85edo: Difference between revisions

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== Theory ==

Since 85 {{=}} 5 × 17, ~~and~~ 85edo shares the same 3.9-cent-sharp fifth as [[17edo|17]], [[34edo|34]], and [[68edo|68]]. ~~The~~ [[patent val]] [[tempering ~~out|tempers~~ out]] [[3125/3072]] in the [[5-limit]] and [[225/224]], [[245/243]], and [[875/864]] in the [[7-limit~~]], so that it [[support]]s [[magic~~]]. It tempers out [[100/99]] and [[385/384]] in the [[11-limit]], supporting 11-limit magic, and [[847/845]], [[1188/1183]], and [[1575/1573]] in the 13-limit. It provides the [[optimal patent val]] for the 13-limit 36ce & 49f temperament tempering out 100/99, 540/539, 847/845 and 1575/1573.

Since 85 {{=}} 5 × 17, 85edo shares the same 3.9-cent-sharp fifth as [[17edo|17]], [[34edo|34]], and [[68edo|68]]. 3/1 is therefore divisible into 5, and the [[patent val]] correspondingly supports [[magic]], [[tempering out]] [[3125/3072]] in the [[5-limit]] and [[225/224]], [[245/243]], and [[875/864]] in the [[7-limit]]. It tempers out [[100/99]] and [[385/384]] in the [[11-limit]], supporting 11-limit magic, and [[847/845]], [[1188/1183]], and [[1575/1573]] in the 13-limit. It provides the [[optimal patent val]] for the 13-limit 36ce & 49f temperament tempering out 100/99, 540/539, 847/845 and 1575/1573. The 85c val, with a very sharp 5/4 of 395.3{{c}}, supports 7-limit [[myna]].

=== Odd harmonics ===

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=== Subsets and supersets ===

85edo contains [[5edo]] and [[17edo]] as subsets. [[255edo]], which triples it, is a notable tuning.

== Interval table ==

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[[Category:Magic]]

== Instruments ==

A [[Lumatone mapping for 85edo]] is available.

== Music ==

; [[Bryan Deister]]

* [https://www.youtube.com/shorts/DbVsxzfKr7I ''microtonal improvisation in 85edo''] (2025)

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 == Theory ==
-Since 85 {{=}} 5 × 17, and 85edo shares the same 3.9-cent-sharp fifth as [[17edo|17]], [[34edo|34]], and [[68edo|68]]. The [[patent val]] [[tempering out|tempers out]] [[3125/3072]] in the [[5-limit]] and [[225/224]], [[245/243]], and [[875/864]] in the [[7-limit]], so that it [[support]]s [[magic]]. It tempers out [[100/99]] and [[385/384]] in the [[11-limit]], supporting 11-limit magic, and [[847/845]], [[1188/1183]], and [[1575/1573]] in the 13-limit. It provides the [[optimal patent val]] for the 13-limit 36ce & 49f temperament tempering out 100/99, 540/539, 847/845 and 1575/1573.
+Since 85 {{=}} 5 × 17, 85edo shares the same 3.9-cent-sharp fifth as [[17edo|17]], [[34edo|34]], and [[68edo|68]]. 3/1 is therefore divisible into 5, and the [[patent val]] correspondingly supports [[magic]], [[tempering out]] [[3125/3072]] in the [[5-limit]] and [[225/224]], [[245/243]], and [[875/864]] in the [[7-limit]]. It tempers out [[100/99]] and [[385/384]] in the [[11-limit]], supporting 11-limit magic, and [[847/845]], [[1188/1183]], and [[1575/1573]] in the 13-limit. It provides the [[optimal patent val]] for the 13-limit 36ce & 49f temperament tempering out 100/99, 540/539, 847/845 and 1575/1573. The 85c val, with a very sharp 5/4 of 395.3{{c}}, supports 7-limit [[myna]].
 === Odd harmonics ===
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 === Subsets and supersets ===
 edo contains [[5edo]] and [[17edo]] as subsets. [[255edo]], which triples it, is a notable tuning.
 == Interval table ==
@@ Line 18: / Line 18: @@
 [[Category:Magic]]
+== Instruments ==
+A [[Lumatone mapping for 85edo]] is available.
+== Music ==
+; [[Bryan Deister]]
+* [https://www.youtube.com/shorts/DbVsxzfKr7I ''microtonal improvisation in 85edo''] (2025)