MOS scale family tree: Difference between revisions

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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.

=== 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 ==

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== See also ==

* [[Catalog of MOS]]

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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.
-=== 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 ==
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 == See also ==
 * [[Catalog of MOS]]