MOS cradle: Difference between revisions
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Wikispaces>Andrew_Heathwaite **Imported revision 413597300 - Original comment: Reverted to Oct 5, 2008 6:39 pm: spammed!** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2013-03-10 13:25:10 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>413597300</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt>Reverted to Oct 5, 2008 6:39 pm: spammed!</tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<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> | <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= | <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 [[ | 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 & share the results here. | ||
Check out & add to a growing repository of MOS Cradle Scales [[ | Check out & 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 [[ | 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 & the perfect fifth as the generator. | ||
For this tutorial, I will limit us to MOS scales as subsets of [[ | 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]] & [[JustIntonation|JI]] scales just as easily & 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, & the octave as our period. At five notes, we close on a pentatonic scale, a subset of [[ | 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 [[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 29: | Line 29: | ||
===Using L=== | ===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 [[ | 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 [[9edo]]. So let's try a few: | ||
generator 1/9: | generator 1/9: | ||
| Line 84: | Line 84: | ||
==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 [[ | 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 [[ | 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: | ||
2 4 2 4 2 | 2 4 2 4 2 | ||
| Line 99: | Line 99: | ||
==A Cradle in a Cradle== | ==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 [[ | 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 [[11edo]]: | ||
2 3 1 3 2 | 2 3 1 3 2 | ||
| Line 111: | Line 111: | ||
__**3 1**__ 6 2 __**1 3**__ | __**3 1**__ 6 2 __**1 3**__ | ||
This new scale, a subset of [[ | This new scale, a subset of [[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 [[ | (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 & add your findings. & when you design lovely new MOS Cradle Scales, do add them to the [[ | 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 [[MOS Cradle Scales|repository]]!</pre></div> | ||
<h4>Original HTML content:</h4> | <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"><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> | <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"><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=" | refers to a technique of embedding one <a class="wiki_link" href="/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 /> | <br /> | ||
Check out &amp; add to a growing repository of MOS Cradle Scales <a class="wiki_link" href=" | Check out &amp; add to a growing repository of MOS Cradle Scales <a class="wiki_link" href="/MOS%20Cradle%20Scales">here</a>.<br /> | ||
<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=" | 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="/Pythagorean%20Scale">Pythagorean Scale</a>, built using the octave as the period &amp; the perfect fifth as the generator.<br /> | ||
<br /> | <br /> | ||
For this tutorial, I will limit us to MOS scales as subsets of <a class="wiki_link" href=" | For this tutorial, I will limit us to MOS scales as subsets of <a class="wiki_link" href="/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="/nonoctave">nonoctave</a> &amp; <a class="wiki_link" href="/JustIntonation">JI</a> scales just as easily &amp; with just as interesting results!<br /> | ||
<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> | <!-- 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 /> | <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=" | 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="/31edo">31edo</a>. Throughout this tutorial, I will show the scales as step degrees of the superscale, like this:<br /> | ||
<br /> | <br /> | ||
9 2 9 2 9<br /> | 9 2 9 2 9<br /> | ||
| Line 143: | Line 140: | ||
<!-- 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> | <!-- 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 /> | <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=" | 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="/9edo">9edo</a>. So let's try a few:<br /> | ||
<br /> | <br /> | ||
generator 1/9:<br /> | generator 1/9:<br /> | ||
| Line 198: | Line 195: | ||
<!-- 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> | <!-- 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 /> | <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=" | 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="/7edo">7edo</a>:<br /> | ||
<br /> | <br /> | ||
1 2 1 2 1<br /> | 1 2 1 2 1<br /> | ||
<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=" | 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="/14edo">14edo</a>, you get:<br /> | ||
<br /> | <br /> | ||
2 4 2 4 2<br /> | 2 4 2 4 2<br /> | ||
| Line 213: | Line 210: | ||
<!-- 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> | <!-- 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 /> | <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=" | 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="/11edo">11edo</a>:<br /> | ||
<br /> | <br /> | ||
2 3 1 3 2<br /> | 2 3 1 3 2<br /> | ||
| Line 225: | Line 222: | ||
<u><strong>3 1</strong></u> 6 2 <u><strong>1 3</strong></u><br /> | <u><strong>3 1</strong></u> 6 2 <u><strong>1 3</strong></u><br /> | ||
<br /> | <br /> | ||
This new scale, a subset of <a class="wiki_link" href=" | This new scale, a subset of <a class="wiki_link" href="/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 /> | <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="/44edo">44edo</a>: 6 2 7 5 4 5 7 2 6!)<br /> | |||
<br /> | <br /> | ||
<a class=" | 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="/MOS%20Cradle%20Scales">repository</a>!</body></html></pre></div> | ||