Recursive structure of MOS scales: Difference between revisions
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You can build this generator on all of the chunk boundaries. All but one of these will be perfect. The perfect ones will have their right endpoint be a chunk boundary, as I just showed before. So this is an interval that's on all but one tone of the reduced mos. That's a generator. | You can build this generator on all of the chunk boundaries. All but one of these will be perfect. The perfect ones will have their right endpoint be a chunk boundary, as I just showed before. So this is an interval that's on all but one tone of the reduced mos. That's a generator. | ||
To complete the proof that the generator of a mos is unique, just reduce all the way down to nL1s for some n. Any generator of the original mos must be a generator of this nL1s. The generator of nL1s is obviously unique, so the generator of the original mos is unique. | |||
== Tree of MOS patterns == | == Tree of MOS patterns == | ||