94edo: Difference between revisions

Line 909:

=== Sagittal ===

94edo can be notated in [[Sagittal notation|Sagittal]] using the [[Sagittal_notation#Athenian_extension_single-shaft|Athenian extension]], with the apotome equal to 9 edosteps and the limma to 7 edosteps.

Thus, the JI chord 16:17:18:19:20:21:22:23:24:25:26:27:28:30 from D would be written D{{sagittal||//|}}:E{{sagittal|(!!(}}:E{{sagittal||//|}}:F{{sagittal||//|}}:F{{sagittal|||\}}:G{{sagittal|\!}}:G{{sagittal|/|\}}:G{{sagittal|~|||(}}:A{{sagittal||//|}}:A{{sagittal|(|)}}:B{{sagittal|(!)}}:B{{sagittal||//|}}:C{{sagittal|\!}}:C{{sagittal|||\}}. Music that doesn't modulate much in the 2.3.5.7.11.13.19 subgroup can be notated by only using {{sagittal|/|}} {{sagittal|/|\}} / {{sagittal|\!}} {{sagittal|\!/}} and their apotome complements; where naturals are used for 3 and 19, {{sagittal|/|}} / {{sagittal|\!}} for 5 and 7, and {{sagittal|/|\}} / {{sagittal|\!/}} for 11 and 13.

{| class="wikitable" style="text-align: center;"

!Degree

~~| '''−9'''~~

~~| −8~~

~~| −7~~

~~| −6~~

~~| −5~~

~~| −4~~

~~| −3~~

~~| −2~~

~~| −1~~

|'''0'''

| +1

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Line 923:

|-

!Evo

~~|{{sagittal|b}}~~

| rowspan="2" |<big>{{sagittal||//|}}</big>

~~|{{sagittal|b}}{{sagittal|~|(}}~~

| rowspan="2" |<big>{{sagittal|~|(}}</big>

~~|{{sagittal|b}}{{sagittal|/|}}~~

| rowspan="2" |<big>{{sagittal|/|}}</big>

~~|{{sagittal|b}}{{sagittal|(|(}}~~

| rowspan="2" |<big>{{sagittal|(|(}}</big>

~~|{{sagittal|b}}{{sagittal|/|\}}~~

| rowspan="2" |<big>{{sagittal|/|\}}</big>

~~| rowspan="2" |{{sagittal|\!/}}~~

|{{sagittal|#}}{{sagittal|\!/}}

~~| rowspan="2" |{{sagittal|(!(}}~~

|{{sagittal|#}}{{sagittal|(!(}}

~~| rowspan="2" |{{sagittal|\!}}~~

|{{sagittal|#}}{{sagittal|\!}}

~~| rowspan="2" |{{sagittal|~!(}}~~

|{{sagittal|#}}{{sagittal|~!(}}

| rowspan="2" |{{sagittal||//|}}

|{{sagittal|#}}

| rowspan="2" |{{sagittal|~|(}}

| rowspan="2" |{{sagittal|/|}}

| rowspan="2" |{{sagittal|(|(}}

| rowspan="2" |{{sagittal|/|\}}

|{{sagittal|#}}{{sagittal|\!/}}

|{{sagittal|#}}{{sagittal|(!(}}

|{{sagittal|#}}{{sagittal|\!}}

|{{sagittal|#}}{{sagittal|~!(}}

|{{sagittal|#}}

|-

!Revo

|~~{{sagittal|\!!/}}~~

|<big>{{sagittal|(|)}}</big>

~~|{{sagittal|(!!(}}~~

|<big>{{sagittal|~||(}}</big>

~~|{{sagittal|!!/}}~~

|<big>{{sagittal|||\}}</big>

~~|{{sagittal|~!!(}}~~

|<big>{{sagittal|(||(}}</big>

~~|{{sagittal|(!)}}~~

|<big>{{sagittal|/||\}}</big>

|{{sagittal|(|)}}

|{{sagittal|~||(}}

|{{sagittal|||\}}

|{{sagittal|(||(}}

|{{sagittal|/||\}}

|}

The following enharmonics from the Athenian set are present (comma tempered out):

* {{sagittal|//|}} = {{Sagittal|/|)}} = {{Sagittal|/|\}} ([[325/324]], [[352/351]])

* {{sagittal|/|}} = {{sagittal||)}} = {{sagittal||\}} ([[225/224]], [[2200/2187]])

* {{sagittal|)|(}} = {{sagittal|~|(}} ([[3680721/3670016]])

* {{sagittal|(|}} = {{sagittal|(|(}} ([[5120/5103]])

* {{sagittal||(}} = {{sagittal||//|}} ([[5120/5103]])

See [[Sagittal notation#Revo|apotome complements]] for equivalent accidental pairs.

The JI chord 16:17:18:19:20:21:22:23:24:25:26:27:28:30 from D would be written D{{sagittal||//|}}:E{{sagittal|(!!(}}:E{{sagittal||//|}}:F{{sagittal||//|}}:F{{sagittal|||\}}:G{{sagittal|\!}}:G{{sagittal|/|\}}:G{{sagittal|~|||(}}:A{{sagittal||//|}}:A{{sagittal|(|)}}:B{{sagittal|(!)}}:B{{sagittal||//|}}:C{{sagittal|\!}}:C{{sagittal|||\}}. Music that doesn't modulate much in the 2.3.5.7.11.13.19 subgroup can be notated by only using {{sagittal|/|}} {{sagittal|/|\}} / {{sagittal|\!}} {{sagittal|\!/}} and their apotome complements; where naturals are used for 3 and 19, {{sagittal|/|}} / {{sagittal|\!}} for 5 and 7, and {{sagittal|/|\}} / {{sagittal|\!/}} for 11 and 13.

== Regular temperament properties ==

@@ Line 909: / Line 909: @@
 === Sagittal ===
 edo can be notated in [[Sagittal notation|Sagittal]] using the [[Sagittal_notation#Athenian_extension_single-shaft|Athenian extension]], with the apotome equal to 9 edosteps and the limma to 7 edosteps.
-Thus, the JI chord 16:17:18:19:20:21:22:23:24:25:26:27:28:30 from D would be written D{{sagittal||//|}}:E{{sagittal|(!!(}}:E{{sagittal||//|}}:F{{sagittal||//|}}:F{{sagittal|||\}}:G{{sagittal|\!}}:G{{sagittal|/|\}}:G{{sagittal|~|||(}}:A{{sagittal||//|}}:A{{sagittal|(|)}}:B{{sagittal|(!)}}:B{{sagittal||//|}}:C{{sagittal|\!}}:C{{sagittal|||\}}. Music that doesn't modulate much in the 2.3.5.7.11.13.19 subgroup can be notated by only using {{sagittal|/|}} {{sagittal|/|\}} / {{sagittal|\!}} {{sagittal|\!/}} and their apotome complements; where naturals are used for 3 and 19, {{sagittal|/|}} / {{sagittal|\!}} for 5 and 7, and {{sagittal|/|\}} / {{sagittal|\!/}} for 11 and 13.
 {| class="wikitable" style="text-align: center;"
 !Degree
-| '''−9'''
-| −8
-| −7
-| −6
-| −5
-| −4
-| −3
-| −2
-| −1
 |'''0'''
 | +1
@@ Line 935: / Line 923: @@
 |-
 !Evo
-|{{sagittal|b}}
+| rowspan="2" |<big>{{sagittal||//|}}</big>
-|{{sagittal|b}}{{sagittal|~|(}}
+| rowspan="2" |<big>{{sagittal|~|(}}</big>
-|{{sagittal|b}}{{sagittal|/|}}
+| rowspan="2" |<big>{{sagittal|/|}}</big>
-|{{sagittal|b}}{{sagittal|(|(}}
+| rowspan="2" |<big>{{sagittal|(|(}}</big>
-|{{sagittal|b}}{{sagittal|/|\}}
+| rowspan="2" |<big>{{sagittal|/|\}}</big>
-| rowspan="2" |{{sagittal|\!/}}
+|<small>{{sagittal|#}}{{sagittal|\!/}}</small>
-| rowspan="2" |{{sagittal|(!(}}
+|<small>{{sagittal|#}}{{sagittal|(!(}}</small>
-| rowspan="2" |{{sagittal|\!}}
+|<small>{{sagittal|#}}{{sagittal|\!}}</small>
-| rowspan="2" |{{sagittal|~!(}}
+|<small>{{sagittal|#}}{{sagittal|~!(}}</small>
-| rowspan="2" |{{sagittal||//|}}
+|<small>{{sagittal|#}}</small>
-| rowspan="2" |{{sagittal|~|(}}
-| rowspan="2" |{{sagittal|/|}}
-| rowspan="2" |{{sagittal|(|(}}
-| rowspan="2" |{{sagittal|/|\}}
-|{{sagittal|#}}{{sagittal|\!/}}
-|{{sagittal|#}}{{sagittal|(!(}}
-|{{sagittal|#}}{{sagittal|\!}}
-|{{sagittal|#}}{{sagittal|~!(}}
-|{{sagittal|#}}
 |-
 !Revo
-|{{sagittal|\!!/}}
+|<big>{{sagittal|(|)}}</big>
-|{{sagittal|(!!(}}
+|<big>{{sagittal|~||(}}</big>
-|{{sagittal|!!/}}
+|<big>{{sagittal|||\}}</big>
-|{{sagittal|~!!(}}
+|<big>{{sagittal|(||(}}</big>
-|{{sagittal|(!)}}
+|<big>{{sagittal|/||\}}</big>
-|{{sagittal|(|)}}
-|{{sagittal|~||(}}
-|{{sagittal|||\}}
-|{{sagittal|(||(}}
-|{{sagittal|/||\}}
 |}
+The following enharmonics from the Athenian set are present (comma tempered out):
+* {{sagittal|//|}} = {{Sagittal|/|)}} = {{Sagittal|/|\}} ([[325/324]], [[352/351]])
+* {{sagittal|/|}} = {{sagittal||)}} = {{sagittal||\}} ([[225/224]], [[2200/2187]])
+* {{sagittal|)|(}} = {{sagittal|~|(}} ([[3680721/3670016]])
+* {{sagittal|(|}} = {{sagittal|(|(}} ([[5120/5103]])
+* {{sagittal||(}} = {{sagittal||//|}} ([[5120/5103]])
+See [[Sagittal notation#Revo|apotome complements]] for equivalent accidental pairs.
+The JI chord 16:17:18:19:20:21:22:23:24:25:26:27:28:30 from D would be written D{{sagittal||//|}}:E{{sagittal|(!!(}}:E{{sagittal||//|}}:F{{sagittal||//|}}:F{{sagittal|||\}}:G{{sagittal|\!}}:G{{sagittal|/|\}}:G{{sagittal|~|||(}}:A{{sagittal||//|}}:A{{sagittal|(|)}}:B{{sagittal|(!)}}:B{{sagittal||//|}}:C{{sagittal|\!}}:C{{sagittal|||\}}. Music that doesn't modulate much in the 2.3.5.7.11.13.19 subgroup can be notated by only using {{sagittal|/|}} {{sagittal|/|\}} / {{sagittal|\!}} {{sagittal|\!/}} and their apotome complements; where naturals are used for 3 and 19, {{sagittal|/|}} / {{sagittal|\!}} for 5 and 7, and {{sagittal|/|\}} / {{sagittal|\!/}} for 11 and 13.
 == Regular temperament properties ==