41edo: Difference between revisions

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== Notations ==

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

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

~~41edo can be notated with~~ [[~~ups and downs~~]]~~, spoken as up, dup, downsharp, sharp, upsharp etc.~~ and ~~down, dud, upflat etc. Note that dup is equivalent to dudsharp~~ and ~~dud is equivalent to dupflat.~~

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

~~41edo can also be notated with quarter-tone accidentals and [[Alternative symbols for ups and downs notation#Sharp-3|ups and downs]].~~

The notes within an octave from A are thus:

~~{{Ups and downs sharpness|41|true}}~~

~~Arrows borrowed from extended [[Helmholtz–Ellis notation]] can also be used:~~

A, B{{sesquiflat2}}, A{{demisharp2}}, B♭, A♯, B{{demiflat2}}, A{{sesquisharp2}}, B, C{{demiflat2}}, B{{demisharp2}}, C, D{{sesquiflat2}}, C{{demisharp2}}, D♭, C♯, D{{demiflat2}}, C{{sesquisharp2}}, D, E{{sesquiflat2}}, D{{demisharp2}}, E♭, D♯, E{{demiflat2}}, D{{sesquisharp2}}, E, F{{demiflat2}}, E{{demisharp2}}, F, G{{sesquiflat2}}, F{{demisharp2}}, G♭, F♯, G{{demiflat2}}, F{{sesquisharp2}}, G, A{{sesquiflat2}}, G{{demisharp2}}, A♭, G♯, A{{demiflat2}}, G{{sesquisharp2}}, A

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

41edo can also be notated with [[Kite's ups and downs notation|Kite's ups and downs]], spoken as up, dup, downsharp, sharp, upsharp etc. and down, dud, upflat etc. Note that dup is equivalent to dudsharp and dud is equivalent to dupflat.

~~The notes within an octave from A are thus~~:

Half-sharps and half-flats can be used to avoid double arrows:

A, B{{sesquiflat2}}, A{{demisharp2}}, B♭, A♯, B{{demiflat2}}, A{{sesquisharp2}}, B, C{{demiflat2}}, B{{demisharp2}}, C, D{{sesquiflat2}}, C{{demisharp2}}, D♭, C♯, D{{demiflat2}}, C{{sesquisharp2}}, D, E{{sesquiflat2}}, D{{demisharp2}}, E♭, D♯, E{{demiflat2}}, D{{sesquisharp2}}, E, F{{demiflat2}}, E{{demisharp2}}, F, G{{sesquiflat2}}, F{{demisharp2}}, G♭, F♯, G{{demiflat2}}, F{{sesquisharp2}}, G, A{{sesquiflat2}}, G{{demisharp2}}, A♭, G♯, A{{demiflat2}}, G{{~~sesquisharp2~~}}~~, A~~

=== Red-Blue notation ===

A red-note/blue-note system, similar to the one proposed for [[36edo]], is another option for notating 41edo. This is a special case of Kite's [[color notation]], treating 41edo as a temperament of the 2.3.7 subgroup. We have the "white key" albitonic notes A–G (7 in total), the "black key" sharps and flats (10 in total), a "red" and "blue" version of each albitonic note (14 in total), a "red" (dark red?) version of each sharp and a "blue" (dark blue?) version of each flat (10 in total), adding up to 41. This would result in quite a colorful keyboard! Note that there are no red flats or blue sharps. Using this nomenclature the notes are:

A red-note/blue-note system, similar to the one proposed for [[36edo]], is another option for notating 41edo. This is a special case of [[Kite's color notation]], treating 41edo as a temperament of the 2.3.7 subgroup. We have the "white key" albitonic notes A–G (7 in total), the "black key" sharps and flats (10 in total), a "red" and "blue" version of each albitonic note (14 in total), a "red" (dark red?) version of each sharp and a "blue" (dark blue?) version of each flat (10 in total), adding up to 41. This would result in quite a colorful keyboard! Note that there are no red flats or blue sharps. Using this nomenclature the notes are:

{{colored note|A}}, {{colored note|red|A}}, {{colored note|blue|B♭}}, {{colored note|B♭}}, {{colored note|A♯}}, {{colored note|red|A♯}}, {{colored note|blue|B}}, {{colored note|B}}, {{colored note|red|B}}, {{colored note|blue|C}}, {{colored note|C}}, {{colored note|red|C}}, {{colored note|blue|D♭}}, {{colored note|D♭}}, {{colored note|C♯}}, {{colored note|red|C♯}}, {{colored note|blue|D}}, {{colored note|D}}, {{colored note|red|D}}, {{colored note|blue|E♭}}, {{colored note|E♭}}, {{colored note|D♯}}, {{colored note|red|D♯}}, {{colored note|blue|E}}, {{colored note|E}}, {{colored note|red|E}}, {{colored note|blue|F}}, {{colored note|F}}, {{colored note|red|F}}, {{colored note|blue|G♭}}, {{colored note|G♭}}, {{colored note|F♯}}, {{colored note|red|F♯}}, {{colored note|blue|G}}, {{colored note|G}}, {{colored note|red|G}}, {{colored note|blue|A♭}}, {{colored note|A♭}}, {{colored note|G♯}}, {{colored note|red|G♯}}, {{colored note|blue|A}}, {{colored note|A}}

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The step size of 41edo is small enough that the smallest interval (the "red/blue unison", seventh-tone, comma, diesis or whatever you want to call it) is actually fairly consonant with most timbres; it resembles a "noticeably out of tune unison" rather than a minor second, and has its own distinct character and appeal.

If "red" is replaced by "up", "blue" by "down", and "neutral" by "mid", and if "gray" is omitted, this notation becomes essentially the same as ~~[[Ups and downs notation|~~ups and downs notation]]. The only difference is the use of minor tritone and major tritone.

If "red" is replaced by "up", "blue" by "down", and "neutral" by "mid", and if "gray" is omitted, this notation becomes essentially the same as Kite's ups and downs notation. The only difference is the use of minor tritone and major tritone.

=== Sagittal notation ===

41edo can be notated in [[Sagittal notation|Sagittal]] using the [[Sagittal notation #Spartan single-shaft|Spartan ~~extension~~]], with the apotome equal to 4 edosteps and the limma to 3 edosteps. Since the apotome can be split in two and the [[243/242|rastma]] is tempered out, a SZ half-sharp and a half-flat may be used instead of pakai/pakao. Here is a simplified table:

41edo can be notated in [[Sagittal notation|Sagittal]] using the [[Sagittal notation #Spartan single-shaft|Spartan set]], with the apotome equal to 4 edosteps and the limma to 3 edosteps. Since the apotome can be split in two and the [[243/242|rastma]] is tempered out, a Stein–Zimmermann half-sharp and a half-flat may be used instead of pakai/pakao. Here is a simplified table:

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

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|-

! rowspan="3" |Symbol

! Evo+SZ

! Evo-SZ

| rowspan="3" | <big>{{sagittal||//|}}</big>

| rowspan="3" | <big>{{sagittal| |//| }}</big>

| rowspan="3" | <big>{{sagittal|/|}}</big>

| rowspan="3" | <big>{{sagittal| /| }}</big>

| <big>{{Sagittal|t}}</big>

| <big>{{Sagittal| t }}</big>

| <~~small~~>{{~~Sagittal~~|t}}{{sagittal||\}}</~~small~~>

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

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

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

|-

! Evo

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

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

~~| <small>{{sagittal|#}}{{sagittal|!/}}</small~~>

|-

! Revo

| <big>{{sagittal|(|~~3=)~~}}</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| /|) }} = {{sagittal| /|\ }} ([[325/324]], [[352/351]])

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

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

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

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

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

@@ Line 845: / Line 845: @@
 == Notations ==
-=== Ups and downs notation ===
+=== Stein–Zimmermann–Gould notation ===
-edo can be notated with [[ups and downs]], spoken as up, dup, downsharp, sharp, upsharp etc. and down, dud, upflat etc. Note that dup is equivalent to dudsharp and dud is equivalent to dupflat.
+[[Stein–Zimmermann–Gould notation]] uses sharps and flats combined with quartertone accidentals and arrows:
-{{Ups and downs sharpness}}
+{{Sharpness-sharp4-szg}}
-edo can also be notated with quarter-tone accidentals and [[Alternative symbols for ups and downs notation#Sharp-3|ups and downs]].
+The notes within an octave from A are thus:
-{{Ups and downs sharpness|41|true}}
-Arrows borrowed from extended [[Helmholtz–Ellis notation]] can also be used:
+A, B{{sesquiflat2}}, A{{demisharp2}}, B♭, A♯, B{{demiflat2}}, A{{sesquisharp2}}, B, C{{demiflat2}}, B{{demisharp2}}, C, D{{sesquiflat2}}, C{{demisharp2}}, D♭, C♯, D{{demiflat2}}, C{{sesquisharp2}}, D, E{{sesquiflat2}}, D{{demisharp2}}, E♭, D♯, E{{demiflat2}}, D{{sesquisharp2}}, E, F{{demiflat2}}, E{{demisharp2}}, F, G{{sesquiflat2}}, F{{demisharp2}}, G♭, F♯, G{{demiflat2}}, F{{sesquisharp2}}, G, A{{sesquiflat2}}, G{{demisharp2}}, A♭, G♯, A{{demiflat2}}, G{{sesquisharp2}}, A
-{{Sharpness-sharp4}}
+=== 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, downsharp, sharp, upsharp etc. and down, dud, upflat etc. Note that dup is equivalent to dudsharp and dud is equivalent to dupflat.
+{{Ups and downs sharpness}}
-The notes within an octave from A are thus:
+Half-sharps and half-flats can be used to avoid double arrows:
+{{Ups and downs sharpness|41|true}}
-A, B{{sesquiflat2}}, A{{demisharp2}}, B♭, A♯, B{{demiflat2}}, A{{sesquisharp2}}, B, C{{demiflat2}}, B{{demisharp2}}, C, D{{sesquiflat2}}, C{{demisharp2}}, D♭, C♯, D{{demiflat2}}, C{{sesquisharp2}}, D, E{{sesquiflat2}}, D{{demisharp2}}, E♭, D♯, E{{demiflat2}}, D{{sesquisharp2}}, E, F{{demiflat2}}, E{{demisharp2}}, F, G{{sesquiflat2}}, F{{demisharp2}}, G♭, F♯, G{{demiflat2}}, F{{sesquisharp2}}, G, A{{sesquiflat2}}, G{{demisharp2}}, A♭, G♯, A{{demiflat2}}, G{{sesquisharp2}}, A
 === Red-Blue notation ===
-A red-note/blue-note system, similar to the one proposed for [[36edo]], is another option for notating 41edo. This is a special case of Kite's [[color notation]], treating 41edo as a temperament of the 2.3.7 subgroup. We have the "white key" albitonic notes A–G (7 in total), the "black key" sharps and flats (10 in total), a "red" and "blue" version of each albitonic note (14 in total), a "red" (dark red?) version of each sharp and a "blue" (dark blue?) version of each flat (10 in total), adding up to 41. This would result in quite a colorful keyboard! Note that there are no red flats or blue sharps. Using this nomenclature the notes are:
+A red-note/blue-note system, similar to the one proposed for [[36edo]], is another option for notating 41edo. This is a special case of [[Kite's color notation]], treating 41edo as a temperament of the 2.3.7 subgroup. We have the "white key" albitonic notes A–G (7 in total), the "black key" sharps and flats (10 in total), a "red" and "blue" version of each albitonic note (14 in total), a "red" (dark red?) version of each sharp and a "blue" (dark blue?) version of each flat (10 in total), adding up to 41. This would result in quite a colorful keyboard! Note that there are no red flats or blue sharps. Using this nomenclature the notes are:
 {{colored note|A}}, {{colored note|red|A}}, {{colored note|blue|B♭}}, {{colored note|B♭}}, {{colored note|A♯}}, {{colored note|red|A♯}}, {{colored note|blue|B}}, {{colored note|B}}, {{colored note|red|B}}, {{colored note|blue|C}}, {{colored note|C}}, {{colored note|red|C}}, {{colored note|blue|D♭}}, {{colored note|D♭}}, {{colored note|C♯}}, {{colored note|red|C♯}}, {{colored note|blue|D}}, {{colored note|D}}, {{colored note|red|D}}, {{colored note|blue|E♭}}, {{colored note|E♭}}, {{colored note|D♯}}, {{colored note|red|D♯}}, {{colored note|blue|E}}, {{colored note|E}}, {{colored note|red|E}}, {{colored note|blue|F}}, {{colored note|F}}, {{colored note|red|F}}, {{colored note|blue|G♭}}, {{colored note|G♭}}, {{colored note|F♯}}, {{colored note|red|F♯}}, {{colored note|blue|G}}, {{colored note|G}}, {{colored note|red|G}}, {{colored note|blue|A♭}}, {{colored note|A♭}}, {{colored note|G♯}}, {{colored note|red|G♯}}, {{colored note|blue|A}}, {{colored note|A}}
@@ Line 869: / Line 869: @@
 The step size of 41edo is small enough that the smallest interval (the "red/blue unison", seventh-tone, comma, diesis or whatever you want to call it) is actually fairly consonant with most timbres; it resembles a "noticeably out of tune unison" rather than a minor second, and has its own distinct character and appeal.
-If "red" is replaced by "up", "blue" by "down", and "neutral" by "mid", and if "gray" is omitted, this notation becomes essentially the same as [[Ups and downs notation|ups and downs notation]]. The only difference is the use of minor tritone and major tritone.
+If "red" is replaced by "up", "blue" by "down", and "neutral" by "mid", and if "gray" is omitted, this notation becomes essentially the same as Kite's ups and downs notation. The only difference is the use of minor tritone and major tritone.
 === Sagittal notation ===
-edo can be notated in [[Sagittal notation|Sagittal]] using the [[Sagittal notation #Spartan single-shaft|Spartan extension]], with the apotome equal to 4 edosteps and the limma to 3 edosteps. Since the apotome can be split in two and the [[243/242|rastma]] is tempered out, a SZ half-sharp and a half-flat may be used instead of pakai/pakao. Here is a simplified table:
+edo can be notated in [[Sagittal notation|Sagittal]] using the [[Sagittal notation #Spartan single-shaft|Spartan set]], with the apotome equal to 4 edosteps and the limma to 3 edosteps. Since the apotome can be split in two and the [[243/242|rastma]] is tempered out, a Stein–Zimmermann half-sharp and a half-flat may be used instead of pakai/pakao. Here is a simplified table:
 {| class="wikitable" style="text-align: center;"
@@ Line 883: / Line 883: @@
 |-
 ! rowspan="3" |Symbol
-! Evo+SZ
+! Evo-SZ
-| rowspan="3" | <big>{{sagittal||//|}}</big>
+| rowspan="3" | <big>{{sagittal| |//| }}</big>
-| rowspan="3" | <big>{{sagittal|/|}}</big>
+| rowspan="3" | <big>{{sagittal| /| }}</big>
-| <big>{{Sagittal|t}}</big>
+| <big>{{Sagittal| t }}</big>
-| <small>{{Sagittal|t}}{{sagittal||\}}</small>
+| rowspan="2" | <big>{{sagittal| \! }}{{sagittal| # }}</big>
-| rowspan="2" | <big>{{sagittal|#}}</big>
+| rowspan="2" | <big>{{sagittal| # }}</big>
 |-
 ! Evo
-| rowspan="2" | <big>{{sagittal|/|\}}</big>
+| rowspan="2" | <big>{{sagittal| /|\ }}</big>
-| <small>{{sagittal|#}}{{sagittal|!/}}</small>
 |-
 ! Revo
-| <big>{{sagittal|(|3=)}}</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| /|) }} = {{sagittal| /|\ }} ([[325/324]], [[352/351]])
-* {{Sagittal|/|}} = {{sagittal||)}} ([[225/224]])
+* {{Sagittal| /| }} = {{sagittal| |) }} ([[225/224]])
-* {{Sagittal||(}} = {{sagittal||//|}} ([[5120/5103]])
+* {{Sagittal| |( }} = {{sagittal| |//| }} ([[5120/5103]])
 See [[Sagittal notation #Revo|apotome complements]] for equivalent accidental pairs.