124edo: Difference between revisions
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124edo is closely related to [[31edo]], but the patent | == Theory == | ||
124edo is closely related to [[31edo]], but the [[patent val]]s differ on the [[mapping]] for [[3/1|3]]. The equal temperament [[tempering out|tempers out]] 2048/2025 ([[diaschisma]]) and {{monzo| -6 -24 19 }} in the 5-limit. Using the patent val, it tempers out [[3136/3125]], [[4000/3969]], and 33614/32805 in the 7-limit; [[385/384]], 1232/1215, 1331/1323, and 3773/3750 in the 11-limit; [[196/195]], [[364/363]], 572/567, [[625/624]], and [[1001/1000]] in the 13-limit. Note that although its sharp fifth is slightly closer to just, both fifths are about equally off in both directions, and its [[9/1|9th harmonic]] is especially accurate as a result, so it can be considered a [[dual-fifth system]], in which it performs very well in the 2.9.5.7.11.13.17.19.23.37 [[subgroup]] (the dual-fifth no-31's [[37-limit]]), which is arguably the right way to analyze its approximations of JI. Also interesting is that one may want to double the number of notes to add a fifth closer to just, but this causes the relative errors of other primes to double leading to [[consistency|inconsistencies]], so its most reasonable and capable conceptualization seems to be that of a dual-fifth system. | |||
== | === Odd harmonics === | ||
{{Harmonics in equal|124|columns=12}} | {{Harmonics in equal|124|columns=12}} | ||
{{Harmonics in equal|124|columns=12|start=13|collapsed=1|title=Approximation of odd harmonics in 124edo (continued)}} | {{Harmonics in equal|124|columns=12|start=13|collapsed=1|title=Approximation of odd harmonics in 124edo (continued)}} | ||
==Intervals== | == Intervals == | ||
{| class="wikitable mw-collapsible mw-collapsed" | {| class="wikitable mw-collapsible mw-collapsed" | ||
|+124 EDO Table of Intervals | |+124 EDO Table of Intervals | ||