Step pattern product: Difference between revisions
Wikispaces>xenwolf **Imported revision 275510936 - Original comment: I hope I did nothing wrong with this "improvements" :)** |
Wikispaces>keenanpepper **Imported revision 275798788 - Original comment: ** |
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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: | : This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-11-15 16:00:17 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>275798788</tt>.<br> | ||
: The revision comment was: <tt> | : 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> | 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> | <h4>Original Wikitext content:</h4> | ||
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For example, the product word of "aabaaab" and "xxyxyxy" is "(a,x)(a,x)(b,y)(a,x)(a,y)(a,x)(b,y)". For brevity, we can substitute each ordered pair of letters by a new single letter and say this is equivalent to the word "rrsrtrs". This construction has an obvious generalization to the product of three or more words. | For example, the product word of "aabaaab" and "xxyxyxy" is "(a,x)(a,x)(b,y)(a,x)(a,y)(a,x)(b,y)". For brevity, we can substitute each ordered pair of letters by a new single letter and say this is equivalent to the word "rrsrtrs". This construction has an obvious generalization to the product of three or more words. | ||
The importance of product words in music theory is that every [[Fokker blocks|Fokker block]] can be expressed as the product word of two or more [[distributional evenness|distributionally even]] scales in a unique way. Fokker blocks are therefore equivalent to product words of DE scales of the same size. If one or both of the DE scales are rotated (into different [[mode|modes]]), then the product Fokker block scale is not always a mode, but is often a [[dome]] instead.</pre></div> | The importance of product words in music theory is that every [[Fokker blocks|Fokker block]] can be expressed as the product word of two or more [[distributional evenness|distributionally even]] scales in a unique way. Fokker blocks are therefore equivalent to product words of DE scales of the same size. If one or both of the DE scales are rotated (into different [[mode|modes]]), then the product Fokker block scale is not always a mode, but is often a [[dome]] instead.</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
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For example, the product word of &quot;aabaaab&quot; and &quot;xxyxyxy&quot; is &quot;(a,x)(a,x)(b,y)(a,x)(a,y)(a,x)(b,y)&quot;. For brevity, we can substitute each ordered pair of letters by a new single letter and say this is equivalent to the word &quot;rrsrtrs&quot;. This construction has an obvious generalization to the product of three or more words.<br /> | For example, the product word of &quot;aabaaab&quot; and &quot;xxyxyxy&quot; is &quot;(a,x)(a,x)(b,y)(a,x)(a,y)(a,x)(b,y)&quot;. For brevity, we can substitute each ordered pair of letters by a new single letter and say this is equivalent to the word &quot;rrsrtrs&quot;. This construction has an obvious generalization to the product of three or more words.<br /> | ||
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The importance of product words in music theory is that every <a class="wiki_link" href="/Fokker%20blocks">Fokker block</a> can be expressed as the product word of two or more <a class="wiki_link" href="/distributional%20evenness">distributionally even</a> scales in a unique way. Fokker blocks are therefore equivalent to product words of DE scales of the same size. If one or both of the DE scales are rotated (into different <a class="wiki_link" href="/mode">modes</a>), then the product Fokker block scale is not always a mode, but is often a <a class="wiki_link" href="/dome">dome</a> instead.</body></html></pre></div> | The importance of product words in music theory is that every <a class="wiki_link" href="/Fokker%20blocks">Fokker block</a> can be expressed as the product word of two or more <a class="wiki_link" href="/distributional%20evenness">distributionally even</a> scales in a unique way. Fokker blocks are therefore equivalent to product words of DE scales of the same size. If one or both of the DE scales are rotated (into different <a class="wiki_link" href="/mode">modes</a>), then the product Fokker block scale is not always a mode, but is often a <a class="wiki_link" href="/dome">dome</a> instead.</body></html></pre></div> | ||