82edo: Difference between revisions

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== 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 ===

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== Intervals ==

{| class="wikitable right-1 right-2 left-3 left-4 left-5"

|+

|-

! #

! rowspan="2" | #

! Cents

! rowspan="2" | Cents

! Approximate ~~Ratios~~*

! rowspan="2" | Approximate ratios*

! Additional ~~Ratios<br>with 11's (~~82e ~~Val)~~

! colspan="2" | Additional ratios

! ~~Additional Ratios<br>with 11's (Patent Val)~~

|-

! Using the 82e val

! Using the patent val

|-

| 0

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|

|}

<nowiki>*~~</nowiki> as~~ a no-11 19-limit temperament

<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:

== Instruments ==

* [[Lumatone mapping for 82edo]]

== Music ==

; [[Bryan Deister]]

* [https://www.youtube.com/shorts/p9xUY8EU7Zg ''microtonal improvisation in 82edo''] (2025)

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|82}}
+{{ED intro}}
 == Theory ==
-edo'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.
+edo'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 ===
@@ Line 15: / Line 15: @@
 == Intervals ==
 {| class="wikitable right-1 right-2 left-3 left-4 left-5"
-|+
+|-
-! #
+! rowspan="2" | &#35;
-! Cents
+! rowspan="2" | Cents
-! Approximate Ratios*
+! rowspan="2" | Approximate ratios*
-! Additional Ratios<br>with 11's (82e Val)
+! colspan="2" | Additional ratios
-! Additional Ratios<br>with 11's (Patent Val)
+|-
+! Using the 82e val
+! Using the patent val
 |-
 | 0
@@ Line 280: / Line 282: @@
 |
 |}
-<nowiki>*</nowiki> as a no-11 19-limit temperament
+<nowiki />* As a no-11 19-limit temperament
+== Notation ==
+=== Ups and downs notation ===
+edo 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)