Warped diatonic: Difference between revisions
Wikispaces>keenanpepper **Imported revision 283510854 - Original comment: ** |
Wikispaces>keenanpepper **Imported revision 283870338 - 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:keenanpepper|keenanpepper]] and made on <tt>2011-12- | : This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-12-08 15:56:35 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>283870338</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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||~ 2x+y ||~ Formula ||~ Temperaments/names ||~ 5L2s substrings ||~ Comments || | ||~ 2x+y ||~ Formula ||~ Temperaments/names ||~ 5L2s substrings ||~ Comments || | ||
|| 8 || [[3L 2s]] || Father || LsLLsL || || | || 8 || [[3L 2s]] || Father || LsLLsL || || | ||
|| 9 || [[4L 1s]] || Bug, superpelog || LLLsLL, LLsLLL || || | || 9 || [[4L 1s]] || Bug, superpelog || LLLsLL, LLsLLL || || | ||
|| 10 || [[4L 2s]] || Decimal, lemba || LLsLLsLL || "Remove one L" || | || 10 || [[4L 2s]] || Decimal, lemba || LLsLLsLL || "Remove one L" || | ||
|| 11 || [[4L 3s]] || Orgone, keemun || LsLLsL || "Replace one L with s" || | || 11 || [[4L 3s]] || Orgone, keemun || LsLLsL || "Replace one L with s" || | ||
|| 11 || [[5L 1s]] || Machine, gorgo || LLLsLL, LLsLLL || "Remove one s" || | || 11 || [[5L 1s]] || Machine, gorgo || LLLsLL, LLsLLL || "Remove one s" || | ||
|| **12** || **[[5L 2s]]** || **Ordinary diatonic** || (infinitely long) || || | || **12** || **[[5L 2s]]** || **Ordinary diatonic** || (infinitely long) || || | ||
|| 13 || [[5L 3s]] || Oneirotonic, father || LsLLsLL, LLsLLsL || "Add one s" || | || 13 || [[5L 3s]] || Oneirotonic, father || LsLLsLL, LLsLLsL || "Add one s" || | ||
|| 13 || [[6L 1s]] || Archeotonic, leantone, tetracot || LLLsLL, LLsLLL || "Replace one s with L" || | || 13 || [[6L 1s]] || Archeotonic, leantone, tetracot || LLLsLL, LLsLLL || "Replace one s with L" || | ||
|| 14 || [[5L 4s]] || Superpelog, godzilla || LsLLsL || "Add two s's" || | || 14 || [[5L 4s]] || Superpelog, godzilla || LsLLsL || "Add two s's" || | ||
|| 14 || [[6L 2s]] || Hedgehog || LLsLLLsLL || "Add one L" || | || 14 || [[6L 2s]] || Hedgehog || LLsLLLsLL || "Add one L" || | ||
|| 15 || [[6L 3s]] || Triforce || LLsLLsLL || || | || 15 || [[6L 3s]] || Triforce || LLsLLsLL || || | ||
|| 15 || [[7L 1s]] || Porcupine || LLLsLL, LLsLLL || || | || 15 || [[7L 1s]] || Porcupine || LLLsLL, LLsLLL || || | ||
|| 16 || [[6L 4s]] || Lemba, antikythera || LsLLsL || || | || 16 || [[6L 4s]] || Lemba, antikythera || LsLLsL || || | ||
|| 16 || [[7L 2s]] || Mavila || LLsLLLsLL || ||</pre></div> | || 16 || [[7L 2s]] || Mavila || LLsLLLsLL || || | ||
=Example: Godzilla[9]= | |||
Godzilla[9] in [[19edo]] is 3 3 1 3 1 3 1 3 1. That's LLsLsLsLs where L is 189.5 cents and s is 63.2 cents. These step sizes are well within the range where they are "recognized" as diatonic scale steps. If you play 0 3 6 7 10 in 19edo (with no drone or harmony, just the melody) it will sound like "do re mi fa sol", leading you to believe that "sol" is a 3/2 interval above "do", but in fact it's not - it's closer to 10/7. The "real" 3/2 is another small step above that, in the melodic position of a flatted "la". | |||
Here's a summary of all the contradicted expectations in godzilla[9], of which there are many: | |||
* 2L+s, which is expected to be 4/3, is really more like 9/7. | |||
* 2L+2s, which is expected to be a "dissonant tritone" like 10/7, is actually the "real" 4/3. In "ti do re mi fa", the ti-fa interval is a tempered 4/3. | |||
* 3L+s, which is expected to be 3/2, is really more like 10/7. | |||
* 3L+2s, which is expected to be an 8/5, is actually the "real" 3/2. In the "minor" scale "la ti do re mi fa", it's the "fa" rather than the "mi" that forms a 3/2 with the root "la". | |||
* 4L+2s, which is expected to be a "minor seventh" (16/9~9/5), is actually 5/3. So in the "natural minor" scale "la ti do re mi fa sol", the outer la-sol interval is the easily recognizable consonance 5/3, but that's the "wrong" consonance for a diatonically-conditioned listener. | |||
* L+2s, which is not found in the ordinary diatonic scale but is familiar from the melodic and harmonic minor scales, is expected to be something close to a "major third" (in 12edo it's 400 cents, in meantone it's a tempered 9/7). In godzilla[9] it's the just minor third 6/5. | |||
* Finally, although there are 7 or even 8 consecutive notes of the scale that sound melodically familiar, the way the scale closes at the 2/1 is very unexpected and jarring for a diatonically-conditioned listener. When you get to 5L+3s that sounds melodically like it ought to be at least an "octave", probably something larger like an "augmented octave". But the real 2/1 is actually one small step beyond that, at 5L+4s.</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>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 /> | <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>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 /> | ||
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</table> | </table> | ||
</body></html></pre></div> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Example: Godzilla[9]"></a><!-- ws:end:WikiTextHeadingRule:0 -->Example: Godzilla[9]</h1> | ||
Godzilla[9] in <a class="wiki_link" href="/19edo">19edo</a> is 3 3 1 3 1 3 1 3 1. That's LLsLsLsLs where L is 189.5 cents and s is 63.2 cents. These step sizes are well within the range where they are &quot;recognized&quot; as diatonic scale steps. If you play 0 3 6 7 10 in 19edo (with no drone or harmony, just the melody) it will sound like &quot;do re mi fa sol&quot;, leading you to believe that &quot;sol&quot; is a 3/2 interval above &quot;do&quot;, but in fact it's not - it's closer to 10/7. The &quot;real&quot; 3/2 is another small step above that, in the melodic position of a flatted &quot;la&quot;.<br /> | |||
Here's a summary of all the contradicted expectations in godzilla[9], of which there are many:<br /> | |||
<ul><li>2L+s, which is expected to be 4/3, is really more like 9/7.</li><li>2L+2s, which is expected to be a &quot;dissonant tritone&quot; like 10/7, is actually the &quot;real&quot; 4/3. In &quot;ti do re mi fa&quot;, the ti-fa interval is a tempered 4/3.</li><li>3L+s, which is expected to be 3/2, is really more like 10/7.</li><li>3L+2s, which is expected to be an 8/5, is actually the &quot;real&quot; 3/2. In the &quot;minor&quot; scale &quot;la ti do re mi fa&quot;, it's the &quot;fa&quot; rather than the &quot;mi&quot; that forms a 3/2 with the root &quot;la&quot;.</li><li>4L+2s, which is expected to be a &quot;minor seventh&quot; (16/9~9/5), is actually 5/3. So in the &quot;natural minor&quot; scale &quot;la ti do re mi fa sol&quot;, the outer la-sol interval is the easily recognizable consonance 5/3, but that's the &quot;wrong&quot; consonance for a diatonically-conditioned listener.</li><li>L+2s, which is not found in the ordinary diatonic scale but is familiar from the melodic and harmonic minor scales, is expected to be something close to a &quot;major third&quot; (in 12edo it's 400 cents, in meantone it's a tempered 9/7). In godzilla[9] it's the just minor third 6/5.</li><li>Finally, although there are 7 or even 8 consecutive notes of the scale that sound melodically familiar, the way the scale closes at the 2/1 is very unexpected and jarring for a diatonically-conditioned listener. When you get to 5L+3s that sounds melodically like it ought to be at least an &quot;octave&quot;, probably something larger like an &quot;augmented octave&quot;. But the real 2/1 is actually one small step beyond that, at 5L+4s.</li></ul></body></html></pre></div> | |||