85edo: Difference between revisions

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~~The 85 equal temperament divides the octave in 85 equal parts of 14.458 cents each.~~ 85 = 5 * 17, ~~and it~~ shares the same 3.9 cent sharp fifth as 17, 34, and 68. ~~The~~ patent val ~~tempers~~ out 3125/3072 in the 5-limit and ~~875~~/~~864~~, 245/243 and ~~225~~/~~224~~ in the 7-limit~~, so that it supports magic~~. It tempers out 100/99 and ~~245~~/~~243~~ in the 11-limit, supporting 11-limit magic, and 1188/1183, ~~847/845~~ and 1575/1573 in the 13-limit. It provides the optimal patent val for the 13-limit temperament tempering out 100/99, 540/539, 847/845 and 1575/1573.

== Theory ==

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 ===

=== Subsets and supersets ===

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

== Interval table ==

== Scales ==

* Amulet{{idiosyncratic}}, (approximated from [[25edo]], subset of [[magic]]): 7 3 7 7 3 7 10 7 7 3 7 10 7

[[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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-The 85 equal temperament divides the octave in 85 equal parts of 14.458 cents each. 85 = 5 * 17, and it shares the same 3.9 cent sharp fifth as 17, 34, and 68. The patent val tempers out 3125/3072 in the 5-limit and 875/864, 245/243 and 225/224 in the 7-limit, so that it supports magic. It tempers out 100/99 and 245/243 in the 11-limit, supporting 11-limit magic, and 1188/1183, 847/845 and 1575/1573 in the 13-limit. It provides the optimal patent val for the 13-limit temperament tempering out 100/99, 540/539, 847/845 and 1575/1573.
+{{Infobox ET}}
+{{ED intro}}
+== Theory ==
+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 ===
+{{Harmonics in equal|85}}
+=== Subsets and supersets ===
+edo contains [[5edo]] and [[17edo]] as subsets. [[255edo]], which triples it, is a notable tuning.
+== Interval table ==
+{{Interval table}}
+== Scales ==
+* Amulet{{idiosyncratic}}, (approximated from [[25edo]], subset of [[magic]]): 7 3 7 7 3 7 10 7 7 3 7 10 7
+[[Category:Magic]]
+== Instruments ==
+A [[Lumatone mapping for 85edo]] is available.
+== Music ==
+; [[Bryan Deister]]
+* [https://www.youtube.com/shorts/DbVsxzfKr7I ''microtonal improvisation in 85edo''] (2025)