82edo: Difference between revisions
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→Instruments: Insert music section after this, starting with Bryan Deister's ''microtonal improvisation in 82edo'' (2025) |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
82edo's [[patent val]] is [[contorted]] in the [[11-limit]], | 82edo's [[patent val]] is [[contorted]] in the [[11-limit]], since {{nowrap|82 {{=}} 2 × 41}}. In the [[13-limit]] the patent val tempers out [[169/168]] and [[676/675]], and in the [[17-limit]] tempers out [[273/272]]. It provides the optimal patent val for [[soothsaying]] temperament and [[support]]s [[baladic]] temperament. The 82d val tempers out [[50/49]] and is an excellent tuning for [[astrology]] and [[byhearted]], surpassing their optimal patent vals. The alternative 82e val tempers out [[121/120]] instead. | ||
=== Prime harmonics === | === Prime harmonics === | ||
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== Approximation to JI == | == Approximation to JI == | ||
=== Zeta peak index === | === Zeta peak index === | ||
{ | {{ZPI | ||
| zpi = 448 | |||
| steps = 81.9541455954050 | |||
| step size = 14.6423343356444 | |||
| tempered height = 6.653983 | |||
| pure height = 5.154524 | |||
| integral = 0.941321 | |||
| gap = 14.718732 | |||
| octave = 1200.67141552284 | |||
| consistent = 8 | |||
| distinct = 8 | |||
}} | |||
== Instruments == | |||
* [[Lumatone mapping for 82edo]] | |||
== Music == | |||
; [[Bryan Deister]] | |||
* [https://www.youtube.com/shorts/p9xUY8EU7Zg ''microtonal improvisation in 82edo''] (2025) | |||
| 14.6423343356444 | |||
| 6.653983 | |||
| 0.941321 | |||
| 14.718732 | |||
| | |||
| 8 | |||
| 8 | |||