MOS scale family tree - Revision history

FloraC: FloraC moved page MOS Scale Family Tree to MOS scale family tree: WP:NCCAPS

2023-12-22T08:07:06Z

FloraC moved page MOS Scale Family Tree to MOS scale family tree: WP:NCCAPS

← Older revision	Revision as of 08:07, 22 December 2023
(No difference)

Ganaram inukshuk: /* History */ Rewrote the conventions section

2022-11-24T07:52:40Z

History: Rewrote the conventions section

← Older revision		Revision as of 07:52, 24 November 2022
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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.		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 ==		== 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.		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.		* 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:		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.		This pattern is repeated indefinitely to each new node added to the tree, or for however many generations are desired.

Xenllium at 07:05, 19 October 2022

2022-10-19T07:05:38Z

← Older revision		Revision as of 07:05, 19 October 2022
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	\|		\|
	\|-		\|-
	\|[[13L 8]]		\|[[13L 8s]]
	\|}		\|}

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	Since a tree structure is built such that each node connects back to a unique parent (except for the root), there are no looping paths, so every path between any two nodes is unique. In [[regular temperament theory]], scales are described as being generated from stacking an interval repeatedly, with moment-of-symmetry scales resulting from this process. Since the sizes of the generating intervals are necessarily described, this means temperaments describe a specific path down the family tree.		Since a tree structure is built such that each node connects back to a unique parent (except for the root), there are no looping paths, so every path between any two nodes is unique. In [[regular temperament theory]], scales are described as being generated from stacking an interval repeatedly, with moment-of-symmetry scales resulting from this process. Since the sizes of the generating intervals are necessarily described, this means temperaments describe a specific path down the family tree.

	=== Relation to ~~edos~~ ===		=== Relation to EDOs ===
	Since every interval available to an [[EDO~~\|edo~~]] can be used as a generating interval, repeatedly stacking such an interval will necessarily produce mosses. Each mos produced this way will describe a unique path on the mos family tree, starting at 1L 1s and terminating right before a pair of sister scales whose note count is equal to the number of equal divisions. Combining all of these paths into a tree will form a subset of the infinite mos family tree, where each path represents a different sequence of mosses that all have the same generating intervals.		Since every interval available to an [[EDO]] can be used as a generating interval, repeatedly stacking such an interval will necessarily produce mosses. Each mos produced this way will describe a unique path on the mos family tree, starting at 1L 1s and terminating right before a pair of sister scales whose note count is equal to the number of equal divisions. Combining all of these paths into a tree will form a subset of the infinite mos family tree, where each path represents a different sequence of mosses that all have the same generating intervals.

	== External links ==		== External links ==
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	== See also ==		== See also ==

	* [[Catalog of MOS]]		* [[Catalog of MOS]]

Ganaram inukshuk: Clarified differences between the MOS family tree and other trees. Clarified page-specific conventions (namely the tree depicted here is sideways, relative to other trees)

2022-08-22T02:12:55Z

Clarified differences between the MOS family tree and other trees. Clarified page-specific conventions (namely the tree depicted here is sideways, relative to other trees)

Ganaram inukshuk: Added: mos family tree organizes scales by the step pattern alone

2022-08-07T20:04:37Z

Added: mos family tree organizes scales by the step pattern alone

← Older revision		Revision as of 20:04, 7 August 2022
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	{{Todo\| expand\| comment=This page is a work-in-progress; feel free to edit as needed. \| inline=1}}		{{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.		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.
	[[File:Family Tree of MOS-MV2 Scales.svg\|thumb\|649x649px\|The family tree of moment-of-symmetry scales, recreated by a xen wiki user.]]		[[File:Family Tree of MOS-MV2 Scales.svg\|thumb\|649x649px\|The family tree of moment-of-symmetry scales, recreated by a xen wiki user.]]

Ganaram inukshuk: Simplified todo

2022-07-30T21:01:01Z

Simplified todo

← Older revision		Revision as of 21:01, 30 July 2022
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	{{Todo\| expand~~, visualizations for observations section needed~~ \| comment=This page is a work-in-progress; feel free to edit as needed. \| inline=1}}		{{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.		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.

Ganaram inukshuk: Added todo

2022-07-30T20:57:41Z

Added todo

← Older revision		Revision as of 20:57, 30 July 2022
Line 1:		Line 1:
			{{Todo\| expand, visualizations for observations section needed \| 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.		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.
	[[File:Family Tree of MOS-MV2 Scales.svg\|thumb\|649x649px\|The family tree of moment-of-symmetry scales, recreated by a xen wiki user.]]		[[File:Family Tree of MOS-MV2 Scales.svg\|thumb\|649x649px\|The family tree of moment-of-symmetry scales, recreated by a xen wiki user.]]

Ganaram inukshuk: Populating page with initial information; needs a todo section

2022-07-30T20:54:01Z

Populating page with initial information; needs a todo section

Show changes

Ganaram inukshuk: Initial creation of page

2022-07-30T20:17:53Z

Initial creation of page

New page

The mos scale family tree (or mos family tree) is an infinite binary tree that organizes 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.

← Older revision		Revision as of 20:04, 7 August 2022
Line 1:		Line 1:
	{{Todo\| expand\| comment=This page is a work-in-progress; feel free to edit as needed. \| inline=1}}		{{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.		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.
	[[File:Family Tree of MOS-MV2 Scales.svg\|thumb\|649x649px\|The family tree of moment-of-symmetry scales, recreated by a xen wiki user.]]		[[File:Family Tree of MOS-MV2 Scales.svg\|thumb\|649x649px\|The family tree of moment-of-symmetry scales, recreated by a xen wiki user.]]

← Older revision		Revision as of 20:57, 30 July 2022
Line 1:		Line 1:
			{{Todo\| expand, visualizations for observations section needed \| 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.		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.
	[[File:Family Tree of MOS-MV2 Scales.svg\|thumb\|649x649px\|The family tree of moment-of-symmetry scales, recreated by a xen wiki user.]]		[[File:Family Tree of MOS-MV2 Scales.svg\|thumb\|649x649px\|The family tree of moment-of-symmetry scales, recreated by a xen wiki user.]]

← Older revision		Revision as of 02:12, 22 August 2022
Line 1:		Line 1:
	{{Todo\| expand\| comment=This page is a work-in-progress; feel free to edit as needed. \| inline=1}}		{{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 ==		== 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 ===		=== 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:		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.		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 ==		== Family tree as a table ==