MOS cradle

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

Check out & add to a growing repository of MOS Cradle Scales [[xenharmonic/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 [[xenharmonic/Pythagorean Scale|Pythagorean Scale]], built using the octave as the period & the perfect fifth as the generator.

For this tutorial, I will limit us to MOS scales as subsets of [[xenharmonic/edo|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 [[xenharmonic/nonoctave|nonoctave]] & [[xenharmonic/JustIntonation|JI]] scales just as easily & with just as interesting results!

==The "Parent"== 

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

9 2 9 2 9

A nice little scale. Tune your synth up to it & give it a whirl. The MOS Cradle technique will give us a new way to elaborate on this basic structure. We'll use it as the "parent" scale.

==The "Cradle"== 

Our parent scale has two different step sizes. The large step = L = 9. The small step = s = 2. We will select one of these step sizes to use as a "cradle" for new pitches.

===Using L=== 

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

generator 1/9:
1 8
1 7 1
1 1 5 1 1
1 1 1 3 1 1 1

generator 2/9:
2 7
2 5 2
2 2 1 2 2

generator 3/9:
3 6

generator 4/9

4 5
4 1 4
1 3 1 3 1
1 2 1 1 1 2 1

Now that we have some MOS shapes, we can cut up our original L's back in the parent scale using any of these shapes. I'll show just a few, with the orignal L = 9 in bold & underlined:

__**4 5**__ 2 __**4 5**__ 2 __**4 5**__
__**1 7 1**__ 2 __**1 7 1**__ 2 __**1 7 1**__
__**1 3 1 3 1**__ 2 __**1 3 1 3 1**__ 2 __**1 3 1 3 1**__

===Using s=== 

Let's see what happens if we use s = 2 as the cradle. We have only one way to break down 2:

1 1

So if we insert 1 1 for 2, we get:

9 __**1 1**__ 9 __**1 1**__ 9

===Using both=== 

Let's insert 4 5 for 9 & 1 1 for 2:

__**4 5**__ __**1 1**__ __**4 5**__ __**1 1**__ __**4 5**__

==Some Observations== 

Using this method, you arrive at new scales which contain the parent scale, plus a few extra notes. You can consider the extra notes "ornamental," secondary to the notes of the parent scale, or you can think of the whole scale as a brand new entity.

Often, the new scale will contain three step sizes, instead of the original two. So in addition to L & s, you'd have M. You can design your scale so that the three step sizes have interesting ratios to one another, if you like. I think it sounds nice when the step sizes don't add or multiply together to make each other.

Sometimes this technique will produce a scale you might have gotten to another way -- like a classic MOS scale.

==Doubling/Tripling the edo== 

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 [[xenharmonic/7edo|7edo]]:

1 2 1 2 1

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 [[xenharmonic/14edo|14edo]], you get:

2 4 2 4 2

& this scale you can easily alter with MOS Cradle:

2 __**3 1**__ 2 __**3 1**__ 2
__**1 1**__ 4 __**1 1**__ 4 __**1 1**__

==A Cradle in a Cradle== 

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

2 3 1 3 2

A fine little scale, I think. Now let's double it:

4 6 2 6 4

& apply MOS Cradle to it:

__**3 1**__ 6 2 __**1 3**__

This new scale, a subset of [[xenharmonic/22edo|22edo]], has four step sizes (1, 2, 3, 6) & contains both th original MOS & 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 [[xenharmonic/44edo|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 & add your findings. & when you design lovely new MOS Cradle Scales, do add them to the [[xenharmonic/MOS Cradle Scales|repository]]!


[[http://www.newswire.net/newsroom/financial/71283-ecommerce-mastery-review-by-sam-england.html|Make money from online shops]]

Original HTML content:

<html><head><title>MOS Cradle</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="MOS Cradle"></a><!-- ws:end:WikiTextHeadingRule:0 -->MOS Cradle</h1>
 refers to a technique of embedding one <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS scale</a> inside another, to create a new hybrid scale, a MOS Cradle Scale. I (Andrew Heathwaite) invite you to experiment &amp; share the results here.<br />
<br />
Check out &amp; add to a growing repository of MOS Cradle Scales <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOS%20Cradle%20Scales">here</a>.<br />
<br />
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 <strong>generator</strong>) within a <strong>period</strong> 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 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Pythagorean%20Scale">Pythagorean Scale</a>, built using the octave as the period &amp; the perfect fifth as the generator.<br />
<br />
For this tutorial, I will limit us to MOS scales as subsets of <a class="wiki_link" href="http://xenharmonic.wikispaces.com/edo">edo</a>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 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/nonoctave">nonoctave</a> &amp; <a class="wiki_link" href="http://xenharmonic.wikispaces.com/JustIntonation">JI</a> scales just as easily &amp; with just as interesting results!<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="MOS Cradle-The &quot;Parent&quot;"></a><!-- ws:end:WikiTextHeadingRule:2 -->The &quot;Parent&quot;</h2>
 <br />
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 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/31edo">31edo</a>. Throughout this tutorial, I will show the scales as step degrees of the superscale, like this:<br />
<br />
9 2 9 2 9<br />
<br />
A nice little scale. Tune your synth up to it &amp; give it a whirl. The MOS Cradle technique will give us a new way to elaborate on this basic structure. We'll use it as the &quot;parent&quot; scale.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="MOS Cradle-The &quot;Cradle&quot;"></a><!-- ws:end:WikiTextHeadingRule:4 -->The &quot;Cradle&quot;</h2>
 <br />
Our parent scale has two different step sizes. The large step = L = 9. The small step = s = 2. We will select one of these step sizes to use as a &quot;cradle&quot; for new pitches.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="MOS Cradle-The &quot;Cradle&quot;-Using L"></a><!-- ws:end:WikiTextHeadingRule:6 -->Using L</h3>
 <br />
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 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/9edo">9edo</a>. So let's try a few:<br />
<br />
generator 1/9:<br />
1 8<br />
1 7 1<br />
1 1 5 1 1<br />
1 1 1 3 1 1 1<br />
<br />
generator 2/9:<br />
2 7<br />
2 5 2<br />
2 2 1 2 2<br />
<br />
generator 3/9:<br />
3 6<br />
<br />
generator 4/9<br />
<br />
4 5<br />
4 1 4<br />
1 3 1 3 1<br />
1 2 1 1 1 2 1<br />
<br />
Now that we have some MOS shapes, we can cut up our original L's back in the parent scale using any of these shapes. I'll show just a few, with the orignal L = 9 in bold &amp; underlined:<br />
<br />
<u><strong>4 5</strong></u> 2 <u><strong>4 5</strong></u> 2 <u><strong>4 5</strong></u><br />
<u><strong>1 7 1</strong></u> 2 <u><strong>1 7 1</strong></u> 2 <u><strong>1 7 1</strong></u><br />
<u><strong>1 3 1 3 1</strong></u> 2 <u><strong>1 3 1 3 1</strong></u> 2 <u><strong>1 3 1 3 1</strong></u><br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="MOS Cradle-The &quot;Cradle&quot;-Using s"></a><!-- ws:end:WikiTextHeadingRule:8 -->Using s</h3>
 <br />
Let's see what happens if we use s = 2 as the cradle. We have only one way to break down 2:<br />
<br />
1 1<br />
<br />
So if we insert 1 1 for 2, we get:<br />
<br />
9 <u><strong>1 1</strong></u> 9 <u><strong>1 1</strong></u> 9<br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="MOS Cradle-The &quot;Cradle&quot;-Using both"></a><!-- ws:end:WikiTextHeadingRule:10 -->Using both</h3>
 <br />
Let's insert 4 5 for 9 &amp; 1 1 for 2:<br />
<br />
<u><strong>4 5</strong></u> <u><strong>1 1</strong></u> <u><strong>4 5</strong></u> <u><strong>1 1</strong></u> <u><strong>4 5</strong></u><br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="MOS Cradle-Some Observations"></a><!-- ws:end:WikiTextHeadingRule:12 -->Some Observations</h2>
 <br />
Using this method, you arrive at new scales which contain the parent scale, plus a few extra notes. You can consider the extra notes &quot;ornamental,&quot; secondary to the notes of the parent scale, or you can think of the whole scale as a brand new entity.<br />
<br />
Often, the new scale will contain three step sizes, instead of the original two. So in addition to L &amp; s, you'd have M. You can design your scale so that the three step sizes have interesting ratios to one another, if you like. I think it sounds nice when the step sizes don't add or multiply together to make each other.<br />
<br />
Sometimes this technique will produce a scale you might have gotten to another way -- like a classic MOS scale.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="MOS Cradle-Doubling/Tripling the edo"></a><!-- ws:end:WikiTextHeadingRule:14 -->Doubling/Tripling the edo</h2>
 <br />
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 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/7edo">7edo</a>:<br />
<br />
1 2 1 2 1<br />
<br />
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 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/14edo">14edo</a>, you get:<br />
<br />
2 4 2 4 2<br />
<br />
&amp; this scale you can easily alter with MOS Cradle:<br />
<br />
2 <u><strong>3 1</strong></u> 2 <u><strong>3 1</strong></u> 2<br />
<u><strong>1 1</strong></u> 4 <u><strong>1 1</strong></u> 4 <u><strong>1 1</strong></u><br />
<br />
<!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="MOS Cradle-A Cradle in a Cradle"></a><!-- ws:end:WikiTextHeadingRule:16 -->A Cradle in a Cradle</h2>
 <br />
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 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/11edo">11edo</a>:<br />
<br />
2 3 1 3 2<br />
<br />
A fine little scale, I think. Now let's double it:<br />
<br />
4 6 2 6 4<br />
<br />
&amp; apply MOS Cradle to it:<br />
<br />
<u><strong>3 1</strong></u> 6 2 <u><strong>1 3</strong></u><br />
<br />
This new scale, a subset of <a class="wiki_link" href="http://xenharmonic.wikispaces.com/22edo">22edo</a>, has four step sizes (1, 2, 3, 6) &amp; contains both th original MOS &amp; th Cradle Scale Swooning Rushes. Not bad!<br />
<br />
(This can go on forever, in theory. If we double it again, we might get this scale, a subset of <a class="wiki_link" href="http://xenharmonic.wikispaces.com/44edo">44edo</a>: 6 2 7 5 4 5 7 2 6!)<br />
<br />
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 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOS%20Cradle%20Scales">repository</a>!<br />
<br />
<br />
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