109edo: Difference between revisions

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Eliora (talk | contribs)
Theory: rework
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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. The error on the 7th harmonic is exceptionally small due to 109 being a denominator of [[semiconvergent]] to log<sub>2</sub>7.
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.  


=== Prime harmonics ===
=== Prime harmonics ===