User:Ganaram inukshuk/Tables: Difference between revisions

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!17\19 - 2\19

!16\19 - 3\19

!15\19 - 4\19

!'''15\19 - 4\19'''

!14\19 - 5\19

!13\19 - 6\19

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This tree can be thought of as a pruned mos family tree, where every leaf node ~~has the~~ step ratio of ~~L:s =~~ 2:1. To conceptualize this tree better, consider the leaf node 7L 5s. Since the entire structure is a binary tree (that is, there are no loopy paths), there is one and only one unique path that starts from 1L 1s and ends at 7L 5s. Likewise, all other leaf nodes have a unique path that merges back with 1L 1s.

This tree can be thought of as a pruned mos family tree, where every leaf node corresponds to a mos available to 19edo with a step ratio of 2:1. To conceptualize this tree better, consider the leaf node 7L 5s. Since the entire structure is a binary tree (that is, there are no loopy paths), there is one and only one unique path that starts from 1L 1s and ends at 7L 5s. Likewise, all other leaf nodes have a unique path that, when traversed backwards, merges back with 1L 1s.

Note that all of these paths inevitably overlap. It's important to note that these overlaps are due to each path having multiple mosses in common with one another, ~~despite having differing~~ generator ~~pairs or step ratios~~. Pruning a mos tree by generator pair isolates a single linear path between 1L 1s and the leaf node with the step ratio of 2:1; put another way, the tree is pruned down to a single branch.

Note that all of these paths inevitably overlap. It's important to note that these overlaps are due to each path having multiple mosses in common with one another. It's important to note that, for a node with two child nodes, the two child scales don't share the same generator pair, only a common mos from the parent node. Pruning a mos tree by generator pair isolates a single linear path between 1L 1s and the leaf node with the step ratio of 2:1; put another way, the tree would be pruned down to a single, finite branch.

Note the curious case of 1L 7s in this example. It should be the leaf node for the generator pair 17\19 and 2\19, but since that scale is also available to the generator pair of 18\19 and 1\19, it's not and that branch continues to 1L 17s. Technically speaking, the branches for the generator pairs of 18\19-1\19 and 17\19-2\19 coincide.

@@ Line 2,456: / Line 2,456: @@
 !17\19 - 2\19
 !16\19 - 3\19
-!15\19 - 4\19
+!'''15\19 - 4\19'''
 !14\19 - 5\19
 !13\19 - 6\19
@@ Line 2,624: / Line 2,624: @@
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 |}
-This tree can be thought of as a pruned mos family tree, where every leaf node has the step ratio of L:s = 2:1. To conceptualize this tree better, consider the leaf node 7L 5s. Since the entire structure is a binary tree (that is, there are no loopy paths), there is one and only one unique path that starts from 1L 1s and ends at 7L 5s. Likewise, all other leaf nodes have a unique path that merges back with 1L 1s.
+This tree can be thought of as a pruned mos family tree, where every leaf node corresponds to a mos available to 19edo with a step ratio of 2:1. To conceptualize this tree better, consider the leaf node 7L 5s. Since the entire structure is a binary tree (that is, there are no loopy paths), there is one and only one unique path that starts from 1L 1s and ends at 7L 5s. Likewise, all other leaf nodes have a unique path that, when traversed backwards, merges back with 1L 1s.
-Note that all of these paths inevitably overlap. It's important to note that these overlaps are due to each path having multiple mosses in common with one another, despite having differing generator pairs or step ratios. Pruning a mos tree by generator pair isolates a single linear path between 1L 1s and the leaf node with the step ratio of 2:1; put another way, the tree is pruned down to a single branch.
+Note that all of these paths inevitably overlap. It's important to note that these overlaps are due to each path having multiple mosses in common with one another. It's important to note that, for a node with two child nodes, the two child scales don't share the same generator pair, only a common mos from the parent node. Pruning a mos tree by generator pair isolates a single linear path between 1L 1s and the leaf node with the step ratio of 2:1; put another way, the tree would be pruned down to a single, finite branch.
 Note the curious case of 1L 7s in this example. It should be the leaf node for the generator pair 17\19 and 2\19, but since that scale is also available to the generator pair of 18\19 and 1\19, it's not and that branch continues to 1L 17s. Technically speaking, the branches for the generator pairs of 18\19-1\19 and 17\19-2\19 coincide.