Corollaries: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
Corollaries are things that anyone could say: there is a quality of self-evidence to them.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">Corollaries are things that anyone could say.


Corollaries are obvious to some, not-so-obvious to others. They are useful to have a grip on.</pre></div>
Corollaries are obvious to some, not-so-obvious to others. They are useful to have a grip on.
<h4>Original HTML content:</h4>
 
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Corollaries&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Corollaries are things that anyone could say.&lt;br /&gt;
* [[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]]?)
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Corollaries are obvious to some, not-so-obvious to others. They are useful to have a grip on.&lt;/body&gt;&lt;/html&gt;</pre></div>
* [[Prime_edo|Prime edos]] make every interval repeated cycle through the whole thing. --[[William Lynch]].
 
* [[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]].
[[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]]

Latest revision as of 08:53, 4 December 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?)
  • 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.
  • "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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