MOS cradle: Difference between revisions
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'''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. | |||
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 | == 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 [[ | 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 == | |||
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|31edo]]. Throughout this tutorial, I will show the scales as step degrees of the superscale, like this: | ||
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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 | == 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|9edo]]. So let's try a few: | ||
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===Using s=== | ===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: | ||
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===Using both=== | ===Using both=== | ||
Let's insert 4 5 for 9 & 1 1 for 2: | 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> | <u>'''4 5'''</u> <u>'''1 1'''</u> <u>'''4 5'''</u> <u>'''1 1'''</u> <u>'''4 5'''</u> | ||
==Some | ==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. | ||
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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/ | ==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|7edo]]: | ||
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<u>'''1 1'''</u> 4 <u>'''1 1'''</u> 4 <u>'''1 1'''</u> | <u>'''1 1'''</u> 4 <u>'''1 1'''</u> 4 <u>'''1 1'''</u> | ||
==A | == 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]]: | 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]]: | ||
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(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 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!) | ||
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]]! | ||
== References == | |||
<references /> | |||
[[Category:MOS scale]] | |||