MOS cradle
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author Andrew_Heathwaite and made on 2008-10-05 21:39:16 UTC.
- The original revision id was 40812555.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
=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 & share the results here. 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 [[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 [[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"== 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 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 [[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 [[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 [[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 [[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 [[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 [[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 [[MOS Cradle Scales|repository]]!
Original HTML content:
<html><head><title>MOS Cradle</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><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="/MOSScales">MOS scale</a> inside another, to create a new hybrid scale, a MOS Cradle Scale. I (Andrew Heathwaite) invite you to experiment & share the results here.<br /> <br /> Check out & add to a growing repository of MOS Cradle Scales <a class="wiki_link" href="/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="/Pythagorean%20Scale">Pythagorean Scale</a>, built using the octave as the period & 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="/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> & <a class="wiki_link" href="/JustIntonation">JI</a> scales just as easily & with just as interesting results!<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="MOS Cradle-The "Parent""></a><!-- ws:end:WikiTextHeadingRule:2 -->The "Parent"</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, & 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 /> 9 2 9 2 9<br /> <br /> 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.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="MOS Cradle-The "Cradle""></a><!-- ws:end:WikiTextHeadingRule:4 -->The "Cradle"</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 "cradle" for new pitches.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h3> --><h3 id="toc3"><a name="MOS Cradle-The "Cradle"-Using L"></a><!-- ws:end:WikiTextHeadingRule:6 -->Using L</h3> <br /> 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 <a class="wiki_link" href="/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 & 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:<h3> --><h3 id="toc4"><a name="MOS Cradle-The "Cradle"-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:<h3> --><h3 id="toc5"><a name="MOS Cradle-The "Cradle"-Using both"></a><!-- ws:end:WikiTextHeadingRule:10 -->Using both</h3> <br /> Let's insert 4 5 for 9 & 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:<h2> --><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 "ornamental," 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 & 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:<h2> --><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="/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="/14edo">14edo</a>, you get:<br /> <br /> 2 4 2 4 2<br /> <br /> & 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:<h2> --><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 & 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 /> 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 /> & 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="/22edo">22edo</a>, has four step sizes (1, 2, 3, 6) & contains both th original MOS & 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="/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 & add your findings. & 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>