Re: Riffs & Rotes

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R&R.  Note 73

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Note To Self --

|  odd  odd  odd  odd # of nodes
|  i_1  e_1  i_k  e_k
|   o----o    o----o
|    \  ...  /
|     \  |  /
|      \ | /
|       \|/
|        O Odd # of nodes

the rote is a tree of odd order, so if you are standing
at the root there are an even number of non-root nodes.

pick one of the nodes that are adjacent to the root.  call it node 1.
the subtree planted on the edge between the root and node 1 is a rote.
call it r_1.

standing at node 1 and looking away from the root (radifugally?) at the
remaining subtrees, there is a unique odd tree among them -- call that
the "exponent" e_1 of r_1.  deleting e_1, the remaining subtree rooted
at node 1 is called the "index" i_1 of r_1.

let numb(r) be the number assigned to the rote r.
then numb(r_1) = (prime(numb(i_1))^numb(e_1).

Jon Awbrey

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