MOS cradle: Difference between revisions

: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2008-10-05 21:39:16 UTC</tt>.<br>

: The original revision id was <tt>40812555</tt>.<br>

refers to a technique of embedding one [[MOSScales|MOS scale]] inside another, to create a new hybrid scale, a MOS Cradle Scale. I (Andrew Heathwaite) invite you to experiment &amp; share the results here.

Check out &amp; add to a growing repository of MOS Cradle Scales [[MOS Cradle Scales|here]].

For this tutorial, I assume basic knowledge of Moment of Symmetry scale design. To summarize, you can design scales by building a chain of one interval (the **generator**) within a **period** of another interval -- often, but not always, the octave. When the resulting set of notes has exactly two step sizes, we call the scale a Moment of Symmetry, or MOS, scale. A prime example: the [[Pythagorean Scale]], built using the octave as the period &amp; the perfect fifth as the generator.

For this tutorial, I will limit us to MOS scales as subsets of [[edo]]s, because we can easily show the steps as degrees in the superscale. But do keep in mind that you can apply these ideas to [[nonoctave]] &amp; [[JustIntonation|JI]] scales just as easily &amp; with just as interesting results!

We begin with a classic MOS scale. So, just to get us started, we'll use 11/31 of an octave as our generator, &amp; the octave as our period. At five notes, we close on a pentatonic scale, a subset of [[31edo]]. Throughout this tutorial, I will show the scales as step degrees of the superscale, like this:

Let's use L = 9. We take those 9 degrees &amp; look at ways of making new MOS scales within that, just as we'd do if we wanted MOS scales in [[9edo]]. So let's try a few:

If you want to use MOS Cradle to elaborate on a scale in a small edo, consider doubling or tripling, etc., the number of notes. Say you want to use the pentatonic scale in [[7edo]]:

You can't use L or s as a cradle here to get a new scale. But, if you double the number of pitches, going into the territory of [[14edo]], you get:

One can, of course, perform MOS Cradle on MOS Cradle scales &amp; produce scales w/ four step sizes. Let's start with Swooning Rushes, a subset of [[11edo]]:

This new scale, a subset of [[22edo]], has four step sizes (1, 2, 3, 6) &amp; contains both th original MOS &amp; th Cradle Scale Swooning Rushes. Not bad!

(This can go on forever, in theory. If we double it again, we might get this scale, a subset of [[44edo]]: 6 2 7 5 4 5 7 2 6!)

Now I think I've given more than enough examples for you to get started on your own! If you discover other neat properties of these scales, feel free to edit this page &amp; add your findings. &amp; when you design lovely new MOS Cradle Scales, do add them to the [[MOS Cradle Scales|repository]]!</pre></div>

  refers to a technique of embedding one &lt;a class="wiki_link" href="/MOSScales"&gt;MOS scale&lt;/a&gt; inside another, to create a new hybrid scale, a MOS Cradle Scale. I (Andrew Heathwaite) invite you to experiment &amp;amp; share the results here.&lt;br /&gt;

Check out &amp;amp; add to a growing repository of MOS Cradle Scales &lt;a class="wiki_link" href="/MOS%20Cradle%20Scales"&gt;here&lt;/a&gt;.&lt;br /&gt;

For this tutorial, I assume basic knowledge of Moment of Symmetry scale design. To summarize, you can design scales by building a chain of one interval (the &lt;strong&gt;generator&lt;/strong&gt;) within a &lt;strong&gt;period&lt;/strong&gt; of another interval -- often, but not always, the octave. When the resulting set of notes has exactly two step sizes, we call the scale a Moment of Symmetry, or MOS, scale. A prime example: the &lt;a class="wiki_link" href="/Pythagorean%20Scale"&gt;Pythagorean Scale&lt;/a&gt;, built using the octave as the period &amp;amp; the perfect fifth as the generator.&lt;br /&gt;

For this tutorial, I will limit us to MOS scales as subsets of &lt;a class="wiki_link" href="/edo"&gt;edo&lt;/a&gt;s, because we can easily show the steps as degrees in the superscale. But do keep in mind that you can apply these ideas to &lt;a class="wiki_link" href="/nonoctave"&gt;nonoctave&lt;/a&gt; &amp;amp; &lt;a class="wiki_link" href="/JustIntonation"&gt;JI&lt;/a&gt; scales just as easily &amp;amp; with just as interesting results!&lt;br /&gt;

We begin with a classic MOS scale. So, just to get us started, we'll use 11/31 of an octave as our generator, &amp;amp; the octave as our period. At five notes, we close on a pentatonic scale, a subset of &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;. Throughout this tutorial, I will show the scales as step degrees of the superscale, like this:&lt;br /&gt;

Let's use L = 9. We take those 9 degrees &amp;amp; look at ways of making new MOS scales within that, just as we'd do if we wanted MOS scales in &lt;a class="wiki_link" href="/9edo"&gt;9edo&lt;/a&gt;. So let's try a few:&lt;br /&gt;

If you want to use MOS Cradle to elaborate on a scale in a small edo, consider doubling or tripling, etc., the number of notes. Say you want to use the pentatonic scale in &lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt;:&lt;br /&gt;

You can't use L or s as a cradle here to get a new scale. But, if you double the number of pitches, going into the territory of &lt;a class="wiki_link" href="/14edo"&gt;14edo&lt;/a&gt;, you get:&lt;br /&gt;

One can, of course, perform MOS Cradle on MOS Cradle scales &amp;amp; produce scales w/ four step sizes. Let's start with Swooning Rushes, a subset of &lt;a class="wiki_link" href="/11edo"&gt;11edo&lt;/a&gt;:&lt;br /&gt;

This new scale, a subset of &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;, has four step sizes (1, 2, 3, 6) &amp;amp; contains both th original MOS &amp;amp; th Cradle Scale Swooning Rushes. Not bad!&lt;br /&gt;

Now I think I've given more than enough examples for you to get started on your own! If you discover other neat properties of these scales, feel free to edit this page &amp;amp; add your findings. &amp;amp; when you design lovely new MOS Cradle Scales, do add them to the &lt;a class="wiki_link" href="/MOS%20Cradle%20Scales"&gt;repository&lt;/a&gt;!&lt;/body&gt;&lt;/html&gt;</pre></div>