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>
: This revision was by author [[User:xenjacob|xenjacob]] and made on <tt>2007-04-11 01:48:21 UTC</tt>.<br>
: The original revision id was <tt>3731360</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<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: 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.
Corollaries are obvious to some, not-so-obvious to others. They are useful to have a grip on.


Equal temperaments are equal. But only if you're on the logarithmic scale. 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?)</pre></div>
* [[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]]?)
<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: there is a quality of self-evidence to them.&lt;br /&gt;
* [[Prime_edo|Prime edos]] make every interval repeated cycle through the whole thing. --[[William Lynch]].
&lt;br /&gt;
 
Corollaries are obvious to some, not-so-obvious to others. They are useful to have a grip on.&lt;br /&gt;
* [[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.
&lt;br /&gt;
 
Equal temperaments are equal. But only if you're on the logarithmic scale. 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?)&lt;/body&gt;&lt;/html&gt;</pre></div>
* 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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