2460edo: Difference between revisions

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 edo is [[consistency|distinctly consistent]] through to the [[27-odd-limit]], which is not very remarkable in itself ([[388edo]] is the first such system), but what is remarkable is the degree of accuracy to which it represents the 27-odd-limit intervals (see [[#Approximation to JI]]). It is also a [[zeta peak edo]], and it has been used in [[Sagittal notation]] to define the ''olympian level'' of JI notation.
-As a micro- (or nano-) temperament, it is a [[landscape]] system in the [[7-limit]], [[tempering out]] [[250047/250000]], and in the [[11-limit]] it tempers out [[9801/9800]]. Beyond that, it tempers out [[10648/10647]] in the [[13-limit]], [[12376/12375]] in the [[17-limit]], 5929/5928 and 6860/6859 in the [[19-limit]]; and 8281/8280 in the [[23-limit]].
+In higher limits, it is ''almost'' consistent in the [[29-odd-limit]] missing [[29/22]], [[29/17]], [[34/29]], [[44/29]]. It is also fully consistent in the no-29 [[39-odd-limit]].
+As a micro- (or nano-) temperament, it tempers [[Kirnberger's atom]] in the [[5-limit]], [[250047/250000]] (landscape comma) in the [[7-limit]], [[9801/9800]] [kalisma] in the [[11-limit]], [[10648/10647]] [harmonisma] in the [[13-limit]], [[12376/12375]] in the [[17-limit]], 5929/5928 and 6860/6859 in the [[19-limit]]; and 8281/8280 in the [[23-limit]].
 === Prime harmonics ===
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 == Notation ==
-edo is special in the [[Sagittal notation]], as it has been the model for the Olympian set, which offers "extreme" precision. The diacritics are independent of the sagittals.
+edo is special in the [[Sagittal notation]], as it has been the model for the Olympian set, which offers "extreme" precision. The diacritics are independent of the sagittals. Scroll the table to see accidentals for use in Revo flavor 145\2460 onwards).
-{| class="wikitable"
+<div style="overflow-x:auto;">
-|+Sagittal notation - Evo compatible sagittals
+{| class="wikitable" style="text-align:center"
-!Steps
+|-
-!0
+!'''Steps'''
-!7
+! 0 !! 7 !! 8
-!8
 !18
 !20
@@ Line 50: / Line 51: @@
 !112
 !116
+|'''121'''
+|'''124'''
+|'''131'''
+|'''133'''
+|'''138'''
+|'''145'''
+|'''150'''
+|'''153'''
+!'''155'''
+|'''160'''
+|'''165'''
+|'''168'''
+|'''170'''
+|'''177'''
+|'''184'''
+|'''189'''
+|'''192'''
+|'''197'''
+|'''199'''
+|'''203'''
+|'''208'''
+|'''213'''
+|'''215'''
+|'''225'''
+|'''226'''
+|'''233'''
 |-
-|Sym.
+|Symbol
 |<big>{{sagittal|h}}</big>
 |<big>{{sagittal|)|}}</big>
@@ Line 79: / Line 106: @@
 |<big>{{sagittal|(/|}}</big>
 |<big>{{sagittal|)/|\}}</big>
-|}
+|<big>{{sagittal||\)}}</big>
-{| class="wikitable mw-collapsible mw-collapsed"
+|<big>{{sagittal|(|)}}</big>
-|+Sagittal notation - Apotome complements
+|<big>{{sagittal||\\}}</big>
-!'''Steps'''
+|<big>{{sagittal|(|\}}</big>
-|'''170'''
+|<big>{{sagittal|)|\\}}</big>
-|'''168'''
+|<big>{{sagittal|)||(}}</big>
-|'''165'''
+|<big>{{sagittal|)~||}}</big>
-|'''160'''
+|<big>{{sagittal|~||(}}</big>
-!'''155'''
+|<big>{{sagittal|||~}}</big>
-|'''153'''
+|<big>{{sagittal|~~||}}</big>
-|'''150'''
+|<big>{{sagittal|)||~}}</big>
-|'''145'''
+|<big>{{sagittal|/||}}</big>
-|'''138'''
-|'''133'''
-|'''131'''
-|'''124'''
-|'''121'''
-|-
-|Symbol
 |<big>{{sagittal|)/||}}</big>
-|<big>{{sagittal|/||}}</big>
+|<big>{{sagittal|||)}}</big>
+|<big>{{sagittal|)||)}}</big>
+|<big>{{sagittal|||\}}</big>
+|<big>{{sagittal|(||}}</big>
+|<big>{{sagittal|~||)}}</big>
+|<big>{{sagittal|/||~}}</big>
+|<big>{{sagittal|(||(}}</big>
+|<big>{{sagittal|~||\}}</big>
+|<big>{{sagittal|//||}}</big>
+|<big>{{sagittal|)//||}}</big>
+|<big>{{sagittal|/||)}}</big>
 |<big>{{sagittal|(||~}}</big>
-|<big>{{sagittal|~~||}}</big>
-|<big>{{sagittal|||~}}</big>
-|<big>{{sagittal|~||(}}</big>
-|<big>{{sagittal|)~||}}</big>
-|<big>{{sagittal|)||(}}</big>
-|<big>{{sagittal|)|\\}}</big>
-|<big>{{sagittal|(|\}}</big>
-|<big>{{sagittal||\\}}</big>
-|<big>{{sagittal|(|)}}</big>
-|<big>{{sagittal||\)}}</big>
-|-
-!'''Steps'''
-|'''233'''
-|'''226'''
-|'''225'''
-|'''215'''
-|'''213'''
-|'''208'''
-|'''203'''
-|'''199'''
-|'''197'''
-|'''192'''
-|'''189'''
-|'''184'''
-|'''177'''
-|-
-|Symbol
 |<big>{{sagittal|/||\}}</big>
-|<big>{{sagittal|(||~}}</big>
-|<big>{{sagittal|/||)}}</big>
-|<big>{{sagittal|)//||}}</big>
-|<big>{{sagittal|//||}}</big>
-|<big>{{sagittal|~||\}}</big>
-|<big>{{sagittal|(||(}}</big>
-|<big>{{sagittal|/||~}}</big>
-|<big>{{sagittal|~||)}}</big>
-|<big>{{sagittal|(||}}</big>
-|<big>{{sagittal|||\}}</big>
-|<big>{{sagittal|)||)}}</big>
-|<big>{{sagittal|||)}}</big>
 |}
-{| class="wikitable mw-collapsible mw-collapsed"
+</div>
-|+Sagittal notation - Diacritics
+{| class="wikitable data-darkreader-inline-color="
+|+Olympian diacritics
 !'''Steps'''
 |1
@@ Line 285: / Line 277: @@
 | [[Minutes]]
 |}
-<nowiki/>* [[Normal forms|Octave-reduced form]], reduced to the first half-octave, and [[normal forms|minimal form]] in parentheses if distinct
+<nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct
 [[Category:Mina]]