User:Ganaram inukshuk/Diagrams

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 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: 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. It turns out this is a 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:

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

1. Generation 2
   1. 1L 2s and 2L 1s - A pair of tritonic "scales". These are children of 1L 1s.
2. Generation 3
   1. 1L 3s and 3L 1s - A pair of tetratonic scales. These are children of 1L 2s.
   2. 2L 3s and 3L 2s - A pair of pentatonic scales representing pentic (classic pentatonic) and antipentic, children of 2L 1s.
3. Generation 4
   1. 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.)
   2. 3L 4s and 4L 3s - A pair of heptatonic scales representing mosh and smitonic, children of 3L 1s.
   3. 2L 5s and 5L 2s - A pair of heptatonic scales representing antidiatonic and diatonic, children of 2L 3s.
   4. 3L 5s and 5L 3s - A pair of octatonic scales representing sensoid and oneirotonic, children of 3L 2s.
4. Generation 5
   1. 1L 5s and 5L 1s - A pair of hexatonic scales representing antimachinoid and machinoid, children of 1L 4s.
   2. 4L 5s and 5L 4s - A pair of nonatonic scales representing orwelloid and semiquartal, children of 4L 1s.
   3. 3L 7s and 7L 3s - A pair of decatonic scales representing sephiroid and dicotonic, children of 3L 4s.
   4. 4L 7s and 7L 4s - A pair of undecatonic scales. These scales are unnamed as of writing; these are children of 4L 3s.
   5. 2L 7s and 7L 2s - A pair of nonatonic scales representing joanatonic and superdiatonic, children of 2L 5s.
   6. 5L 7s and 7L 5s - A pair of dodecatonic scales representing p-chromatic (Pythagorean chromatic) and m-chromatic (meantone chromatic), children of 5L 2s.
   7. 3L 8s and 8L 3s - A pair of undecatonic scales. These scales are unnamed as of writing; these are children of 3L 5s.
   8. 5L 8s and 8L 5s. A pair of tridecatonic scales. These scales are unnamed as of writing; these are children of 5L 3s.

Including Multi-period MOSses

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

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.