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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | A macrotonal edonoi would be, by definition, a scale which meets two constraints: |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2009-12-27 23:11:12 UTC</tt>.<br>
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| : The original revision id was <tt>111123201</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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| <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">A macrotonal edonoi would be, by definition, a scale which meets two constraints:
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| * [[macrotonal]] - all steps are larger than a semitone
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| * [[edonoi]] - short for "equal divisions of a non-octave interval" - the scale consists of a single step stacked over and over which does not repeat at an octave
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| Examples include equal-tempered [[BP|Bohlen Pierce]] (a.k.a. the 13th root of 3), the [[square root of 13 over 10|square root of 13:10]], the [[12edt|12th root of 3]], the [[4edf|4th root of 3:2]], and the [[6edf|6th root of 3:2]].
| | <ul><li>[[macrotonal|macrotonal]] - all steps are larger than a semitone</li><li>[[edonoi|edonoi]] - short for "equal divisions of a non-octave interval" - the scale consists of a single step stacked over and over which does not repeat at an octave</li></ul> |
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| <span style="font-size: 17px; line-height: 25px;">**Macrotonal edos** </span>
| | Examples include equal-tempered [[BP|Bohlen Pierce]] (a.k.a. the 13th root of 3), the [[square_root_of_13_over_10|square root of 13:10]], the [[12edt|12th root of 3]], the [[4edf|4th root of 3:2]], and the [[6edf|6th root of 3:2]]. |
| Macrotonal edonoi are related, in step-size and equality of steps, to [[macrotonal edos]], but while macrotonal edos are a finite set, macrotonal edonoi are theoretically infinite. Macrotonal edos are extremely [[redundancy|redundant]] systems. Not only is there a very limited set of intervals in one octave of a macrotonal edo, but thanks to octave equivalency, that small set repeats at every octave. | | |
| | <span style="font-size: 17px; line-height: 25px;">'''Macrotonal edos''' </span> |
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| | Macrotonal edonoi are related, in step-size and equality of steps, to [[macrotonal_edos|macrotonal edos]], but while macrotonal edos are a finite set, macrotonal edonoi are theoretically infinite. Macrotonal edos are extremely [[redundancy|redundant]] systems. Not only is there a very limited set of intervals in one octave of a macrotonal edo, but thanks to octave equivalency, that small set repeats at every octave. |
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| Macrotonal edonoi, by not containing octaves at all, take away the redundancy of octave equivalence, and are thus much more complex systems to compose in. Each new step further out produces a brand new interval, with no octave-equivalent complement that came before it. | | Macrotonal edonoi, by not containing octaves at all, take away the redundancy of octave equivalence, and are thus much more complex systems to compose in. Each new step further out produces a brand new interval, with no octave-equivalent complement that came before it. |
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| If we consider macrotonal edos as distinct stopping-places in a continuum of scales with decreasing step size (from the 1200-cent step of 1edo, down to the 100-cent step of [[12edo]] which defines the edge of "macrotonal"), then macrotonal edonoi represent unique universes that are "in the cracks". | | If we consider macrotonal edos as distinct stopping-places in a continuum of scales with decreasing step size (from the 1200-cent step of 1edo, down to the 100-cent step of [[12edo|12edo]] which defines the edge of "macrotonal"), then macrotonal edonoi represent unique universes that are "in the cracks". |
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| ==Equal Divisions of Compound Octaves== | | ==Equal Divisions of Compound Octaves== |
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| What about dividing a compound octave, say, 4:1 or 8:1? Examples of this kind of scale would include the 15th root of 4 and the 22nd root of 8. I don't know whether or not we should use the term edonoi for these. | | What about dividing a compound octave, say, 4:1 or 8:1? Examples of this kind of scale would include the 15th root of 4 and the 22nd root of 8. I don't know whether or not we should use the term edonoi for these. |
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| These kinds of scales, equal divisions of compound octaves, represent a middle-ground in terms of redundancy and complexity of an equal-step system. For instance, the 15th root of 4 can be arrived at by taking every other tone in [[15edo]]. It doesn't repeat at one octave, but it repeats at two octaves, after having generated 15 tones. From there, the system is redundant with itself, as it now produces the same intervals two octaves higher than where they first appeared. </pre></div> | | These kinds of scales, equal divisions of compound octaves, represent a middle-ground in terms of redundancy and complexity of an equal-step system. For instance, the 15th root of 4 can be arrived at by taking every other tone in [[15edo|15edo]]. It doesn't repeat at one octave, but it repeats at two octaves, after having generated 15 tones. From there, the system is redundant with itself, as it now produces the same intervals two octaves higher than where they first appeared. |
| <h4>Original HTML content:</h4>
| | [[Category:edonoi]] |
| <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>macrotonal edonois</title></head><body>A macrotonal edonoi would be, by definition, a scale which meets two constraints:<br />
| | [[Category:macrotonal]] |
| <ul><li><a class="wiki_link" href="/macrotonal">macrotonal</a> - all steps are larger than a semitone</li><li><a class="wiki_link" href="/edonoi">edonoi</a> - short for &quot;equal divisions of a non-octave interval&quot; - the scale consists of a single step stacked over and over which does not repeat at an octave</li></ul><br />
| | [[Category:theory]] |
| Examples include equal-tempered <a class="wiki_link" href="/BP">Bohlen Pierce</a> (a.k.a. the 13th root of 3), the <a class="wiki_link" href="/square%20root%20of%2013%20over%2010">square root of 13:10</a>, the <a class="wiki_link" href="/12edt">12th root of 3</a>, the <a class="wiki_link" href="/4edf">4th root of 3:2</a>, and the <a class="wiki_link" href="/6edf">6th root of 3:2</a>.<br />
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| <span style="font-size: 17px; line-height: 25px;"><strong>Macrotonal edos</strong> </span><br />
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| Macrotonal edonoi are related, in step-size and equality of steps, to <a class="wiki_link" href="/macrotonal%20edos">macrotonal edos</a>, but while macrotonal edos are a finite set, macrotonal edonoi are theoretically infinite. Macrotonal edos are extremely <a class="wiki_link" href="/redundancy">redundant</a> systems. Not only is there a very limited set of intervals in one octave of a macrotonal edo, but thanks to octave equivalency, that small set repeats at every octave.<br />
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| <br />
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| Macrotonal edonoi, by not containing octaves at all, take away the redundancy of octave equivalence, and are thus much more complex systems to compose in. Each new step further out produces a brand new interval, with no octave-equivalent complement that came before it.<br />
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| <br />
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| If we consider macrotonal edos as distinct stopping-places in a continuum of scales with decreasing step size (from the 1200-cent step of 1edo, down to the 100-cent step of <a class="wiki_link" href="/12edo">12edo</a> which defines the edge of &quot;macrotonal&quot;), then macrotonal edonoi represent unique universes that are &quot;in the cracks&quot;.<br />
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| <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Equal Divisions of Compound Octaves"></a><!-- ws:end:WikiTextHeadingRule:0 -->Equal Divisions of Compound Octaves</h2>
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| <br />
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| What about dividing a compound octave, say, 4:1 or 8:1? Examples of this kind of scale would include the 15th root of 4 and the 22nd root of 8. I don't know whether or not we should use the term edonoi for these.<br />
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| These kinds of scales, equal divisions of compound octaves, represent a middle-ground in terms of redundancy and complexity of an equal-step system. For instance, the 15th root of 4 can be arrived at by taking every other tone in <a class="wiki_link" href="/15edo">15edo</a>. It doesn't repeat at one octave, but it repeats at two octaves, after having generated 15 tones. From there, the system is redundant with itself, as it now produces the same intervals two octaves higher than where they first appeared.</body></html></pre></div>
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