8404edo - Revision history

FloraC: Note the possibility of an adaptive approach

2025-02-22T10:14:09Z

Note the possibility of an adaptive approach

← Older revision		Revision as of 10:14, 22 February 2025
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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 ~~most~~ 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.		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, ~~its~~ [[3/2\|perfect fifth]] comes from [[2101edo]].		Like 16808edo, 8404edo's [[3/2\|perfect fifth]] comes from [[2101edo]].

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

FloraC: Just reference 16808edo

2025-02-22T09:52:13Z

Just reference 16808edo

← Older revision		Revision as of 09:52, 22 February 2025
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	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 most 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.		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 most 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.

	~~Its~~ [[3/2\|perfect fifth]] ~~ultimately~~ comes from [[2101edo]].		Like 16808edo, its [[3/2\|perfect fifth]] comes from [[2101edo]].

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

FloraC: Created page with "{{Infobox ET}} {{ED intro}} 8404edo is consistent to the 13-odd-limit, but both harmonics 5 and 13 are about halfway between its steps. It is mos..."

2025-02-22T09:31:49Z

Created page with "{{Infobox ET}} {{ED intro}} 8404edo is consistent to the 13-odd-limit, but both harmonics 5 and 13 are about halfway between its steps. It is mos..."

New page

{{Infobox ET}}
{{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 most 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.

Its [[3/2|perfect fifth]] ultimately comes from [[2101edo]].

=== Prime harmonics ===
{{Harmonics in equal|8404|intervals=prime}}

=== Subsets and supersets ===
Since 8404 factors into primes as {{nowrap| 2<sup>2</sup> × 11 × 191 }}, 8404edo contains subset edos 2, 4, 11, 22, 44, 191, 382, 764, 2101, and 4202. One step of 8404edo is exactly 2 jinns.