Macrotonal edonois - Revision history

Fredg999 category edits: Removing from Category:Theory using Cat-a-lot

2023-03-04T20:25:21Z

Removing from Category:Theory using Cat-a-lot

← Older revision		Revision as of 20:25, 4 March 2023
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	[[Category:edonoi]]		[[Category:edonoi]]
	[[Category:macrotonal]]		[[Category:macrotonal]]
	~~[[Category:theory]]~~

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

← Older revision		Revision as of 00:00, 17 July 2018
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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>~~
	~~: This revision was by author [[User:Andrew_Heathwaite\|Andrew_Heathwaite]] and made on <tt>2009-12-27 23:11:12 UTC</tt>.<br>~~
	~~: The original revision id was <tt>111123201</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">A macrotonal edonoi would be, by definition, a scale which meets two constraints:
	* [[macrotonal]] - all steps are larger than a semitone
	* [[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

	~~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>

	~~<~~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>

			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.

	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.

	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".

	==Equal Divisions of Compound Octaves==		==Equal Divisions of Compound Octaves==

	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.

	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 />
	~~<br />~~
	~~<span style="font-size: 17px; line-height~~: ~~25px;"><strong>Macrotonal edos</strong> </span><br />~~
	~~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 />
	~~<br />~~
	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 />
	~~<br />~~
	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 />
	~~<br />~~
	~~<!-- 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>
	~~<br />~~
	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 />
	~~<br />~~
	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>

Wikispaces>Andrew_Heathwaite: Imported revision 111123201 - Original comment:

2009-12-27T23:11:12Z

**Imported revision 111123201 - Original comment: **

← Older revision		Revision as of 23:11, 27 December 2009
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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:Andrew_Heathwaite\|Andrew_Heathwaite]] and made on <tt>2009-12-~~24 19~~:10:00 UTC</tt>.<br>		: This revision was by author [[User:Andrew_Heathwaite\|Andrew_Heathwaite]] and made on <tt>2009-12-27 23:11:12 UTC</tt>.<br>
	: The original revision id was <tt>~~111025587~~</tt>.<br>		: The original revision id was <tt>111123201</tt>.<br>
	: The revision comment was: <tt></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>		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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	<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:		<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:
	* [[macrotonal]] - all steps are larger than a semitone		* [[macrotonal]] - all steps are larger than a semitone
	* [[edonoi]] - it consists of a single step stacked over and over which does not repeat at an octave		* [[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

	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]].		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]].

	~~They~~ 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.		<span style="font-size: 17px; line-height: 25px;">Macrotonal edos </span>
			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.

	~~==equal divisions~~ of ~~compound octaves==~~		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.

	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. Do they ~~count as edonoi?~~</pre></div>		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".

			==Equal Divisions of Compound Octaves==

			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.

			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>
	<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>macrotonal edonois</title></head><body>A macrotonal edonoi would be, by definition, a scale which meets two constraints:<br />		<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 />
	<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> - it consists of a single step stacked over and over which does not repeat at an octave</li></ul><br />		<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 />
	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 />		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 />
	<br />		<br />
	~~They~~ 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.<br />		<span style="font-size: 17px; line-height: 25px;"><strong>Macrotonal edos</strong> </span><br />
			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 />
			<br />
			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 />
	<br />		<br />
	<!-- 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>		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 />
			<br />
			<!-- 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>
	<br />		<br />
	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. Do they ~~count as edonoi?~~</body></html></pre></div>		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 />
			<br />
			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>

Wikispaces>Andrew_Heathwaite: Imported revision 111025587 - Original comment:

2009-12-24T19:10:00Z

**Imported revision 111025587 - Original comment: **

← Older revision		Revision as of 19:10, 24 December 2009
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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:~~seraph57~~\|~~seraph57~~]] and made on <tt>2009-12-24 18:34:49 UTC</tt>.<br>		: This revision was by author [[User:Andrew_Heathwaite\|Andrew_Heathwaite]] and made on <tt>2009-12-24 19:10:00 UTC</tt>.<br>
	: The original revision id was <tt>~~111024993~~</tt>.<br>		: The original revision id was <tt>111025587</tt>.<br>
	: The revision comment was: <tt>~~added link~~</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>		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">~~EDONOI is short for "equal divisions~~ of a ~~non-~~octave ~~interval".~~		<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:
			* [[macrotonal]] - all steps are larger than a semitone
			* [[edonoi]] - it consists of a single step stacked over and over which does not repeat at an octave

	Examples include ~~the~~ equal-tempered [[BP\|Bohlen-Pierce ~~scale~~]] (a.k.a. the 13th root of 3), [[~~Carlos Alpha]], [[Carlos Beta]], [[Carlos Gamma~~]], the [[~~19ED3~~\|~~19th~~ root of 3]], the [[~~6edf~~\|~~6th~~ root of 3:2]] , ~~[[88cET]]~~ and the [[~~square root of 13 over 10~~\|~~square~~ root of 13:10]] .		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]].

	~~Some EDONOI contain an interval close~~ to ~~a 2:1 that might function like a stretched or squashed octave. They can thus be considered variations on~~ [[~~edo~~]]s.		They 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.

	~~Other EDONOI contain no approximation~~ of ~~an octave or a~~ compound octave (at least, not for a while), and continue generating new tones as they continue upward or downward. Such scales lack a very familiar compositional [[redundancy]], that of octave equivalence, and thus require special attention.		==equal divisions of compound octaves==

	~~==EDONOI Forum==~~		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. Do they count as edonoi?</pre></div>
	~~[[http~~:~~//xenharmonic.ning~~.~~com/group/equaldivisionofnonoctaveintervals\|EDONOI Forum at Xenharmonic Alliance]]~~</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>macrotonal edonois</title></head><body>~~EDONOI is short for~~ &~~amp~~;~~quot~~;equal ~~divisions~~ of a ~~non-octave interval~~&~~amp~~;~~quot~~;.<br />		<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 />
			<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> - it consists of a single step stacked over and over which does not repeat at an octave</li></ul><br />
			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 />
	<br />		<br />
	~~Examples include the equal~~-~~tempered <a class="wiki_link" href="/BP">Bohlen-Pierce scale</a> (a.k.a. the 13th root~~ of 3), <a class="wiki_link" href="/~~Carlos~~%~~20Alpha~~">~~Carlos Alpha~~</a>, ~~<~~a ~~class="wiki_link" href="/Carlos%20Beta">Carlos Beta</a>, <a class="wiki_link" href="/Carlos%20Gamma">Carlos Gamma</a>~~, the <a class="wiki_link" href="/19ED3">19th root of 3</a>, the <a class="wiki_link" href="/6edf">6th root of 3:2</a> , <a class="wiki_link" href="/88cET">88cET</a> and the <a class="wiki_link" href="/square%20root%20of%2013%20over%2010">square root of 13:10</a> .<br />		They 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.<br />
	<br />		<br />
	Some EDONOI contain an interval close to a 2:1 that might function like a stretched or squashed octave. They can thus be considered variations on <a class="wiki_link" href="/edo">edo</a>s.<br />		<!-- 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>
	~~<br />~~		<br />
	Other EDONOI contain no approximation of an octave or a compound octave (at least, not for a while), and continue generating new tones as they continue upward or downward. Such scales lack a very familiar compositional <a class="wiki_link" href="/redundancy">redundancy</a>, that of octave equivalence, and thus require special attention.<br />		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. Do they count as edonoi?</body></html></pre></div>
	~~<br />~~
	<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-~~EDONOI Forum~~"></a><!-- ws:end:WikiTextHeadingRule:0 -->~~EDONOI Forum~~</h2>
	<~~a class="wiki_link_ext" href="http:/~~/~~xenharmonic.ning.com/group/equaldivisionofnonoctaveintervals" rel="nofollow"~~>~~EDONOI Forum at Xenharmonic Alliance</~~a~~>~~</body></html></pre></div>

Wikispaces>seraph57: Imported revision 111024993 - Original comment: added link

2009-12-24T18:34:49Z

**Imported revision 111024993 - Original comment: added link**

← Older revision		Revision as of 18:34, 24 December 2009
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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:~~Andrew_Heathwaite~~\|~~Andrew_Heathwaite~~]] and made on <tt>2009-12-24 18:05:24 UTC</tt>.<br>		: This revision was by author [[User:seraph57\|seraph57]] and made on <tt>2009-12-24 18:34:49 UTC</tt>.<br>
	: The original revision id was <tt>~~111024331~~</tt>.<br>		: The original revision id was <tt>111024993</tt>.<br>
	: The revision comment was: <tt></tt><br>		: The revision comment was: <tt>added link</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>
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	Some EDONOI contain an interval close to a 2:1 that might function like a stretched or squashed octave. They can thus be considered variations on [[edo]]s.		Some EDONOI contain an interval close to a 2:1 that might function like a stretched or squashed octave. They can thus be considered variations on [[edo]]s.

	Other EDONOI contain no approximation of an octave or a compound octave (at least, not for a while), and continue generating new tones as they continue upward or downward. Such scales lack a very familiar compositional [[redundancy]], that of octave equivalence, and thus require special attention.</pre></div>		Other EDONOI contain no approximation of an octave or a compound octave (at least, not for a while), and continue generating new tones as they continue upward or downward. Such scales lack a very familiar compositional [[redundancy]], that of octave equivalence, and thus require special attention.

			==EDONOI Forum==
			[[http://xenharmonic.ning.com/group/equaldivisionofnonoctaveintervals\|EDONOI Forum at Xenharmonic Alliance]]</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>macrotonal edonois</title></head><body>EDONOI is short for &quot;equal divisions of a non-octave interval&quot;.<br />		<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>EDONOI is short for &quot;equal divisions of a non-octave interval&quot;.<br />
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	Some EDONOI contain an interval close to a 2:1 that might function like a stretched or squashed octave. They can thus be considered variations on <a class="wiki_link" href="/edo">edo</a>s.<br />		Some EDONOI contain an interval close to a 2:1 that might function like a stretched or squashed octave. They can thus be considered variations on <a class="wiki_link" href="/edo">edo</a>s.<br />
	<br />		<br />
	Other EDONOI contain no approximation of an octave or a compound octave (at least, not for a while), and continue generating new tones as they continue upward or downward. Such scales lack a very familiar compositional <a class="wiki_link" href="/redundancy">redundancy</a>, that of octave equivalence, and thus require special attention.</body></html></pre></div>		Other EDONOI contain no approximation of an octave or a compound octave (at least, not for a while), and continue generating new tones as they continue upward or downward. Such scales lack a very familiar compositional <a class="wiki_link" href="/redundancy">redundancy</a>, that of octave equivalence, and thus require special attention.<br />
			<br />
			<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-EDONOI Forum"></a><!-- ws:end:WikiTextHeadingRule:0 -->EDONOI Forum</h2>
			<a class="wiki_link_ext" href="http://xenharmonic.ning.com/group/equaldivisionofnonoctaveintervals" rel="nofollow">EDONOI Forum at Xenharmonic Alliance</a></body></html></pre></div>

Wikispaces>Andrew_Heathwaite: Imported revision 111024331 - Original comment:

2009-12-24T18:05:24Z

**Imported revision 111024331 - Original comment: **

Wikispaces>Andrew_Heathwaite: Imported revision 111024307 - Original comment:

2009-12-24T18:04:43Z

**Imported revision 111024307 - Original comment: **

Wikispaces>Andrew_Heathwaite: Imported revision 111024283 - Original comment:

2009-12-24T18:04:14Z

**Imported revision 111024283 - Original comment: **

New page

<h2>IMPORTED REVISION FROM WIKISPACES</h2>
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>2009-12-24 18:04:14 UTC</tt>.<br>
: The original revision id was <tt>111024283</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">EDONOI is short for "equal divisions of a non-octave interval".

Examples include the equal-tempered [[BP|Bohlen-Pierce scale]] (a.k.a. the 13th root of 3), [[Carlos Alpha]], [[Carlos Beta]], [[Carlos Gamma]], the [[19ED3|19th root of 3]], the [[6df|6th root of 3:2]], [[88cET]] and the [[square root of 13:10]].

Some EDONOI contain an interval close to a 2:1 that might function like a stretched or squashed octave. They can thus be considered variations on [[edo]]s.

Other EDONOI contain no approximation of an octave or a compound octave (at least, not for a while), and continue generating new tones as they continue upward or downward. Such scales lack a very familiar compositional [[redundancy]], that of octave equivalence, and thus require special attention.</pre></div>
<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>macrotonal edonois</title></head><body>EDONOI is short for &quot;equal divisions of a non-octave interval&quot;.<br />
<br />
Examples include the equal-tempered <a class="wiki_link" href="/BP">Bohlen-Pierce scale</a> (a.k.a. the 13th root of 3), <a class="wiki_link" href="/Carlos%20Alpha">Carlos Alpha</a>, <a class="wiki_link" href="/Carlos%20Beta">Carlos Beta</a>, <a class="wiki_link" href="/Carlos%20Gamma">Carlos Gamma</a>, the <a class="wiki_link" href="/19ED3">19th root of 3</a>, the <a class="wiki_link" href="/6df">6th root of 3:2</a>, <a class="wiki_link" href="/88cET">88cET</a> and the [[square root of 13:10]].<br />
<br />
Some EDONOI contain an interval close to a 2:1 that might function like a stretched or squashed octave. They can thus be considered variations on <a class="wiki_link" href="/edo">edo</a>s.<br />
<br />
Other EDONOI contain no approximation of an octave or a compound octave (at least, not for a while), and continue generating new tones as they continue upward or downward. Such scales lack a very familiar compositional <a class="wiki_link" href="/redundancy">redundancy</a>, that of octave equivalence, and thus require special attention.</body></html></pre></div>

← Older revision		Revision as of 18:05, 24 December 2009
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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:Andrew_Heathwaite\|Andrew_Heathwaite]] and made on <tt>2009-12-24 18:04:43 UTC</tt>.<br>		: This revision was by author [[User:Andrew_Heathwaite\|Andrew_Heathwaite]] and made on <tt>2009-12-24 18:05:24 UTC</tt>.<br>
	: The original revision id was <tt>~~111024307~~</tt>.<br>		: The original revision id was <tt>111024331</tt>.<br>
	: The revision comment was: <tt></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>		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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	<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">EDONOI is short for "equal divisions of a non-octave interval".		<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">EDONOI is short for "equal divisions of a non-octave interval".

	Examples include the equal-tempered [[BP\|Bohlen-Pierce scale]] (a.k.a. the 13th root of 3), [[Carlos Alpha]], [[Carlos Beta]], [[Carlos Gamma]], the [[19ED3\|19th root of 3]], the [[6edf\|6th root of 3:2]] , [[88cET]] and the [[square root of 13/10]].		Examples include the equal-tempered [[BP\|Bohlen-Pierce scale]] (a.k.a. the 13th root of 3), [[Carlos Alpha]], [[Carlos Beta]], [[Carlos Gamma]], the [[19ED3\|19th root of 3]], the [[6edf\|6th root of 3:2]] , [[88cET]] and the [[square root of 13 over 10\|square root of 13:10]] .

	Some EDONOI contain an interval close to a 2:1 that might function like a stretched or squashed octave. They can thus be considered variations on [[edo]]s.		Some EDONOI contain an interval close to a 2:1 that might function like a stretched or squashed octave. They can thus be considered variations on [[edo]]s.
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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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>macrotonal edonois</title></head><body>EDONOI is short for &quot;equal divisions of a non-octave interval&quot;.<br />		<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>EDONOI is short for &quot;equal divisions of a non-octave interval&quot;.<br />
	<br />		<br />
	Examples include the equal-tempered <a class="wiki_link" href="/BP">Bohlen-Pierce scale</a> (a.k.a. the 13th root of 3), <a class="wiki_link" href="/Carlos%20Alpha">Carlos Alpha</a>, <a class="wiki_link" href="/Carlos%20Beta">Carlos Beta</a>, <a class="wiki_link" href="/Carlos%20Gamma">Carlos Gamma</a>, the <a class="wiki_link" href="/19ED3">19th root of 3</a>, the <a class="wiki_link" href="/6edf">6th root of 3:2</a> , <a class="wiki_link" href="/88cET">88cET</a> and the [[square root of 13/~~10]]~~.<br />		Examples include the equal-tempered <a class="wiki_link" href="/BP">Bohlen-Pierce scale</a> (a.k.a. the 13th root of 3), <a class="wiki_link" href="/Carlos%20Alpha">Carlos Alpha</a>, <a class="wiki_link" href="/Carlos%20Beta">Carlos Beta</a>, <a class="wiki_link" href="/Carlos%20Gamma">Carlos Gamma</a>, the <a class="wiki_link" href="/19ED3">19th root of 3</a>, the <a class="wiki_link" href="/6edf">6th root of 3:2</a> , <a class="wiki_link" href="/88cET">88cET</a> and the <a class="wiki_link" href="/square%20root%20of%2013%20over%2010">square root of 13:10</a> .<br />
	<br />		<br />
	Some EDONOI contain an interval close to a 2:1 that might function like a stretched or squashed octave. They can thus be considered variations on <a class="wiki_link" href="/edo">edo</a>s.<br />		Some EDONOI contain an interval close to a 2:1 that might function like a stretched or squashed octave. They can thus be considered variations on <a class="wiki_link" href="/edo">edo</a>s.<br />
	<br />		<br />
	Other EDONOI contain no approximation of an octave or a compound octave (at least, not for a while), and continue generating new tones as they continue upward or downward. Such scales lack a very familiar compositional <a class="wiki_link" href="/redundancy">redundancy</a>, that of octave equivalence, and thus require special attention.</body></html></pre></div>		Other EDONOI contain no approximation of an octave or a compound octave (at least, not for a while), and continue generating new tones as they continue upward or downward. Such scales lack a very familiar compositional <a class="wiki_link" href="/redundancy">redundancy</a>, that of octave equivalence, and thus require special attention.</body></html></pre></div>

← Older revision		Revision as of 18:04, 24 December 2009
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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:Andrew_Heathwaite\|Andrew_Heathwaite]] and made on <tt>2009-12-24 18:04:14 UTC</tt>.<br>		: This revision was by author [[User:Andrew_Heathwaite\|Andrew_Heathwaite]] and made on <tt>2009-12-24 18:04:43 UTC</tt>.<br>
	: The original revision id was <tt>~~111024283~~</tt>.<br>		: The original revision id was <tt>111024307</tt>.<br>
	: The revision comment was: <tt></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>		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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	<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">EDONOI is short for "equal divisions of a non-octave interval".		<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">EDONOI is short for "equal divisions of a non-octave interval".

	Examples include the equal-tempered [[BP\|Bohlen-Pierce scale]] (a.k.a. the 13th root of 3), [[Carlos Alpha]], [[Carlos Beta]], [[Carlos Gamma]], the [[19ED3\|19th root of 3]], the [[~~6df~~\|6th root of 3:2]], [[88cET]] and the [[square root of 13:10]].		Examples include the equal-tempered [[BP\|Bohlen-Pierce scale]] (a.k.a. the 13th root of 3), [[Carlos Alpha]], [[Carlos Beta]], [[Carlos Gamma]], the [[19ED3\|19th root of 3]], the [[6edf\|6th root of 3:2]] , [[88cET]] and the [[square root of 13/10]].

	Some EDONOI contain an interval close to a 2:1 that might function like a stretched or squashed octave. They can thus be considered variations on [[edo]]s.		Some EDONOI contain an interval close to a 2:1 that might function like a stretched or squashed octave. They can thus be considered variations on [[edo]]s.
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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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>macrotonal edonois</title></head><body>EDONOI is short for &quot;equal divisions of a non-octave interval&quot;.<br />		<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>EDONOI is short for &quot;equal divisions of a non-octave interval&quot;.<br />
	<br />		<br />
	Examples include the equal-tempered <a class="wiki_link" href="/BP">Bohlen-Pierce scale</a> (a.k.a. the 13th root of 3), <a class="wiki_link" href="/Carlos%20Alpha">Carlos Alpha</a>, <a class="wiki_link" href="/Carlos%20Beta">Carlos Beta</a>, <a class="wiki_link" href="/Carlos%20Gamma">Carlos Gamma</a>, the <a class="wiki_link" href="/19ED3">19th root of 3</a>, the <a class="wiki_link" href="/~~6df~~">6th root of 3:2</a>, <a class="wiki_link" href="/88cET">88cET</a> and the [[square root of 13:10]].<br />		Examples include the equal-tempered <a class="wiki_link" href="/BP">Bohlen-Pierce scale</a> (a.k.a. the 13th root of 3), <a class="wiki_link" href="/Carlos%20Alpha">Carlos Alpha</a>, <a class="wiki_link" href="/Carlos%20Beta">Carlos Beta</a>, <a class="wiki_link" href="/Carlos%20Gamma">Carlos Gamma</a>, the <a class="wiki_link" href="/19ED3">19th root of 3</a>, the <a class="wiki_link" href="/6edf">6th root of 3:2</a> , <a class="wiki_link" href="/88cET">88cET</a> and the [[square root of 13/10]].<br />
	<br />		<br />
	Some EDONOI contain an interval close to a 2:1 that might function like a stretched or squashed octave. They can thus be considered variations on <a class="wiki_link" href="/edo">edo</a>s.<br />		Some EDONOI contain an interval close to a 2:1 that might function like a stretched or squashed octave. They can thus be considered variations on <a class="wiki_link" href="/edo">edo</a>s.<br />
	<br />		<br />
	Other EDONOI contain no approximation of an octave or a compound octave (at least, not for a while), and continue generating new tones as they continue upward or downward. Such scales lack a very familiar compositional <a class="wiki_link" href="/redundancy">redundancy</a>, that of octave equivalence, and thus require special attention.</body></html></pre></div>		Other EDONOI contain no approximation of an octave or a compound octave (at least, not for a while), and continue generating new tones as they continue upward or downward. Such scales lack a very familiar compositional <a class="wiki_link" href="/redundancy">redundancy</a>, that of octave equivalence, and thus require special attention.</body></html></pre></div>

Macrotonal edonois - Revision history

Fredg999 category edits: Removing from Category:Theory using Cat-a-lot

Wikispaces>FREEZE at 00:00, 17 July 2018

Wikispaces>Andrew_Heathwaite: **Imported revision 111123201 - Original comment: **

Wikispaces>Andrew_Heathwaite: **Imported revision 111025587 - Original comment: **

Wikispaces>seraph57: **Imported revision 111024993 - Original comment: added link**

Wikispaces>Andrew_Heathwaite: **Imported revision 111024331 - Original comment: **