Generator form manipulation: Difference between revisions
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=== beyond rank-2 === | === beyond rank-2 === | ||
[[File:Generator step by step manipulation.png|thumb|600px|A demonstration of how one might transform the size of a generator of a rank-3 temperament.]] | |||
These two tricks should enable us to attain any valid generator sizes we may wish for a given temperament. And these tricks work for any rank<ref>past 1, anyway; of course, rank 1 temperaments are somewhat inflexible in their single generator's size.</ref>, not only rank 2 like we've looked at thus far with 5-limit meantone examples. To be clear, for a rank <span><math>r</math></span> temperament, adding or subtracting <span><math>R_a</math></span> from another generator will only affect the size of <span><math>G_a</math></span>. | These two tricks should enable us to attain any valid generator sizes we may wish for a given temperament. And these tricks work for any rank<ref>past 1, anyway; of course, rank 1 temperaments are somewhat inflexible in their single generator's size.</ref>, not only rank 2 like we've looked at thus far with 5-limit meantone examples. To be clear, for a rank <span><math>r</math></span> temperament, adding or subtracting <span><math>R_a</math></span> from another generator will only affect the size of <span><math>G_a</math></span>. | ||