Corollaries: Difference between revisions

Revision as of 07:10, 20 October 2024

Corollaries are things that anyone could say: there is a quality of self-evidence to them.

Corollaries are obvious to some, not-so-obvious to others. They are useful to have a grip on.

Equal temperaments are equal on the logarithmic scale, and harmonic series are equal on the frequency scale. The logarithmic scale is the logarithm of the frequency scale. (Could a logarithm of the logarithm scale be useful? Or an exponential of the frequency scale? Or a power of any one of these? - see PFDO?)

Prime edos make every interval repeated cycle through the whole thing. --William Lynch.

Dyads are distributionally even by definition, but "real" triads must not be distributionally even; and distributionally even interlaced tetrads and cannot exist in equal divisions of a cardinality relatively prime to 4 or 6.

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 Corollaries are obvious to some, not-so-obvious to others. They are useful to have a grip on.
-* [[Equal temperament]]s are equal on the logarithmic scale, and [[harmonic series]] are equal on the frequency scale. The logarithmic scale is the logarithm of the frequency scale. (Could a logarithm of the logarithm scale be useful? Or an exponential of the frequency scale? Or a power of any one of these?)
+* [[Equal temperament]]s are equal on the logarithmic scale, and [[harmonic series]] are equal on the frequency scale. The logarithmic scale is the logarithm of the frequency scale. (Could a logarithm of the logarithm scale be useful? Or an exponential of the frequency scale? Or a power of any one of these? - see [[PFDO]]?)
 * [[Prime_edo|Prime edos]] make every interval repeated cycle through the whole thing. --[[William Lynch]].