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.

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? - see [[PFDO]]?)

[[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]]

* "''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]]

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 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? - see [[PFDO]]?)
-[[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]]
+* "''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]]