64edo: Difference between revisions

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64be val is a tuning for the [[beatles]] temperament and for the [[rank-3]] temperaments [[heimlaug]] and [[vili]] in the 17-limit. 64bccc tunes [[dichotic]], although that is an [[exotemperament]]. 64cdf is a tuning for [[vibhu]].

The patent val of 64edo is the first patent val to represent the intervals 5/4, 81/64, 14/11, 9/7, 13/10, 21/16, and 4/3 distinctly, although in 64edo they are not in the correct order.

The patent val of 64edo is the first patent val to represent the intervals 5/4, 81/64, 14/11, 9/7, 13/10, 21/16, and 4/3 distinctly, although in 64edo they are not in the correct order. [[72edo]] represents all of these intervals distinctly and in the correct order.

=== Odd harmonics ===

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== 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 =====

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</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 =====

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; [[Bryan Deister]]

* [https://www.youtube.com/shorts/ag1FbgAuR6I ''microtonal improvisation in 64edo''] (2025)

* [https://www.youtube.com/shorts/cwEY-eXjMFw ''Servant of Evil - Mothy (microtonal cover in 64edo)''] (2026)

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 be val is a tuning for the [[beatles]] temperament and for the [[rank-3]] temperaments [[heimlaug]] and [[vili]] in the 17-limit. 64bccc tunes [[dichotic]], although that is an [[exotemperament]]. 64cdf is a tuning for [[vibhu]].
-The patent val of 64edo is the first patent val to represent the intervals 5/4, 81/64, 14/11, 9/7, 13/10, 21/16, and 4/3 distinctly, although in 64edo they are not in the correct order.
+The patent val of 64edo is the first patent val to represent the intervals 5/4, 81/64, 14/11, 9/7, 13/10, 21/16, and 4/3 distinctly, although in 64edo they are not in the correct order. [[72edo]] represents all of these intervals distinctly and in the correct order.
 === Odd harmonics ===
@@ 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 =====
@@ Line 112: / Line 114: @@
 ; [[Bryan Deister]]
 * [https://www.youtube.com/shorts/ag1FbgAuR6I ''microtonal improvisation in 64edo''] (2025)
+* [https://www.youtube.com/shorts/cwEY-eXjMFw ''Servant of Evil - Mothy (microtonal cover in 64edo)''] (2026)