64edo: Difference between revisions

(One intermediate revision by one other user not shown)

Line 15:

=== Subsets and supersets ===

64edo is the 6th power of ~~[[2edo]]~~, and it has subset edos {{EDOs| 2, 4, 8, 16, 32 }}. [[128edo]], which doubles it, corrects its approximation to many of the lower harmonics.

64edo is the 6th power of two edo, and it has subset edos {{EDOs| 2, 4, 8, 16, 32 }}. [[128edo]], which doubles it, corrects its approximation to many of the lower harmonics.

== Intervals ==

Line 21:

== Notation ==

=== ~~Ups~~ and downs notation ===

=== Stein–Zimmermann–Gould notation ===

64edo can be notated with [[Stein–Zimmermann–Gould notation]]:

Here, a sharp raises by three steps, and a flat lowers by three steps, so arrows can be used to fill in the gap. If the arrows are taken to have their own layer of enharmonic spellings, some notes may be best spelled with double arrows.

=== Kite's ups and downs notation ===

Spoken as up, downsharp, sharp, upsharp, etc. Note that downsharp can be respelled as dup (double-up), and upflat as dud.

~~Using [[Helmholtz–Ellis]] accidentals, 64edo can also be notated using [[Alternative symbols for ups and downs notation#Sharp-3|alternative ups and downs]]:~~

~~{{Sharpness-sharp3}}~~

Here, a sharp raises by three steps, and a flat lowers by three steps, so arrows can be used to fill in the gap. If the arrows are taken to have their own layer of enharmonic spellings, some notes may be best spelled with double arrows.

=== Sagittal notation ===

==== Best fifth notation ====

This notation uses the same sagittal sequence as ~~EDOs~~ [[50edo#Sagittal notation|50]], [[57edo#Sagittal notation|57]], and [[71edo#Second-best fifth notation|71b]].

This notation uses the same sagittal sequence as edos [[50edo #Sagittal notation|50]], [[57edo #Sagittal notation|57]], and [[71edo #Second-best fifth notation|71b]].

===== Evo flavor =====

Line 53:

Line 55:

</imagemap>

In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this ~~EDO~~.

In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation #Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this edo.

==== Second-best fifth notation ====

This notation is a superset of the notation for [[32edo#Sagittal notation|~~32-EDO~~]].

This notation is a superset of the notation for [[32edo #Sagittal notation|32edo]].

===== Evo flavor =====

@@ Line 15: / Line 15: @@
 === Subsets and supersets ===
-edo is the 6th power of [[2edo]], and it has subset edos {{EDOs| 2, 4, 8, 16, 32 }}. [[128edo]], which doubles it, corrects its approximation to many of the lower harmonics.
+edo is the 6th power of two edo, and it has subset edos {{EDOs| 2, 4, 8, 16, 32 }}. [[128edo]], which doubles it, corrects its approximation to many of the lower harmonics.
 == Intervals ==
@@ Line 21: / Line 21: @@
 == Notation ==
-=== Ups and downs notation ===
+=== Stein–Zimmermann–Gould notation ===
+edo can be notated with [[Stein–Zimmermann–Gould notation]]:
+{{Sharpness-sharp3-szg}}
+Here, a sharp raises by three steps, and a flat lowers by three steps, so arrows can be used to fill in the gap. If the arrows are taken to have their own layer of enharmonic spellings, some notes may be best spelled with double arrows.
+=== Kite's ups and downs notation ===
 Spoken as up, downsharp, sharp, upsharp, etc. Note that downsharp can be respelled as dup (double-up), and upflat as dud.
 {{sharpness-sharp3a}}
-Using [[Helmholtz–Ellis]] accidentals, 64edo can also be notated using [[Alternative symbols for ups and downs notation#Sharp-3|alternative ups and downs]]:
-{{Sharpness-sharp3}}
-Here, a sharp raises by three steps, and a flat lowers by three steps, so arrows can be used to fill in the gap. If the arrows are taken to have their own layer of enharmonic spellings, some notes may be best spelled with double arrows.
 === Sagittal notation ===
 ==== Best fifth notation ====
-This notation uses the same sagittal sequence as EDOs [[50edo#Sagittal notation|50]], [[57edo#Sagittal notation|57]], and [[71edo#Second-best fifth notation|71b]].
+This notation uses the same sagittal sequence as edos [[50edo #Sagittal notation|50]], [[57edo #Sagittal notation|57]], and [[71edo #Second-best fifth notation|71b]].
 ===== Evo flavor =====
@@ Line 53: / Line 55: @@
 </imagemap>
-In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO.
+In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation #Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this edo.
 ==== Second-best fifth notation ====
-This notation is a superset of the notation for [[32edo#Sagittal notation|32-EDO]].
+This notation is a superset of the notation for [[32edo #Sagittal notation|32edo]].
 ===== Evo flavor =====