420edo: Difference between revisions
m +categories |
|||
| (2 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
420edo is [[enfactoring|enfactored]] in the 7-limit, with the same tuning of [[harmonic]]s [[3/1|3]], [[5/1|5]], and [[7/1|7]] as [[140edo]]. The [[13/1|13th harmonic]] is also present in 140edo, and ultimately derives from [[10edo]]. The [[29/1|29th harmonic]], while having significantly drifted in terms of [[relative interval error]], has retained its step position from [[7edo]]. In addition, in the 29-limit, only the harmonics 11 and 17 have step numbers coprime with 420. This means that all other approximations are preserved from smaller edos, thus enabling edo mergers and mashups. | 420edo is [[enfactoring|enfactored]] in the 7-limit, with the same tuning of [[harmonic]]s [[3/1|3]], [[5/1|5]], and [[7/1|7]] as [[140edo]]. The [[13/1|13th harmonic]] is also present in 140edo, and ultimately derives from [[10edo]]. The [[29/1|29th harmonic]], while having significantly drifted in terms of [[relative interval error]], has retained its step position from [[7edo]]. In addition, in the 29-limit, only the harmonics 11 and 17 have step numbers coprime with 420. This means that all other approximations are preserved from smaller edos, thus enabling edo mergers and mashups. | ||
420edo is good at the 2.5.7.11.13.19.23 [[subgroup]], and has a great potential as a near-just xenharmonic system. It also works satisfactorily with the 29-limit as a whole, though in[[consistent]]. In the 11-limit, it notably tempers out [[4000/3993]], and in the 13-limit, [[10648/10647]]. | 420edo is good at the 2.5.7.11.13.19.23 [[subgroup]], and has a great potential as a near-just xenharmonic system. In the 2.7.11.19 subgroup, it supports the [[30th-octave temperaments#Oyster|oyster]] temperament. It also works satisfactorily with the 29-limit as a whole, though in[[consistent]]. In the 11-limit, it notably tempers out [[4000/3993]], and in the 13-limit, [[10648/10647]]. | ||
=== Odd harmonics === | === Odd harmonics === | ||
| Line 18: | Line 18: | ||
== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
|- | |||
! rowspan="2" | [[Subgroup]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" | [[Comma list|Comma List]] | ! rowspan="2" | [[Comma list|Comma List]] | ||
| Line 30: | Line 31: | ||
| 2401/2400, 4000/3993, 5120/5103, 15625/15552 | | 2401/2400, 4000/3993, 5120/5103, 15625/15552 | ||
| {{mapping| 420 666 975 1179 1453 }} | | {{mapping| 420 666 975 1179 1453 }} | ||
| | | −0.051 | ||
| 0.278 | | 0.278 | ||
| 9.74 | | 9.74 | ||
|- | |- style="border-top: double;" | ||
| 2.5.7.11.13.19.23 | |||
| 875/874, 5635/5632, 10241/10240, 12103/12100, 11875/11858, 10985/10976 | |||
| {{mapping| 420 975 1179 1453 1554 1784 1900 }} | |||
| | | +0.069 | ||
| 0.104 | |||
| 3.62 | |||
|} | |} | ||