Maximal harmony epimorphic scales - Revision history

ArrowHead294: Clean up

2025-02-11T20:10:27Z

Clean up

← Older revision		Revision as of 20:10, 11 February 2025
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	If we look at all periodic scales [[Periodic_scale#Epimorphism\|epimorphic]] with respect to a given val, a certain number will achieve the maximal possible number of consonant dyads with respect to a given consonance set. In the 5-limit, that set will be the 5-limit diamond, {6/5, 5/4, 4/3, 3/2, 8/5, 5/3}. In case of a tie, the tie can sometimes be broken by means of larger chords (triads, tetrads etc.) Connectivity of the [[Graph-theoretic_properties_of_scales\|graph of the scale]] is another way of rating harmonic content; algebraic connectivity is especially useful for this because it can take non-integer values and is easy to compute. Below we list a few examples.		If we look at all periodic scales [[Periodic_scale#Epimorphism\|epimorphic]] with respect to a given val, a certain number will achieve the maximal possible number of consonant dyads with respect to a given consonance set. In the 5-limit, that set will be the 5-limit diamond, {6/5, 5/4, 4/3, 3/2, 8/5, 5/3}. In case of a tie, the tie can sometimes be broken by means of larger chords (triads, tetrads etc.) Connectivity of the [[Graph-theoretic_properties_of_scales\|graph of the scale]] is another way of rating harmonic content; algebraic connectivity is especially useful for this because it can take non-integer values and is easy to compute. Below we list a few examples.

	=5-limit=		= 5-limit =
			== Five notes ==
			[[semilim2]]

	~~==Five notes==~~		[[semilim3]]
	[[~~semilim2\|semilim2~~]]

	[[~~semilim3\|semilim3~~]]		== Six notes, 6b val ==
			[[dwarf6_5]]

	~~==Six notes, 6b val==~~		[[cluster6e]]
	[[~~dwarf6_5\|dwarf6_5]]~~

	~~[[cluster6e\|~~cluster6e]]

	[[x-wing1\|x-wing1]]		[[x-wing1\|x-wing1]]
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	[[x-wing2\|x-wing2]]		[[x-wing2\|x-wing2]]

	==Seven notes==		== Seven notes ==
	[[zarlino~~\|zarlino]]~~		[[zarlino]]

	~~[[mavchrome6\|mavchrome6]]~~

	~~==Eight notes==~~
	~~[[semimaj1\|semimaj1~~]]

	[[~~semimaj2\|semimaj2~~]]		[[mavchrome6]]

	==~~Nine~~ notes==		== Eight notes ==
	[[~~mavdie1\|mavdie1~~]]		[[semimaj1]]

	~~==Ten notes==~~		[[semimaj2]]
	[[~~blackchrome1\|blackchrome1~~]]

	[[~~blackchrome2\|blackchrome2~~]]		== Nine notes ==
			[[mavdie1]]

	=~~7 odd limit~~=		== Ten notes ==
			[[blackchrome1]]

	~~==Seven notes==~~		[[blackchrome2]]
	[[~~maxsev1\|maxsev1~~]]

	[[~~maxsev2\|maxsev2~~]]		= 7 odd limit =
			== Seven notes ==
			[[maxsev1]]

	~~=Seven limit marvel=~~		[[maxsev2]]

	==Seven notes==		= Seven limit marvel =
			== Seven notes ==
	[[Gypsy_scale\|Gypsy scale]]		[[Gypsy_scale\|Gypsy scale]]

	=Eleven limit marvel=		= Eleven limit marvel =
			== Seven notes ==
	==Seven notes==		[[marvel11max7a]]
	[[~~marvel11max7a\|~~marvel11max7a]]

	[[~~marvel11max7b\|~~marvel11max7b]]		[[marvel11max7b]]

	~~<br>~~		{{Navbox scale gallery}}
	{{~~Scale~~ gallery}}

	[[Category:Lists of scales]]		[[Category:Lists of scales]]

BudjarnLambeth at 04:40, 2 December 2024

2024-12-02T04:40:13Z

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	[[marvel11max7b\|marvel11max7b]]		[[marvel11max7b\|marvel11max7b]]

			<br>
	{{Scale gallery}}		{{Scale gallery}}

	[[Category:Lists of scales]]		[[Category:Lists of scales]]

BudjarnLambeth at 04:40, 2 December 2024

2024-12-02T04:40:02Z

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	[[marvel11max7b\|marvel11max7b]]		[[marvel11max7b\|marvel11max7b]]


	{{Scale gallery}}		{{Scale gallery}}

	[[Category:Lists of scales]]		[[Category:Lists of scales]]

BudjarnLambeth: {{Scale gallery}}

2024-12-02T04:39:50Z

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	[[marvel11max7b\|marvel11max7b]]		[[marvel11max7b\|marvel11max7b]]

			{{Scale gallery}}

	[[Category:Lists of scales]]		[[Category:Lists of scales]]

Fredg999: Fixed broken internal link

2023-05-02T05:01:37Z

Fixed broken internal link

← Older revision		Revision as of 05:01, 2 May 2023
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	If we look at all periodic scales [[Periodic_scale#~~Epimorphic~~\|epimorphic]] with respect to a given val, a certain number will achieve the maximal possible number of consonant dyads with respect to a given consonance set. In the 5-limit, that set will be the 5-limit diamond, {6/5, 5/4, 4/3, 3/2, 8/5, 5/3}. In case of a tie, the tie can sometimes be broken by means of larger chords (triads, tetrads etc.) Connectivity of the [[Graph-theoretic_properties_of_scales\|graph of the scale]] is another way of rating harmonic content; algebraic connectivity is especially useful for this because it can take non-integer values and is easy to compute. Below we list a few examples.		If we look at all periodic scales [[Periodic_scale#Epimorphism\|epimorphic]] with respect to a given val, a certain number will achieve the maximal possible number of consonant dyads with respect to a given consonance set. In the 5-limit, that set will be the 5-limit diamond, {6/5, 5/4, 4/3, 3/2, 8/5, 5/3}. In case of a tie, the tie can sometimes be broken by means of larger chords (triads, tetrads etc.) Connectivity of the [[Graph-theoretic_properties_of_scales\|graph of the scale]] is another way of rating harmonic content; algebraic connectivity is especially useful for this because it can take non-integer values and is easy to compute. Below we list a few examples.

	=5-limit=		=5-limit=

BudjarnLambeth: Categorised this uncategorised page

2023-04-26T01:15:27Z

Categorised this uncategorised page

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	[[marvel11max7b\|marvel11max7b]]		[[marvel11max7b\|marvel11max7b]]
			[[Category:Lists of scales]]

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>~~		If we look at all periodic scales [[Periodic_scale#Epimorphic\|epimorphic]] with respect to a given val, a certain number will achieve the maximal possible number of consonant dyads with respect to a given consonance set. In the 5-limit, that set will be the 5-limit diamond, {6/5, 5/4, 4/3, 3/2, 8/5, 5/3}. In case of a tie, the tie can sometimes be broken by means of larger chords (triads, tetrads etc.) Connectivity of the [[Graph-theoretic_properties_of_scales\|graph of the scale]] is another way of rating harmonic content; algebraic connectivity is especially useful for this because it can take non-integer values and is easy to compute. Below we list a few examples.
	~~This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>~~
	~~: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2013-12-13 16:13:59 UTC</tt>.<br>~~
	~~: The original revision id was <tt>477287794</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">If we look at all periodic scales [[~~Periodic scale~~#Epimorphic\|epimorphic]] with respect to a given val, a certain number will achieve the maximal possible number of consonant dyads with respect to a given consonance set. In the 5-limit, that set will be the 5-limit diamond, {6/5, 5/4, 4/3, 3/2, 8/5, 5/3}. In case of a tie, the tie can sometimes be broken by means of larger chords (triads, tetrads etc.) Connectivity of the [[Graph-~~theoretic properties of scales~~\|graph of the scale]] is another way of rating harmonic content; algebraic connectivity is especially useful for this because it can take non-integer values and is easy to compute. Below we list a few examples.

	=5-limit=		=5-limit=

	==Five notes==		==Five notes==
	[[semilim2]]		[[semilim2\|semilim2]]
	[[semilim3]]
			[[semilim3\|semilim3]]

	==Six notes, 6b val==		==Six notes, 6b val==
	[[dwarf6_5]]		[[dwarf6_5\|dwarf6_5]]
	[[cluster6e]]
	[[x-wing1]]		[[cluster6e\|cluster6e]]
	[[x-wing2]]
			[[x-wing1\|x-wing1]]

			[[x-wing2\|x-wing2]]

	==Seven notes==		==Seven notes==
	[[zarlino]]		[[zarlino\|zarlino]]
	[[mavchrome6]]
			[[mavchrome6\|mavchrome6]]

	==Eight notes==		==Eight notes==
	[[semimaj1]]		[[semimaj1\|semimaj1]]
	[[semimaj2]]
			[[semimaj2\|semimaj2]]

	==Nine notes==		==Nine notes==
	[[mavdie1]]		[[mavdie1\|mavdie1]]

	==Ten notes==		==Ten notes==
	[[blackchrome1]]		[[blackchrome1\|blackchrome1]]
	[[blackchrome2]]
			[[blackchrome2\|blackchrome2]]

	=7 odd limit=		=7 odd limit=

	==Seven notes==		==Seven notes==
	[[maxsev1]]		[[maxsev1\|maxsev1]]
	[[maxsev2]]
			[[maxsev2\|maxsev2]]

	=Seven limit marvel=		=Seven limit marvel=

	==Seven notes==		==Seven notes==
	[[Gypsy scale]]		[[Gypsy_scale\|Gypsy scale]]

	=Eleven limit marvel=		=Eleven limit marvel=

	==Seven notes==		==Seven notes==
	[[marvel11max7a]]		[[marvel11max7a\|marvel11max7a]]
	[[marvel11max7b]]~~</pre></div>~~
	~~<h4>Original HTML content:</h4>~~		[[marvel11max7b\|marvel11max7b]]
	<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>Maximal harmony epimorphic scales</title></head><body>If we look at all periodic scales <a class="wiki_link" href="/Periodic%20scale#Epimorphic">epimorphic</a> with respect to a given val, a certain number will achieve the maximal possible number of consonant dyads with respect to a given consonance set. In the 5-limit, that set will be the 5-limit diamond, {6/5, 5/4, 4/3, 3/2, 8/5, 5/3}. In case of a tie, the tie can sometimes be broken by means of larger chords (triads, tetrads etc.) Connectivity of the <a class="wiki_link" href="/Graph-theoretic%20properties%20of%20scales">graph of the scale</a> is another way of rating harmonic content; algebraic connectivity is especially useful for this because it can take non-integer values and is easy to compute. Below we list a few examples.<br />
	~~<br />~~
	~~<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x5-limit"></a><!-- ws:end:WikiTextHeadingRule:0 -->5-limit</h1>~~
	~~<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x5-limit-Five notes"></a><!-- ws:end:WikiTextHeadingRule:2 -->Five notes</h2>~~
	~~<a class="wiki_link" href="/semilim2">semilim2</a><br />~~
	~~<a class="wiki_link" href="/semilim3">semilim3</a><br />~~
	~~<br />~~
	<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x5-limit-Six notes, 6b val"></a><!-- ws:end:WikiTextHeadingRule:4 -->Six notes, 6b val</h2>
	~~<a class="wiki_link" href="/dwarf6_5">dwarf6_5</a><br />~~
	~~<a class="wiki_link" href="/cluster6e">cluster6e</a><br />~~
	~~<a class="wiki_link" href="/x-wing1">x-wing1</a><br />~~
	~~<a class="wiki_link" href="/x-wing2">x-wing2</a><br />~~
	~~<br />~~
	~~<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x5-limit-Seven notes"></a><!-- ws:end:WikiTextHeadingRule:6 -->Seven notes</h2>~~
	~~<a class="wiki_link" href="/zarlino">zarlino</a><br />~~
	~~<a class="wiki_link" href="/mavchrome6">mavchrome6</a><br />~~
	~~<br />~~
	~~<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="x5-limit-Eight notes"></a><!-- ws:end:WikiTextHeadingRule:8 -->Eight notes</h2>~~
	~~<a class="wiki_link" href="/semimaj1">semimaj1</a><br />~~
	~~<a class="wiki_link" href="/semimaj2">semimaj2</a><br />~~
	~~<br />~~
	~~<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x5-limit-Nine notes"></a><!-- ws:end:WikiTextHeadingRule:10 -->Nine notes</h2>~~
	~~<a class="wiki_link" href="/mavdie1">mavdie1</a><br />~~
	~~<br />~~
	~~<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="x5-limit-Ten notes"></a><!-- ws:end:WikiTextHeadingRule:12 -->Ten notes</h2>~~
	~~<a class="wiki_link" href="/blackchrome1">blackchrome1</a><br />~~
	~~<a class="wiki_link" href="/blackchrome2">blackchrome2</a><br />~~
	~~<br />~~
	~~<!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="x7 odd limit"></a><!-- ws:end:WikiTextHeadingRule:14 -->7 odd limit</h1>~~
	<!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="x7 odd limit-Seven notes"></a><!-- ws:end:WikiTextHeadingRule:16 -->Seven notes</h2>
	~~<a class="wiki_link" href="/maxsev1">maxsev1</a><br />~~
	~~<a class="wiki_link" href="/maxsev2">maxsev2</a><br />~~
	~~<br />~~
	<!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Seven limit marvel"></a><!-- ws:end:WikiTextHeadingRule:18 -->Seven limit marvel</h1>
	<!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Seven limit marvel-Seven notes"></a><!-- ws:end:WikiTextHeadingRule:20 -->Seven notes</h2>
	~~<a class="wiki_link" href="/Gypsy%20scale">Gypsy scale</a><br />~~
	~~<br />~~
	<!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="Eleven limit marvel"></a><!-- ws:end:WikiTextHeadingRule:22 -->Eleven limit marvel</h1>
	<!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Eleven limit marvel-Seven notes"></a><!-- ws:end:WikiTextHeadingRule:24 -->Seven notes</h2>
	~~<a class="wiki_link" href="/marvel11max7a">marvel11max7a</a><br />~~
	~~<a class="wiki_link" href="/marvel11max7b">marvel11max7b</a></body></html></pre></div>~~

Wikispaces>genewardsmith: Imported revision 477287794 - Original comment:

2013-12-13T16:13:59Z

**Imported revision 477287794 - Original comment: **

← Older revision		Revision as of 16:13, 13 December 2013
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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:genewardsmith\|genewardsmith]] and made on <tt>2013-02-~~14 12~~:08:22 UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2013-12-13 16:13:59 UTC</tt>.<br>
	: The original revision id was <tt>~~407006390~~</tt>.<br>		: The original revision id was <tt>477287794</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>
	<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">If we look at all periodic scales epimorphic with respect to a given val, a certain number will achieve the maximal possible number of consonant dyads with respect to a given consonance set. In the 5-limit, that set will be the 5-limit diamond, {6/5, 5/4, 4/3, 3/2, 8/5, 5/3}. In case of a tie, the tie can sometimes be broken by means of larger chords (triads, tetrads etc.) Connectivity of the [[Graph-theoretic properties of scales\|graph of the scale]] is another way of rating harmonic content; algebraic connectivity is especially useful for this because it can take non-integer values and is easy to compute. Below we list a few examples.		<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">If we look at all periodic scales [[Periodic scale#Epimorphic\|epimorphic]] with respect to a given val, a certain number will achieve the maximal possible number of consonant dyads with respect to a given consonance set. In the 5-limit, that set will be the 5-limit diamond, {6/5, 5/4, 4/3, 3/2, 8/5, 5/3}. In case of a tie, the tie can sometimes be broken by means of larger chords (triads, tetrads etc.) Connectivity of the [[Graph-theoretic properties of scales\|graph of the scale]] is another way of rating harmonic content; algebraic connectivity is especially useful for this because it can take non-integer values and is easy to compute. Below we list a few examples.

	=5-limit=		=5-limit=
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	[[marvel11max7b]]</pre></div>		[[marvel11max7b]]</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>Maximal harmony epimorphic scales</title></head><body>If we look at all periodic scales epimorphic with respect to a given val, a certain number will achieve the maximal possible number of consonant dyads with respect to a given consonance set. In the 5-limit, that set will be the 5-limit diamond, {6/5, 5/4, 4/3, 3/2, 8/5, 5/3}. In case of a tie, the tie can sometimes be broken by means of larger chords (triads, tetrads etc.) Connectivity of the <a class="wiki_link" href="/Graph-theoretic%20properties%20of%20scales">graph of the scale</a> is another way of rating harmonic content; algebraic connectivity is especially useful for this because it can take non-integer values and is easy to compute. Below we list a few examples.<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>Maximal harmony epimorphic scales</title></head><body>If we look at all periodic scales <a class="wiki_link" href="/Periodic%20scale#Epimorphic">epimorphic</a> with respect to a given val, a certain number will achieve the maximal possible number of consonant dyads with respect to a given consonance set. In the 5-limit, that set will be the 5-limit diamond, {6/5, 5/4, 4/3, 3/2, 8/5, 5/3}. In case of a tie, the tie can sometimes be broken by means of larger chords (triads, tetrads etc.) Connectivity of the <a class="wiki_link" href="/Graph-theoretic%20properties%20of%20scales">graph of the scale</a> is another way of rating harmonic content; algebraic connectivity is especially useful for this because it can take non-integer values and is easy to compute. Below we list a few examples.<br />
	<br />		<br />
	<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x5-limit"></a><!-- ws:end:WikiTextHeadingRule:0 -->5-limit</h1>		<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x5-limit"></a><!-- ws:end:WikiTextHeadingRule:0 -->5-limit</h1>

Wikispaces>genewardsmith: Imported revision 407006390 - Original comment:

2013-02-14T12:08:22Z

**Imported revision 407006390 - Original comment: **

← Older revision		Revision as of 12:08, 14 February 2013
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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:genewardsmith\|genewardsmith]] and made on <tt>2013-02-14 11:34:52 UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2013-02-14 12:08:22 UTC</tt>.<br>
	: The original revision id was <tt>~~406993954~~</tt>.<br>		: The original revision id was <tt>407006390</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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	=Seven limit marvel=		=Seven limit marvel=
	==Seven notes==		==Seven notes==
	[[Gypsy scale]]</pre></div>		[[Gypsy scale]]

			=Eleven limit marvel=
			==Seven notes==
			[[marvel11max7a]]
			[[marvel11max7b]]</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>Maximal harmony epimorphic scales</title></head><body>If we look at all periodic scales epimorphic with respect to a given val, a certain number will achieve the maximal possible number of consonant dyads with respect to a given consonance set. In the 5-limit, that set will be the 5-limit diamond, {6/5, 5/4, 4/3, 3/2, 8/5, 5/3}. In case of a tie, the tie can sometimes be broken by means of larger chords (triads, tetrads etc.) Connectivity of the <a class="wiki_link" href="/Graph-theoretic%20properties%20of%20scales">graph of the scale</a> is another way of rating harmonic content; algebraic connectivity is especially useful for this because it can take non-integer values and is easy to compute. Below we list a few examples.<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>Maximal harmony epimorphic scales</title></head><body>If we look at all periodic scales epimorphic with respect to a given val, a certain number will achieve the maximal possible number of consonant dyads with respect to a given consonance set. In the 5-limit, that set will be the 5-limit diamond, {6/5, 5/4, 4/3, 3/2, 8/5, 5/3}. In case of a tie, the tie can sometimes be broken by means of larger chords (triads, tetrads etc.) Connectivity of the <a class="wiki_link" href="/Graph-theoretic%20properties%20of%20scales">graph of the scale</a> is another way of rating harmonic content; algebraic connectivity is especially useful for this because it can take non-integer values and is easy to compute. Below we list a few examples.<br />
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	<!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Seven limit marvel"></a><!-- ws:end:WikiTextHeadingRule:18 -->Seven limit marvel</h1>		<!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Seven limit marvel"></a><!-- ws:end:WikiTextHeadingRule:18 -->Seven limit marvel</h1>
	<!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Seven limit marvel-Seven notes"></a><!-- ws:end:WikiTextHeadingRule:20 -->Seven notes</h2>		<!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Seven limit marvel-Seven notes"></a><!-- ws:end:WikiTextHeadingRule:20 -->Seven notes</h2>
	<a class="wiki_link" href="/Gypsy%20scale">Gypsy scale</a></body></html></pre></div>		<a class="wiki_link" href="/Gypsy%20scale">Gypsy scale</a><br />
			<br />
			<!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="Eleven limit marvel"></a><!-- ws:end:WikiTextHeadingRule:22 -->Eleven limit marvel</h1>
			<!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Eleven limit marvel-Seven notes"></a><!-- ws:end:WikiTextHeadingRule:24 -->Seven notes</h2>
			<a class="wiki_link" href="/marvel11max7a">marvel11max7a</a><br />
			<a class="wiki_link" href="/marvel11max7b">marvel11max7b</a></body></html></pre></div>

Wikispaces>genewardsmith: Imported revision 406993954 - Original comment:

2013-02-14T11:34:52Z

**Imported revision 406993954 - Original comment: **

← Older revision		Revision as of 11:34, 14 February 2013
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	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:genewardsmith\|genewardsmith]] and made on <tt>2013-02-14 11:34:20 UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2013-02-14 11:34:52 UTC</tt>.<br>
	: The original revision id was <tt>~~406993732~~</tt>.<br>		: The original revision id was <tt>406993954</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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	[[maxsev2]]		[[maxsev2]]

	=~~Marvel~~=		=Seven limit marvel=
	==Seven notes==		==Seven notes==
	[[Gypsy scale]]</pre></div>		[[Gypsy scale]]</pre></div>
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	<a class="wiki_link" href="/maxsev2">maxsev2</a><br />		<a class="wiki_link" href="/maxsev2">maxsev2</a><br />
	<br />		<br />
	<!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="~~Marvel~~"></a><!-- ws:end:WikiTextHeadingRule:18 -->~~Marvel~~</h1>		<!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Seven limit marvel"></a><!-- ws:end:WikiTextHeadingRule:18 -->Seven limit marvel</h1>
	<!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="~~Marvel~~-Seven notes"></a><!-- ws:end:WikiTextHeadingRule:20 -->Seven notes</h2>		<!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Seven limit marvel-Seven notes"></a><!-- ws:end:WikiTextHeadingRule:20 -->Seven notes</h2>
	<a class="wiki_link" href="/Gypsy%20scale">Gypsy scale</a></body></html></pre></div>		<a class="wiki_link" href="/Gypsy%20scale">Gypsy scale</a></body></html></pre></div>

Maximal harmony epimorphic scales - Revision history

ArrowHead294: Clean up

BudjarnLambeth at 04:40, 2 December 2024

BudjarnLambeth at 04:40, 2 December 2024

BudjarnLambeth: {{Scale gallery}}

Fredg999: Fixed broken internal link

BudjarnLambeth: Categorised this uncategorised page

Wikispaces>FREEZE at 00:00, 17 July 2018

Wikispaces>genewardsmith: **Imported revision 477287794 - Original comment: **

Wikispaces>genewardsmith: **Imported revision 407006390 - Original comment: **

Wikispaces>genewardsmith: **Imported revision 406993954 - Original comment: **

Wikispaces>genewardsmith: Imported revision 477287794 - Original comment:

Wikispaces>genewardsmith: Imported revision 407006390 - Original comment:

Wikispaces>genewardsmith: Imported revision 406993954 - Original comment: