User:BudjarnLambeth/12edo as a 2.3.5.17.19 tuning: Difference between revisions

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'''This page is only opinion, not fact.'''

~~This user page details ''how I personally'' assign each [[EDO]] to~~ a ~~[[subgroup]] of [[just intonation]]… This changes all the time because I can’t make up my mind~~.

Interpreting 12edo as a 2.3.5.17.19 system:

~~== Types of subgroups ==~~

== Intervals ==

~~'''WIP: I plan to heavily rewrite this section after carefully studying the new ''[[User:Dummy index/Heuristics for picking a nonstandard basis of JI subgroup]]''.'''~~

~~== Procedure for choosing a subgroup ==~~

~~'''WIP: I plan to heavily rewrite this section after carefully studying the new ''[[User:Dummy index/Heuristics for picking a nonstandard basis of JI subgroup]]''.'''~~

~~== List of subgroups by EDO ==~~

~~'''WIP: I plan to heavily rewrite this section after carefully studying the new ''[[User:Dummy index/Heuristics for picking a nonstandard basis of JI subgroup]]''.'''~~

~~Size categories taken from my [[human EDO size categorization]] (HUECAT).~~

~~For the purposes of this list, if prime N is mapped to A steps in an EDO, then “<N“ means N but mapped to A-1 steps, and “N>” means N but mapped to A+1 steps.~~

~~=== Picnic EDOs    (1-4) ===~~

~~=== Birthday EDOs    (5-19) ===~~

~~=== Carousel EDOs    (20-34) ===~~

~~=== Schoolbus EDOs    (35-54) ===~~

~~=== Double-decker EDOs    (55-74) ===~~

~~== Notation of dual-3 EDOs ==~~

Most EDO notation systems, including the near-universal [[ups and downs notation]], are built upon [[chain-of-fifths notation]]. How then should an EDO be notated if it’s dual-fifth, i.e. it has two mappings of 3: 3+ and 3-?

The most straightforward solution is to just choose whichever 3 is closer to just 3/1, and pretend that’s the "real 3" for notation purposes. Treat the other 3 as just another prime, like 5 or 7. In most cases, I advise to do that.

If you happen to be mainly using an EDO as a tuning for one specific non-dual [[regular temperament]] like meantone, mavila, etc., then pretend that temperament’s mapping of 3 is the ‘real’ one for the purpose of notation, and pretend the other 3 is just like any other larger prime.

Of course, this results in multiple notation systems for the same EDO, since different people use different temperaments or none at all, but that’s already the case. All of those notation systems already exist, I’m not adding any new ones, I’m just saying that the ones we already have all have a valid place and it’s okay to use one some day and another some other day on a project-by-project basis.

As long as you name and briefly explain your notation system at the start of your score, use whatever system you want. Use whichever one works in practice for you and the musicians collaborating with you. Invent one, if the existing ones don’t work. It’s fine. Not everything has to be standardized and homogenized.

Because I’m personally a fan of mixing and matching multiple temperaments, and other things that aren’t temperaments like approximated [[JI]] scales, [[MOS scale]]s, [[MODMOS]] & [[inflected MOS]] scales and even randomly generated scales, I usually like to go with the first option: ups and downs notation, in particular using whichever 3 is closest to just for its chain of fifths, and the other 3 being treated as just another available prime like 5, 7 or 11.

~~== Interpreting 12edo as a 2.3.5.17.19 system==~~

=== Intervals ===

<br>

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=== Chords ===

== Chords ==

<br>

==== Common chords ====

=== Common chords ===

My interpretation of what the just harmonies are, hiding behind common practice chords.

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==== Parent chords ====

=== Parent chords ===

My list of in my opinion the most harmonious 'parent chords' in 12edo, which you can use as palettes to build novel and pretty smaller chords. Choose one of these chords, take any subset of 2 or more notes from it, and you will make another, also harmonious chord.

@@ Line 5: / Line 5: @@
 '''This page is only opinion, not fact.'''
-This user page details ''how I personally'' assign each [[EDO]] to a [[subgroup]] of [[just intonation]]… This changes all the time because I can’t make up my mind.
+Interpreting 12edo as a 2.3.5.17.19 system:
-== Types of subgroups ==
+== Intervals ==
-'''WIP: I plan to heavily rewrite this section after carefully studying the new ''[[User:Dummy index/Heuristics for picking a nonstandard basis of JI subgroup]]''.'''
-== Procedure for choosing a subgroup ==
-'''WIP: I plan to heavily rewrite this section after carefully studying the new ''[[User:Dummy index/Heuristics for picking a nonstandard basis of JI subgroup]]''.'''
-== List of subgroups by EDO ==
-'''WIP: I plan to heavily rewrite this section after carefully studying the new ''[[User:Dummy index/Heuristics for picking a nonstandard basis of JI subgroup]]''.'''
-Size categories taken from my [[human EDO size categorization]] (HUECAT).
-For the purposes of this list, if prime N is mapped to A steps in an EDO, then “<N“ means N but mapped to A-1 steps, and “N>” means N but mapped to A+1 steps.
-=== Picnic EDOs    (1-4) ===
-=== Birthday EDOs    (5-19) ===
-=== Carousel EDOs    (20-34) ===
-=== Schoolbus EDOs    (35-54) ===
-=== Double-decker EDOs    (55-74) ===
-== Notation of dual-3 EDOs ==
-Most EDO notation systems, including the near-universal [[ups and downs notation]], are built upon [[chain-of-fifths notation]]. How then should an EDO be notated if it’s dual-fifth, i.e. it has two mappings of 3: 3+ and 3-?
-The most straightforward solution is to just choose whichever 3 is closer to just 3/1, and pretend that’s the "real 3" for notation purposes. Treat the other 3 as just another prime, like 5 or 7. In most cases, I advise to do that.
-If you happen to be mainly using an EDO as a tuning for one specific non-dual [[regular temperament]] like meantone, mavila, etc., then pretend that temperament’s mapping of 3 is the ‘real’ one for the purpose of notation, and pretend the other 3 is just like any other larger prime.
-Of course, this results in multiple notation systems for the same EDO, since different people use different temperaments or none at all, but that’s already the case. All of those notation systems already exist, I’m not adding any new ones, I’m just saying that the ones we already have all have a valid place and it’s okay to use one some day and another some other day on a project-by-project basis.
-As long as you name and briefly explain your notation system at the start of your score, use whatever system you want. Use whichever one works in practice for you and the musicians collaborating with you. Invent one, if the existing ones don’t work. It’s fine. Not everything has to be standardized and homogenized.
-Because I’m personally a fan of mixing and matching multiple temperaments, and other things that aren’t temperaments like approximated [[JI]] scales, [[MOS scale]]s, [[MODMOS]] & [[inflected MOS]] scales and even randomly generated scales, I usually like to go with the first option: ups and downs notation, in particular using whichever 3 is closest to just for its chain of fifths, and the other 3 being treated as just another available prime like 5, 7 or 11.
-== Interpreting 12edo as a 2.3.5.17.19 system==
-=== Intervals ===
 <br>
@@ Line 113: / Line 76: @@
-=== Chords ===
+== Chords ==
 <br>
-==== Common chords ====
+=== Common chords ===
 My interpretation of what the just harmonies are, hiding behind common practice chords.
@@ Line 337: / Line 300: @@
-==== Parent chords ====
+=== Parent chords ===
 My list of in my opinion the most harmonious 'parent chords' in 12edo, which you can use as palettes to build novel and pretty smaller chords. Choose one of these chords, take any subset of 2 or more notes from it, and you will make another, also harmonious chord.