Superparticular-Nonoctave-MOS
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=Superparticular-Nonoctave-MOS= A few years ago, inspired by a fantastic scale revealed by Jacky Ligon on th nonoctave forum, I (Andrew Heathwaite) embarked on a quest to discover scales that meet these three criteria: 1. [[Superparticular]] - meaning that th steps of th scale represent th intervals between adjacent notes in th harmonic series. You can identify these intervals easily, because they appear in th form //n/n-1.// Examples: 5/4, 7/6, 13/12, 122/121, etc. 2. [[Nonoctave]] - meaning that th 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. 3. [[Moment of Symmetry]] - meaning that th scale contain exactly two step sizes, spaced out as evenly as possible w/i th scale. Normally, you build MOS scales by continuously adding notes a given interval, called th generator, away from one another in one long chain until th resulting scale has only two step sizes. Pythagorean scales use 3/2 (th perfect fifth) as th generator. In 12edo, we can identify th standard pentatonic scale & th 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 fits as Superparticular because its intervals, 9/8 & 12/11, both fit th form //n/n-1//. It fits as nonoctave (more accurately, near-octave) because it repeats at 1214.2 cents. It fits as MOS because it contains exactly two step sizes, spaced out as evenly as possible w/i th scale. Inspired by th peculiar musical qualities of this scale, I set about looking for others, & found quite a few. I gave some of them quirky nicknames. No doubt, I have missed some interesting ones, so if you do come across some scales of this type, do add them to this list, I implore you! I invite you to play & share yr results! ===Pentatonic:=== [[SNM-05-13]] 13/12, 5/4, 13/12, 5/4, 13/12 = 1188.3 cents [[SNM-06-14]] 6/5,14/13,6/5,14/13,6/5 = 1203.5 cents [[SNM-07-09]] 7/6,9/8,7/6,9/8,7/6 = 1208.4 cents ===Heptatonic:=== === === [[SNM-05-21]] : Mercury Sand 21/20, 5/4, 21/20, 21/20, 21/20, 5/4, 21/20 = 1195.0 cents [[SNM-07-18]] : Philter 18/17, 7/6, 18/17, 7/6, 18/17, 7/6, 18/17 = 1196.4 cents [[SNM-08-14]] : Temple Stones 14/13, 8/7, 14/13, 8/7, 14/13, 8/7, 14/13 = 1206.7 cents [[SNM-08-20]] 8/7, 20/19, 8/7, 20/19, 8/7, 20/19, 8/7 = 1191.1 cents [[SNM-09-12]] : Jacky Ligon's scale 9/8, 12/11, 9/8, 12/11, 9/8, 12/11, 12/11 = 1214.2 cents ===Octatonic:=== [[SNM-09-32]] : Snowflake 9/8, 9/8, 32/31, 9/8, 9/8, 32/31, 9/8, 32/31 = 1184.4 cents [[SNM-10-19]] 10/9, 10/9, 19/18, 10/9, 10/9, 19/18, 10/9, 19/18 = 1192.8 cents [[SNM-11-13]] 13/12, 13/12, 11/10, 13/12, 13/12, 11/10, 13/12, 11/10 = 1187.9 cents ===Nonatonic:=== [[SNM-12-23]] 12/11, 12/11, 23/22, 12/11, 12/11, 12/11, 23/22, 12/11, 12/11 = 1208.3 cents ===Dekatonic:=== [[SNM-11-18]] : Philter 2 18/17, 18/17, 18/17, 11/10, 18/17, 18/17, 11/10, 18/17, 18/17, 11/10 = 1187.7 cents ===Hendekatonic:=== ====[[SNM-11-40]] : Rollalong==== 11/10, 40/39, 11/10, 40/39, 11/10, 40/39, 11/10, 40/39, 11/10, 40/39, 11/10 = 1209.2 cents
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 /> A few years ago, inspired by a fantastic scale revealed by Jacky Ligon on th nonoctave forum, I (Andrew Heathwaite) embarked on a quest to discover scales that meet these three criteria:<br /> <br /> 1. <a class="wiki_link" href="/Superparticular">Superparticular</a> - meaning that th steps of th scale represent th intervals between adjacent notes in th harmonic series. You can identify these intervals easily, because they appear in th form <em>n/n-1.</em> Examples: 5/4, 7/6, 13/12, 122/121, etc.<br /> <br /> 2. <a class="wiki_link" href="/Nonoctave">Nonoctave</a> - meaning that th 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.<br /> <br /> 3. <a class="wiki_link" href="/Moment%20of%20Symmetry">Moment of Symmetry</a> - meaning that th scale contain exactly two step sizes, spaced out as evenly as possible w/i th scale. Normally, you build MOS scales by continuously adding notes a given interval, called th generator, away from one another in one long chain until th resulting scale has only two step sizes. Pythagorean scales use 3/2 (th perfect fifth) as th generator. In 12edo, we can identify th standard pentatonic scale & th various diatonic scales as MOS scales because you can build them using a chain of fifths.<br /> <br /> Jacky Ligon's scale meets these three criteria. I will use it as an example:<br /> <br /> Steps:<br /> 9/8, 12/11, 9/8, 12/11, 9/8, 12/11, 12/11<br /> <br /> It fits as Superparticular because its intervals, 9/8 & 12/11, both fit th form <em>n/n-1</em>.<br /> It fits as nonoctave (more accurately, near-octave) because it repeats at 1214.2 cents.<br /> It fits as MOS because it contains exactly two step sizes, spaced out as evenly as possible w/i th scale.<br /> <br /> Inspired by th peculiar musical qualities of this scale, I set about looking for others, & found quite a few. I gave some of them quirky nicknames. No doubt, I have missed some interesting ones, so if you do come across some scales of this type, do add them to this list, I implore you!<br /> <br /> I invite you to play & share yr results!<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h3> --><h3 id="toc1"><a name="Superparticular-Nonoctave-MOS--Pentatonic:"></a><!-- ws:end:WikiTextHeadingRule:2 -->Pentatonic:</h3> <a class="wiki_link" href="/SNM-05-13">SNM-05-13</a><br /> 13/12, 5/4, 13/12, 5/4, 13/12 = 1188.3 cents<br /> <br /> <a class="wiki_link" href="/SNM-06-14">SNM-06-14</a><br /> 6/5,14/13,6/5,14/13,6/5 = 1203.5 cents<br /> <br /> <a class="wiki_link" href="/SNM-07-09">SNM-07-09</a><br /> 7/6,9/8,7/6,9/8,7/6 = 1208.4 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h3> --><h3 id="toc2"><a name="Superparticular-Nonoctave-MOS--Heptatonic:"></a><!-- ws:end:WikiTextHeadingRule:4 -->Heptatonic:</h3> <!-- ws:start:WikiTextHeadingRule:6:<h3> --><h3 id="toc3"><!-- ws:end:WikiTextHeadingRule:6 --> </h3> <a class="wiki_link" href="/SNM-05-21">SNM-05-21</a> : Mercury Sand<br /> 21/20, 5/4, 21/20, 21/20, 21/20, 5/4, 21/20 = 1195.0 cents<br /> <br /> <a class="wiki_link" href="/SNM-07-18">SNM-07-18</a> : Philter<br /> 18/17, 7/6, 18/17, 7/6, 18/17, 7/6, 18/17 = 1196.4 cents<br /> <br /> <a class="wiki_link" href="/SNM-08-14">SNM-08-14</a> : Temple Stones<br /> 14/13, 8/7, 14/13, 8/7, 14/13, 8/7, 14/13 = 1206.7 cents<br /> <br /> <a class="wiki_link" href="/SNM-08-20">SNM-08-20</a><br /> 8/7, 20/19, 8/7, 20/19, 8/7, 20/19, 8/7 = 1191.1 cents<br /> <br /> <a class="wiki_link" href="/SNM-09-12">SNM-09-12</a> : Jacky Ligon's scale<br /> 9/8, 12/11, 9/8, 12/11, 9/8, 12/11, 12/11 = 1214.2 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h3> --><h3 id="toc4"><a name="Superparticular-Nonoctave-MOS--Octatonic:"></a><!-- ws:end:WikiTextHeadingRule:8 -->Octatonic:</h3> <a class="wiki_link" href="/SNM-09-32">SNM-09-32</a> : Snowflake<br /> 9/8, 9/8, 32/31, 9/8, 9/8, 32/31, 9/8, 32/31 = 1184.4 cents<br /> <br /> <a class="wiki_link" href="/SNM-10-19">SNM-10-19</a><br /> 10/9, 10/9, 19/18, 10/9, 10/9, 19/18, 10/9, 19/18 = 1192.8 cents<br /> <br /> <a class="wiki_link" href="/SNM-11-13">SNM-11-13</a><br /> 13/12, 13/12, 11/10, 13/12, 13/12, 11/10, 13/12, 11/10 = 1187.9 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h3> --><h3 id="toc5"><a name="Superparticular-Nonoctave-MOS--Nonatonic:"></a><!-- ws:end:WikiTextHeadingRule:10 -->Nonatonic:</h3> <a class="wiki_link" href="/SNM-12-23">SNM-12-23</a><br /> 12/11, 12/11, 23/22, 12/11, 12/11, 12/11, 23/22, 12/11, 12/11 = 1208.3 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h3> --><h3 id="toc6"><a name="Superparticular-Nonoctave-MOS--Dekatonic:"></a><!-- ws:end:WikiTextHeadingRule:12 -->Dekatonic:</h3> <a class="wiki_link" href="/SNM-11-18">SNM-11-18</a> : Philter 2<br /> 18/17, 18/17, 18/17, 11/10, 18/17, 18/17, 11/10, 18/17, 18/17, 11/10 = 1187.7 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h3> --><h3 id="toc7"><a name="Superparticular-Nonoctave-MOS--Hendekatonic:"></a><!-- ws:end:WikiTextHeadingRule:14 -->Hendekatonic:</h3> <!-- ws:start:WikiTextHeadingRule:16:<h4> --><h4 id="toc8"><a name="Superparticular-Nonoctave-MOS--Hendekatonic:-SNM-11-40 : Rollalong"></a><!-- ws:end:WikiTextHeadingRule:16 --><a class="wiki_link" href="/SNM-11-40">SNM-11-40</a> : Rollalong</h4> 11/10, 40/39, 11/10, 40/39, 11/10, 40/39, 11/10, 40/39, 11/10, 40/39, 11/10 = 1209.2 cents</body></html>