Wikispaces>Andrew_Heathwaite |
|
| (14 intermediate revisions by 9 users not shown) |
| Line 1: |
Line 1: |
| <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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2008-10-01 19:13:50 UTC</tt>.<br>
| |
| : The original revision id was <tt>40384382</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 & share the results here.
| |
|
| |
|
| Check out & 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 & 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 & 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. | | 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]] & [[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 [[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, & 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 & 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 & 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 & 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 & 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 & 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 & 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**__
| |
|
| |
|
| ===Using s===
| | <u>'''1 7 1'''</u> 2 <u>'''1 7 1'''</u> 2 <u>'''1 7 1'''</u> |
|
| |
|
| | <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=== |
| | Let's insert 4 5 for 9 & 1 1 for 2: |
| | |
| | <u>'''4 5'''</u> <u>'''1 1'''</u> <u>'''4 5'''</u> <u>'''1 1'''</u> <u>'''4 5'''</u> |
| | |
| | ==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|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|14edo]], you get: |
| | |
| | 2 4 2 4 2 |
| | |
| | & this scale you can easily alter with MOS Cradle: |
| | |
| | 2 <u>'''3 1'''</u> 2 <u>'''3 1'''</u> 2 |
|
| |
|
| ===Using both===
| | <u>'''1 1'''</u> 4 <u>'''1 1'''</u> 4 <u>'''1 1'''</u> |
|
| |
|
| Let's insert 4 5 for 9 & 1 1 for 2: | | == 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|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: |
| | |
| | <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) & contains both the original MOS & the Cradle Scale Swooning Rushes. Not bad! |
|
| |
|
| __**4 5**__ __**1 1**__ __**4 5**__ __**1 1**__ __**4 5**__
| | (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!) |
|
| |
|
| ==Some Observations==
| | 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]]! |
|
| |
|
| 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.
| | == References == |
| | <references /> |
|
| |
|
| 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</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"><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="/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="/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 &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="/edo">edo</a>s, because we can easily show the steps as degrees in the superscale.<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="/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="/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</body></html></pre></div>
| |