MOS scale family tree: Difference between revisions

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{{Todo| expand| comment=This page is a work-in-progress; feel free to edit as needed. | inline=1}}

The MOS scale family tree (or mos family tree) is an infinite binary tree that organizes [[MOS scale|moment-of-symmetry scales]] based on the parent-to-child relationship between scales. This tree is ~~distinct from~~ other trees, such as ~~the scale tree (which organizes scales~~ based on ~~the Farey tree) and~~ the Stern-Brocot tree, ~~in that the mos family~~ tree organizes scales ~~regardless of temperament~~, ~~equave, step size, or period. In other words, this is~~ a family tree of step patterns.

The MOS scale family tree (or mos family tree) is an infinite binary tree that organizes [[MOS scale|moment-of-symmetry scales]] based on the parent-to-child relationship between scales. This tree is not to be confused with other scale trees, such as those based on the Stern-Brocot or tree or Farey tree. Rather, this tree organizes MOS scales quite differently, depicting a family tree of step patterns.

~~[[File:Family Tree of MOS-MV2 Scales.svg|thumb|649x649px|The family tree of moment-of-symmetry scales, recreated by a xen wiki user.]]~~

== History ==

[[Erv Wilson]] was the first to describe such a tree using Fibonacci rabbit patterns. One version of his tree is referred to the scale/rhythm tree, and it's this tree that shows the parent-child relationship between all (single-period) moment-of-symmetry scales.

[[File:Family Tree of MOS-MV2 Scales.svg|thumb|663x663px|The family tree of moment-of-symmetry scales, recreated by a xen wiki user. Note that the construction of this tree uses an upper and lower child, as opposed to a left and right child.]][[Erv Wilson]] was the first to describe such a tree using Fibonacci rabbit patterns. One version of his tree is referred to the scale/rhythm tree, and it's this tree that shows the parent-child relationship between all (single-period) moment-of-symmetry scales.

Since the term "scale tree" is already used to describe scales arranged using the Farey ~~tree~~, the term "family tree" is used instead.

Since the term "scale tree" is already used to describe scales arranged using the Farey or Stern-Brocot trees, the term "family tree" is used instead.

=== Differences and conventions ===

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At the root of the tree is the step pattern Ls, representing the mos 1L 1s. The child scales of any node can be constructed as such:

* ~~The upper~~ child starts with a copy of the step pattern of its parent and has every "L" replaced with "Ls" and every "s" is replaced with "s".

* One child starts with a copy of the step pattern of its parent and has every "L" replaced with "Ls" and every "s" is replaced with "s".

* The ~~lower~~ child starts with a reversed copy of the parent's step pattern and has every "L" replaced with "Ls" and every "s" replaced with "L".

* The other child starts with a reversed copy of the parent's step pattern and has every "L" replaced with "Ls" and every "s" replaced with "L".

This pattern is repeated indefinitely to each new node added to the tree, or for however many generations are desired.

An alternate version of the tree can be made by only considering the number of steps there are, ~~not~~ the pattern of steps formed. Again, the tree starts with 1L 1s at the root. The child scales will have the following note counts, given a parent of xL ys:

An alternate version of the tree can be made by only considering the number of steps there are, ignoring the pattern of steps formed. Again, the tree starts with 1L 1s at the root. The child scales will have the following note counts, given a parent of xL ys:

* ~~The upper~~ child will have x large steps and x+y small steps, for a mos of xL (x+y)s.

* One child will have x large steps and x+y small steps, for a mos of xL (x+y)s.

* The ~~lower~~ child will have x+y large steps and x small steps, for a mos of (x+y)L xs.

* The other child will have x+y large steps and x small steps, for a mos of (x+y)L xs.

== Family tree as a table ==

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 {{Todo| expand| comment=This page is a work-in-progress; feel free to edit as needed. | inline=1}}
-The MOS scale family tree (or mos family tree) is an infinite binary tree that organizes [[MOS scale|moment-of-symmetry scales]] based on the parent-to-child relationship between scales. This tree is distinct from other trees, such as the scale tree (which organizes scales based on the Farey tree) and the Stern-Brocot tree, in that the mos family tree organizes scales regardless of temperament, equave, step size, or period. In other words, this is a family tree of step patterns.
+The MOS scale family tree (or mos family tree<!-- Are there any other names this tree goes by? If so, add them here. -->) is an infinite binary tree that organizes [[MOS scale|moment-of-symmetry scales]] based on the parent-to-child relationship between scales. This tree is not to be confused with other scale trees, such as those based on the Stern-Brocot or tree or Farey tree. Rather, this tree organizes MOS scales quite differently, depicting a family tree of step patterns.
-[[File:Family Tree of MOS-MV2 Scales.svg|thumb|649x649px|The family tree of moment-of-symmetry scales, recreated by a xen wiki user.]]
 == History ==
-[[Erv Wilson]] was the first to describe such a tree using Fibonacci rabbit patterns. One version of his tree is referred to the scale/rhythm tree, and it's this tree that shows the parent-child relationship between all (single-period) moment-of-symmetry scales.
+[[File:Family Tree of MOS-MV2 Scales.svg|thumb|663x663px|The family tree of moment-of-symmetry scales, recreated by a xen wiki user. Note that the construction of this tree uses an upper and lower child, as opposed to a left and right child.]][[Erv Wilson]] was the first to describe such a tree using Fibonacci rabbit patterns. One version of his tree is referred to the scale/rhythm tree, and it's this tree that shows the parent-child relationship between all (single-period) moment-of-symmetry scales.
-Since the term "scale tree" is already used to describe scales arranged using the Farey tree, the term "family tree" is used instead.
+Since the term "scale tree" is already used to describe scales arranged using the Farey or Stern-Brocot trees, the term "family tree" is used instead.
 === Differences and conventions ===
@@ Line 18: / Line 16: @@
 At the root of the tree is the step pattern Ls, representing the mos 1L 1s. The child scales of any node can be constructed as such:
-* The upper child starts with a copy of the step pattern of its parent and has every "L" replaced with "Ls" and every "s" is replaced with "s".
+* One child starts with a copy of the step pattern of its parent and has every "L" replaced with "Ls" and every "s" is replaced with "s".
-* The lower child starts with a reversed copy of the parent's step pattern and has every "L" replaced with "Ls" and every "s" replaced with "L".
+* The other child starts with a reversed copy of the parent's step pattern and has every "L" replaced with "Ls" and every "s" replaced with "L".
 This pattern is repeated indefinitely to each new node added to the tree, or for however many generations are desired.
-An alternate version of the tree can be made by only considering the number of steps there are, not the pattern of steps formed. Again, the tree starts with 1L 1s at the root. The child scales will have the following note counts, given a parent of xL ys:
+An alternate version of the tree can be made by only considering the number of steps there are, ignoring the pattern of steps formed. Again, the tree starts with 1L 1s at the root. The child scales will have the following note counts, given a parent of xL ys:
-* The upper child will have x large steps and x+y small steps, for a mos of xL (x+y)s.
+* One child will have x large steps and x+y small steps, for a mos of xL (x+y)s.
-* The lower child will have x+y large steps and x small steps, for a mos of (x+y)L xs.
+* The other child will have x+y large steps and x small steps, for a mos of (x+y)L xs.
 == Family tree as a table ==