and 13 limit [[leapweek]]; plus 109ef provides an excellent tuning for 11- and 13-limit octacot.

109edo ~~[[tempering out|tempers out]] 20000/19683 in the [[~~5~~-limit]]; [[245/243]], 2401/2400 and 65625/65536 in the [[~~7~~-limit]]; [[385/384]], 1375/1372, and 4000/3993 in the [[~~11~~-limit]]~~. ~~It provides the [[optimal patent val]] for 7-limit [[octacot]] temperament~~, and ~~11 and 13 limit [[leapweek]]; plus 109ef provides~~ an ~~excellent tuning for 11- and 13-limit octacot~~.

109edo is a strong 2.5.7.11.19.23.31 subgroup tuning, with errors of less than 10% on all harmonics and an exceptionally small error of 0.16% on the 7th harmonic.

=== Prime harmonics ===

=== Subsets and supersets ===

109edo is the 29th [[prime EDO]].

==Scales==

Since 109edo has a step of 11.009 cents, it also allows one to use its MOS scales as circulating temperaments. It is also the first edo which also allows one to use an MOS scale one octave of which fills a standard piano keyboard as a circulating temperament.

Since 109edo has a step of 11.009 cents, it also allows one to use its MOS scales as circulating temperaments. It is also the first edo which also allows one to use an MOS scale one octave of which fills a standard piano keyboard as a circulating temperament{{clarify}}.

{| class="wikitable mw-collapsible mw-collapsed"

|+Circulating temperaments in 109edo

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 {{Infobox ET}}
 {{EDO intro|109}}
+==Theory==
+edo [[tempering out|tempers out]] 20000/19683 in the [[5-limit]]; [[245/243]], 2401/2400 and 65625/65536 in the [[7-limit]]; [[385/384]], 1375/1372, and 4000/3993 in the [[11-limit]]. It provides the [[optimal patent val]] for 7-limit [[octacot]] temperament, and 11 and 13 limit [[leapweek]]; plus 109ef provides an excellent tuning for 11- and 13-limit octacot.
-edo [[tempering out|tempers out]] 20000/19683 in the [[5-limit]]; [[245/243]], 2401/2400 and 65625/65536 in the [[7-limit]]; [[385/384]], 1375/1372, and 4000/3993 in the [[11-limit]]. It provides the [[optimal patent val]] for 7-limit [[octacot]] temperament, and 11 and 13 limit [[leapweek]]; plus 109ef provides an excellent tuning for 11- and 13-limit octacot.
+edo is a strong 2.5.7.11.19.23.31 subgroup tuning, with errors of less than 10% on all harmonics and an exceptionally small error of 0.16% on the 7th harmonic.
+=== Prime harmonics ===
+{{harmonics in equal|109}}
+=== Subsets and supersets ===
 edo is the 29th [[prime EDO]].
+==Scales==
-Since 109edo has a step of 11.009 cents, it also allows one to use its MOS scales as circulating temperaments. It is also the first edo which also allows one to use an MOS scale one octave of which fills a standard piano keyboard as a circulating temperament.
+Since 109edo has a step of 11.009 cents, it also allows one to use its MOS scales as circulating temperaments. It is also the first edo which also allows one to use an MOS scale one octave of which fills a standard piano keyboard as a circulating temperament{{clarify}}.
 {| class="wikitable mw-collapsible mw-collapsed"
 |+Circulating temperaments in 109edo