82edo: Difference between revisions
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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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== Intervals == | == Intervals == | ||
{| class="wikitable right-1 right-2 left-3 left-4 left-5" | {| class="wikitable right-1 right-2 left-3 left-4 left-5" | ||
| | |- | ||
! # | ! rowspan="2" | # | ||
! Cents | ! rowspan="2" | Cents | ||
! Approximate | ! rowspan="2" | Approximate ratios* | ||
! Additional | ! colspan="2" | Additional ratios | ||
! | |- | ||
! Using the 82e val | |||
! Using the patent val | |||
|- | |- | ||
| 0 | | 0 | ||
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| | | | ||
|} | |} | ||
<nowiki>* | <nowiki />* As a no-11 19-limit temperament | ||
== | |||
=== | == Notation == | ||
{ | === Ups and downs notation === | ||
60edo can be notated using [[ups and downs notation]] using [[Helmholtz–Ellis]] accidentals: | |||
{{Sharpness-sharp8}} | |||
== Instruments == | |||
* [[Lumatone mapping for 82edo]] | |||
== Music == | |||
; [[Bryan Deister]] | |||
* [https://www.youtube.com/shorts/p9xUY8EU7Zg ''microtonal improvisation in 82edo''] (2025) | |||