User:Ganaram inukshuk/Diagrams: Difference between revisions

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== 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 and relates scales by generation rather than by other metrics such as total note count or 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.

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:

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## '''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:~~Family Tree of MOS-MV2 Scales~~.~~svg~~|~~left~~]]

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

@@ Line 2: / Line 2: @@
 == 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 and relates scales by generation rather than by other metrics such as total note count or 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.
+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:
@@ Line 28: / Line 33: @@
 ## '''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:Family Tree of MOS-MV2 Scales.svg|left]]
+[[File:17edo Rectangular Horograms.png|2000x2000px]]