53edo: Difference between revisions

Line 633:

== Notation ==

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

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

53edo can be notated with [[ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).

[[Stein–Zimmermann–Gould notation]] uses sharps and flats with arrows:

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

53edo can also be notated with [[Kite's ups and downs notation|Kite's ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).

Another notation uses [[Alternative symbols for ups and downs notation#Sharp-5|alternative ups and downs]]. Here, this can be done using sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:

~~{{Sharpness-sharp5}}~~

=== Sagittal notation ===

53edo can be notated in [[Sagittal notation|Sagittal]] using the [[Sagittal notation#Spartan extension single-shaft|Spartan extension]], with the apotome equal to 5 edosteps and the limma to 4 edosteps. Here is a simplified table:

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

! colspan="2" |Steps

! colspan="2" | Steps

!'''0'''

! 1

Line 651:

Line 653:

!'''5'''

|-

! rowspan="2" |Symbol

! rowspan="2" | Symbol

!Evo

! Evo

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

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

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

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

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

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

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

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

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

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

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

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

|-

!Revo

! Revo

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

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

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

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

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

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

|}

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

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

* {{sagittal|/|}} = {{sagittal||)}} ([[225/224]])

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

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

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

Featured below is the 53edo gamut notated using the best accidental approximants; in this case, pai/pao and phai/phao.

Line 681:

Line 682:

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.

== Relationship to 12edo ==

@@ Line 633: / Line 633: @@
 == Notation ==
-=== Ups and downs notation ===
+=== Stein–Zimmermann–Gould notation ===
-edo can be notated with [[ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).
+[[Stein–Zimmermann–Gould notation]] uses sharps and flats with arrows:
+{{Sharpness-sharp5-szg}}
+=== Kite's ups and downs notation ===
+edo can also be notated with [[Kite's ups and downs notation|Kite's ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).
 {{Ups and downs sharpness}}
-Another notation uses [[Alternative symbols for ups and downs notation#Sharp-5|alternative ups and downs]]. Here, this can be done using sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:
-{{Sharpness-sharp5}}
 === Sagittal notation ===
 edo can be notated in [[Sagittal notation|Sagittal]] using the [[Sagittal notation#Spartan extension single-shaft|Spartan extension]], with the apotome equal to 5 edosteps and the limma to 4 edosteps. Here is a simplified table:
 {| class="wikitable" style="text-align: center;"
-! colspan="2" |Steps
+! colspan="2" | Steps
 !'''0'''
 ! 1
@@ Line 651: / Line 653: @@
 !'''5'''
 |-
-! rowspan="2" |Symbol
+! rowspan="2" | Symbol
-!Evo
+! Evo
-| rowspan="2" |<big>{{sagittal||//|}}</big>
+| rowspan="2" | <big>{{sagittal||//|}}</big>
-| rowspan="2" |<big>{{sagittal|/|}}</big>
+| rowspan="2" | <big>{{sagittal|/|}}</big>
-| rowspan="2" |<big>{{sagittal|//|}}</big>
+| rowspan="2" | <big>{{sagittal|//|}}</big>
-|<small>{{sagittal|#}}{{sagittal|\\!}}</small>
+| <small>{{sagittal|#}}{{sagittal|\\!}}</small>
-|<small>{{sagittal|#}}{{sagittal|\!}}</small>
+| <small>{{sagittal|#}}{{sagittal|\!}}</small>
-|<big>{{sagittal|#}}</big>
+| <big>{{sagittal|#}}</big>
 |-
-!Revo
+! Revo
-|<big>{{sagittal|)||(}}</big>
+| <big>{{sagittal|)||(}}</big>
-|<big>{{sagittal|||\}}</big>
+| <big>{{sagittal|||\}}</big>
-|<big>{{sagittal|/||\}}</big>
+| <big>{{sagittal|/||\}}</big>
 |}
 The following enharmonics from the Spartan set are present (comma tempered out):
 * {{sagittal|//|}} = {{Sagittal|/|)}} = {{Sagittal|/|\}} ([[325/324]], [[352/351]])
 * {{sagittal|/|}} = {{sagittal||)}} ([[225/224]])
 * {{sagittal||(}} = {{sagittal||//|}} ([[5120/5103]])
-See [[Sagittal notation#Revo|apotome complements]] for equivalent accidental pairs.
+See [[Sagittal notation #Revo|apotome complements]] for equivalent accidental pairs.
 Featured below is the 53edo gamut notated using the best accidental approximants; in this case, pai/pao and phai/phao.
@@ Line 681: / Line 682: @@
 {{Sagittal chart}}
-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.
 == Relationship to 12edo ==