57edo: Difference between revisions

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=== Odd harmonics ===

{{Harmonics in equal|57|intervals=odd|columns=11|prec=2|start=12|collapsed=true|title=Approximation of odd harmonics in 57edo (continued)}}

=== Subsets and supersets ===

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| 25

| 526.32

|[[19/14]], [[23/17]]

|[[19/14]], [[42/31]], [[23/17]]

| {{UDnote|step=25}}

| {{UDnote|fifth=34|step=25}}

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| 35

| 736.84

|[[26/17]], [[32/21]] [[29/19]]

|[[26/17]], [[32/21]], [[29/19]]

| {{UDnote|step=35}}

| {{UDnote|fifth=34|step=35}}

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| {{UDnote|fifth=34|step=57}}

|}

<nowiki>*</nowiki> As a 2.5/3.7.11.13.17.19.23.29.31/3-subgroup temperament, in ''italics'' if inconsistent

<nowiki>*</nowiki> As a 2.3.5.7.11.13.17.19.23.29.31-subgroup temperament, in ''italics'' if inconsistent

== Notation ==

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

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

57edo can be notated using [[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, 57edo 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 ===

This notation uses the same sagittal sequence as ~~EDOs~~ [[50edo#Sagittal notation|50]], [[64edo#Sagittal notation|64]], and [[71edo#Sagittal notation|71b]], and is a superset of the notation for [[19edo#Sagittal notation|~~19-EDO~~]].

This notation uses the same sagittal sequence as edos [[50edo #Sagittal notation|50]], [[64edo #Sagittal notation|64]], and [[71edo #Sagittal notation|71b]], and is a superset of the notation for [[19edo #Sagittal notation|19edo]].

==== 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.

== Scales ==

@@ Line 9: / Line 9: @@
 === Odd harmonics ===
 {{Harmonics in equal|57}}
+{{Harmonics in equal|57|intervals=odd|columns=11|prec=2|start=12|collapsed=true|title=Approximation of odd harmonics in 57edo (continued)}}
 === Subsets and supersets ===
@@ Line 174: / Line 175: @@
 | 25
 | 526.32
-|[[19/14]], [[23/17]]
+|[[19/14]], [[42/31]], [[23/17]]
 | {{UDnote|step=25}}
 | {{UDnote|fifth=34|step=25}}
@@ Line 234: / Line 235: @@
 | 35
 | 736.84
-|[[26/17]], [[32/21]] [[29/19]]
+|[[26/17]], [[32/21]], [[29/19]]
 | {{UDnote|step=35}}
 | {{UDnote|fifth=34|step=35}}
@@ Line 370: / Line 371: @@
 | {{UDnote|fifth=34|step=57}}
 |}
-<nowiki>*</nowiki> As a 2.5/3.7.11.13.17.19.23.29.31/3-subgroup temperament, in ''italics'' if inconsistent
+<nowiki>*</nowiki> As a 2.3.5.7.11.13.17.19.23.29.31-subgroup temperament, in ''italics'' if inconsistent
 == Notation ==
-=== Ups and downs notation ===
+=== Stein–Zimmermann–Gould notation ===
+edo can be notated using [[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.
 {{Ups and downs sharpness}}
-Using [[Helmholtz–Ellis]] accidentals, 57edo 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 ===
-This notation uses the same sagittal sequence as EDOs [[50edo#Sagittal notation|50]], [[64edo#Sagittal notation|64]], and [[71edo#Sagittal notation|71b]], and is a superset of the notation for [[19edo#Sagittal notation|19-EDO]].
+This notation uses the same sagittal sequence as edos [[50edo #Sagittal notation|50]], [[64edo #Sagittal notation|64]], and [[71edo #Sagittal notation|71b]], and is a superset of the notation for [[19edo #Sagittal notation|19edo]].
 ==== Evo flavor ====
@@ Line 404: / Line 407: @@
 </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.
 == Scales ==