8404edo: Difference between revisions
Just reference 16808edo |
Note the possibility of an adaptive approach |
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{{ED intro}} | {{ED intro}} | ||
8404edo is [[consistent]] to the [[13-odd-limit]], but both [[harmonic]]s [[5/1|5]] and [[13/1|13]] are about halfway between its steps. It is | 8404edo is [[consistent]] to the [[13-odd-limit]], but both [[harmonic]]s [[5/1|5]] and [[13/1|13]] are about halfway between its steps. It is perhaps more interesting as every other step of the monstrous [[16808edo]], with the same extraordinary accuracy in the 2.3.25.7.11.17.23.31 subgroup. Moreover, it can be used adaptively to mimic 16808edo by alternating the sharp and flat mappings of the inaccurate primes, if you believe the full 16808edo is not worth going the extra mile. [[8269edo]] and [[8539edo]] are similarly sized edos that legit approximate JI without this trick, though they do best in the [[23-limit]], not the [[31-limit]]. | ||
Like 16808edo, | Like 16808edo, 8404edo's [[3/2|perfect fifth]] comes from [[2101edo]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||