Kite's Genchain mode numbering: Difference between revisions
Wikispaces>TallKite **Imported revision 593196904 - Original comment: ** |
Wikispaces>TallKite **Imported revision 593196918 - Original comment: ** |
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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:TallKite|TallKite]] and made on <tt>2016-09-24 03: | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-09-24 03:56:23 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>593196918</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">= = | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=MOS Scales= | ||
[[toc]] | [[toc]] | ||
**Mode numbers** provide a way to name MOS, MODMOS and even non-MOS rank-2 scales and modes systematically. Like [[xenharmonic/Modal UDP notation|Modal UDP notation]], it starts with the convention of using //some-temperament-name//[//some-number//] to create a generator-chain, and adds a way to number each mode uniquely. For example, here are all the modes of Meantone[7], using ~3/2 as the generator: | **Mode numbers** provide a way to name MOS, MODMOS and even non-MOS rank-2 scales and modes systematically. Like [[xenharmonic/Modal UDP notation|Modal UDP notation]], it starts with the convention of using //some-temperament-name//[//some-number//] to create a generator-chain, and adds a way to number each mode uniquely. | ||
For example, here are all the modes of Meantone[7], using ~3/2 as the generator: | |||
|| old scale name || new scale name || sL pattern || example on white keys || genchain || | || old scale name || new scale name || sL pattern || example on white keys || genchain || | ||
|| Lydian || 1st Meantone [7] || LLLs LLs || F G A B C D E F || __**F**__ C G D A E B || | || Lydian || 1st Meantone [7] || LLLs LLs || F G A B C D E F || __**F**__ C G D A E B || | ||
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==[[#Rank-2 scales that are neither MOS nor MODMOS]]** | ==[[#Rank-2 scales that are neither MOS nor MODMOS]]**__Other rank-2 scales__**== | ||
Some scales have too many or too few notes to be MOS. If they have an unbroken genchain, they can be named Meantone [6], Meantone [8], etc. Curly brackets can be used to distinguish them from MOS scales: Meantone {6} and Meantone {8}. | Some scales have too many or too few notes to be MOS or MODMOS. If they have an unbroken genchain, they can be named Meantone [6], Meantone [8], etc. Curly brackets can be used to distinguish them from MOS scales: Meantone {6} and Meantone {8}. | ||
However chromatic alterations create genchains with gaps that are very difficult to name. These scales must be named as MOS scales with notes added or removed, using "add" and "no", analogous to chord names. As with MODMOS scales, there is often more than one name for a scale. | However chromatic alterations create genchains with gaps that are very difficult to name. These scales must be named as MOS scales with notes added or removed, using "add" and "no", analogous to chord names. As with MODMOS scales, there is often more than one name for a scale. | ||
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==[[#Explanation / Rationale]] | ==[[#Explanation / Rationale]]__Explanation__== | ||
**__Why not number the modes in the order they occur in the scale?__** | **__Why not number the modes in the order they occur in the scale?__** | ||
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Furthermore, UDP uses the more mathematical [[https://en.wikipedia.org/wiki/Zero-based_numbering|zero-based counting]] and Mode Numbers notation uses the more intuitive one-based counting. UDP is mathematician-oriented whereas Mode Numbers notation is musician-oriented.</pre></div> | Furthermore, UDP uses the more mathematical [[https://en.wikipedia.org/wiki/Zero-based_numbering|zero-based counting]] and Mode Numbers notation uses the more intuitive one-based counting. UDP is mathematician-oriented whereas Mode Numbers notation is musician-oriented.</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>Naming Rank-2 Scales using Mode Numbers</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><!-- ws:end:WikiTextHeadingRule:0 --> </h1> | <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>Naming Rank-2 Scales using Mode Numbers</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="MOS Scales"></a><!-- ws:end:WikiTextHeadingRule:0 -->MOS Scales</h1> | ||
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<!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --><div style="margin-left: 2em;"><a href="# | <!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --><div style="margin-left: 2em;"><a href="#MOS Scales-Fractional-octave periods">Fractional-octave periods</a></div> | ||
<!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --><div style="margin-left: 2em;"><a href="# | <!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --><div style="margin-left: 2em;"><a href="#MOS Scales-Other rank-2 scales">Other rank-2 scales</a></div> | ||
<!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --><div style="margin-left: 2em;"><a href="# | <!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --><div style="margin-left: 2em;"><a href="#MOS Scales-Numbering considerations">Numbering considerations</a></div> | ||
<!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --><div style="margin-left: 2em;"><a href="#MOS Scales-Explanation">Explanation</a></div> | |||
<!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --></div> | <!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --></div> | ||
<!-- ws:end:WikiTextTocRule:19 --><strong>Mode numbers</strong> provide a way to name MOS, MODMOS and even non-MOS rank-2 scales and modes systematically. Like <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Modal%20UDP%20notation">Modal UDP notation</a>, it starts with the convention of using <em>some-temperament-name</em>[<em>some-number</em>] to create a generator-chain, and adds a way to number each mode uniquely. For example, here are all the modes of Meantone[7], using ~3/2 as the generator:<br /> | <!-- ws:end:WikiTextTocRule:19 --><strong>Mode numbers</strong> provide a way to name MOS, MODMOS and even non-MOS rank-2 scales and modes systematically. Like <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Modal%20UDP%20notation">Modal UDP notation</a>, it starts with the convention of using <em>some-temperament-name</em>[<em>some-number</em>] to create a generator-chain, and adds a way to number each mode uniquely. <br /> | ||
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For example, here are all the modes of Meantone[7], using ~3/2 as the generator:<br /> | |||
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<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name=" | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="MOS Scales-MODMOS scales"></a><!-- ws:end:WikiTextHeadingRule:2 --><!-- ws:start:WikiTextAnchorRule:20:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@How to name rank-2 scales-MODMOS scales&quot; title=&quot;Anchor: How to name rank-2 scales-MODMOS scales&quot;/&gt; --><a name="How to name rank-2 scales-MODMOS scales"></a><!-- ws:end:WikiTextAnchorRule:20 --><strong><u>MODMOS scales</u></strong></h2> | ||
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<a class="wiki_link" href="/MODMOS%20Scales">MODMOS</a> scales are named as chromatic alterations of a MOS scale, similar to UDP notation. The ascending melodic minor scale is 5th Meantone [7] #6 #7. The &quot;#&quot; symbol means moved N steps forwards on the genchain, whether the generator is chroma-positive or not. This scale has the same name in 16edo, even though in 16edo, G# is actually flat of G.<br /> | <a class="wiki_link" href="/MODMOS%20Scales">MODMOS</a> scales are named as chromatic alterations of a MOS scale, similar to UDP notation. The ascending melodic minor scale is 5th Meantone [7] #6 #7. The &quot;#&quot; symbol means moved N steps forwards on the genchain, whether the generator is chroma-positive or not. This scale has the same name in 16edo, even though in 16edo, G# is actually flat of G.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name=" | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="MOS Scales-Fractional-octave periods"></a><!-- ws:end:WikiTextHeadingRule:4 --><!-- ws:start:WikiTextAnchorRule:21:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Fractional-octave periods&quot; title=&quot;Anchor: Fractional-octave periods&quot;/&gt; --><a name="Fractional-octave periods"></a><!-- ws:end:WikiTextAnchorRule:21 --><strong><u>Fractional-octave periods</u></strong></h2> | ||
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Fractional-period rank-2 temperaments have multiple genchains running in parallel. Multiple genchains occur because a rank-2 genchain is really a 2 dimensional &quot;genweb&quot;, running in octaves (or whatever the period is) vertically and fifths (or whatever the generator is) horizontally.<br /> | Fractional-period rank-2 temperaments have multiple genchains running in parallel. Multiple genchains occur because a rank-2 genchain is really a 2 dimensional &quot;genweb&quot;, running in octaves (or whatever the period is) vertically and fifths (or whatever the generator is) horizontally.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name=" | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="MOS Scales-Other rank-2 scales"></a><!-- ws:end:WikiTextHeadingRule:6 --><!-- ws:start:WikiTextAnchorRule:22:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Rank-2 scales that are neither MOS nor MODMOS&quot; title=&quot;Anchor: Rank-2 scales that are neither MOS nor MODMOS&quot;/&gt; --><a name="Rank-2 scales that are neither MOS nor MODMOS"></a><!-- ws:end:WikiTextAnchorRule:22 --><strong><u>Other rank-2 scales</u></strong></h2> | ||
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Some scales have too many or too few notes to be MOS. If they have an unbroken genchain, they can be named Meantone [6], Meantone [8], etc. Curly brackets can be used to distinguish them from MOS scales: Meantone {6} and Meantone {8}.<br /> | Some scales have too many or too few notes to be MOS or MODMOS. If they have an unbroken genchain, they can be named Meantone [6], Meantone [8], etc. Curly brackets can be used to distinguish them from MOS scales: Meantone {6} and Meantone {8}.<br /> | ||
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However chromatic alterations create genchains with gaps that are very difficult to name. These scales must be named as MOS scales with notes added or removed, using &quot;add&quot; and &quot;no&quot;, analogous to chord names. As with MODMOS scales, there is often more than one name for a scale.<br /> | However chromatic alterations create genchains with gaps that are very difficult to name. These scales must be named as MOS scales with notes added or removed, using &quot;add&quot; and &quot;no&quot;, analogous to chord names. As with MODMOS scales, there is often more than one name for a scale.<br /> | ||
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As long as we stick to MOS scales, terms like Meantone [5] or Meantone {6} are fine. But when we alter, add or drop notes, we need to define what &quot;#4&quot; means in a pentatonic or hexatonic context.<br /> | As long as we stick to MOS scales, terms like Meantone [5] or Meantone {6} are fine. But when we alter, add or drop notes, we need to define what &quot;#4&quot; means in a pentatonic or hexatonic context.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name=" | <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="MOS Scales-Explanation"></a><!-- ws:end:WikiTextHeadingRule:10 --><!-- ws:start:WikiTextAnchorRule:24:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Explanation / Rationale&quot; title=&quot;Anchor: Explanation / Rationale&quot;/&gt; --><a name="Explanation / Rationale"></a><!-- ws:end:WikiTextAnchorRule:24 --><u>Explanation</u></h2> | ||
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<strong><u>Why not number the modes in the order they occur in the scale?</u></strong><br /> | <strong><u>Why not number the modes in the order they occur in the scale?</u></strong><br /> | ||