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}}
{{EDO intro|82}}
{{ED intro}}


== Theory ==
== Theory ==
82edo's [[patent val]] is [[contorted]] in the [[11-limit]], from 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]] & [[byhearted]], surpassing their optimal patent vals. The alternative 82e val tempers out [[121/120]] instead.  
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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{{Sharpness-sharp8}}
{{Sharpness-sharp8}}


== Zeta properties ==
== Approximation to JI ==
=== Zeta peak index ===
=== Zeta peak index ===
{| class="wikitable"
{{ZPI
|-
| zpi = 448
! colspan="3" | Tuning
| steps = 81.9541455954050
! colspan="3" | Strength
| step size = 14.6423343356444
! colspan="2" | Closest EDO
| tempered height = 6.653983
! colspan="2" | Integer limit
| pure height = 5.154524
|-
| integral = 0.941321
! ZPI
| gap = 14.718732
! Steps per octave
| octave = 1200.67141552284
! Step size (cents)
| consistent = 8
! Height
| distinct = 8
! Integral
}}
! Gap
 
! EDO
== Instruments ==
! Octave (cents)
* [[Lumatone mapping for 82edo]]
! Consistent
 
! Distinct
== Music ==
|-
; [[Bryan Deister]]
| [[448zpi]]
* [https://www.youtube.com/shorts/p9xUY8EU7Zg ''microtonal improvisation in 82edo''] (2025)
| 81.9541455954050
| 14.6423343356444
| 6.653983
| 0.941321
| 14.718732
| 82edo
| 1200.67141552284
| 8
| 8
|}