Corollaries: Difference between revisions

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


[[Prime_edo|Prime edos]] make every interval repeated cycle through the whole thing. --William Lynch.
* [[Prime_edo|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 hexatonic scales cannot exist in equal divisions of a cardinality relatively prime to 4 or 6.
* [[Dyad]]s are distributionally even by definition, but "real" [[triad]]s must not be distributionally even; and distributionally even interlaced [[tetrad]]s and [[Category:6-tone scales|hexatonic scales]] 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,
* A [[tenth]] splits the difference between the [[octave]] and the [[twelfth]].
[[Category:Lists]]
[[Category:Lists]]

Revision as of 23:27, 18 September 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?)
  • 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.