Superparticular-Nonoctave-MOS: Difference between revisions

: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2008-05-01 23:31:07 UTC</tt>.<br>

: The original revision id was <tt>23287421</tt>.<br>

: The revision comment was: <tt>I set some limits w/i which I intend to find every possible scale. ... .. .</tt><br>

NOTE: I haven't completed th list of scales on this page. Consider that part under construction. You can check th intro &amp; th few scales I have in th meantime, tho!

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 new scales that meet these three criteria:

# [[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, 41:40, etc.

# [[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.

# [[MOSScales|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.

# It fits as Superparticular because its intervals, 9/8 &amp; 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, &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 w/i these (admittedly arbitrary) limits:

Even w/ these limits in place, this produces a multitude of fascinating scales for our enjoyment &amp; fascination. I invite you to play &amp; share yr results!

NOTE: I haven't completed th list of scales on this page. Consider that part under construction. You can check th intro &amp;amp; th few scales I have in th meantime, tho!&lt;br /&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 new scales that meet these three criteria:&lt;br /&gt;

&lt;ol&gt;&lt;li&gt;&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, 41:40, etc.&lt;/li&gt;&lt;li&gt;&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;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/MOSScales"&gt;Moment of Symmetry&lt;/a&gt; - 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;amp; th various diatonic scales as MOS scales because you can build them using a chain of fifths.&lt;/li&gt;&lt;/ol&gt;&lt;br /&gt;

&lt;ol&gt;&lt;li&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;/li&gt;&lt;li&gt;It fits as nonoctave (more accurately, near-octave) because it repeats at 1214.2 cents.&lt;/li&gt;&lt;li&gt;It fits as MOS because it contains exactly two step sizes, spaced out as evenly as possible w/i th scale.&lt;/li&gt;&lt;/ol&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. I have since then embarked on a search for all scales of this type w/i these (admittedly arbitrary) limits:&lt;br /&gt;

Even w/ these limits in place, this produces a multitude of fascinating scales for our enjoyment &amp;amp; fascination. I invite you to play &amp;amp; share yr results!&lt;br /&gt;