User:Ganaram inukshuk/Diagrams: Difference between revisions

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This page is for xen-related diagrams that I've made but don't have an exact place elsewhere on the wiki.

This page is for xen-related diagrams that I've made but don't have an exact place elsewhere on the wiki (yet).

== Family Tree of MOSses ==

This is a family tree of MOSses based on using the production rules L->Ls, s->s and L->Ls, s->L on the brightest and darkest mode respectively on a parent scale to produce a pair of sister scales. The result is a binary tree that ~~(as far as I can tell)~~ only includes single-period MOSses and organizes scales by generation rather than by other metrics such as total note count or ~~by relation by~~ Farey sums. This tree is five layers deep.

This is a family tree of MOSses based on using the production rules L->Ls, s->s and L->Ls, s->L on the brightest and darkest mode respectively on a parent scale to produce a pair of sister scales. The result is a binary tree that only includes single-period MOSses and organizes and relates scales by generation rather than by other metrics such as total note count or Farey sums. This tree is five layers deep.

[[File:Family ~~Tree~~ of MOS~~-MV2 Scales~~.~~svg~~|~~left~~]]

Personal note: <s>I don't think I've ever seen a scale tree organized like this, but I'd be curious to know if it's been conceived elsewhere. The fact that it only contains single-period scales makes it unusual compared to other scale trees.</s> It turns out this is a [[wikipedia:Stern–Brocot_tree|Stern-Brocot tree]] adapted to show the relationship between MOSses. SB trees only ever show ratios in their reduced form, hence why the MOS family tree only shows single-period MOSses.

Update (2022-07-28): This type of diagram was already by described by Erv Wilson, with connections to Fibonacci's "rabbit sequence". http://anaphoria.com/RabbitSequence.pdf

=== Single-period MOSses only ===

The scales depicted here are as follows, using TAMNAMS names wherever possible:

# Generation 1

## '''1L 1s''' - This is the progenitor scale for all scales and consists of two steps.

# Generation 2

## '''1L 2s''' and '''2L 1s''' - A pair of tritonic "scales". These are children of 1L 1s.

# Generation 3

## '''1L 3s''' and '''3L 1s''' - A pair of tetratonic scales. These are children of 1L 2s.

## '''2L 3s''' and '''3L 2s''' - A pair of pentatonic scales representing '''pentic''' (classic pentatonic) and '''antipentic''', children of 2L 1s.

# Generation 4

## '''1L 4s''' and '''4L 1s''' - A pair of pentatonic scales representing '''''antimanic''''' and '''manic''', children of 1L 3s. (TAMNAMS does not name 1L ns scales, but for completeness, the names for such scales are borrowed from the sister scale of nL 1s with the anti- prefix added.)

## '''3L 4s''' and '''4L 3s''' - A pair of heptatonic scales representing '''mosh''' and '''smitonic''', children of 3L 1s.

## '''2L 5s''' and '''5L 2s''' - A pair of heptatonic scales representing '''antidiatonic''' and '''diatonic''', children of 2L 3s.

## '''3L 5s''' and '''5L 3s''' - A pair of octatonic scales representing '''sensoid''' and '''oneirotonic''', children of 3L 2s.

# Generation 5

## '''1L 5s''' and '''5L 1s''' - A pair of hexatonic scales representing '''''antimachinoid''''' and '''machinoid''', children of 1L 4s.

## '''4L 5s''' and '''5L 4s''' - A pair of nonatonic scales representing '''orwelloid''' and '''semiquartal''', children of 4L 1s.

## '''3L 7s''' and '''7L 3s''' - A pair of decatonic scales representing '''sephiroid''' and '''dicotonic''', children of 3L 4s.

## '''4L 7s''' and '''7L 4s''' - A pair of undecatonic scales. These scales are unnamed as of writing; these are children of 4L 3s.

## '''2L 7s''' and '''7L 2s''' - A pair of nonatonic scales representing '''joanatonic''' and '''superdiatonic''', children of 2L 5s.

## '''5L 7s''' and '''7L 5s''' - A pair of dodecatonic scales representing '''p-chromatic''' (Pythagorean chromatic) and '''m-chromatic''' (meantone chromatic), children of 5L 2s.

## '''3L 8s''' and '''8L 3s''' - A pair of undecatonic scales. These scales are unnamed as of writing; these are children of 3L 5s.

## '''5L 8s''' and '''8L 5s'''. A pair of tridecatonic scales. These scales are unnamed as of writing; these are children of 5L 3s.

[[File:Family_Tree_of_MOS-MV2_Scales.svg|alt=|1500x1500px]]

=== Including Multi-period MOSses ===

By including multi-period MOSses, the family tree's similarity to the Stern-Brocot tree becomes more apparent.

[[File:Family tree of mv2 scales with multi period scales.svg|frameless|1500x1500px]]

== MOS Diagrams for a Specific EDO ==

I've found it easier to conceptualize the relationship between scales with a given generator pair if it's represented rectangularly instead of circularly. Here's an example of a "rectangular horogram" for 17edo.

[[File:17edo Rectangular Horograms.png|2000x2000px]]

@@ Line 1: / Line 1: @@
-This page is for xen-related diagrams that I've made but don't have an exact place elsewhere on the wiki.
+This page is for xen-related diagrams that I've made but don't have an exact place elsewhere on the wiki (yet).
 == Family Tree of MOSses ==
-This is a family tree of MOSses based on using the production rules L->Ls, s->s and L->Ls, s->L on the brightest and darkest mode respectively on a parent scale to produce a pair of sister scales. The result is a binary tree that (as far as I can tell) only includes single-period MOSses and organizes scales by generation rather than by other metrics such as total note count or by relation by Farey sums. This tree is five layers deep.
+This is a family tree of MOSses based on using the production rules L->Ls, s->s and L->Ls, s->L on the brightest and darkest mode respectively on a parent scale to produce a pair of sister scales. The result is a binary tree that only includes single-period MOSses and organizes and relates scales by generation rather than by other metrics such as total note count or Farey sums. This tree is five layers deep.
-[[File:Family Tree of MOS-MV2 Scales.svg|left]]
+Personal note: <s>I don't think I've ever seen a scale tree organized like this, but I'd be curious to know if it's been conceived elsewhere. The fact that it only contains single-period scales makes it unusual compared to other scale trees.</s> It turns out this is a [[wikipedia:Stern–Brocot_tree|Stern-Brocot tree]] adapted to show the relationship between MOSses. SB trees only ever show ratios in their reduced form, hence why the MOS family tree only shows single-period MOSses.
+Update (2022-07-28): This type of diagram was already by described by Erv Wilson, with connections to Fibonacci's "rabbit sequence". http://anaphoria.com/RabbitSequence.pdf
+=== Single-period MOSses only ===
+The scales depicted here are as follows, using TAMNAMS names wherever possible:
+# Generation 1
+## '''1L 1s''' - This is the progenitor scale for all scales and consists of two steps.
+# Generation 2
+## '''1L 2s''' and '''2L 1s''' - A pair of tritonic "scales". These are children of 1L 1s.
+# Generation 3
+## '''1L 3s''' and '''3L 1s''' - A pair of tetratonic scales. These are children of 1L 2s.
+## '''2L 3s''' and '''3L 2s''' - A pair of pentatonic scales representing '''pentic''' (classic pentatonic) and '''antipentic''', children of 2L 1s.
+# Generation 4
+## '''1L 4s''' and '''4L 1s''' - A pair of pentatonic scales representing '''''antimanic''''' and '''manic''', children of 1L 3s. (TAMNAMS does not name 1L ns scales, but for completeness, the names for such scales are borrowed from the sister scale of nL 1s with the anti- prefix added.)
+## '''3L 4s''' and '''4L 3s''' - A pair of heptatonic scales representing '''mosh''' and '''smitonic''', children of 3L 1s.
+## '''2L 5s''' and '''5L 2s''' - A pair of heptatonic scales representing '''antidiatonic''' and '''diatonic''', children of 2L 3s.
+## '''3L 5s''' and '''5L 3s''' - A pair of octatonic scales representing '''sensoid''' and '''oneirotonic''', children of 3L 2s.
+# Generation 5
+## '''1L 5s''' and '''5L 1s''' - A pair of hexatonic scales representing '''''antimachinoid''''' and '''machinoid''', children of 1L 4s.
+## '''4L 5s''' and '''5L 4s''' - A pair of nonatonic scales representing '''orwelloid''' and '''semiquartal''', children of 4L 1s.
+## '''3L 7s''' and '''7L 3s''' - A pair of decatonic scales representing '''sephiroid''' and '''dicotonic''', children of 3L 4s.
+## '''4L 7s''' and '''7L 4s''' - A pair of undecatonic scales. These scales are unnamed as of writing; these are children of 4L 3s.
+## '''2L 7s''' and '''7L 2s''' - A pair of nonatonic scales representing '''joanatonic''' and '''superdiatonic''', children of 2L 5s.
+## '''5L 7s''' and '''7L 5s''' - A pair of dodecatonic scales representing '''p-chromatic''' (Pythagorean chromatic) and '''m-chromatic''' (meantone chromatic), children of 5L 2s.
+## '''3L 8s''' and '''8L 3s''' - A pair of undecatonic scales. These scales are unnamed as of writing; these are children of 3L 5s.
+## '''5L 8s''' and '''8L 5s'''. A pair of tridecatonic scales. These scales are unnamed as of writing; these are children of 5L 3s.
+[[File:Family_Tree_of_MOS-MV2_Scales.svg|alt=|1500x1500px]]
+=== Including Multi-period MOSses ===
+By including multi-period MOSses, the family tree's similarity to the Stern-Brocot tree becomes more apparent.
+[[File:Family tree of mv2 scales with multi period scales.svg|frameless|1500x1500px]]
+== MOS Diagrams for a Specific EDO ==
+I've found it easier to conceptualize the relationship between scales with a given generator pair if it's represented rectangularly instead of circularly. Here's an example of a "rectangular horogram" for 17edo.
+[[File:17edo Rectangular Horograms.png|2000x2000px]]