Maximum variety: Difference between revisions
Wikispaces>guest **Imported revision 388139476 - Original comment: ** |
Wikispaces>guest **Imported revision 388770004 - Original comment: Reverted to Nov 12, 2011 1:11 pm: page was spammed** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:guest|guest]] and made on <tt>2012-12- | : This revision was by author [[User:guest|guest]] and made on <tt>2012-12-03 20:43:18 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>388770004</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt>Reverted to Nov 12, 2011 1:11 pm: page was spammed</tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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Any scale with all equal steps (such as an [[EDO]]) has maximum variety 1. All [[MOSScales|MOS]] and [[distributional evenness|distributionally even]] scales have maximum variety 2 (in fact this can be taken as the definition of distributional evenness). An example of a scale with high max variety is the [[harmonic series]], because the steps get gradually smaller as you go up the scale, and none of them are equal. | Any scale with all equal steps (such as an [[EDO]]) has maximum variety 1. All [[MOSScales|MOS]] and [[distributional evenness|distributionally even]] scales have maximum variety 2 (in fact this can be taken as the definition of distributional evenness). An example of a scale with high max variety is the [[harmonic series]], because the steps get gradually smaller as you go up the scale, and none of them are equal. | ||
== | ==Max-variety-3 scales== | ||
**Max-variety-3** scales are an attempt to generalize distributional evenness (closely related to the MOS property) to scales with three different step sizes rather than two (for example, those related to rank-3 [[Regular Temperaments|regular temperaments]]). The construction of max-variety-3 scales is significantly more complicated than that of MOSes, but not much more difficult to understand if the right approach is used. | **Max-variety-3** scales are an attempt to generalize distributional evenness (closely related to the MOS property) to scales with three different step sizes rather than two (for example, those related to rank-3 [[Regular Temperaments|regular temperaments]]). The construction of max-variety-3 scales is significantly more complicated than that of MOSes, but not much more difficult to understand if the right approach is used. | ||
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Any scale with all equal steps (such as an <a class="wiki_link" href="/EDO">EDO</a>) has maximum variety 1. All <a class="wiki_link" href="/MOSScales">MOS</a> and <a class="wiki_link" href="/distributional%20evenness">distributionally even</a> scales have maximum variety 2 (in fact this can be taken as the definition of distributional evenness). An example of a scale with high max variety is the <a class="wiki_link" href="/harmonic%20series">harmonic series</a>, because the steps get gradually smaller as you go up the scale, and none of them are equal.<br /> | Any scale with all equal steps (such as an <a class="wiki_link" href="/EDO">EDO</a>) has maximum variety 1. All <a class="wiki_link" href="/MOSScales">MOS</a> and <a class="wiki_link" href="/distributional%20evenness">distributionally even</a> scales have maximum variety 2 (in fact this can be taken as the definition of distributional evenness). An example of a scale with high max variety is the <a class="wiki_link" href="/harmonic%20series">harmonic series</a>, because the steps get gradually smaller as you go up the scale, and none of them are equal.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Max-variety-3 scales"></a><!-- ws:end:WikiTextHeadingRule:0 -- | <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Max-variety-3 scales"></a><!-- ws:end:WikiTextHeadingRule:0 -->Max-variety-3 scales</h2> | ||
<strong>Max-variety-3</strong> scales are an attempt to generalize distributional evenness (closely related to the MOS property) to scales with three different step sizes rather than two (for example, those related to rank-3 <a class="wiki_link" href="/Regular%20Temperaments">regular temperaments</a>). The construction of max-variety-3 scales is significantly more complicated than that of MOSes, but not much more difficult to understand if the right approach is used.<br /> | <strong>Max-variety-3</strong> scales are an attempt to generalize distributional evenness (closely related to the MOS property) to scales with three different step sizes rather than two (for example, those related to rank-3 <a class="wiki_link" href="/Regular%20Temperaments">regular temperaments</a>). The construction of max-variety-3 scales is significantly more complicated than that of MOSes, but not much more difficult to understand if the right approach is used.<br /> | ||
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