MOS scale family tree: Difference between revisions

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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.

== History ==

[[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.

[[File:Family Tree of MOS-MV2 Scales.svg|thumb|811x811px|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 or Stern-Brocot trees, the term "family tree" is used instead.

=== ~~Differences~~ and ~~conventions~~ ===

=== Conventions and other differences ===

~~Although~~ the tree ~~described here~~ is ~~ultimately based on~~ Wilson~~'s description and therefore shows the same information~~, ~~the tree described in this article deviates from Wilson's description. The main~~ differences ~~are~~ listed below:

For the purposes of this article, the mos family tree will be depicted sideways and with an "upper" and "lower" child mos, rather than a left and right child, as typical with binary trees. This is exactly how Wilson initially described his tree, but with a few additional differences, listed below:

* Scale step patterns may not be shown; preferably, the mos in its xL ys form will be shown instead of a step pattern.

* Scale step patterns may not be shown. If ~~they~~ are shown, ~~scale step patterns~~ will always be shown in both its brightest and darkest modes. One way to think of this is the brightest mode will have as many L's to the left as possible while still preserving the mos property, and the darkest mode will have as many L's to the right as possible while still preserving the mos property.

* If step patterns are shown, they will always be shown in both its brightest and darkest modes.

* The construction rules described here result in a tree that is upside-down relative to Wilson's description.

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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:

* 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".

* One child (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".

* 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".

* The other child (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".

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

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 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.
 == History ==
-[[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.
+[[File:Family Tree of MOS-MV2 Scales.svg|thumb|811x811px|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 or Stern-Brocot trees, the term "family tree" is used instead.
-=== Differences and conventions ===
+=== Conventions and other differences ===
-Although the tree described here is ultimately based on Wilson's description and therefore shows the same information, the tree described in this article deviates from Wilson's description. The main differences are listed below:
+For the purposes of this article, the mos family tree will be depicted sideways and with an "upper" and "lower" child mos, rather than a left and right child, as typical with binary trees. This is exactly how Wilson initially described his tree, but with a few additional differences, listed below:
+* Scale step patterns may not be shown; preferably, the mos in its xL ys form will be shown instead of a step pattern.
-* Scale step patterns may not be shown. If they are shown, scale step patterns will always be shown in both its brightest and darkest modes. One way to think of this is the brightest mode will have as many L's to the left as possible while still preserving the mos property, and the darkest mode will have as many L's to the right as possible while still preserving the mos property.
+* If step patterns are shown, they will always be shown in both its brightest and darkest modes.
 * The construction rules described here result in a tree that is upside-down relative to Wilson's description.
@@ Line 16: / 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:
-* 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".
+* One child (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".
-* 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".
+* The other child (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".
 This pattern is repeated indefinitely to each new node added to the tree, or for however many generations are desired.