MOS scale: Difference between revisions
Wikispaces>hstraub **Imported revision 3495411 - Original comment: ** |
Wikispaces>hstraub **Imported revision 3495483 - 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:hstraub|hstraub]] and made on <tt>2007-03-27 13: | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2007-03-27 13:22:22 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>3495483</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> | ||
| Line 26: | Line 26: | ||
which is a linear diophantine equation! This means that given a, b and n, all possible MOS types can be calculated via the general solution of the corresponding linear diophantine equation. | which is a linear diophantine equation! This means that given a, b and n, all possible MOS types can be calculated via the general solution of the corresponding linear diophantine equation. | ||
Below is a list of MOS with number of elements from 5 to 10, in equal temperaments | Below is a list of MOS with number of elements from 5 to 10, in equal temperaments up to 36. | ||
Not all mathematical possibilities are listed - solutions of the equation that would yield too "exotic" scale steps (too small/tto big diffference between s and L) are excluded. (The concrete restrictions applied were: a solution appears if 7/6 < L/s < 5.) | Not all mathematical possibilities are listed - solutions of the equation that would yield too "exotic" scale steps (too small/tto big diffference between s and L) are excluded. (The concrete restrictions applied were: a solution appears if 7/6 < L/s < 5.) | ||
| Line 33: | Line 33: | ||
[[HeptatonicMOS|Heptatonic MOS]] | [[HeptatonicMOS|Heptatonic MOS]] | ||
[[OctatonicMOS|Octatonic MOS]] | [[OctatonicMOS|Octatonic MOS]] | ||
[[NonatonicMOS|Nonatonic MOS]]</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>MOSScales</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="MOS scales"></a><!-- ws:end:WikiTextHeadingRule:0 -->MOS scales</h1> | <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>MOSScales</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="MOS scales"></a><!-- ws:end:WikiTextHeadingRule:0 -->MOS scales</h1> | ||
| Line 55: | Line 55: | ||
which is a linear diophantine equation! This means that given a, b and n, all possible MOS types can be calculated via the general solution of the corresponding linear diophantine equation.<br /> | which is a linear diophantine equation! This means that given a, b and n, all possible MOS types can be calculated via the general solution of the corresponding linear diophantine equation.<br /> | ||
<br /> | <br /> | ||
Below is a list of MOS with number of elements from 5 to 10, in equal temperaments | Below is a list of MOS with number of elements from 5 to 10, in equal temperaments up to 36.<br /> | ||
Not all mathematical possibilities are listed - solutions of the equation that would yield too &quot;exotic&quot; scale steps (too small/tto big diffference between s and L) are excluded. (The concrete restrictions applied were: a solution appears if 7/6 &lt; L/s &lt; 5.)<br /> | Not all mathematical possibilities are listed - solutions of the equation that would yield too &quot;exotic&quot; scale steps (too small/tto big diffference between s and L) are excluded. (The concrete restrictions applied were: a solution appears if 7/6 &lt; L/s &lt; 5.)<br /> | ||
<br /> | <br /> | ||
| Line 62: | Line 62: | ||
<a class="wiki_link" href="/HeptatonicMOS">Heptatonic MOS</a><br /> | <a class="wiki_link" href="/HeptatonicMOS">Heptatonic MOS</a><br /> | ||
<a class="wiki_link" href="/OctatonicMOS">Octatonic MOS</a><br /> | <a class="wiki_link" href="/OctatonicMOS">Octatonic MOS</a><br /> | ||
& | <a class="wiki_link" href="/NonatonicMOS">Nonatonic MOS</a></body></html></pre></div> | ||