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Wikispaces>Andrew_Heathwaite **Imported revision 23287421 - Original comment: I set some limits w/i which I intend to find every possible scale. ... .. .** |
Wikispaces>spt3125 **Imported revision 504166090 - 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: | : This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-04-23 19:02:31 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>504166090</tt>.<br> | ||
: The revision comment was: <tt> | : 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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">=Superparticular-Nonoctave-MOS= | <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;white-space: pre-wrap ! important" class="old-revision-html">=Superparticular-Nonoctave-MOS= | ||
NOTE: I haven't completed | NOTE: I haven't completed the list of scales on this page. Consider that part under construction. You can check the intro & the few scales I have in the meantime, though! | ||
... | ... | ||
A few years ago, inspired by a fantastic scale revealed by Jacky Ligon on | A few years ago, inspired by a fantastic scale revealed by Jacky Ligon on the nonoctave forum, I (Andrew Heathwaite) embarked on a quest to discover new scales that meet these three criteria: | ||
# [[Superparticular]] - meaning that | # [[Superparticular]] - meaning that the steps of the scale represent the intervals between adjacent notes in the harmonic series. You can identify these intervals easily, because they appear in the form //n/n-1.// Examples: 5:4, 7:6, 13:12, 41:40, etc. | ||
# [[Nonoctave]] - meaning that | # [[Nonoctave]] - meaning that the scale repeats at an interval other than an octave. In fact, for this project I wanted near-octaves, intervals like 1193 cents, 1221 cents, & so on. These intervals can sound very harsh, but they can also sound incredibly rich & dynamic. Timbre plays an important role here in making these near-octave intervals function as octaves. | ||
# [[MOSScales|Moment of Symmetry]] - meaning that | # [[MOSScales|Moment of Symmetry]] - meaning that the scale contains exactly two step sizes, spaced out as evenly as possible within the scale. Normally, you build MOS scales by continuously adding notes a given interval, called the generator, away from one another in one long chain until the resulting scale has only two step sizes. Pythagorean scales use 3/2 (the perfect fifth) as the generator. In 12edo, we can identify the standard pentatonic scale & the various diatonic scales as MOS scales because you can build them using a chain of fifths. | ||
Jacky Ligon's scale meets these three criteria. I will use it as an example: | Jacky Ligon's scale meets these three criteria. I will use it as an example: | ||
| Line 22: | Line 22: | ||
//Steps: 9:8, 12:11, 9:8, 12:11, 9:8, 12:11, 12:11// | //Steps: 9:8, 12:11, 9:8, 12:11, 9:8, 12:11, 12:11// | ||
# It | # It is superparticular because its intervals, 9/8 & 12/11, both fit the form //n/n-1//. | ||
# It | # It is nonoctave (more accurately, near-octave) because it repeats at 1214.2 cents. | ||
# It | # It is MOS because it contains exactly two step sizes, spaced out as evenly as possible within the scale. | ||
Inspired by | Inspired by the peculiar musical qualities of this scale, I set about looking for others, & found quite a few. I gave some of them quirky nicknames. I have since then embarked on a search for all scales of this type within these (admittedly arbitrary) limits: | ||
# Superparticular Limit: smallest interval: 41/40 = 42.8 cents. | # Superparticular Limit: smallest interval: 41/40 = 42.8 cents. | ||
| Line 32: | Line 32: | ||
# Moment of Symmetry Limit: greatest number of notes in a scale = 10. | # Moment of Symmetry Limit: greatest number of notes in a scale = 10. | ||
Even | Even with these limits in place, this produces a multitude of fascinating scales for our enjoyment & fascination. I invite you to play & share your results! | ||
==Pentatonic (5-note) Scales:== | ==Pentatonic (5-note) Scales:== | ||
| Line 41: | Line 41: | ||
SNM320614 : //6:5, 14:13, 6:5, 14:13, 6:5 = 1203.5 cents// | SNM320614 : //6:5, 14:13, 6:5, 14:13, 6:5 = 1203.5 cents// | ||
SNM320615 : //6:5, 15:14, 6:5, 15:14, 6:5 = 1185.8 cents// | SNM320615 : //6:5, 15:14, 6:5, 15:14, 6:5 = 1185.8 cents// | ||
==Heptatonic (7-note) Scales:== | ==Heptatonic (7-note) Scales:== | ||
===MOS 2+5 : sLsssLs=== | ===MOS 2+5 : sLsssLs=== | ||
| Line 70: | Line 71: | ||
<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>Superparticular-Nonoctave-MOS</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Superparticular-Nonoctave-MOS"></a><!-- ws:end:WikiTextHeadingRule:0 -->Superparticular-Nonoctave-MOS</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>Superparticular-Nonoctave-MOS</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Superparticular-Nonoctave-MOS"></a><!-- ws:end:WikiTextHeadingRule:0 -->Superparticular-Nonoctave-MOS</h1> | ||
<br /> | <br /> | ||
NOTE: I haven't completed | NOTE: I haven't completed the list of scales on this page. Consider that part under construction. You can check the intro &amp; the few scales I have in the meantime, though!<br /> | ||
<br /> | <br /> | ||
...<br /> | ...<br /> | ||
<br /> | <br /> | ||
A few years ago, inspired by a fantastic scale revealed by Jacky Ligon on | A few years ago, inspired by a fantastic scale revealed by Jacky Ligon on the nonoctave forum, I (Andrew Heathwaite) embarked on a quest to discover new scales that meet these three criteria:<br /> | ||
<br /> | <br /> | ||
<ol><li><a class="wiki_link" href="/Superparticular">Superparticular</a> - meaning that | <ol><li><a class="wiki_link" href="/Superparticular">Superparticular</a> - meaning that the steps of the scale represent the intervals between adjacent notes in the harmonic series. You can identify these intervals easily, because they appear in the form <em>n/n-1.</em> Examples: 5:4, 7:6, 13:12, 41:40, etc.</li><li><a class="wiki_link" href="/Nonoctave">Nonoctave</a> - meaning that the scale repeats at an interval other than an octave. In fact, for this project I wanted near-octaves, intervals like 1193 cents, 1221 cents, &amp; so on. These intervals can sound very harsh, but they can also sound incredibly rich &amp; dynamic. Timbre plays an important role here in making these near-octave intervals function as octaves.</li><li><a class="wiki_link" href="/MOSScales">Moment of Symmetry</a> - meaning that the scale contains exactly two step sizes, spaced out as evenly as possible within the scale. Normally, you build MOS scales by continuously adding notes a given interval, called the generator, away from one another in one long chain until the resulting scale has only two step sizes. Pythagorean scales use 3/2 (the perfect fifth) as the generator. In 12edo, we can identify the standard pentatonic scale &amp; the various diatonic scales as MOS scales because you can build them using a chain of fifths.</li></ol><br /> | ||
Jacky Ligon's scale meets these three criteria. I will use it as an example:<br /> | Jacky Ligon's scale meets these three criteria. I will use it as an example:<br /> | ||
<br /> | <br /> | ||
<em>Steps: 9:8, 12:11, 9:8, 12:11, 9:8, 12:11, 12:11</em><br /> | <em>Steps: 9:8, 12:11, 9:8, 12:11, 9:8, 12:11, 12:11</em><br /> | ||
<br /> | <br /> | ||
<ol><li>It | <ol><li>It is superparticular because its intervals, 9/8 &amp; 12/11, both fit the form <em>n/n-1</em>.</li><li>It is nonoctave (more accurately, near-octave) because it repeats at 1214.2 cents.</li><li>It is MOS because it contains exactly two step sizes, spaced out as evenly as possible within the scale.</li></ol><br /> | ||
Inspired by | Inspired by the peculiar musical qualities of this scale, I set about looking for others, &amp; found quite a few. I gave some of them quirky nicknames. I have since then embarked on a search for all scales of this type within these (admittedly arbitrary) limits:<br /> | ||
<br /> | <br /> | ||
<ol><li>Superparticular Limit: smallest interval: 41/40 = 42.8 cents.</li><li>Nonoctave Limit: greatest deviation from octave allowed = 25 cents.</li><li>Moment of Symmetry Limit: greatest number of notes in a scale = 10.</li></ol><br /> | <ol><li>Superparticular Limit: smallest interval: 41/40 = 42.8 cents.</li><li>Nonoctave Limit: greatest deviation from octave allowed = 25 cents.</li><li>Moment of Symmetry Limit: greatest number of notes in a scale = 10.</li></ol><br /> | ||
Even | Even with these limits in place, this produces a multitude of fascinating scales for our enjoyment &amp; fascination. I invite you to play &amp; share your results!<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Superparticular-Nonoctave-MOS-Pentatonic (5-note) Scales:"></a><!-- ws:end:WikiTextHeadingRule:2 -->Pentatonic (5-note) Scales:</h2> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Superparticular-Nonoctave-MOS-Pentatonic (5-note) Scales:"></a><!-- ws:end:WikiTextHeadingRule:2 -->Pentatonic (5-note) Scales:</h2> | ||
| Line 94: | Line 95: | ||
SNM320614 : <em>6:5, 14:13, 6:5, 14:13, 6:5 = 1203.5 cents</em><br /> | SNM320614 : <em>6:5, 14:13, 6:5, 14:13, 6:5 = 1203.5 cents</em><br /> | ||
SNM320615 : <em>6:5, 15:14, 6:5, 15:14, 6:5 = 1185.8 cents</em><br /> | SNM320615 : <em>6:5, 15:14, 6:5, 15:14, 6:5 = 1185.8 cents</em><br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Superparticular-Nonoctave-MOS-Heptatonic (7-note) Scales:"></a><!-- ws:end:WikiTextHeadingRule:8 -->Heptatonic (7-note) Scales:</h2> | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Superparticular-Nonoctave-MOS-Heptatonic (7-note) Scales:"></a><!-- ws:end:WikiTextHeadingRule:8 -->Heptatonic (7-note) Scales:</h2> | ||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="Superparticular-Nonoctave-MOS-Heptatonic (7-note) Scales:-MOS 2+5 : sLsssLs"></a><!-- ws:end:WikiTextHeadingRule:10 -->MOS 2+5 : sLsssLs</h3> | <!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="Superparticular-Nonoctave-MOS-Heptatonic (7-note) Scales:-MOS 2+5 : sLsssLs"></a><!-- ws:end:WikiTextHeadingRule:10 -->MOS 2+5 : sLsssLs</h3> | ||
Revision as of 19:02, 23 April 2014
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author spt3125 and made on 2014-04-23 19:02:31 UTC.
- The original revision id was 504166090.
- 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:
=Superparticular-Nonoctave-MOS= NOTE: I haven't completed the list of scales on this page. Consider that part under construction. You can check the intro & the few scales I have in the meantime, though! ... A few years ago, inspired by a fantastic scale revealed by Jacky Ligon on the nonoctave forum, I (Andrew Heathwaite) embarked on a quest to discover new scales that meet these three criteria: # [[Superparticular]] - meaning that the steps of the scale represent the intervals between adjacent notes in the harmonic series. You can identify these intervals easily, because they appear in the form //n/n-1.// Examples: 5:4, 7:6, 13:12, 41:40, etc. # [[Nonoctave]] - meaning that the scale repeats at an interval other than an octave. In fact, for this project I wanted near-octaves, intervals like 1193 cents, 1221 cents, & so on. These intervals can sound very harsh, but they can also sound incredibly rich & dynamic. Timbre plays an important role here in making these near-octave intervals function as octaves. # [[MOSScales|Moment of Symmetry]] - meaning that the scale contains exactly two step sizes, spaced out as evenly as possible within the scale. Normally, you build MOS scales by continuously adding notes a given interval, called the generator, away from one another in one long chain until the resulting scale has only two step sizes. Pythagorean scales use 3/2 (the perfect fifth) as the generator. In 12edo, we can identify the standard pentatonic scale & the various diatonic scales as MOS scales because you can build them using a chain of fifths. Jacky Ligon's scale meets these three criteria. I will use it as an example: //Steps: 9:8, 12:11, 9:8, 12:11, 9:8, 12:11, 12:11// # It is superparticular because its intervals, 9/8 & 12/11, both fit the form //n/n-1//. # It is nonoctave (more accurately, near-octave) because it repeats at 1214.2 cents. # It is MOS because it contains exactly two step sizes, spaced out as evenly as possible within the scale. Inspired by the peculiar musical qualities of this scale, I set about looking for others, & found quite a few. I gave some of them quirky nicknames. I have since then embarked on a search for all scales of this type within these (admittedly arbitrary) limits: # Superparticular Limit: smallest interval: 41/40 = 42.8 cents. # Nonoctave Limit: greatest deviation from octave allowed = 25 cents. # Moment of Symmetry Limit: greatest number of notes in a scale = 10. Even with these limits in place, this produces a multitude of fascinating scales for our enjoyment & fascination. I invite you to play & share your results! ==Pentatonic (5-note) Scales:== ===MOS 2+3 : sLsLs=== [[SNM230513]] : //13:12, 5:4, 13:12, 5:4, 13:12 = 1188.3 cents// SNM230610 : //10:9, 6:5, 10:9, 6:5, 10:9 = 1178.5 cents// ===MOS 3+2 : LsLsL=== SNM320614 : //6:5, 14:13, 6:5, 14:13, 6:5 = 1203.5 cents// SNM320615 : //6:5, 15:14, 6:5, 15:14, 6:5 = 1185.8 cents// ==Heptatonic (7-note) Scales:== ===MOS 2+5 : sLsssLs=== [[SNM250520]] : //20:19, 5:4, 20:19, 20:19, 20:19, 5:4, 20:19 = 1216.6 cents// [[SNM250521]] : //21:20, 5:4, 21:20, 21:20, 21:20, 5:4, 21:20 = 1195.0 cents (nickname: Mercury Sand)// SNM250616 : //16:15, 6:5, 16:15, 16:15, 16:15, 6:5, 16:15 = 1189.9 cents// ===MOS 3+4 : sLsLsLs=== ===MOS 4+3 : LsLsLsL=== ===MOS 5+2 : LsLLLsL=== ==Octatonic (8-note) Scales:== ===MOS 3+5 : sLssLsLs=== ===MOS 5+3 : LsLLsLsL=== ==Nonatonic (9-note) Scales:== ===MOS 2+7 : ssLsssLss=== [[SNM270528]] : //28:27, 28:27, 5:4, 28:27, 28:27, 28:27, 5:4, 28:27, 28:27 = 1213.4 cents// [[SNM270529]] : //29:28, 29:28, 5:4, 29:28, 29:28, 29:28, 5:4, 29:28, 29:28 = 1197.9 cents// [[SNM270530]] : //30:29, 30:29, 5:4, 30:29, 30:29, 30:29, 5:4, 30:29, 30:29 = 1183.5 cents// SNM270622 : //22:21, 22:21, 6:5, 22:21, 22:21, 22:21, 6:5, 22:21, 22:21 = 1195.0 cents// ===MOS 4+5 : LsLsLsLsL=== ===MOS 5+4 : sLsLsLsLs=== ===MOS 7+2 : LLsLLLsLL=== ==Dekatonic (10-note) Scales:== ===MOS 3+7 : sLsssLssLs=== ===MOS 7+3 : LsLLLsLLsL===
Original HTML content:
<html><head><title>Superparticular-Nonoctave-MOS</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Superparticular-Nonoctave-MOS"></a><!-- ws:end:WikiTextHeadingRule:0 -->Superparticular-Nonoctave-MOS</h1> <br /> NOTE: I haven't completed the list of scales on this page. Consider that part under construction. You can check the intro & the few scales I have in the meantime, though!<br /> <br /> ...<br /> <br /> A few years ago, inspired by a fantastic scale revealed by Jacky Ligon on the nonoctave forum, I (Andrew Heathwaite) embarked on a quest to discover new scales that meet these three criteria:<br /> <br /> <ol><li><a class="wiki_link" href="/Superparticular">Superparticular</a> - meaning that the steps of the scale represent the intervals between adjacent notes in the harmonic series. You can identify these intervals easily, because they appear in the form <em>n/n-1.</em> Examples: 5:4, 7:6, 13:12, 41:40, etc.</li><li><a class="wiki_link" href="/Nonoctave">Nonoctave</a> - meaning that the scale repeats at an interval other than an octave. In fact, for this project I wanted near-octaves, intervals like 1193 cents, 1221 cents, & so on. These intervals can sound very harsh, but they can also sound incredibly rich & dynamic. Timbre plays an important role here in making these near-octave intervals function as octaves.</li><li><a class="wiki_link" href="/MOSScales">Moment of Symmetry</a> - meaning that the scale contains exactly two step sizes, spaced out as evenly as possible within the scale. Normally, you build MOS scales by continuously adding notes a given interval, called the generator, away from one another in one long chain until the resulting scale has only two step sizes. Pythagorean scales use 3/2 (the perfect fifth) as the generator. In 12edo, we can identify the standard pentatonic scale & the various diatonic scales as MOS scales because you can build them using a chain of fifths.</li></ol><br /> Jacky Ligon's scale meets these three criteria. I will use it as an example:<br /> <br /> <em>Steps: 9:8, 12:11, 9:8, 12:11, 9:8, 12:11, 12:11</em><br /> <br /> <ol><li>It is superparticular because its intervals, 9/8 & 12/11, both fit the form <em>n/n-1</em>.</li><li>It is nonoctave (more accurately, near-octave) because it repeats at 1214.2 cents.</li><li>It is MOS because it contains exactly two step sizes, spaced out as evenly as possible within the scale.</li></ol><br /> Inspired by the peculiar musical qualities of this scale, I set about looking for others, & found quite a few. I gave some of them quirky nicknames. I have since then embarked on a search for all scales of this type within these (admittedly arbitrary) limits:<br /> <br /> <ol><li>Superparticular Limit: smallest interval: 41/40 = 42.8 cents.</li><li>Nonoctave Limit: greatest deviation from octave allowed = 25 cents.</li><li>Moment of Symmetry Limit: greatest number of notes in a scale = 10.</li></ol><br /> Even with these limits in place, this produces a multitude of fascinating scales for our enjoyment & fascination. I invite you to play & share your results!<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="Superparticular-Nonoctave-MOS-Pentatonic (5-note) Scales:"></a><!-- ws:end:WikiTextHeadingRule:2 -->Pentatonic (5-note) Scales:</h2> <!-- ws:start:WikiTextHeadingRule:4:<h3> --><h3 id="toc2"><a name="Superparticular-Nonoctave-MOS-Pentatonic (5-note) Scales:-MOS 2+3 : sLsLs"></a><!-- ws:end:WikiTextHeadingRule:4 -->MOS 2+3 : sLsLs</h3> <a class="wiki_link" href="/SNM230513">SNM230513</a> : <em>13:12, 5:4, 13:12, 5:4, 13:12 = 1188.3 cents</em><br /> SNM230610 : <em>10:9, 6:5, 10:9, 6:5, 10:9 = 1178.5 cents</em><br /> <!-- ws:start:WikiTextHeadingRule:6:<h3> --><h3 id="toc3"><a name="Superparticular-Nonoctave-MOS-Pentatonic (5-note) Scales:-MOS 3+2 : LsLsL"></a><!-- ws:end:WikiTextHeadingRule:6 -->MOS 3+2 : LsLsL</h3> SNM320614 : <em>6:5, 14:13, 6:5, 14:13, 6:5 = 1203.5 cents</em><br /> SNM320615 : <em>6:5, 15:14, 6:5, 15:14, 6:5 = 1185.8 cents</em><br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><a name="Superparticular-Nonoctave-MOS-Heptatonic (7-note) Scales:"></a><!-- ws:end:WikiTextHeadingRule:8 -->Heptatonic (7-note) Scales:</h2> <!-- ws:start:WikiTextHeadingRule:10:<h3> --><h3 id="toc5"><a name="Superparticular-Nonoctave-MOS-Heptatonic (7-note) Scales:-MOS 2+5 : sLsssLs"></a><!-- ws:end:WikiTextHeadingRule:10 -->MOS 2+5 : sLsssLs</h3> <a class="wiki_link" href="/SNM250520">SNM250520</a> : <em>20:19, 5:4, 20:19, 20:19, 20:19, 5:4, 20:19 = 1216.6 cents</em><br /> <a class="wiki_link" href="/SNM250521">SNM250521</a> : <em>21:20, 5:4, 21:20, 21:20, 21:20, 5:4, 21:20 = 1195.0 cents (nickname: Mercury Sand)</em><br /> SNM250616 : <em>16:15, 6:5, 16:15, 16:15, 16:15, 6:5, 16:15 = 1189.9 cents</em><br /> <!-- ws:start:WikiTextHeadingRule:12:<h3> --><h3 id="toc6"><a name="Superparticular-Nonoctave-MOS-Heptatonic (7-note) Scales:-MOS 3+4 : sLsLsLs"></a><!-- ws:end:WikiTextHeadingRule:12 -->MOS 3+4 : sLsLsLs</h3> <!-- ws:start:WikiTextHeadingRule:14:<h3> --><h3 id="toc7"><a name="Superparticular-Nonoctave-MOS-Heptatonic (7-note) Scales:-MOS 4+3 : LsLsLsL"></a><!-- ws:end:WikiTextHeadingRule:14 -->MOS 4+3 : LsLsLsL</h3> <!-- ws:start:WikiTextHeadingRule:16:<h3> --><h3 id="toc8"><a name="Superparticular-Nonoctave-MOS-Heptatonic (7-note) Scales:-MOS 5+2 : LsLLLsL"></a><!-- ws:end:WikiTextHeadingRule:16 -->MOS 5+2 : LsLLLsL</h3> <br /> <!-- ws:start:WikiTextHeadingRule:18:<h2> --><h2 id="toc9"><a name="Superparticular-Nonoctave-MOS-Octatonic (8-note) Scales:"></a><!-- ws:end:WikiTextHeadingRule:18 -->Octatonic (8-note) Scales:</h2> <!-- ws:start:WikiTextHeadingRule:20:<h3> --><h3 id="toc10"><a name="Superparticular-Nonoctave-MOS-Octatonic (8-note) Scales:-MOS 3+5 : sLssLsLs"></a><!-- ws:end:WikiTextHeadingRule:20 -->MOS 3+5 : sLssLsLs</h3> <!-- ws:start:WikiTextHeadingRule:22:<h3> --><h3 id="toc11"><a name="Superparticular-Nonoctave-MOS-Octatonic (8-note) Scales:-MOS 5+3 : LsLLsLsL"></a><!-- ws:end:WikiTextHeadingRule:22 -->MOS 5+3 : LsLLsLsL</h3> <br /> <!-- ws:start:WikiTextHeadingRule:24:<h2> --><h2 id="toc12"><a name="Superparticular-Nonoctave-MOS-Nonatonic (9-note) Scales:"></a><!-- ws:end:WikiTextHeadingRule:24 -->Nonatonic (9-note) Scales:</h2> <!-- ws:start:WikiTextHeadingRule:26:<h3> --><h3 id="toc13"><a name="Superparticular-Nonoctave-MOS-Nonatonic (9-note) Scales:-MOS 2+7 : ssLsssLss"></a><!-- ws:end:WikiTextHeadingRule:26 -->MOS 2+7 : ssLsssLss</h3> <a class="wiki_link" href="/SNM270528">SNM270528</a> : <em>28:27, 28:27, 5:4, 28:27, 28:27, 28:27, 5:4, 28:27, 28:27 = 1213.4 cents</em><br /> <a class="wiki_link" href="/SNM270529">SNM270529</a> : <em>29:28, 29:28, 5:4, 29:28, 29:28, 29:28, 5:4, 29:28, 29:28 = 1197.9 cents</em><br /> <a class="wiki_link" href="/SNM270530">SNM270530</a> : <em>30:29, 30:29, 5:4, 30:29, 30:29, 30:29, 5:4, 30:29, 30:29 = 1183.5 cents</em><br /> SNM270622 : <em>22:21, 22:21, 6:5, 22:21, 22:21, 22:21, 6:5, 22:21, 22:21 = 1195.0 cents</em><br /> <!-- ws:start:WikiTextHeadingRule:28:<h3> --><h3 id="toc14"><a name="Superparticular-Nonoctave-MOS-Nonatonic (9-note) Scales:-MOS 4+5 : LsLsLsLsL"></a><!-- ws:end:WikiTextHeadingRule:28 -->MOS 4+5 : LsLsLsLsL</h3> <!-- ws:start:WikiTextHeadingRule:30:<h3> --><h3 id="toc15"><a name="Superparticular-Nonoctave-MOS-Nonatonic (9-note) Scales:-MOS 5+4 : sLsLsLsLs"></a><!-- ws:end:WikiTextHeadingRule:30 -->MOS 5+4 : sLsLsLsLs</h3> <!-- ws:start:WikiTextHeadingRule:32:<h3> --><h3 id="toc16"><a name="Superparticular-Nonoctave-MOS-Nonatonic (9-note) Scales:-MOS 7+2 : LLsLLLsLL"></a><!-- ws:end:WikiTextHeadingRule:32 -->MOS 7+2 : LLsLLLsLL</h3> <br /> <!-- ws:start:WikiTextHeadingRule:34:<h2> --><h2 id="toc17"><a name="Superparticular-Nonoctave-MOS-Dekatonic (10-note) Scales:"></a><!-- ws:end:WikiTextHeadingRule:34 -->Dekatonic (10-note) Scales:</h2> <!-- ws:start:WikiTextHeadingRule:36:<h3> --><h3 id="toc18"><a name="Superparticular-Nonoctave-MOS-Dekatonic (10-note) Scales:-MOS 3+7 : sLsssLssLs"></a><!-- ws:end:WikiTextHeadingRule:36 -->MOS 3+7 : sLsssLssLs</h3> <!-- ws:start:WikiTextHeadingRule:38:<h3> --><h3 id="toc19"><a name="Superparticular-Nonoctave-MOS-Dekatonic (10-note) Scales:-MOS 7+3 : LsLLLsLLsL"></a><!-- ws:end:WikiTextHeadingRule:38 -->MOS 7+3 : LsLLLsLLsL</h3> </body></html>