Andrew Heathwaite's MOS Investigations: Difference between revisions
Wikispaces>Andrew_Heathwaite **Imported revision 286336532 - Original comment: ** |
Wikispaces>Andrew_Heathwaite **Imported revision 287568464 - 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>2011-12- | : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-12-20 00:56:01 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>287568464</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> | ||
<h4>Original Wikitext content:</h4> | <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"> | <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">This is a page for me, Andrew Heathwaite, to organize my thoughts and questions regarding [[MOSScales|Moment of Symmetry Scales]]. I'm using it primarily to provoke and organize conversations with myself. It's a sort of personal sandbox. If it provokes conversations with others, all the better! You *yes you* are more than welcome to correct obvious errors, add clearly-demarked related material, and comment through the comments tab -- ask questions, tell me where you think I'm totally bonkers, connect me to similar ideas that you may know about, give a hurrah or two -- whatever you find suitable. | ||
==Expanding on "Maximal Evenness"== | ==Expanding on "Maximal Evenness"== | ||
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[[image:137edo_MOS_031_demo_correction.png]] | [[image:137edo_MOS_031_demo_correction.png]] | ||
[[image:137edo_MOS_032_demo.png]] | [[image:137edo_MOS_032_demo.png]] | ||
Update: I decided to go with [[127edo]] and have completed the visual study. See [[MOS Scales of 127edo]]. | |||
==Notes on Keenan Pepper's Diatonic-like MOS Scales== | ==Notes on Keenan Pepper's Diatonic-like MOS Scales== | ||
In the Xenharmonic Alliance Facebook Group, on Dec. 1, 2011, Keenan Pepper posted a short list of MOS scales, introducing them, '<span class="messageBody">The diatonic scale has both an extremely low average harmonic entropy, and also a very nearly maximum 'categorical channel capacity' (something I'm currently working on defining properly in terms of information theory - it basically means 'ability to tell different intervals and modes apart').</span>" I'm using this space to take some notes on the scales | In the Xenharmonic Alliance Facebook Group, on Dec. 1, 2011, Keenan Pepper posted a short list of MOS scales, introducing them, '<span class="messageBody">The diatonic scale has both an extremely low average harmonic entropy, and also a very nearly maximum 'categorical channel capacity' (something I'm currently working on defining properly in terms of information theory - it basically means 'ability to tell different intervals and modes apart').</span>" | ||
This sounds interesting. I'm using this space to take some notes on the scales he lists: | |||
||~ Scale Name ||~ Generator ||~ L ||~ s ||~ c ||~ L:s ||~ s:c || | ||~ Scale Name ||~ Generator ||~ L ||~ s ||~ c ||~ L:s ||~ s:c || | ||
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=Porcupine Chromaticism= | =Porcupine Chromaticism= | ||
Mike Battaglia has brought up this idea of Porcupine Chromaticism and given MODMOS Scales of Porcupine as specific examples. So to start that exploration, I've made a diagram of all the MOS scales that Porcupine makes possible, starting at Porcupine[7], and terminating at [[140edo]], which is arguably an optimal tuning for Porcupine. Take a look: | Mike Battaglia has brought up this idea of Porcupine Chromaticism and given [[MODMOS Scales]] of Porcupine as specific examples. So to start that exploration, I've made a diagram of all the MOS scales that Porcupine makes possible, starting at Porcupine[7], and terminating at [[140edo]], which is arguably an optimal tuning for Porcupine. Take a look: | ||
[[image:porcupine_mos_overview_140edo.jpg]] | [[image:porcupine_mos_overview_140edo.jpg]] | ||
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<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> | <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> | <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>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>. I'm using it primarily to provoke and organize conversations with myself. It's a sort of personal sandbox. If it provokes conversations with others, all the better! You *yes you* are more than welcome to correct obvious errors, add clearly-demarked related material, and comment through the comments tab -- ask questions, tell me where you think I'm totally bonkers, connect me to similar ideas that you may know about, give a hurrah or two -- whatever you find suitable.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Expanding on &quot;Maximal Evenness&quot;"></a><!-- ws:end:WikiTextHeadingRule:0 -->Expanding on &quot;Maximal Evenness&quot;</h2> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Expanding on &quot;Maximal Evenness&quot;"></a><!-- ws:end:WikiTextHeadingRule:0 -->Expanding on &quot;Maximal Evenness&quot;</h2> | ||
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Update: I decided to go with <a class="wiki_link" href="/127edo">127edo</a> and have completed the visual study. See <a class="wiki_link" href="/MOS%20Scales%20of%20127edo">MOS Scales of 127edo</a>.<br /> | |||
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<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x-Notes on Keenan Pepper's Diatonic-like MOS Scales"></a><!-- ws:end:WikiTextHeadingRule:4 -->Notes on Keenan Pepper's Diatonic-like MOS Scales</h2> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x-Notes on Keenan Pepper's Diatonic-like MOS Scales"></a><!-- ws:end:WikiTextHeadingRule:4 -->Notes on Keenan Pepper's Diatonic-like MOS Scales</h2> | ||
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In the Xenharmonic Alliance Facebook Group, on Dec. 1, 2011, Keenan Pepper posted a short list of MOS scales, introducing them, '<span class="messageBody">The diatonic scale has both an extremely low average harmonic entropy, and also a very nearly maximum 'categorical channel capacity' (something I'm currently working on defining properly in terms of information theory - it basically means 'ability to tell different intervals and modes apart').</span>&quot; I'm using this space to take some notes on the scales | In the Xenharmonic Alliance Facebook Group, on Dec. 1, 2011, Keenan Pepper posted a short list of MOS scales, introducing them, '<span class="messageBody">The diatonic scale has both an extremely low average harmonic entropy, and also a very nearly maximum 'categorical channel capacity' (something I'm currently working on defining properly in terms of information theory - it basically means 'ability to tell different intervals and modes apart').</span>&quot;<br /> | ||
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This sounds interesting. I'm using this space to take some notes on the scales he lists:<br /> | |||
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<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Porcupine Chromaticism"></a><!-- ws:end:WikiTextHeadingRule:8 -->Porcupine Chromaticism</h1> | <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Porcupine Chromaticism"></a><!-- ws:end:WikiTextHeadingRule:8 -->Porcupine Chromaticism</h1> | ||
<br /> | <br /> | ||
Mike Battaglia has brought up this idea of Porcupine Chromaticism and given MODMOS Scales of Porcupine as specific examples. So to start that exploration, I've made a diagram of all the MOS scales that Porcupine makes possible, starting at Porcupine[7], and terminating at <a class="wiki_link" href="/140edo">140edo</a>, which is arguably an optimal tuning for Porcupine. Take a look:<br /> | Mike Battaglia has brought up this idea of Porcupine Chromaticism and given <a class="wiki_link" href="/MODMOS%20Scales">MODMOS Scales</a> of Porcupine as specific examples. So to start that exploration, I've made a diagram of all the MOS scales that Porcupine makes possible, starting at Porcupine[7], and terminating at <a class="wiki_link" href="/140edo">140edo</a>, which is arguably an optimal tuning for Porcupine. Take a look:<br /> | ||
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<!-- ws:start:WikiTextLocalImageRule:320:&lt;img src=&quot;/file/view/porcupine_mos_overview_140edo.jpg/271210382/porcupine_mos_overview_140edo.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/porcupine_mos_overview_140edo.jpg/271210382/porcupine_mos_overview_140edo.jpg" alt="porcupine_mos_overview_140edo.jpg" title="porcupine_mos_overview_140edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:320 --><br /> | <!-- ws:start:WikiTextLocalImageRule:320:&lt;img src=&quot;/file/view/porcupine_mos_overview_140edo.jpg/271210382/porcupine_mos_overview_140edo.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/porcupine_mos_overview_140edo.jpg/271210382/porcupine_mos_overview_140edo.jpg" alt="porcupine_mos_overview_140edo.jpg" title="porcupine_mos_overview_140edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:320 --><br /> | ||