Ternary scale theorems: Difference between revisions

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Proof:

* A.1. Say that the generator of ''T'' has ''k'' steps.

* A.2.i. ~~Each slice/occurrence~~ of ~~the (perfect) generator in the template MOS~~ ''T'' ~~contains a certain number of '''X''' steps, and the imperfect generator~~ occurs only at one position. Call the unique imperfect position ''p''.

* A.2.i. The imperfect generator of ''T'' occurs only at one position. Call the unique imperfect position ''p''.

* A.2.ii. Say that the number of '''X''' steps in a ''perfect'' generator is ''i'', and the number of '''W''' steps in a ''perfect'' generator is ''j'', we have that {{nowrap|''k'' {{=}} ''i'' + ''j''.}}

* A.2.iii. We know from MOS theory that letter counts in ''k''-steps (for any fixed ''k'') differ by at most 1. Assume, possibly after taking the equave complement, that the imperfect generator has one ''more'' '''X''': the imperfect generator has {{nowrap|(''i'' + 1)-many}} '''X''''s, and {{nowrap|(''j'' − 1)-many}} '''W''''s.

@@ Line 90: / Line 90: @@
 Proof:
 * A.1. Say that the generator of ''T'' has ''k'' steps.
-* A.2.i. Each slice/occurrence of the (perfect) generator in the template MOS ''T'' contains a certain number of '''X''' steps, and the imperfect generator occurs only at one position. Call the unique imperfect position ''p''.
+* A.2.i. The imperfect generator of ''T'' occurs only at one position. Call the unique imperfect position ''p''.
 * A.2.ii. Say that the number of '''X''' steps in a ''perfect'' generator is ''i'', and the number of '''W''' steps in a ''perfect'' generator is ''j'', we have that {{nowrap|''k'' {{=}} ''i'' + ''j''.}}
 * A.2.iii. We know from MOS theory that letter counts in ''k''-steps (for any fixed ''k'') differ by at most 1. Assume, possibly after taking the equave complement, that the imperfect generator has one ''more'' '''X''': the imperfect generator has {{nowrap|(''i'' + 1)-many}} '''X''''s, and {{nowrap|(''j'' &minus; 1)-many}} '''W''''s.