3L 4s: Difference between revisions
Wikispaces>Andrew_Heathwaite **Imported revision 105851379 - Original comment: ** |
Wikispaces>Andrew_Heathwaite **Imported revision 201369348 - 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> | : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-02-13 17:10:22 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>201369348</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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MOS scales of this form are built from a generator that falls between 1\3 (one degree of [[3edo]] - 400 cents) and 2\7 (two degrees of [[7edo]] - 343 cents. | MOS scales of this form are built from a generator that falls between 1\3 (one degree of [[3edo]] - 400 cents) and 2\7 (two degrees of [[7edo]] - 343 cents. | ||
It has the form s L s L s L s and its various "modes" (with nicknames coined by | It has the form s L s L s L s and its various "modes" (with nicknames coined by [[Andrew Heathwaite]]) are: | ||
|| s L s L s L s || bish || | || s L s L s L s || bish || | ||
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One can build a continuum of equal-tempered scales between 1\3 and 2\7 by taking "freshman sums," adding together the numerators, then adding together the denominators. | One can build a continuum of equal-tempered scales between 1\3 and 2\7 by taking "freshman sums," adding together the numerators, then adding together the denominators. | ||
||||||||||~ generator || g || 2g || 3g || 4g (-1200) || | ||||||||||~ generator || g || 2g || 3g || 4g (-1200) || | ||
|| 1\3 || || || || || 400.000 || 800.000 || 1200.000 || 400.000 || || | || 1\3 || || || || || 400.000 || 800.000 || 1200.000 || 400.000 || || | ||
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|| 2\7 || || || || || 342.847 || 685.714 || 1028.571 || 171.429 || || | || 2\7 || || || || || 342.847 || 685.714 || 1028.571 || 171.429 || || | ||
3\10 on this chart represents a dividing line between | 3\10 on this chart represents a dividing line between "neutral third scales" on the bottom (eg. [[17edo neutral scale]]), and something else I don't have a name for yet on the top, with [[10edo]] standing in between. (What do you call this region, dear reader?) MOS-wise, the neutral third scales, after three more generations, make MOS [[7L 3s]] ("unfair mosh"); the other scales make MOS [[3L 7s]] ("fair mosh"). | ||
In "neural scale territory," the generators are all "neutral thirds," and two of them make an approximation of the "perfect fifth." Additionally, the L of the scale is somewhere around a "whole tone" and the s of the scale is somewhere around a "neutral tone". | In "neural third scale territory," the generators are all "neutral thirds," and two of them make an approximation of the "perfect fifth." Additionally, the L of the scale is somewhere around a "whole tone" and the s of the scale is somewhere around a "neutral tone". | ||
In the as-yet unnamed northern territory, the generators are major thirds (including some very flat ones), and two generators are definitely sharp of a perfect fifth. L ranges from a "supermajor second" to a "major third" and s is a "semitone" or smaller.</pre></div> | In the as-yet unnamed northern territory, the generators are major thirds (including some very flat ones), and two generators are definitely sharp of a perfect fifth. L ranges from a "supermajor second" to a "major third" and s is a "semitone" or smaller.</pre></div> | ||
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MOS scales of this form are built from a generator that falls between 1\3 (one degree of <a class="wiki_link" href="/3edo">3edo</a> - 400 cents) and 2\7 (two degrees of <a class="wiki_link" href="/7edo">7edo</a> - 343 cents.<br /> | MOS scales of this form are built from a generator that falls between 1\3 (one degree of <a class="wiki_link" href="/3edo">3edo</a> - 400 cents) and 2\7 (two degrees of <a class="wiki_link" href="/7edo">7edo</a> - 343 cents.<br /> | ||
<br /> | <br /> | ||
It has the form s L s L s L s and its various &quot;modes&quot; (with nicknames coined by | It has the form s L s L s L s and its various &quot;modes&quot; (with nicknames coined by <a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a>) are:<br /> | ||
<br /> | <br /> | ||
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One can build a continuum of equal-tempered scales between 1\3 and 2\7 by taking &quot;freshman sums,&quot; adding together the numerators, then adding together the denominators.<br /> | One can build a continuum of equal-tempered scales between 1\3 and 2\7 by taking &quot;freshman sums,&quot; adding together the numerators, then adding together the denominators.<br /> | ||
<br /> | <br /> | ||
<br /> | |||
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<br /> | <br /> | ||
3\10 on this chart represents a dividing line between | 3\10 on this chart represents a dividing line between &quot;neutral third scales&quot; on the bottom (eg. <a class="wiki_link" href="/17edo%20neutral%20scale">17edo neutral scale</a>), and something else I don't have a name for yet on the top, with <a class="wiki_link" href="/10edo">10edo</a> standing in between. (What do you call this region, dear reader?) MOS-wise, the neutral third scales, after three more generations, make MOS <a class="wiki_link" href="/7L%203s">7L 3s</a> (&quot;unfair mosh&quot;); the other scales make MOS <a class="wiki_link" href="/3L%207s">3L 7s</a> (&quot;fair mosh&quot;).<br /> | ||
<br /> | <br /> | ||
In &quot;neural scale territory,&quot; the generators are all &quot;neutral thirds,&quot; and two of them make an approximation of the &quot;perfect fifth.&quot; Additionally, the L of the scale is somewhere around a &quot;whole tone&quot; and the s of the scale is somewhere around a &quot;neutral tone&quot;.<br /> | In &quot;neural third scale territory,&quot; the generators are all &quot;neutral thirds,&quot; and two of them make an approximation of the &quot;perfect fifth.&quot; Additionally, the L of the scale is somewhere around a &quot;whole tone&quot; and the s of the scale is somewhere around a &quot;neutral tone&quot;.<br /> | ||
<br /> | <br /> | ||
In the as-yet unnamed northern territory, the generators are major thirds (including some very flat ones), and two generators are definitely sharp of a perfect fifth. L ranges from a &quot;supermajor second&quot; to a &quot;major third&quot; and s is a &quot;semitone&quot; or smaller.</body></html></pre></div> | In the as-yet unnamed northern territory, the generators are major thirds (including some very flat ones), and two generators are definitely sharp of a perfect fifth. L ranges from a &quot;supermajor second&quot; to a &quot;major third&quot; and s is a &quot;semitone&quot; or smaller.</body></html></pre></div> | ||