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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:genewardsmith|genewardsmith]] and made on <tt>2012-04-17 12:01:01 UTC</tt>.<br> | | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-04-18 14:17:58 UTC</tt>.<br> |
| : The original revision id was <tt>321558490</tt>.<br> | | : The original revision id was <tt>322228346</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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| When R is less than 1, it represents the ratio in (logarithmic) size between the smaller and the larger step. When it is greater than 1, it is larger/smaller. By replacing g with 1 - g if necessary, we can reduce always to the case where R>1 (or R<1 if we prefer.) | | When R is less than 1, it represents the ratio in (logarithmic) size between the smaller and the larger step. When it is greater than 1, it is larger/smaller. By replacing g with 1 - g if necessary, we can reduce always to the case where R>1 (or R<1 if we prefer.) |
|
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| =Catalog of MOS=
| |
| Below is a list of MOS with number of elements from 5 to 10, plus some of the more significant larger MOS.
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|
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| || [[PentatonicMOS|Pentatonic MOS]] || || || || || || || [[1L 4s]] || || [[2L 3s]] || || [[3L 2s]] || || [[4L 1s]] || || || || || || ||
| |
| || [[HexatonicMOS|Hexatonic MOS]] || || || || || || [[1L 5s]] || || [[2L 4s]] || || [[3L 3s]] || || [[4L 2s]] || || [[5L 1s]] || || || || || ||
| |
| || [[HeptatonicMOS|Heptatonic MOS]] || || || || || [[1L 6s]] || || [[2L 5s]] || || [[3L 4s]] || || [[4L 3s]] || || [[5L 2s]] || || [[6L 1s]] || || || || ||
| |
| || [[OctatonicMOS|Octatonic MOS]] || || || || [[1L 7s]] || || [[2L 6s]] || || [[3L 5s]] || || [[4L 4s]] || || [[5L 3s]] || || [[6L 2s]] || || [[7L 1s]] || || || ||
| |
| || [[NonatonicMOS|Nonatonic MOS]] || || || [[1L 8s]] || || [[2L 7s]] || || [[3L 6s]] || || [[4L 5s]] || || [[5L 4s]] || || [[6L 3s]] || || [[7L 2s]] || || [[8L 1s]] || || ||
| |
| || [[DecatonicMOS|Decatonic MOS]] || || [[1L 9s]] || || [[2L 8s]] || || [[3L 7s]] || || [[4L 6s]] || || [[5L 5s]] || || [[6L 4s]] || || [[7L 3s]] || || [[8L 2s]] || || [[9L 1s]] || ||
| |
| || [[Hendecatonic MOS]] || [[1L 10s]] || || [[2L 9s]] || || [[3L 8s]] || || [[4L 7s]] || || [[5L 6s]] || || [[6L 5s]] || || [[7L 4s]] || || [[8L 3s]] || || [[9L 2s]] || || [[10L 1s]] ||
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|
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| Sensi[11] [[[8L 3s]]]
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| Slendric[11] [[[5L 6s]]]
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| Keemun[11] [[[4L 7s]]]
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|
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| Pajara[12] [[[10L 2s]]]
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| Meantone[12] [[[7L 5s]]]
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| Superpyth[12] [[[5L 7s]]]
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| Augene[12] [[[3L 9s]]]
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| Injera[12] [[[2L 10s]]]
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|
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| Orwell[13] [[[4L 9s]]]
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| Magic[13] [[[3L 10s]]]
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|
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| See: [[Tridecatonic MOS]]
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|
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| Injera[14] [[[12L 2s]]]
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| [WITNOTS{14}] [[[11L 3s]]]
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| Godzilla[14] [[[5L 9s]]]
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| Doublewide[14] [[[4L 10s]]]
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|
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| Superkleismic[15] [[[11L 4s]]]
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| Porcupine[15] [[[7L 8s]]]
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| Myna[15] [[[4L 11s]]]
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| Valentine[15] [[[1L 14s]]]
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|
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| Wizard[16] [[[6L 10s]]]
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| Mothra[16], Shoe[16] [[[5L 11s]]]
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|
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| Squares[17] [[[14L 3s]]]
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| Garibaldi[17] [[[12L 5s]]]
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| Beatles[17] [[[10L 7s]]]
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| Mohajira[17] [[[7L 10s]]]
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|
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| Muggles[19] [[[16L 3s]]]
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| Meantone[19] [[[12L 7s]]]
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| Negri[19] [[[10L 9s]]]
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| Sensi[19] [[[8L 11s]]]
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| Flattone[19] [[[7L 12s]]]
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| Hemiwuerschmidt[19] [[[6L 13s]]]
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| Myna[19] [[[4L 15s]]]
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| Magic[19] [[[3L 16s]]]
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| Tritonic[19] [[[2L 17s]]]
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|
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| Roman[20] [[[3L 17s]]]
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|
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| Miracle[21] [[[10L 11s]]]
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| Rodan[21] [[[5L 16s]]]
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| Tritonic[21] [[[2L 19s]]]
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|
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| Magic[22] [[[19L 3s]]]
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| Orwell[22] [[[9L 13s]]]
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| Wizard[22] [[[6L 16s]]]
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| Diaschismic[22] [[[12L 10s]]]
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| Shrutar[22] [[[2L 20s]]]
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| Coendou[22] [[[7L 15s]]]
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|
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| Hemikleismic[23] [[[15L 8s]]]
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| Unidec[23] [[[13L 10s]]]
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| Roman[23] [[[3L 20s]]]
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|
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| Mohajira[24] [[[7L 17s]]]
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|
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| Luna[25] [[[6L 19s]]]
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|
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| Ennealimmal[27] [[[18L 9s]]]
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| Octacot[27] [[[14L 13s]]]
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|
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| Leapday[29], Grackle[29] [[[17L 12s]]]
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| Garibaldi[29] [[[12L 17s]]]
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|
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| =Variations on MOS Scales= | | =Variations on MOS Scales= |
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| ==[[MOSDiagrams]]== </pre></div> | | ==[[MOSDiagrams]]== </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:WikiTextTocRule:28:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><a href="#Definition">Definition</a><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --> | <a href="#Mathematical Definition">Mathematical Definition</a><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> | <a href="#Mathematical Properties of MOS">Mathematical Properties of MOS</a><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --> | <a href="#Visualizing MOS: Generator Chains, Pitch Space, and Hierarchies">Visualizing MOS: Generator Chains, Pitch Space, and Hierarchies</a><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --> | <a href="#Classification of MOS">Classification of MOS</a><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --> | <a href="#Catalog of MOS">Catalog of MOS</a><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --> | <a href="#Variations on MOS Scales">Variations on MOS Scales</a><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --> | <a href="#MOS As Applied To Rhythms">MOS As Applied To Rhythms</a><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --> | <a href="#Algorithms">Algorithms</a><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --> | | <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:WikiTextTocRule:26:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --><a href="#Definition">Definition</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --> | <a href="#Mathematical Definition">Mathematical Definition</a><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --> | <a href="#Mathematical Properties of MOS">Mathematical Properties of MOS</a><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --> | <a href="#Visualizing MOS: Generator Chains, Pitch Space, and Hierarchies">Visualizing MOS: Generator Chains, Pitch Space, and Hierarchies</a><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> | <a href="#Classification of MOS">Classification of MOS</a><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --> | <a href="#Variations on MOS Scales">Variations on MOS Scales</a><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --> | <a href="#MOS As Applied To Rhythms">MOS As Applied To Rhythms</a><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --> | <a href="#Algorithms">Algorithms</a><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --> |
| <!-- ws:end:WikiTextTocRule:43 --><hr /> | | <!-- ws:end:WikiTextTocRule:40 --><hr /> |
| <br /> | | <br /> |
| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Definition"></a><!-- ws:end:WikiTextHeadingRule:0 -->Definition</h1> | | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Definition"></a><!-- ws:end:WikiTextHeadingRule:0 -->Definition</h1> |
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| Since the generator chain and logarithmic pitch space are both 1-dimensional, it may be helpful to graph them together in 2 dimensions. Here is a diagram for sensi[8], an octatonic <a class="wiki_link" href="/3L%205s">3L 5s</a> MOS scale with a generator of about 444¢. The x-axis shows the generator chain and the y-axis shows the nine tones (eight plus octave) in logarithmic pitch space. You can see that the vertical lines are evenly-spaced (since every generator is the same), while the horizontal lines have large and small gaps, representing the large and small steps of sensi[8].<br /> | | Since the generator chain and logarithmic pitch space are both 1-dimensional, it may be helpful to graph them together in 2 dimensions. Here is a diagram for sensi[8], an octatonic <a class="wiki_link" href="/3L%205s">3L 5s</a> MOS scale with a generator of about 444¢. The x-axis shows the generator chain and the y-axis shows the nine tones (eight plus octave) in logarithmic pitch space. You can see that the vertical lines are evenly-spaced (since every generator is the same), while the horizontal lines have large and small gaps, representing the large and small steps of sensi[8].<br /> |
| <br /> | | <br /> |
| <!-- ws:start:WikiTextLocalImageRule:425:&lt;img src=&quot;/file/view/map_of_sensi%5B8%5D.png/287845258/map_of_sensi%5B8%5D.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/map_of_sensi%5B8%5D.png/287845258/map_of_sensi%5B8%5D.png" alt="map_of_sensi[8].png" title="map_of_sensi[8].png" /><!-- ws:end:WikiTextLocalImageRule:425 --><br /> | | <!-- ws:start:WikiTextLocalImageRule:126:&lt;img src=&quot;/file/view/map_of_sensi%5B8%5D.png/287845258/map_of_sensi%5B8%5D.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/map_of_sensi%5B8%5D.png/287845258/map_of_sensi%5B8%5D.png" alt="map_of_sensi[8].png" title="map_of_sensi[8].png" /><!-- ws:end:WikiTextLocalImageRule:126 --><br /> |
| <br /> | | <br /> |
| And another way to visualize MOS scales is hierarchically. Every MOS scale with 3 or more tones:<br /> | | And another way to visualize MOS scales is hierarchically. Every MOS scale with 3 or more tones:<br /> |
| <ol><li>contains at least one MOS scale with fewer tones (and in fact, more than one instance of it), and</li><li>is contained (more than once) in either<ol><li>an MOS scale with more tones, or</li><li>an equal scale (when L:s = 2:1).</li></ol></li></ol><br /> | | <ol><li>contains at least one MOS scale with fewer tones (and in fact, more than one instance of it), and</li><li>is contained (more than once) in either<ol><li>an MOS scale with more tones, or</li><li>an equal scale (when L:s = 2:1).</li></ol></li></ol><br /> |
| Below is a diagram showing four MOS scales in logarithmic pitch space generated by 7\<a class="wiki_link" href="/37edo">37edo</a> (approx. 227¢). Each contains the ones above it and is contained by the ones below it. There are additional MOS scales that would appear above the first line with 1, 2, 3, 4, and 5 tones, but they have been omitted. The bottom line is a case where L:s=2:1, which means that there are no more MOS scales to be had -- the next stopping point is at a complete chromatic scale of <a class="wiki_link" href="/37edo">37edo</a>.<br /> | | Below is a diagram showing four MOS scales in logarithmic pitch space generated by 7\<a class="wiki_link" href="/37edo">37edo</a> (approx. 227¢). Each contains the ones above it and is contained by the ones below it. There are additional MOS scales that would appear above the first line with 1, 2, 3, 4, and 5 tones, but they have been omitted. The bottom line is a case where L:s=2:1, which means that there are no more MOS scales to be had -- the next stopping point is at a complete chromatic scale of <a class="wiki_link" href="/37edo">37edo</a>.<br /> |
| <!-- ws:start:WikiTextLocalImageRule:426:&lt;img src=&quot;/file/view/37edo_mos_07.png/285321926/37edo_mos_07.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/37edo_mos_07.png/285321926/37edo_mos_07.png" alt="37edo_mos_07.png" title="37edo_mos_07.png" /><!-- ws:end:WikiTextLocalImageRule:426 --><br /> | | <!-- ws:start:WikiTextLocalImageRule:127:&lt;img src=&quot;/file/view/37edo_mos_07.png/285321926/37edo_mos_07.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/37edo_mos_07.png/285321926/37edo_mos_07.png" alt="37edo_mos_07.png" title="37edo_mos_07.png" /><!-- ws:end:WikiTextLocalImageRule:127 --><br /> |
| For more images showing the hierarchical arrangement of MOS scales, see <a class="wiki_link" href="/MOS%20scales%20of%2017edo">MOS scales of 17edo</a>, <a class="wiki_link" href="/31edo%20MOS%20scales">31edo MOS scales</a>, <a class="wiki_link" href="/MOS%20Scales%20of%2037edo">MOS Scales of 37edo</a>, and <a class="wiki_link" href="/MOS%20Scales%20of%20127edo">MOS Scales of 127edo</a>.<br /> | | For more images showing the hierarchical arrangement of MOS scales, see <a class="wiki_link" href="/MOS%20scales%20of%2017edo">MOS scales of 17edo</a>, <a class="wiki_link" href="/31edo%20MOS%20scales">31edo MOS scales</a>, <a class="wiki_link" href="/MOS%20Scales%20of%2037edo">MOS Scales of 37edo</a>, and <a class="wiki_link" href="/MOS%20Scales%20of%20127edo">MOS Scales of 127edo</a>.<br /> |
| <br /> | | <br /> |
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| When R is less than 1, it represents the ratio in (logarithmic) size between the smaller and the larger step. When it is greater than 1, it is larger/smaller. By replacing g with 1 - g if necessary, we can reduce always to the case where R&gt;1 (or R&lt;1 if we prefer.)<br /> | | When R is less than 1, it represents the ratio in (logarithmic) size between the smaller and the larger step. When it is greater than 1, it is larger/smaller. By replacing g with 1 - g if necessary, we can reduce always to the case where R&gt;1 (or R&lt;1 if we prefer.)<br /> |
| <br /> | | <br /> |
| <!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Catalog of MOS"></a><!-- ws:end:WikiTextHeadingRule:18 -->Catalog of MOS</h1> | | <!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Variations on MOS Scales"></a><!-- ws:end:WikiTextHeadingRule:18 -->Variations on MOS Scales</h1> |
| Below is a list of MOS with number of elements from 5 to 10, plus some of the more significant larger MOS.<br />
| |
| <br />
| |
| | |
| | |
| <table class="wiki_table">
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| <tr>
| |
| <td><a class="wiki_link" href="/PentatonicMOS">Pentatonic MOS</a><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><a class="wiki_link" href="/1L%204s">1L 4s</a><br />
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| </td>
| |
| <td><br />
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| </td>
| |
| <td><a class="wiki_link" href="/2L%203s">2L 3s</a><br />
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| </td>
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| <td><br />
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| </td>
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| <td><a class="wiki_link" href="/3L%202s">3L 2s</a><br />
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| </td>
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| <td><br />
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| </td>
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| <td><a class="wiki_link" href="/4L%201s">4L 1s</a><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
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| <tr>
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| <td><a class="wiki_link" href="/HexatonicMOS">Hexatonic MOS</a><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><a class="wiki_link" href="/1L%205s">1L 5s</a><br />
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| </td>
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| <td><br />
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| </td>
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| <td><a class="wiki_link" href="/2L%204s">2L 4s</a><br />
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| </td>
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| <td><br />
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| </td>
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| <td><a class="wiki_link" href="/3L%203s">3L 3s</a><br />
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| </td>
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| <td><br />
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| </td>
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| <td><a class="wiki_link" href="/4L%202s">4L 2s</a><br />
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| </td>
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| <td><br />
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| </td>
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| <td><a class="wiki_link" href="/5L%201s">5L 1s</a><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
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| <tr>
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| <td><a class="wiki_link" href="/HeptatonicMOS">Heptatonic MOS</a><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><a class="wiki_link" href="/1L%206s">1L 6s</a><br />
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| </td>
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| <td><br />
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| </td>
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| <td><a class="wiki_link" href="/2L%205s">2L 5s</a><br />
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| </td>
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| <td><br />
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| </td>
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| <td><a class="wiki_link" href="/3L%204s">3L 4s</a><br />
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| </td>
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| <td><br />
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| </td>
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| <td><a class="wiki_link" href="/4L%203s">4L 3s</a><br />
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| </td>
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| <td><br />
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| </td>
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| <td><a class="wiki_link" href="/5L%202s">5L 2s</a><br />
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| </td>
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| <td><br />
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| </td>
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| <td><a class="wiki_link" href="/6L%201s">6L 1s</a><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/OctatonicMOS">Octatonic MOS</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/1L%207s">1L 7s</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/2L%206s">2L 6s</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/3L%205s">3L 5s</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/4L%204s">4L 4s</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/5L%203s">5L 3s</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/6L%202s">6L 2s</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/7L%201s">7L 1s</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/NonatonicMOS">Nonatonic MOS</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/1L%208s">1L 8s</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/2L%207s">2L 7s</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/3L%206s">3L 6s</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/4L%205s">4L 5s</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/5L%204s">5L 4s</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/6L%203s">6L 3s</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/7L%202s">7L 2s</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/8L%201s">8L 1s</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/DecatonicMOS">Decatonic MOS</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/1L%209s">1L 9s</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/2L%208s">2L 8s</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/3L%207s">3L 7s</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/4L%206s">4L 6s</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/5L%205s">5L 5s</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/6L%204s">6L 4s</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/7L%203s">7L 3s</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/8L%202s">8L 2s</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/9L%201s">9L 1s</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/Hendecatonic%20MOS">Hendecatonic MOS</a><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/1L%2010s">1L 10s</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/2L%209s">2L 9s</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/3L%208s">3L 8s</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/4L%207s">4L 7s</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/5L%206s">5L 6s</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/6L%205s">6L 5s</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/7L%204s">7L 4s</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/8L%203s">8L 3s</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/9L%202s">9L 2s</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/10L%201s">10L 1s</a><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| Sensi[11] [<a class="wiki_link" href="/8L%203s">8L 3s</a>]<br />
| |
| Slendric[11] [<a class="wiki_link" href="/5L%206s">5L 6s</a>]<br />
| |
| Keemun[11] [<a class="wiki_link" href="/4L%207s">4L 7s</a>]<br />
| |
| <br />
| |
| Pajara[12] [<a class="wiki_link" href="/10L%202s">10L 2s</a>]<br />
| |
| Meantone[12] [<a class="wiki_link" href="/7L%205s">7L 5s</a>]<br />
| |
| Superpyth[12] [<a class="wiki_link" href="/5L%207s">5L 7s</a>]<br />
| |
| Augene[12] [<a class="wiki_link" href="/3L%209s">3L 9s</a>]<br />
| |
| Injera[12] [<a class="wiki_link" href="/2L%2010s">2L 10s</a>]<br />
| |
| <br />
| |
| Orwell[13] [<a class="wiki_link" href="/4L%209s">4L 9s</a>]<br />
| |
| Magic[13] [<a class="wiki_link" href="/3L%2010s">3L 10s</a>]<br />
| |
| <br />
| |
| See: <a class="wiki_link" href="/Tridecatonic%20MOS">Tridecatonic MOS</a><br />
| |
| <br />
| |
| Injera[14] [<a class="wiki_link" href="/12L%202s">12L 2s</a>]<br />
| |
| [WITNOTS{14}] [<a class="wiki_link" href="/11L%203s">11L 3s</a>]<br />
| |
| Godzilla[14] [<a class="wiki_link" href="/5L%209s">5L 9s</a>]<br />
| |
| Doublewide[14] [<a class="wiki_link" href="/4L%2010s">4L 10s</a>]<br />
| |
| <br />
| |
| Superkleismic[15] [<a class="wiki_link" href="/11L%204s">11L 4s</a>]<br />
| |
| Porcupine[15] [<a class="wiki_link" href="/7L%208s">7L 8s</a>]<br />
| |
| Myna[15] [<a class="wiki_link" href="/4L%2011s">4L 11s</a>]<br />
| |
| Valentine[15] [<a class="wiki_link" href="/1L%2014s">1L 14s</a>]<br />
| |
| <br />
| |
| Wizard[16] [<a class="wiki_link" href="/6L%2010s">6L 10s</a>]<br />
| |
| Mothra[16], Shoe[16] [<a class="wiki_link" href="/5L%2011s">5L 11s</a>]<br />
| |
| <br />
| |
| Squares[17] [<a class="wiki_link" href="/14L%203s">14L 3s</a>]<br />
| |
| Garibaldi[17] [<a class="wiki_link" href="/12L%205s">12L 5s</a>]<br />
| |
| Beatles[17] [<a class="wiki_link" href="/10L%207s">10L 7s</a>]<br />
| |
| Mohajira[17] [<a class="wiki_link" href="/7L%2010s">7L 10s</a>]<br />
| |
| <br />
| |
| Muggles[19] [<a class="wiki_link" href="/16L%203s">16L 3s</a>]<br />
| |
| Meantone[19] [<a class="wiki_link" href="/12L%207s">12L 7s</a>]<br />
| |
| Negri[19] [<a class="wiki_link" href="/10L%209s">10L 9s</a>]<br />
| |
| Sensi[19] [<a class="wiki_link" href="/8L%2011s">8L 11s</a>]<br />
| |
| Flattone[19] [<a class="wiki_link" href="/7L%2012s">7L 12s</a>]<br />
| |
| Hemiwuerschmidt[19] [<a class="wiki_link" href="/6L%2013s">6L 13s</a>]<br />
| |
| Myna[19] [<a class="wiki_link" href="/4L%2015s">4L 15s</a>]<br />
| |
| Magic[19] [<a class="wiki_link" href="/3L%2016s">3L 16s</a>]<br />
| |
| Tritonic[19] [<a class="wiki_link" href="/2L%2017s">2L 17s</a>]<br />
| |
| <br />
| |
| Roman[20] [<a class="wiki_link" href="/3L%2017s">3L 17s</a>]<br />
| |
| <br />
| |
| Miracle[21] [<a class="wiki_link" href="/10L%2011s">10L 11s</a>]<br />
| |
| Rodan[21] [<a class="wiki_link" href="/5L%2016s">5L 16s</a>]<br />
| |
| Tritonic[21] [<a class="wiki_link" href="/2L%2019s">2L 19s</a>]<br />
| |
| <br />
| |
| Magic[22] [<a class="wiki_link" href="/19L%203s">19L 3s</a>]<br />
| |
| Orwell[22] [<a class="wiki_link" href="/9L%2013s">9L 13s</a>]<br />
| |
| Wizard[22] [<a class="wiki_link" href="/6L%2016s">6L 16s</a>]<br />
| |
| Diaschismic[22] [<a class="wiki_link" href="/12L%2010s">12L 10s</a>]<br />
| |
| Shrutar[22] [<a class="wiki_link" href="/2L%2020s">2L 20s</a>]<br />
| |
| Coendou[22] [<a class="wiki_link" href="/7L%2015s">7L 15s</a>]<br />
| |
| <br />
| |
| Hemikleismic[23] [<a class="wiki_link" href="/15L%208s">15L 8s</a>]<br />
| |
| Unidec[23] [<a class="wiki_link" href="/13L%2010s">13L 10s</a>]<br />
| |
| Roman[23] [<a class="wiki_link" href="/3L%2020s">3L 20s</a>]<br />
| |
| <br />
| |
| Mohajira[24] [<a class="wiki_link" href="/7L%2017s">7L 17s</a>]<br />
| |
| <br />
| |
| Luna[25] [<a class="wiki_link" href="/6L%2019s">6L 19s</a>]<br />
| |
| <br />
| |
| Ennealimmal[27] [<a class="wiki_link" href="/18L%209s">18L 9s</a>]<br />
| |
| Octacot[27] [<a class="wiki_link" href="/14L%2013s">14L 13s</a>]<br />
| |
| <br />
| |
| Leapday[29], Grackle[29] [<a class="wiki_link" href="/17L%2012s">17L 12s</a>]<br />
| |
| Garibaldi[29] [<a class="wiki_link" href="/12L%2017s">12L 17s</a>]<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Variations on MOS Scales"></a><!-- ws:end:WikiTextHeadingRule:20 -->Variations on MOS Scales</h1>
| |
| <ol><li><a class="wiki_link" href="/MODMOS%20Scales">MODMOS Scales</a> are derived from chromatic alterations of one or more tones of an MOS scale, typically by the interval of L-s, the &quot;chroma&quot;.</li><li><a class="wiki_link" href="/Muddle">Muddles</a> are subsets of MOS parent scales with the general shape of a smaller (and possibly unrelated) MOS scale.</li><li><a class="wiki_link" href="/MOS%20Cradle">MOS Cradle</a> is a technique of embedding MOS-like structures inside MOS scales and may or may not produce subsets of MOS scales.</li></ol><br /> | | <ol><li><a class="wiki_link" href="/MODMOS%20Scales">MODMOS Scales</a> are derived from chromatic alterations of one or more tones of an MOS scale, typically by the interval of L-s, the &quot;chroma&quot;.</li><li><a class="wiki_link" href="/Muddle">Muddles</a> are subsets of MOS parent scales with the general shape of a smaller (and possibly unrelated) MOS scale.</li><li><a class="wiki_link" href="/MOS%20Cradle">MOS Cradle</a> is a technique of embedding MOS-like structures inside MOS scales and may or may not produce subsets of MOS scales.</li></ol><br /> |
| <!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="MOS As Applied To Rhythms"></a><!-- ws:end:WikiTextHeadingRule:22 -->MOS As Applied To Rhythms</h1> | | <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="MOS As Applied To Rhythms"></a><!-- ws:end:WikiTextHeadingRule:20 -->MOS As Applied To Rhythms</h1> |
| David Canright was the first to suggest Fibonacci Rhythms in 1/1. This lead to Kraig Grady to be the first to apply MOS patterns to rhythms. Two papers on the subject can be found here <a class="wiki_link_ext" href="http://anaphoria.com/hora.PDF" rel="nofollow">http://anaphoria.com/hora.PDF</a> and <a class="wiki_link_ext" href="http://anaphoria.com/horo2.PDF" rel="nofollow">http://anaphoria.com/horo2.PDF</a><br /> | | David Canright was the first to suggest Fibonacci Rhythms in 1/1. This lead to Kraig Grady to be the first to apply MOS patterns to rhythms. Two papers on the subject can be found here <a class="wiki_link_ext" href="http://anaphoria.com/hora.PDF" rel="nofollow">http://anaphoria.com/hora.PDF</a> and <a class="wiki_link_ext" href="http://anaphoria.com/horo2.PDF" rel="nofollow">http://anaphoria.com/horo2.PDF</a><br /> |
| MOS structures and thinking can be applied to the design of rhythms as well. See <a class="wiki_link" href="/MOS%20Rhythm%20Tutorial">MOS Rhythm Tutorial</a><br /> | | MOS structures and thinking can be applied to the design of rhythms as well. See <a class="wiki_link" href="/MOS%20Rhythm%20Tutorial">MOS Rhythm Tutorial</a><br /> |
| <br /> | | <br /> |
| <!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc12"><a name="Algorithms"></a><!-- ws:end:WikiTextHeadingRule:24 -->Algorithms</h1> | | <!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="Algorithms"></a><!-- ws:end:WikiTextHeadingRule:22 -->Algorithms</h1> |
| Below is some Maple code for various mathematical routines having to do with MOS. If you have access to Maple, you can of course copy and run these programs. Even if you do not, since Maple code makes better pseudocode than most languages or computer algebra packages afford, it can be used as pseudocode. For that purpose, it will be helpful to know that &quot;modp(x, n)&quot; means reducing x mod the integer n to 0, 1, ..., n-1 not only when x is an integer, but also when it is a rational number with denominator prime to n. In that case, p/q mod n = r means p = qr mod n.<br /> | | Below is some Maple code for various mathematical routines having to do with MOS. If you have access to Maple, you can of course copy and run these programs. Even if you do not, since Maple code makes better pseudocode than most languages or computer algebra packages afford, it can be used as pseudocode. For that purpose, it will be helpful to know that &quot;modp(x, n)&quot; means reducing x mod the integer n to 0, 1, ..., n-1 not only when x is an integer, but also when it is a rational number with denominator prime to n. In that case, p/q mod n = r means p = qr mod n.<br /> |
| <br /> | | <br /> |
| Line 937: |
Line 483: |
| evalf(w) end:<br /> | | evalf(w) end:<br /> |
| <br /> | | <br /> |
| <!-- ws:start:WikiTextHeadingRule:26:&lt;h2&gt; --><h2 id="toc13"><a name="Algorithms-MOSDiagrams"></a><!-- ws:end:WikiTextHeadingRule:26 --><a class="wiki_link" href="/MOSDiagrams">MOSDiagrams</a></h2> | | <!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Algorithms-MOSDiagrams"></a><!-- ws:end:WikiTextHeadingRule:24 --><a class="wiki_link" href="/MOSDiagrams">MOSDiagrams</a></h2> |
| </body></html></pre></div> | | </body></html></pre></div> |