Don Page comma: Difference between revisions
Wikispaces>keenanpepper **Imported revision 270052574 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 270098040 - 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:genewardsmith|genewardsmith]] and made on <tt>2011-10-30 20:20:29 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>270098040</tt>.<br> | ||
: The revision comment was: <tt></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> | 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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Successive superparticular ratios such as 10/9 and 11/10 or 12/11 and 13/12 exhibit a distinct tendency to produce strong (in the sense of low badness figures for the corresponding temperament) Don Page commas, but these are by no means the only examples. | Successive superparticular ratios such as 10/9 and 11/10 or 12/11 and 13/12 exhibit a distinct tendency to produce strong (in the sense of low badness figures for the corresponding temperament) Don Page commas, but these are by no means the only examples. | ||
Here are some 5-limit Don Page commas: | |||
DPC(5/3, 2) = 648/625 | |||
DPC(4/3, 9/5) = 81/80 | |||
DPC(5/4, 2) = 128/125 | |||
DPC(4/3, 5/3) = 16875/16384 | |||
DPC(3/2, 5/3) = 20000/19683 | |||
DPC(81/80, 128/125) = |161 -84 -12>, the atom | |||
DPC(81/80, 25/24) = |71 -99 37>, raider | |||
Here are some Don Page commas derived from 9-limit consonances: | Here are some Don Page commas derived from 9-limit consonances: | ||
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Here are some complex Don Page commas derived from other commas: | Here are some complex Don Page commas derived from other commas: | ||
DPC(525/512, 245/243) = |-153 277 -18 -87> | DPC(525/512, 245/243) = |-153 277 -18 -87> | ||
DPC(49/48, 50/49) = |-487 -97 -198 392> | DPC(49/48, 50/49) = |-487 -97 -198 392> | ||
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<br /> | <br /> | ||
Successive superparticular ratios such as 10/9 and 11/10 or 12/11 and 13/12 exhibit a distinct tendency to produce strong (in the sense of low badness figures for the corresponding temperament) Don Page commas, but these are by no means the only examples.<br /> | Successive superparticular ratios such as 10/9 and 11/10 or 12/11 and 13/12 exhibit a distinct tendency to produce strong (in the sense of low badness figures for the corresponding temperament) Don Page commas, but these are by no means the only examples.<br /> | ||
<br /> | |||
Here are some 5-limit Don Page commas:<br /> | |||
<br /> | |||
DPC(5/3, 2) = 648/625<br /> | |||
DPC(4/3, 9/5) = 81/80<br /> | |||
DPC(5/4, 2) = 128/125<br /> | |||
DPC(4/3, 5/3) = 16875/16384<br /> | |||
DPC(3/2, 5/3) = 20000/19683<br /> | |||
DPC(81/80, 128/125) = |161 -84 -12&gt;, the atom<br /> | |||
DPC(81/80, 25/24) = |71 -99 37&gt;, raider<br /> | |||
<br /> | <br /> | ||
Here are some Don Page commas derived from 9-limit consonances:<br /> | Here are some Don Page commas derived from 9-limit consonances:<br /> | ||
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Here are some complex Don Page commas derived from other commas:<br /> | Here are some complex Don Page commas derived from other commas:<br /> | ||
<br /> | <br /> | ||
DPC(525/512, 245/243) = |-153 277 -18 -87&gt;<br /> | DPC(525/512, 245/243) = |-153 277 -18 -87&gt;<br /> | ||
DPC(49/48, 50/49) = |-487 -97 -198 392&gt;<br /> | DPC(49/48, 50/49) = |-487 -97 -198 392&gt;<br /> | ||