User:Ganaram inukshuk/Diagrams: Difference between revisions

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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.

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.

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

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