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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
'''MOS cradle''' is a technique of embedding one [[MOS scale]] inside another, to create a new hybrid scale, a '''MOS cradle scale'''. This method of combining two MOS scales should not be confused with [[Muddle|Muddles]] or a [[Secondary MOS]] although some scales may be able to be constructed both ways.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:guest|guest]] and made on <tt>2013-03-10 23:46:39 UTC</tt>.<br>
: The original revision id was <tt>413713082</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<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">=MOS Cradle=
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]].
Examples of these scales can be found at [[MOS cradle scales]].


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.
== Introduction ==
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 tuning|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!
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; [[JI]] scales just as easily &amp; with just as interesting results!


==The "Parent"==  
== 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, &amp; the octave as our period. At five notes, we close on a pentatonic scale, a subset of [[31edo|31edo]]. Throughout this tutorial, I will show the scales as step degrees of the superscale, like this:
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:


9 2 9 2 9
9 2 9 2 9
Line 23: Line 15:
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 "parent" scale.
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 "parent" scale.


==The "Cradle"==  
== 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.
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===  
=== Using L ===
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|9edo]]. So let's try a few:


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:
generator 1/9:


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


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


generator 3/9:
generator 3/9:
3 6
3 6


Line 48: Line 46:


4 5
4 5
4 1 4
4 1 4
1 3 1 3 1
1 3 1 3 1
1 2 1 1 1 2 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 &amp; underlined:
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:


__**4 5**__ 2 __**4 5**__ 2 __**4 5**__
<u>'''4 5'''</u> 2 <u>'''4 5'''</u> 2 <u>'''4 5'''</u>
__**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**__
<u>'''1 7 1'''</u> 2 <u>'''1 7 1'''</u> 2 <u>'''1 7 1'''</u>


===Using s===
<u>'''1 3 1 3 1'''</u> 2 <u>'''1 3 1 3 1'''</u> 2 <u>'''1 3 1 3 1'''</u>


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


Line 66: Line 68:
So if we insert 1 1 for 2, we get:
So if we insert 1 1 for 2, we get:


9 __**1 1**__ 9 __**1 1**__ 9
9 <u>'''1 1'''</u> 9 <u>'''1 1'''</u> 9
 
===Using both===


===Using both===
Let's insert 4 5 for 9 &amp; 1 1 for 2:
Let's insert 4 5 for 9 &amp; 1 1 for 2:


__**4 5**__ __**1 1**__ __**4 5**__ __**1 1**__ __**4 5**__
<u>'''4 5'''</u> <u>'''1 1'''</u> <u>'''4 5'''</u> <u>'''1 1'''</u> <u>'''4 5'''</u>
 
==Some Observations==


==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.
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.


Line 82: Line 82:
Sometimes this technique will produce a scale you might have gotten to another way -- like a classic MOS scale.
Sometimes this technique will produce a scale you might have gotten to another way -- like a classic MOS scale.


==Doubling/Tripling the edo==  
==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 [[7edo|7edo]]:
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]]:


1 2 1 2 1
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 [[14edo]], you get:
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|14edo]], you get:


2 4 2 4 2
2 4 2 4 2
Line 94: Line 93:
&amp; this scale you can easily alter with MOS Cradle:
&amp; this scale you can easily alter with MOS Cradle:


2 __**3 1**__ 2 __**3 1**__ 2
2 <u>'''3 1'''</u> 2 <u>'''3 1'''</u> 2
__**1 1**__ 4 __**1 1**__ 4 __**1 1**__


==A Cradle in a Cradle==
<u>'''1 1'''</u> 4 <u>'''1 1'''</u> 4 <u>'''1 1'''</u>


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]]:
== A cradle in a cradle ==
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|11edo]]:


2 3 1 3 2
2 3 1 3 2
Line 109: Line 108:
&amp; apply MOS Cradle to it:
&amp; apply MOS Cradle to it:


__**3 1**__ 6 2 6 __**1 3**__
<u>'''3 1'''</u> 6 2 6 <u>'''1 3'''</u>
 
This new scale, a subset of [[22edo|22edo]], has four step sizes (1, 2, 3, 6) &amp; contains both the original MOS &amp; the 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|44edo]]: 6 2 7 5 4 5 7 2 6!)


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!
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]]!


(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!)
== References ==
<references />


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>
[[Category:MOS scale]]
<h4>Original HTML content:</h4>
<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;MOS Cradle&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="MOS Cradle"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;MOS Cradle&lt;/h1&gt;
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;
&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;
&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;
&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;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="MOS Cradle-The &amp;quot;Parent&amp;quot;"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;The &amp;quot;Parent&amp;quot;&lt;/h2&gt;
&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;
&lt;br /&gt;
9 2 9 2 9&lt;br /&gt;
&lt;br /&gt;
A nice little scale. Tune your synth up to it &amp;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 &amp;quot;parent&amp;quot; scale.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="MOS Cradle-The &amp;quot;Cradle&amp;quot;"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;The &amp;quot;Cradle&amp;quot;&lt;/h2&gt;
&lt;br /&gt;
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 &amp;quot;cradle&amp;quot; for new pitches.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="MOS Cradle-The &amp;quot;Cradle&amp;quot;-Using L"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Using L&lt;/h3&gt;
&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;
&lt;br /&gt;
generator 1/9:&lt;br /&gt;
1 8&lt;br /&gt;
1 7 1&lt;br /&gt;
1 1 5 1 1&lt;br /&gt;
1 1 1 3 1 1 1&lt;br /&gt;
&lt;br /&gt;
generator 2/9:&lt;br /&gt;
2 7&lt;br /&gt;
2 5 2&lt;br /&gt;
2 2 1 2 2&lt;br /&gt;
&lt;br /&gt;
generator 3/9:&lt;br /&gt;
3 6&lt;br /&gt;
&lt;br /&gt;
generator 4/9&lt;br /&gt;
&lt;br /&gt;
4 5&lt;br /&gt;
4 1 4&lt;br /&gt;
1 3 1 3 1&lt;br /&gt;
1 2 1 1 1 2 1&lt;br /&gt;
&lt;br /&gt;
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;amp; underlined:&lt;br /&gt;
&lt;br /&gt;
&lt;u&gt;&lt;strong&gt;4 5&lt;/strong&gt;&lt;/u&gt; 2 &lt;u&gt;&lt;strong&gt;4 5&lt;/strong&gt;&lt;/u&gt; 2 &lt;u&gt;&lt;strong&gt;4 5&lt;/strong&gt;&lt;/u&gt;&lt;br /&gt;
&lt;u&gt;&lt;strong&gt;1 7 1&lt;/strong&gt;&lt;/u&gt; 2 &lt;u&gt;&lt;strong&gt;1 7 1&lt;/strong&gt;&lt;/u&gt; 2 &lt;u&gt;&lt;strong&gt;1 7 1&lt;/strong&gt;&lt;/u&gt;&lt;br /&gt;
&lt;u&gt;&lt;strong&gt;1 3 1 3 1&lt;/strong&gt;&lt;/u&gt; 2 &lt;u&gt;&lt;strong&gt;1 3 1 3 1&lt;/strong&gt;&lt;/u&gt; 2 &lt;u&gt;&lt;strong&gt;1 3 1 3 1&lt;/strong&gt;&lt;/u&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="MOS Cradle-The &amp;quot;Cradle&amp;quot;-Using s"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Using s&lt;/h3&gt;
&lt;br /&gt;
Let's see what happens if we use s = 2 as the cradle. We have only one way to break down 2:&lt;br /&gt;
&lt;br /&gt;
1 1&lt;br /&gt;
&lt;br /&gt;
So if we insert 1 1 for 2, we get:&lt;br /&gt;
&lt;br /&gt;
9 &lt;u&gt;&lt;strong&gt;1 1&lt;/strong&gt;&lt;/u&gt; 9 &lt;u&gt;&lt;strong&gt;1 1&lt;/strong&gt;&lt;/u&gt; 9&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="MOS Cradle-The &amp;quot;Cradle&amp;quot;-Using both"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Using both&lt;/h3&gt;
&lt;br /&gt;
Let's insert 4 5 for 9 &amp;amp; 1 1 for 2:&lt;br /&gt;
&lt;br /&gt;
&lt;u&gt;&lt;strong&gt;4 5&lt;/strong&gt;&lt;/u&gt; &lt;u&gt;&lt;strong&gt;1 1&lt;/strong&gt;&lt;/u&gt; &lt;u&gt;&lt;strong&gt;4 5&lt;/strong&gt;&lt;/u&gt; &lt;u&gt;&lt;strong&gt;1 1&lt;/strong&gt;&lt;/u&gt; &lt;u&gt;&lt;strong&gt;4 5&lt;/strong&gt;&lt;/u&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="MOS Cradle-Some Observations"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Some Observations&lt;/h2&gt;
&lt;br /&gt;
Using this method, you arrive at new scales which contain the parent scale, plus a few extra notes. You can consider the extra notes &amp;quot;ornamental,&amp;quot; secondary to the notes of the parent scale, or you can think of the whole scale as a brand new entity.&lt;br /&gt;
&lt;br /&gt;
Often, the new scale will contain three step sizes, instead of the original two. So in addition to L &amp;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.&lt;br /&gt;
&lt;br /&gt;
Sometimes this technique will produce a scale you might have gotten to another way -- like a classic MOS scale.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="MOS Cradle-Doubling/Tripling the edo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Doubling/Tripling the edo&lt;/h2&gt;
&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;
&lt;br /&gt;
1 2 1 2 1&lt;br /&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;
&lt;br /&gt;
2 4 2 4 2&lt;br /&gt;
&lt;br /&gt;
&amp;amp; this scale you can easily alter with MOS Cradle:&lt;br /&gt;
&lt;br /&gt;
2 &lt;u&gt;&lt;strong&gt;3 1&lt;/strong&gt;&lt;/u&gt; 2 &lt;u&gt;&lt;strong&gt;3 1&lt;/strong&gt;&lt;/u&gt; 2&lt;br /&gt;
&lt;u&gt;&lt;strong&gt;1 1&lt;/strong&gt;&lt;/u&gt; 4 &lt;u&gt;&lt;strong&gt;1 1&lt;/strong&gt;&lt;/u&gt; 4 &lt;u&gt;&lt;strong&gt;1 1&lt;/strong&gt;&lt;/u&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="MOS Cradle-A Cradle in a Cradle"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;A Cradle in a Cradle&lt;/h2&gt;
&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;
&lt;br /&gt;
2 3 1 3 2&lt;br /&gt;
&lt;br /&gt;
A fine little scale, I think. Now let's double it:&lt;br /&gt;
&lt;br /&gt;
4 6 2 6 4&lt;br /&gt;
&lt;br /&gt;
&amp;amp; apply MOS Cradle to it:&lt;br /&gt;
&lt;br /&gt;
&lt;u&gt;&lt;strong&gt;3 1&lt;/strong&gt;&lt;/u&gt; 6 2 6 &lt;u&gt;&lt;strong&gt;1 3&lt;/strong&gt;&lt;/u&gt;&lt;br /&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;
&lt;br /&gt;
(This can go on forever, in theory. If we double it again, we might get this scale, a subset of &lt;a class="wiki_link" href="/44edo"&gt;44edo&lt;/a&gt;: 6 2 7 5 4 5 7 2 6!)&lt;br /&gt;
&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>
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