Corollaries

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.

• A tenth splits the difference between the octave and the twelfth.

• "The more subtle refinement is not yet with us and can only come by the use of a scale more minutely divided than our own; this would educate the ear to something finer than we have yet heard." - Edward Elgar