Warped diatonic: Difference between revisions

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**Imported revision 282568100 - Original comment: **
Wikispaces>keenanpepper
**Imported revision 282589914 - Original comment: **
Line 1: Line 1:
<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:keenanpepper|keenanpepper]] and made on <tt>2011-12-05 16:42:04 UTC</tt>.<br>
: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-12-05 17:43:47 UTC</tt>.<br>
: The original revision id was <tt>282568100</tt>.<br>
: The original revision id was <tt>282589914</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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|| 10 || [[4L 2s]] || Decimal || LLsLLsLL ||
|| 10 || [[4L 2s]] || Decimal || LLsLLsLL ||
|| 11 || [[4L 3s]] || Orgone, keemun || LsLLsL ||
|| 11 || [[4L 3s]] || Orgone, keemun || LsLLsL ||
|| 11 || [[5L 1s]] || Machine || LLLsLL, LLsLLL ||
|| 11 || [[5L 1s]] || Machine, gorgo || LLLsLL, LLsLLL ||
|| **12** || **[[5L 2s]]** || **Ordinary diatonic** || (infinitely long) ||
|| **12** || **[[5L 2s]]** || **Ordinary diatonic** || (infinitely long) ||
|| 13 || [[5L 3s]] || Oneirotonic || LsLLsLL, LLsLLsL ||
|| 13 || [[5L 3s]] || Oneirotonic || LsLLsLL, LLsLLsL ||
Line 94: Line 94:
         &lt;td&gt;&lt;a class="wiki_link" href="/5L%201s"&gt;5L 1s&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/5L%201s"&gt;5L 1s&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;Machine&lt;br /&gt;
         &lt;td&gt;Machine, gorgo&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;LLLsLL, LLsLLL&lt;br /&gt;
         &lt;td&gt;LLLsLL, LLsLLL&lt;br /&gt;

Revision as of 17:43, 5 December 2011

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author keenanpepper and made on 2011-12-05 17:43:47 UTC.
The original revision id was 282589914.
The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

A **warped diatonic scale** is a scale (excluding the diatonic scale itself) that contains relatively long substrings of the [[5L 2s]] diatonic scale ("LLsLLLsLLsLLLs...") in its sequence of large and small steps, and such that the sizes of those steps are similar to those of the diatonic scale (namely, in the ballpark of 200 and 100 cents).
Such scales may mislead a diatonic-conditioned listener into assigning the intervals to diatonic scale categories, but the categorization will be violated when either (1) the part of the scale that doesn't agree with 5L2s is reached, or (2) the harmonic nature of the intervals is drastically different than what's expected from the diatonic scale.

Combinatorically, most [[distributionally even]] scales with more L steps than s steps do have significantly long substrings of the 5L2s diatonic scale in them. So, when searching for distributionally even warped diatonics, we can use the simple figure of merit that xLys is a good warped diatonic when x > y and 2x+y is in the vicinity of 12. If 2x+y is much less than 12, the steps will be too large to be recognized as the diatonic scale; conversely if 2x+y is much more than 12, the steps will be too small.

The scales at the top and bottom of this table are questionable as "warped diatonics", but the ones near 2x+y=12 are good examples.

||~ 2x+y ||~ Formula ||~ Names ||~ 5L2s substrings ||
|| 8 || [[3L 2s]] || Father || LsLLsL ||
|| 9 || [[4L 1s]] || Bug, superpelog || LLLsLL, LLsLLL ||
|| 10 || [[4L 2s]] || Decimal || LLsLLsLL ||
|| 11 || [[4L 3s]] || Orgone, keemun || LsLLsL ||
|| 11 || [[5L 1s]] || Machine, gorgo || LLLsLL, LLsLLL ||
|| **12** || **[[5L 2s]]** || **Ordinary diatonic** || (infinitely long) ||
|| 13 || [[5L 3s]] || Oneirotonic || LsLLsLL, LLsLLsL ||
|| 13 || [[6L 1s]] || Archeotonic || LLLsLL, LLsLLL ||
|| 14 || [[5L 4s]] || Superpelog, godzilla || LsLLsL ||
|| 14 || [[6L 2s]] || Hedgehog || LLsLLLsLL ||
|| 15 || [[6L 3s]] || Triforce || LLsLLsLL ||
|| 15 || [[7L 1s]] || Porcupine || LLLsLL, LLsLLL ||
|| 16 || [[6L 4s]] || Lemba, antikythera || LsLLsL ||
|| 16 || [[7L 2s]] || Mavila || LLsLLLsLL ||

Original HTML content:

<html><head><title>Warped diatonic</title></head><body>A <strong>warped diatonic scale</strong> is a scale (excluding the diatonic scale itself) that contains relatively long substrings of the <a class="wiki_link" href="/5L%202s">5L 2s</a> diatonic scale (&quot;LLsLLLsLLsLLLs...&quot;) in its sequence of large and small steps, and such that the sizes of those steps are similar to those of the diatonic scale (namely, in the ballpark of 200 and 100 cents).<br />
Such scales may mislead a diatonic-conditioned listener into assigning the intervals to diatonic scale categories, but the categorization will be violated when either (1) the part of the scale that doesn't agree with 5L2s is reached, or (2) the harmonic nature of the intervals is drastically different than what's expected from the diatonic scale.<br />
<br />
Combinatorically, most <a class="wiki_link" href="/distributionally%20even">distributionally even</a> scales with more L steps than s steps do have significantly long substrings of the 5L2s diatonic scale in them. So, when searching for distributionally even warped diatonics, we can use the simple figure of merit that xLys is a good warped diatonic when x &gt; y and 2x+y is in the vicinity of 12. If 2x+y is much less than 12, the steps will be too large to be recognized as the diatonic scale; conversely if 2x+y is much more than 12, the steps will be too small.<br />
<br />
The scales at the top and bottom of this table are questionable as &quot;warped diatonics&quot;, but the ones near 2x+y=12 are good examples.<br />
<br />


<table class="wiki_table">
    <tr>
        <th>2x+y<br />
</th>
        <th>Formula<br />
</th>
        <th>Names<br />
</th>
        <th>5L2s substrings<br />
</th>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td><a class="wiki_link" href="/3L%202s">3L 2s</a><br />
</td>
        <td>Father<br />
</td>
        <td>LsLLsL<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td><a class="wiki_link" href="/4L%201s">4L 1s</a><br />
</td>
        <td>Bug, superpelog<br />
</td>
        <td>LLLsLL, LLsLLL<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td><a class="wiki_link" href="/4L%202s">4L 2s</a><br />
</td>
        <td>Decimal<br />
</td>
        <td>LLsLLsLL<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td><a class="wiki_link" href="/4L%203s">4L 3s</a><br />
</td>
        <td>Orgone, keemun<br />
</td>
        <td>LsLLsL<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td><a class="wiki_link" href="/5L%201s">5L 1s</a><br />
</td>
        <td>Machine, gorgo<br />
</td>
        <td>LLLsLL, LLsLLL<br />
</td>
    </tr>
    <tr>
        <td><strong>12</strong><br />
</td>
        <td><strong><a class="wiki_link" href="/5L%202s">5L 2s</a></strong><br />
</td>
        <td><strong>Ordinary diatonic</strong><br />
</td>
        <td>(infinitely long)<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td><a class="wiki_link" href="/5L%203s">5L 3s</a><br />
</td>
        <td>Oneirotonic<br />
</td>
        <td>LsLLsLL, LLsLLsL<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td><a class="wiki_link" href="/6L%201s">6L 1s</a><br />
</td>
        <td>Archeotonic<br />
</td>
        <td>LLLsLL, LLsLLL<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td><a class="wiki_link" href="/5L%204s">5L 4s</a><br />
</td>
        <td>Superpelog, godzilla<br />
</td>
        <td>LsLLsL<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td><a class="wiki_link" href="/6L%202s">6L 2s</a><br />
</td>
        <td>Hedgehog<br />
</td>
        <td>LLsLLLsLL<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td><a class="wiki_link" href="/6L%203s">6L 3s</a><br />
</td>
        <td>Triforce<br />
</td>
        <td>LLsLLsLL<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td><a class="wiki_link" href="/7L%201s">7L 1s</a><br />
</td>
        <td>Porcupine<br />
</td>
        <td>LLLsLL, LLsLLL<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td><a class="wiki_link" href="/6L%204s">6L 4s</a><br />
</td>
        <td>Lemba, antikythera<br />
</td>
        <td>LsLLsL<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td><a class="wiki_link" href="/7L%202s">7L 2s</a><br />
</td>
        <td>Mavila<br />
</td>
        <td>LLsLLLsLL<br />
</td>
    </tr>
</table>

</body></html>
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