Superparticular-Nonoctave-MOS: Difference between revisions

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: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2008-04-27 03:57:35 UTC</tt>.<br>

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<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=

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, &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.

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 &amp; 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:

It fits as MOS because it contains exactly two step sizes, spaced out as evenly as possible w/i th scale.

===Pentatonic:===  

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

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:===  

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:===  

===Dekatonic:===  

====[[SNM-11-40]] : Rollalong====

<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Superparticular-Nonoctave-MOS&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Superparticular-Nonoctave-MOS"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Superparticular-Nonoctave-MOS&lt;/h1&gt;

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:&lt;br /&gt;

1. &lt;a class="wiki_link" href="/Superparticular"&gt;Superparticular&lt;/a&gt; - 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 &lt;em&gt;n/n-1.&lt;/em&gt; Examples: 5/4, 7/6, 13/12, 122/121, etc.&lt;br /&gt;

2. &lt;a class="wiki_link" href="/Nonoctave"&gt;Nonoctave&lt;/a&gt; - 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, &amp;amp; so on. These intervals can sound very harsh, but they can also sound incredibly rich &amp;amp; dynamic. Timbre plays an important role here in making these near-octave intervals function as octaves.&lt;br /&gt;

Steps:&lt;br /&gt;

It fits as Superparticular because its intervals, 9/8 &amp;amp; 12/11, both fit th form &lt;em&gt;n/n-1&lt;/em&gt;.&lt;br /&gt;

Inspired by th peculiar musical qualities of this scale, I set about looking for others, &amp;amp; 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!&lt;br /&gt;