Andrew Heathwaite's MOS Investigations: Difference between revisions
Wikispaces>Andrew_Heathwaite **Imported revision 270690070 - Original comment: ** |
Wikispaces>Andrew_Heathwaite **Imported revision 270703714 - 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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-11-01 | : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-11-01 13:08:37 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>270703714</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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Some kind of augmented step? | Some kind of augmented step? | ||
Mike Battaglia proposes (at least in the case of Porcupine) "d" for s-c and "A" for L+c....</pre></div> | Mike Battaglia proposes (at least in the case of Porcupine) "d" for s-c and "A" for L+c.... | ||
<span class="commentBody">So I posted to XA: "Ok, thinking it over, A and d are interesting choices to describe the additional steps, since they're so general. "d" is the small step minus one chroma, or s-c. But since the chroma itself is L-s, we can define d directly in terms of L a</span><span class="text_exposed_show">nd s as 2s-L. Meanwhile, "A" is the large step plus one chroma, or L+c. Described in terms of L and s, "A" is 2L-s. This allows us to quickly compute c, A, and d quickly, given L and s. As one example, Orwell[9] in 53edo has L=7 and s=5. So c=L-s=7-5=2; d=2s-L=2(5)-7=3; and A=2L-s=2(7)-5=9. Sure enough, a MODMOS of Orwell[9] with all four of these steps can be easily generated. Start with 7 5 7 5 7 5 7 5 5 and shift the second tone up by one chroma (which we computed to be 2\53), producing 9 3 7 5 7 5 7 5 5, which generalizes to AdLsLsLss! (Note that in 53edo Orwell[9] 2s=10 and A=9, not equal; while in 22edo's version of Orwell[9] 2s=4 and A=4, a potential 22edo Orwell pun.)</span><span class="commentBody"> ... (Oh, and another pun is possible here, since c and d are both 1 degree in 22edo but 2 and 3 degrees, respectively, in 53edo.)"</span></pre></div> | |||
<h4>Original HTML content:</h4> | <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"><html><head><title>Andrew Heathwaite's MOS Investigations</title></head><body>Ok, this is a page for me, Andrew Heathwaite, to organize my thoughts and questions regarding <a class="wiki_link" href="/MOSScales">Moment of Symmetry Scales</a>.<br /> | <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"><html><head><title>Andrew Heathwaite's MOS Investigations</title></head><body>Ok, this is a page for me, Andrew Heathwaite, to organize my thoughts and questions regarding <a class="wiki_link" href="/MOSScales">Moment of Symmetry Scales</a>.<br /> | ||
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Some kind of augmented step?<br /> | Some kind of augmented step?<br /> | ||
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Mike Battaglia proposes (at least in the case of Porcupine) &quot;d&quot; for s-c and &quot;A&quot; for L+c....</body></html></pre></div> | Mike Battaglia proposes (at least in the case of Porcupine) &quot;d&quot; for s-c and &quot;A&quot; for L+c....<br /> | ||
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<span class="commentBody">So I posted to XA: &quot;Ok, thinking it over, A and d are interesting choices to describe the additional steps, since they're so general. &quot;d&quot; is the small step minus one chroma, or s-c. But since the chroma itself is L-s, we can define d directly in terms of L a</span><span class="text_exposed_show">nd s as 2s-L. Meanwhile, &quot;A&quot; is the large step plus one chroma, or L+c. Described in terms of L and s, &quot;A&quot; is 2L-s. This allows us to quickly compute c, A, and d quickly, given L and s. As one example, Orwell[9] in 53edo has L=7 and s=5. So c=L-s=7-5=2; d=2s-L=2(5)-7=3; and A=2L-s=2(7)-5=9. Sure enough, a MODMOS of Orwell[9] with all four of these steps can be easily generated. Start with 7 5 7 5 7 5 7 5 5 and shift the second tone up by one chroma (which we computed to be 2\53), producing 9 3 7 5 7 5 7 5 5, which generalizes to AdLsLsLss! (Note that in 53edo Orwell[9] 2s=10 and A=9, not equal; while in 22edo's version of Orwell[9] 2s=4 and A=4, a potential 22edo Orwell pun.)</span><span class="commentBody"> ... (Oh, and another pun is possible here, since c and d are both 1 degree in 22edo but 2 and 3 degrees, respectively, in 53edo.)&quot;</span></body></html></pre></div> | |||