User:TromboneBoi9/Extended Ups and Downs: Difference between revisions

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This is an extension on [[Kite Giedraitis]]'s [[Ups and ~~Downs Notation~~|Ups and Downs notation system]].

This is an extension on [[Kite Giedraitis]]'s [[Ups and downs notation|Ups and Downs notation system]].

Something I noticed in [[Ups and downs notation|regular EDO notation]]~~--relying~~ on [[Pythagorean]] names with an extra layer of accidentals--is that the [[81/64|Pythagorean major third]] in a lot of EDO systems doesn't match the [[5/4|just major third 5/4]]. So, with some thought from Just Intonation notations, I came up with something that I think might be promising.

Something I noticed in [[Ups and downs notation|regular EDO notation]], which rely on [[Pythagorean]] names with an extra layer of accidentals, is that the [[81/64|Pythagorean major third]] in a lot of EDO systems doesn't match the [[5/4|just major third 5/4]]. So, with some thought from common Just Intonation notations (really just [[HEJI]]), I came up with something that I think might be promising.

In essence, instead of solely relying on Pythagorean names and arrows for edosteps in between (which can get unwieldy in larger EDOs, e.g. [[72edo#Intervals|72-EDO]]), I considered giving the [[syntonic comma]] a single symbol instead. That way you can emphasize the [[5-limit]] in your compositions more easily, and it ~~will stay~~ that ~~way when directly read in a different EDO~~.

In essence, instead of solely relying on Pythagorean names and arrows for edosteps in between (which can get unwieldy in larger EDOs, e.g. [[72edo#Intervals|72-EDO]]), I considered giving the [[syntonic comma]] a single symbol instead. That way, you can emphasize the [[5-limit]] in your compositions more easily, and it also means that this system can be used just like any JI notation system up to the 5-limit.

If your EDO has a different pitch for the just major third and the Pythagorean major third, then of course, it has a syntonic comma that hasn't been tempered out. This won't change much notation-wise for EDOs with a syntonic comma of 0 or 1 step, of course, but it could have an effect on even "sharper" systems like 37-EDO with a larger comma.

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|}For systems with a negative syntonic comma (sub-meantone systems), use ''')''' (pitch up) and '''(''' (pitch down) instead of '''/''' and '''\'''.

For ~~anti-diatonic~~ systems, the meantone-favoring flat and sharp symbols are not recommended, but use <u>harmonic notation</u> should they be needed.

For systems with fifths so flat so as to make them [[2L 5s|antidiatonic]] systems, the meantone-favoring flat and sharp symbols are not recommended, but use <u>harmonic notation</u> (where sharps and flats switch functions) should they be needed.

An example in [[13edo|13b-EDO]] where the syntonic comma is -2 steps (technically):

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|D

|}For systems with describable quarter tones, you can optionally use ad-lib ~~quarter tone~~ notation~~. Though~~ for many systems ([[10edo|10]], [[17edo|17]], [[24edo|24]], [[31edo|31]]), the ~~syntonic comma~~ notation ~~makes it~~ redundant; perhaps it could be of use in larger systems like [[41edo|41]], [[48edo|48]], or [[72edo|72]].

|}

[[File:Screenshot_2023-05-19_12.15.58_PM.png|thumb|A previous draft for quartertone accidentals: accidentals for [[5L 2s|diatonic]] systems on the top, accidentals for [[2L 5s|antidiatonic]] systems on the bottom]]

For systems with describable quarter tones, you can optionally use ad-lib quartertone notation, though for many systems ([[10edo|10]], [[17edo|17]], [[24edo|24]], [[31edo|31]]), the previous symbols make quartertone notation redundant; perhaps it could be of use in larger systems like [[41edo|41]], [[48edo|48]], or [[72edo|72]].

An example in [[41edo|41-EDO]] with '''+''' for a quartertone sharp and '''d''' for a quartertone flat:

@@ Line 1: / Line 1: @@
-This is an extension on [[Kite Giedraitis]]'s [[Ups and Downs Notation|Ups and Downs notation system]].
+This is an extension on [[Kite Giedraitis]]'s [[Ups and downs notation|Ups and Downs notation system]].
-Something I noticed in [[Ups and downs notation|regular EDO notation]]--relying on [[Pythagorean]] names with an extra layer of accidentals--is that the [[81/64|Pythagorean major third]] in a lot of EDO systems doesn't match the [[5/4|just major third 5/4]]. So, with some thought from Just Intonation notations, I came up with something that I think might be promising.
+Something I noticed in [[Ups and downs notation|regular EDO notation]], which rely on [[Pythagorean]] names with an extra layer of accidentals, is that the [[81/64|Pythagorean major third]] in a lot of EDO systems doesn't match the [[5/4|just major third 5/4]]. So, with some thought from common Just Intonation notations (really just [[HEJI]]), I came up with something that I think might be promising.
-In essence, instead of solely relying on Pythagorean names and arrows for edosteps in between (which can get unwieldy in larger EDOs, e.g. [[72edo#Intervals|72-EDO]]), I considered giving the [[syntonic comma]] a single symbol instead. That way you can emphasize the [[5-limit]] in your compositions more easily, and it will stay that way when directly read in a different EDO.
+In essence, instead of solely relying on Pythagorean names and arrows for edosteps in between (which can get unwieldy in larger EDOs, e.g. [[72edo#Intervals|72-EDO]]), I considered giving the [[syntonic comma]] a single symbol instead. That way, you can emphasize the [[5-limit]] in your compositions more easily, and it also means that this system can be used just like any JI notation system up to the 5-limit.
 If your EDO has a different pitch for the just major third and the Pythagorean major third, then of course, it has a syntonic comma that hasn't been tempered out. This won't change much notation-wise for EDOs with a syntonic comma of 0 or 1 step, of course, but it could have an effect on even "sharper" systems like 37-EDO with a larger comma.
@@ Line 207: / Line 207: @@
 |}For systems with a negative syntonic comma (sub-meantone systems), use ''')''' (pitch up) and '''(''' (pitch down) instead of '''/''' and '''\'''.
-For anti-diatonic systems, the meantone-favoring flat and sharp symbols are not recommended, but use <u>harmonic notation</u> should they be needed.
+For systems with fifths so flat so as to make them [[2L 5s|antidiatonic]] systems, the meantone-favoring flat and sharp symbols are not recommended, but use <u>harmonic notation</u> (where sharps and flats switch functions) should they be needed.
 An example in [[13edo|13b-EDO]] where the syntonic comma is -2 steps (technically):
@@ Line 285: / Line 285: @@
 |D
 |D
-|}For systems with describable quarter tones, you can optionally use ad-lib quarter tone notation. Though for many systems ([[10edo|10]], [[17edo|17]], [[24edo|24]], [[31edo|31]]), the syntonic comma notation makes it redundant; perhaps it could be of use in larger systems like [[41edo|41]], [[48edo|48]], or [[72edo|72]].
+|}
+[[File:Screenshot_2023-05-19_12.15.58_PM.png|thumb|A previous draft for quartertone accidentals: accidentals for [[5L 2s|diatonic]] systems on the top, accidentals for [[2L 5s|antidiatonic]] systems on the bottom]]
+For systems with describable quarter tones, you can optionally use ad-lib quartertone notation, though for many systems ([[10edo|10]], [[17edo|17]], [[24edo|24]], [[31edo|31]]), the previous symbols make quartertone notation redundant; perhaps it could be of use in larger systems like [[41edo|41]], [[48edo|48]], or [[72edo|72]].
 An example in [[41edo|41-EDO]] with '''+''' for a quartertone sharp and '''d''' for a quartertone flat: