87edo: Difference between revisions
m →Theory: some commentary |
→Theory: hide the second table by default to reduce the noise on the page. And since we're at 71, I don't see a reason to shy away from presenting the qualities of primes as high as 89 |
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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 | 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, which when detempered is the beginning of the construction of [[Ringer scale|Ringer]] 87, 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. | ||
{{Harmonics in equal|87|columns=12}} | |||
{{Harmonics in equal|87|columns= | {{Harmonics in equal|87|columns=12|start=13|collapsed=1|title=Approximation of prime harmonics in 87edo (continued)}} | ||
{{Harmonics in equal|87|columns= | |||
== Intervals == | == Intervals == | ||