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 has an excellent 7th harmonic, being a denominator of [[semiconvergent]] to log<sub>2</sub>7, and it is overall a strong 2.5.7.11.19.23.31.41 subgroup tuning, with errors of less than 10% on all harmonics. Some commas it tempers out in this subgroup are 575/574, 1331/1330, 1375/~~1572~~, 2255/2244, 2300/2299, 6860/6859, 10241/10240.

== Theory ==

109edo [[tempering out|tempers out]] 20000/19683 ([[tetracot comma]]) 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 has an excellent [[7/1|7th harmonic]], being a denominator of [[semiconvergent]] to log<sub>2</sub>7, and it is overall a strong 2.5.7.11.19.23.31.41 [[subgroup]] tuning, with errors of less than 10% on all harmonics. Some commas it tempers out in this subgroup are 575/574, 1331/1330, 1375/1372, 2255/2244, 2300/2299, 6860/6859, 10241/10240.

=== Prime harmonics ===

=== Subsets and supersets ===

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

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

=== Nonoctave temperaments ===

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== Intervals ==

~~[[Category:Equal divisions of the octave|###]]~~

~~[[Category:Prime EDO]]~~

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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 has an excellent 7th harmonic, being a denominator of [[semiconvergent]] to log<sub>2</sub>7, and it is overall a strong 2.5.7.11.19.23.31.41 subgroup tuning, with errors of less than 10% on all harmonics. Some commas it tempers out in this subgroup are 575/574, 1331/1330, 1375/1572, 2255/2244, 2300/2299, 6860/6859, 10241/10240.
+== Theory ==
+edo [[tempering out|tempers out]] 20000/19683 ([[tetracot comma]]) 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 has an excellent [[7/1|7th harmonic]], being a denominator of [[semiconvergent]] to log<sub>2</sub>7, and it is overall a strong 2.5.7.11.19.23.31.41 [[subgroup]] tuning, with errors of less than 10% on all harmonics. Some commas it tempers out in this subgroup are 575/574, 1331/1330, 1375/1372, 2255/2244, 2300/2299, 6860/6859, 10241/10240.
 === Prime harmonics ===
-{{harmonics in equal|109}}
+{{Harmonics in equal|109}}
 === Subsets and supersets ===
-edo is the 29th [[prime EDO]].
+edo is the 29th [[prime edo]].
 === Nonoctave temperaments ===
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 == Intervals ==
 {{Interval table}}
-[[Category:Equal divisions of the octave|###]]<!-- 3-digit number -->
-[[Category:Prime EDO]]