87edo: Difference between revisions
m →Theory: ty for splitting wasnt sure how to do that... |
m →Theory: some commentary |
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=== Prime harmonics === | === Prime harmonics === | ||
In higher limits it excels as a subgroup temperament, especially as an incomplete 71-limit temperament with [[128/127]] and [[129/128]] (the subharmonic and harmonic comma-sized intervals, respectively) mapped accurately to a single step. Generalizing a single step of 87edo harmonically yields harmonics 115 through 138*, (thus) tempering S116 through S137 by patent val and corresponding to the gravity of the fact that 87edo is a circle of [[126/125]]'s, meaning ([[126/125]])<sup>87</sup> only very slightly exceeds the octave. | |||
(*When detempered this is the beginning of the construction of [[Ringer scale|Ringer]] 87.) | |||
{{Harmonics in equal|87|columns=11}} | {{Harmonics in equal|87|columns=11}} | ||
{{Harmonics in equal|87|columns=9|start=12}} | {{Harmonics in equal|87|columns=9|start=12}} | ||