2460edo: Difference between revisions

← Older edit Newer edit →

VisualWikitext

@@ Line 17: / Line 17: @@
 edo is also notable for being the smallest edo that is a multiple of 12 to be [[purely consistent]] in the 15-odd-limit (i.e. it is the smallest edo that is a multiple of 12 which maintains [[relative interval error|relative error]]s of less than 25% on all of the first 16 harmonics of the harmonic series). [[72edo]] comes close, but its approximations to [[13/8]] and [[15/8]] are somewhat inaccurate.
+== 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.
+{| class="wikitable"
+|+Sagittal notation - Evo compatible sagittals
+!Steps
+!0
+!7
+!8
+!18
+!20
+!25
+!30
+!34
+!36
+!41
+!44
+!51
+!56
+!63
+!65
+!68
+!73
+!78
+!80
+!83
+!88
+!95
+!100
+!102
+!109
+!112
+!116
+|-
+|Sym.
+|<big>{{sagittal|h}}</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>
+|<big>{{sagittal|/|\}}</big>
+|<big>{{sagittal|(/|}}</big>
+|<big>{{sagittal|)/|\}}</big>
+|}
+{| class="wikitable mw-collapsible mw-collapsed"
+|+Sagittal notation - Apotome complements
+!'''Steps'''
+|'''170'''
+|'''168'''
+|'''165'''
+|'''160'''
+!'''155'''
+|'''153'''
+|'''150'''
+|'''145'''
+|'''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>
+|-
+!'''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"
+|+Sagittal notation - Diacritics
+!'''Steps'''
+|1
+|2
+|3
+|4
+!5
+|6
+|-
+|Symbol
+|<big>{{sagittal|`}}</big>
+|<big>{{sagittal|``}}</big>
+|<big>{{sagittal|'}}{{sagittal|,}}</big>
+|<big>{{sagittal|'}}</big>
+|<big>{{sagittal|'}}{{sagittal|`}}</big>
+|<big>{{sagittal|'}}{{sagittal|``}}</big>
+|}
 == Approximation to JI ==