User:TromboneBoi9: Difference between revisions

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'''[https://akahler.w3spaces.com/ I have a website!!]'''

=== An idea for notation I had ===

== An idea for notation I had ==

Something I noticed in regular EDO notation, ~~using~~ Pythagorean names, is that the major third in a lot of temperaments is no longer the closest the EDO has to the 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]], relying on Pythagorean names with an extra layer of accidentals, is that the [Pythagorean] major third in a lot of temperaments is no longer the closest the EDO has to 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.

In essence, instead of solely relying on Pythaogrean names and arrows for edosteps in between (which can get unwieldy in larger EDOs), I considered making the arrow represent the [[syntonic comma]] instead. If your EDO has a different pitch for the just major third and the Pythagorean major third, then of course, it has syntonic comma that hasn't been tempered out. This won't change anything for EDOs with a syntonic comma less than or equal to one step, of course, but it could have an effect on even "sharper" systems like 37-EDO.

In essence, instead of solely relying on Pythaogrean names and arrows for edosteps in between (which can get unwieldy in larger EDOs, e.g. [[72edo#Intervals|72-EDO]]), I considered making the arrow represent the [[syntonic comma]] instead. 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 anything for EDOs with a syntonic comma less than or equal to one step, of course, but it could have an effect on even "sharper" systems like 37-EDO.

For single edosteps, we can instead use a sort of slash-like symbol Bosanquet used in his notation, and perhaps stack them on top of each other to use less horizontal space.

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|D

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''I have also devised custom accidentals for quartertones in both diatonic and anti-diatonic systems, but the image uploading process is being weird so I'll have to figure that out at some point.''

=== Cloudy scales ===

== Cloudy scales ==

I don't know about you, but I love the seventh harmonic. These scales are named after the [[cloudy comma]], and use different [[7-limit]] intervals for generators.

=== Cumulus Alpha ===

'''''Cumulus Alpha''''' is a 5L6s [[MOS]] with [[7/4]] as the generator and [[2/1]] as the period. This appears to approximate a subset of [[26edo|26-EDO]]; it approximates the whole of 26-EDO when extended to a 5L21s MOS, which I dub '''''Cumulus Alpha Holo'''''.

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=== Cumulus Beta ===

'''''Cumulus Beta''''' is an 4L5s MOS with [[7/6]] as the generator and [[2/1]] as the period. It approximates all intervals of [[9edo|9-EDO]] within a cent, proving 9-EDO's place as an exceptional 7-limit approximation.

{| class="wikitable mw-collapsible"

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|0.000

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=== Cumulus Gamma ===

'''''Cumulus Gamma''''' is an 3L8s MOS with [[9/7]] as the generator and [[2/1]] as the period. It approximates all intervals of [[11edo|11-EDO]] within 10 cents.

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@@ Line 5: / Line 5: @@
 '''[https://akahler.w3spaces.com/ I have a website!!]'''
-=== An idea for notation I had ===
+== An idea for notation I had ==
-Something I noticed in regular EDO notation, using Pythagorean names, is that the major third in a lot of temperaments is no longer the closest the EDO has to the 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]], relying on Pythagorean names with an extra layer of accidentals, is that the [Pythagorean] major third in a lot of temperaments is no longer the closest the EDO has to 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.
-In essence, instead of solely relying on Pythaogrean names and arrows for edosteps in between (which can get unwieldy in larger EDOs), I considered making the arrow represent the [[syntonic comma]] instead. If your EDO has a different pitch for the just major third and the Pythagorean major third, then of course, it has syntonic comma that hasn't been tempered out. This won't change anything for EDOs with a syntonic comma less than or equal to one step, of course, but it could have an effect on even "sharper" systems like 37-EDO.
+In essence, instead of solely relying on Pythaogrean names and arrows for edosteps in between (which can get unwieldy in larger EDOs, e.g. [[72edo#Intervals|72-EDO]]), I considered making the arrow represent the [[syntonic comma]] instead. 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 anything for EDOs with a syntonic comma less than or equal to one step, of course, but it could have an effect on even "sharper" systems like 37-EDO.
 For single edosteps, we can instead use a sort of slash-like symbol Bosanquet used in his notation, and perhaps stack them on top of each other to use less horizontal space.
@@ Line 288: / Line 288: @@
 |D
 |}
+''I have also devised custom accidentals for quartertones in both diatonic and anti-diatonic systems, but the image uploading process is being weird so I'll have to figure that out at some point.''
-=== Cloudy scales ===
+== Cloudy scales ==
 I don't know about you, but I love the seventh harmonic. These scales are named after the [[cloudy comma]], and use different [[7-limit]] intervals for generators.
+=== Cumulus Alpha ===
 '''''Cumulus Alpha''''' is a 5L6s [[MOS]] with [[7/4]] as the generator and [[2/1]] as the period. This appears to approximate a subset of [[26edo|26-EDO]]; it approximates the whole of 26-EDO when extended to a 5L21s MOS, which I dub '''''Cumulus Alpha Holo'''''.
 {| class="wikitable mw-collapsible"
@@ Line 359: / Line 361: @@
 |26
 |}
+=== Cumulus Beta ===
 '''''Cumulus Beta''''' is an 4L5s MOS with [[7/6]] as the generator and [[2/1]] as the period. It approximates all intervals of [[9edo|9-EDO]] within a cent, proving 9-EDO's place as an exceptional 7-limit approximation.
 {| class="wikitable mw-collapsible"
@@ Line 416: / Line 420: @@
 |0.000
 |}
+=== Cumulus Gamma ===
 '''''Cumulus Gamma''''' is an 3L8s MOS with [[9/7]] as the generator and [[2/1]] as the period. It approximates all intervals of [[11edo|11-EDO]] within 10 cents.
 {| class="wikitable mw-collapsible"