Just intonation: Difference between revisions
Wikispaces>lobawad **Imported revision 241352145 - 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: | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-07-15 02:45:35 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>241450853</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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In languages other than English, the original conceptions of "Just Intonation" are more obviously retained in the terms used in those languages: Reine Stimmung (pure, that is, beatless, tuning) in German, Натуральний стрій in Ukrainian and Gamme naturelle in French, (both referring to the "natural scale", that is, intervals derived from the harmonic partials), Intonazione naturale (natural intonation, once again intervals derived from harmonic partials) in Italian, and so on. | In languages other than English, the original conceptions of "Just Intonation" are more obviously retained in the terms used in those languages: Reine Stimmung (pure, that is, beatless, tuning) in German, Натуральний стрій in Ukrainian and Gamme naturelle in French, (both referring to the "natural scale", that is, intervals derived from the harmonic partials), Intonazione naturale (natural intonation, once again intervals derived from harmonic partials) in Italian, and so on. | ||
In the English language, the term "just" referred to "true, correct", and is still used today in this sense, in the crafts. In printing, to "justify" a line of type is to fit it precisely to a certain measure, for example. The original sense, then, was similar to that sense which is clearly retained in other languages as "natural". | In the English language, the term "just" referred to "true, correct", and is still used today in this sense, in the crafts. In printing, to "justify" a line of type is to fit it precisely to a certain measure, for example. The original sense, then, was similar to that sense which is clearly retained in other languages as "natural". | ||
Of course, an historical description of something as "natural" does not prove that that thing really is "natural", and defining the concept of "natural", especially in the arts, is always very problematic. Nevertheless, the historical meanings of the terms for what we call "Just Intonation" do claim a "natural" status, and Just Intonation is indeed derived from genuine acoustic phenomena. How important, universal, etc., these phenomena are has been a matter of debate for thousands of years. | Of course, an historical description of something as "natural" does not prove that that thing really is "natural", and defining the concept of "natural", especially in the arts, is always very problematic. Nevertheless, the historical meanings of the terms for what we call "Just Intonation" do claim a "natural" status, and Just Intonation is indeed derived from genuine acoustic phenomena. How important, universal, etc., these phenomena are has been a matter of debate for thousands of years. | ||
The current common usage of describing intervals between pitches by specifying ratios of rational numbers is another way of expressing the "natural scale", for it describes ratios between harmonic partials (in their ideal form). So, contemporary usage of the term is in keeping with historical and international usages. However, just as harmonic vocabulary has expanded over the centuries, so has that which falls under "just intonation" expanded. | The current common usage of describing intervals between pitches by specifying ratios of rational numbers is another way of expressing the "natural scale", for it describes ratios between harmonic partials (in their ideal form). So, contemporary usage of the term is in keeping with historical and international usages. However, just as harmonic vocabulary has expanded over the centuries, so has that which falls under "just intonation" expanded. | ||
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You see that the tones share the frequencies of some of the partials. These partials will "meld" when our Do and Sol are played together. This goes by the wonderful name of "Tonverschmelzung" in German. It is a very distinctinctive "blending" sound. Were our Sol at, for example, 148 Hertz, it's second harmonic component would be at 296 Hertz, and the two tones played together would not "melt together" at 300 Hertz, but would "beat". That is, we would hear a throbbing sound, the "beat rate" of which is found by reckoning the distance in Hertz between the two near-coincident partials. In this case, 300-296=4 Hertz, so we'd hear a beating of four times a second (this is like a rhythm of eighth notes at a metronome marking of 120 beats per minute). | You see that the tones share the frequencies of some of the partials. These partials will "meld" when our Do and Sol are played together. This goes by the wonderful name of "Tonverschmelzung" in German. It is a very distinctinctive "blending" sound. Were our Sol at, for example, 148 Hertz, it's second harmonic component would be at 296 Hertz, and the two tones played together would not "melt together" at 300 Hertz, but would "beat". That is, we would hear a throbbing sound, the "beat rate" of which is found by reckoning the distance in Hertz between the two near-coincident partials. In this case, 300-296=4 Hertz, so we'd hear a beating of four times a second (this is like a rhythm of eighth notes at a metronome marking of 120 beats per minute). | ||
One does not need to know of the harmonic series, nor even know how to read, or even count, to sing this. | One does not need to know of the harmonic series, nor even know how to read, or even count, to sing this. | ||
There is more to it than this, of course, but the basic principles of Just Intonation are very simple. Hundreds of years ago, when the intonation of a few well-known intervals were the concern, understanding and defining "Just" was not difficult. These days, though, and going on from these basics, it can get a bit more complicated... | There is more to it than this, of course, but the basic principles of Just Intonation are very simple. Hundreds of years ago, when the intonation of a few well-known intervals were the concern, understanding and defining "Just" was not difficult. These days, though, and going on from these basics, it can get a bit more complicated... | ||
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==Free Style Just== | ==Free Style Just== | ||
Lou Harrison used this term; it means that you choose just-intonation pitches, from the set of all possible just intervals (not from a mode or scale), as you use them in music. Dedicated page -> [[FreeStyleJI]] | [[Lou Harrison]] used this term; it means that you choose just-intonation pitches, from the set of all possible just intervals (not from a mode or scale), as you use them in music. Dedicated page -> [[FreeStyleJI]] | ||
==Constrained Just== | ==Constrained Just== | ||
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* [[http://lumma.org/tuning/gws/commaseq.htm|Comma Sequences]] by Gene Ward Smith [[http://www.webcitation.org/5xe4rPLZ0|Permalink]]</pre></div> | * [[http://lumma.org/tuning/gws/commaseq.htm|Comma Sequences]] by Gene Ward Smith [[http://www.webcitation.org/5xe4rPLZ0|Permalink]]</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>Just intonation</title></head><body><!-- ws:start:WikiTextTocRule: | <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>Just intonation</title></head><body><!-- ws:start:WikiTextTocRule:16:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --><a href="#Just Intonation explained">Just Intonation explained</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#x&quot;Pure&quot;? &quot;Rational&quot;? Various shades of &quot;Just&quot; Intonation">&quot;Pure&quot;? &quot;Rational&quot;? Various shades of &quot;Just&quot; Intonation</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | <a href="#Just Intonation in use">Just Intonation in use</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | <a href="#Variations on 'Just'">Variations on 'Just'</a><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --> | <a href="#Links">Links</a><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> | <a href="#Articles">Articles</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:25 --><hr /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Just Intonation explained"></a><!-- ws:end:WikiTextHeadingRule:0 -->Just Intonation explained</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Just Intonation explained"></a><!-- ws:end:WikiTextHeadingRule:0 -->Just Intonation explained</h1> | ||
&quot;Just Intonation&quot;, as we find it commonly used today, describes <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">intervals</a> between pitches by specifying ratios (of <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Rational_number" rel="nofollow">rational numbers</a>) between the frequencies of pitches.<br /> | &quot;Just Intonation&quot;, as we find it commonly used today, describes <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">intervals</a> between pitches by specifying ratios (of <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Rational_number" rel="nofollow">rational numbers</a>) between the frequencies of pitches.<br /> | ||
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In languages other than English, the original conceptions of &quot;Just Intonation&quot; are more obviously retained in the terms used in those languages: Reine Stimmung (pure, that is, beatless, tuning) in German, Натуральний стрій in Ukrainian and Gamme naturelle in French, (both referring to the &quot;natural scale&quot;, that is, intervals derived from the harmonic partials), Intonazione naturale (natural intonation, once again intervals derived from harmonic partials) in Italian, and so on.<br /> | In languages other than English, the original conceptions of &quot;Just Intonation&quot; are more obviously retained in the terms used in those languages: Reine Stimmung (pure, that is, beatless, tuning) in German, Натуральний стрій in Ukrainian and Gamme naturelle in French, (both referring to the &quot;natural scale&quot;, that is, intervals derived from the harmonic partials), Intonazione naturale (natural intonation, once again intervals derived from harmonic partials) in Italian, and so on.<br /> | ||
<br /> | <br /> | ||
In the English language, the term &quot;just&quot; referred to &quot;true, correct&quot;, and is still used today in this sense, in the crafts. In printing, to &quot;justify&quot; a line of type is to fit it precisely to a certain measure, for example. The original sense, then, was similar to that sense which is clearly retained in other languages as &quot;natural&quot;. <br /> | In the English language, the term &quot;just&quot; referred to &quot;true, correct&quot;, and is still used today in this sense, in the crafts. In printing, to &quot;justify&quot; a line of type is to fit it precisely to a certain measure, for example. The original sense, then, was similar to that sense which is clearly retained in other languages as &quot;natural&quot;.<br /> | ||
<br /> | <br /> | ||
Of course, an historical description of something as &quot;natural&quot; does not prove that that thing really is &quot;natural&quot;, and defining the concept of &quot;natural&quot;, especially in the arts, is always very problematic. Nevertheless, the historical meanings of the terms for what we call &quot;Just Intonation&quot; do claim a &quot;natural&quot; status, and Just Intonation is indeed derived from genuine acoustic phenomena. How important, universal, etc., these phenomena are has been a matter of debate for thousands of years. <br /> | Of course, an historical description of something as &quot;natural&quot; does not prove that that thing really is &quot;natural&quot;, and defining the concept of &quot;natural&quot;, especially in the arts, is always very problematic. Nevertheless, the historical meanings of the terms for what we call &quot;Just Intonation&quot; do claim a &quot;natural&quot; status, and Just Intonation is indeed derived from genuine acoustic phenomena. How important, universal, etc., these phenomena are has been a matter of debate for thousands of years.<br /> | ||
<br /> | <br /> | ||
The current common usage of describing intervals between pitches by specifying ratios of rational numbers is another way of expressing the &quot;natural scale&quot;, for it describes ratios between harmonic partials (in their ideal form). So, contemporary usage of the term is in keeping with historical and international usages. However, just as harmonic vocabulary has expanded over the centuries, so has that which falls under &quot;just intonation&quot; expanded.<br /> | The current common usage of describing intervals between pitches by specifying ratios of rational numbers is another way of expressing the &quot;natural scale&quot;, for it describes ratios between harmonic partials (in their ideal form). So, contemporary usage of the term is in keeping with historical and international usages. However, just as harmonic vocabulary has expanded over the centuries, so has that which falls under &quot;just intonation&quot; expanded.<br /> | ||
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You see that the tones share the frequencies of some of the partials. These partials will &quot;meld&quot; when our Do and Sol are played together. This goes by the wonderful name of &quot;Tonverschmelzung&quot; in German. It is a very distinctinctive &quot;blending&quot; sound. Were our Sol at, for example, 148 Hertz, it's second harmonic component would be at 296 Hertz, and the two tones played together would not &quot;melt together&quot; at 300 Hertz, but would &quot;beat&quot;. That is, we would hear a throbbing sound, the &quot;beat rate&quot; of which is found by reckoning the distance in Hertz between the two near-coincident partials. In this case, 300-296=4 Hertz, so we'd hear a beating of four times a second (this is like a rhythm of eighth notes at a metronome marking of 120 beats per minute).<br /> | You see that the tones share the frequencies of some of the partials. These partials will &quot;meld&quot; when our Do and Sol are played together. This goes by the wonderful name of &quot;Tonverschmelzung&quot; in German. It is a very distinctinctive &quot;blending&quot; sound. Were our Sol at, for example, 148 Hertz, it's second harmonic component would be at 296 Hertz, and the two tones played together would not &quot;melt together&quot; at 300 Hertz, but would &quot;beat&quot;. That is, we would hear a throbbing sound, the &quot;beat rate&quot; of which is found by reckoning the distance in Hertz between the two near-coincident partials. In this case, 300-296=4 Hertz, so we'd hear a beating of four times a second (this is like a rhythm of eighth notes at a metronome marking of 120 beats per minute).<br /> | ||
<br /> | <br /> | ||
One does not need to know of the harmonic series, nor even know how to read, or even count, to sing this. <br /> | One does not need to know of the harmonic series, nor even know how to read, or even count, to sing this.<br /> | ||
<br /> | <br /> | ||
There is more to it than this, of course, but the basic principles of Just Intonation are very simple. Hundreds of years ago, when the intonation of a few well-known intervals were the concern, understanding and defining &quot;Just&quot; was not difficult. These days, though, and going on from these basics, it can get a bit more complicated...<br /> | There is more to it than this, of course, but the basic principles of Just Intonation are very simple. Hundreds of years ago, when the intonation of a few well-known intervals were the concern, understanding and defining &quot;Just&quot; was not difficult. These days, though, and going on from these basics, it can get a bit more complicated...<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Just Intonation in use-Free Style Just"></a><!-- ws:end:WikiTextHeadingRule:6 -->Free Style Just</h2> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Just Intonation in use-Free Style Just"></a><!-- ws:end:WikiTextHeadingRule:6 -->Free Style Just</h2> | ||
< | <br /> | ||
<a class="wiki_link" href="/Lou%20Harrison">Lou Harrison</a> used this term; it means that you choose just-intonation pitches, from the set of all possible just intervals (not from a mode or scale), as you use them in music. Dedicated page -&gt; <a class="wiki_link" href="/FreeStyleJI">FreeStyleJI</a><br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Just Intonation in use-Constrained Just"></a><!-- ws:end:WikiTextHeadingRule:8 -->Constrained Just</h2> | ||
(In need of a better name maybe) Here are six ways that musicians and theorists have constrained the field of potential just ratios (from Jacques Dudon, &quot;Differential Coherence&quot;, <em>1/1</em> vol. 11, no. 2: p.1):<br /> | (In need of a better name maybe) Here are six ways that musicians and theorists have constrained the field of potential just ratios (from Jacques Dudon, &quot;Differential Coherence&quot;, <em>1/1</em> vol. 11, no. 2: p.1):<br /> | ||
<br /> | <br /> | ||
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<em>8. While related to the above, the use of recurrent sequences is by some included under JI as it involves whole numbers. Wilson's <a class="wiki_link_ext" href="http://anaphoria.com/wilsonintroMERU.html" rel="nofollow">Meru scales</a> are a good example as well as Jacques Dudon</em><br /> | <em>8. While related to the above, the use of recurrent sequences is by some included under JI as it involves whole numbers. Wilson's <a class="wiki_link_ext" href="http://anaphoria.com/wilsonintroMERU.html" rel="nofollow">Meru scales</a> are a good example as well as Jacques Dudon</em><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Variations on 'Just'"></a><!-- ws:end:WikiTextHeadingRule:10 -->Variations on 'Just'</h1> | ||
<a class="wiki_link" href="/Regular%20Temperaments">Regular Temperaments</a> are just intonation systems of various <a class="wiki_link" href="/harmonic%20limits">harmonic limits</a> with certain commas 'tempered out'<br /> | <a class="wiki_link" href="/Regular%20Temperaments">Regular Temperaments</a> are just intonation systems of various <a class="wiki_link" href="/harmonic%20limits">harmonic limits</a> with certain commas 'tempered out'<br /> | ||
<a class="wiki_link" href="/AdaptiveJI">Adaptive JI</a><br /> | <a class="wiki_link" href="/AdaptiveJI">Adaptive JI</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Links"></a><!-- ws:end:WikiTextHeadingRule:12 -->Links</h1> | ||
<a class="wiki_link" href="/hypergenesis58.scl">58 note 11 limit JI</a> - hyper-Partchian!<br /> | <a class="wiki_link" href="/hypergenesis58.scl">58 note 11 limit JI</a> - hyper-Partchian!<br /> | ||
<a class="wiki_link" href="/Hahn%20distance">Hahn distance</a><br /> | <a class="wiki_link" href="/Hahn%20distance">Hahn distance</a><br /> | ||
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<a class="wiki_link" href="/FiniteSubsetJI">FiniteSubsetJI</a><br /> | <a class="wiki_link" href="/FiniteSubsetJI">FiniteSubsetJI</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="Articles"></a><!-- ws:end:WikiTextHeadingRule:14 -->Articles</h1> | ||
<ul><li><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Just_intonation" rel="nofollow">Wikipedia article on just intonation</a></li><li><a class="wiki_link_ext" href="http://nowitzky.hostwebs.com/justint/" rel="nofollow">Just Intonation</a> by Mark Nowitzky <a class="wiki_link_ext" href="http://www.webcitation.org/5xeAm2lPL" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://www.kylegann.com/tuning.html" rel="nofollow">Just Intonation Explained</a> by Kyle Gann <a class="wiki_link_ext" href="http://www.webcitation.org/5xe2iC7Nq" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://www.kylegann.com/Octave.html" rel="nofollow">Anatomy of an Octave</a> by Kyle Gann <a class="wiki_link_ext" href="http://www.webcitation.org/5xe30LCev" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://www.dbdoty.com/Words/What-is-Just-Intonation.html" rel="nofollow">What is Just Intonation?</a> by David B. Doty <a class="wiki_link_ext" href="http://www.webcitation.org/5xe3MeWVq" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://www.dbdoty.com/Words/werntz.html" rel="nofollow">A Response to Julia Werntz</a> by David B. Doty <a class="wiki_link_ext" href="http://www.webcitation.org/5xe38KWx4" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://lumma.org/tuning/gws/commaseq.htm" rel="nofollow">Comma Sequences</a> by Gene Ward Smith <a class="wiki_link_ext" href="http://www.webcitation.org/5xe4rPLZ0" rel="nofollow">Permalink</a></li></ul></body></html></pre></div> | <ul><li><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Just_intonation" rel="nofollow">Wikipedia article on just intonation</a></li><li><a class="wiki_link_ext" href="http://nowitzky.hostwebs.com/justint/" rel="nofollow">Just Intonation</a> by Mark Nowitzky <a class="wiki_link_ext" href="http://www.webcitation.org/5xeAm2lPL" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://www.kylegann.com/tuning.html" rel="nofollow">Just Intonation Explained</a> by Kyle Gann <a class="wiki_link_ext" href="http://www.webcitation.org/5xe2iC7Nq" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://www.kylegann.com/Octave.html" rel="nofollow">Anatomy of an Octave</a> by Kyle Gann <a class="wiki_link_ext" href="http://www.webcitation.org/5xe30LCev" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://www.dbdoty.com/Words/What-is-Just-Intonation.html" rel="nofollow">What is Just Intonation?</a> by David B. Doty <a class="wiki_link_ext" href="http://www.webcitation.org/5xe3MeWVq" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://www.dbdoty.com/Words/werntz.html" rel="nofollow">A Response to Julia Werntz</a> by David B. Doty <a class="wiki_link_ext" href="http://www.webcitation.org/5xe38KWx4" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://lumma.org/tuning/gws/commaseq.htm" rel="nofollow">Comma Sequences</a> by Gene Ward Smith <a class="wiki_link_ext" href="http://www.webcitation.org/5xe4rPLZ0" rel="nofollow">Permalink</a></li></ul></body></html></pre></div> | ||