Xenharmonic Wiki

Gene Ward Smith: Difference between revisions

← Older editNewer edit →
VisualWikitext
Wikispaces>genewardsmith
**Imported revision 385062730 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 385063008 - Original comment: **
Line 1: Line 1:
<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>2012-11-22 10:59:50 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-11-22 11:01:11 UTC</tt>.<br>
: The original revision id was <tt>385062730</tt>.<br>
: The original revision id was <tt>385063008</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>
Line 12: Line 12:
In music theory, he introduced [[http://en.wikipedia.org/wiki/Exterior_algebra|wedge products]] as a way of classifying [[regular temperaments]].  In this system, a temperament is specified by means of a [[Wedgies and Multivals|wedgie]], which may technically be identified as a point on a [[http://en.wikipedia.org/wiki/Grassmannian|Grassmannian]].  He has long drawn attention to the relationship between [[Equal Temperaments|equal divisions of the octave]] and the [[The Riemann Zeta Function and Tuning|Riemann zeta function]].&lt;ref&gt;Rusin, Dave. "Why 12 tones per octave?" http://www.math.niu.edu/~rusin/uses-math/music/12&lt;/ref&gt;&lt;ref&gt;OEIS. Increasingly large peaks of the Riemann zeta function on the critical line http://oeis.org/A117536&lt;/ref&gt;&lt;ref&gt;OEIS. Increasingly large integrals of the Z function between zeros http://oeis.org/A117538&lt;/ref&gt; He [[http://www.webcitation.org/67ZUSajSK|early on]] identified and emphasized free abelian groups of finite rank and their homomorphisms, and it was from that perspective that he contributed to the creation of the [[http://x31eq.com/paradigm.html|regular mapping paradigm]].
In music theory, he introduced [[http://en.wikipedia.org/wiki/Exterior_algebra|wedge products]] as a way of classifying [[regular temperaments]].  In this system, a temperament is specified by means of a [[Wedgies and Multivals|wedgie]], which may technically be identified as a point on a [[http://en.wikipedia.org/wiki/Grassmannian|Grassmannian]].  He has long drawn attention to the relationship between [[Equal Temperaments|equal divisions of the octave]] and the [[The Riemann Zeta Function and Tuning|Riemann zeta function]].&lt;ref&gt;Rusin, Dave. "Why 12 tones per octave?" http://www.math.niu.edu/~rusin/uses-math/music/12&lt;/ref&gt;&lt;ref&gt;OEIS. Increasingly large peaks of the Riemann zeta function on the critical line http://oeis.org/A117536&lt;/ref&gt;&lt;ref&gt;OEIS. Increasingly large integrals of the Z function between zeros http://oeis.org/A117538&lt;/ref&gt; He [[http://www.webcitation.org/67ZUSajSK|early on]] identified and emphasized free abelian groups of finite rank and their homomorphisms, and it was from that perspective that he contributed to the creation of the [[http://x31eq.com/paradigm.html|regular mapping paradigm]].


In the 1970s, Gene experimented with musical compositions using a device with four square-wave voices, whose tuning was very stable and accurate, being controlled by a [[http://en.wikipedia.org/wiki/Crystal_oscillator|crystal oscillator]]. The device in turn was controlled by HP [[http://en.wikipedia.org/wiki/HP_9800_series_desktop_computers|HP 9800 series desktop computers]], initially the HP 9830A, programmed in HP Basic, later the 9845A. Using this, he explored both just intonation with a particular emphasis on groups of transformations, and [[pajara]].  
In the 1970s, Gene experimented with musical compositions using a device with four square-wave voices, whose tuning was very stable and accurate, being controlled by a [[http://en.wikipedia.org/wiki/Crystal_oscillator|crystal oscillator]]. The device in turn was controlled by [[http://en.wikipedia.org/wiki/HP_9800_series_desktop_computers|HP 9800 series desktop computers]], initially the HP 9830A, programmed in HP Basic, later the 9845A. Using this, he explored both just intonation with a particular emphasis on groups of transformations, and [[pajara]].  


Gene had a basic understanding of the regular mapping paradigm during this period, but it was limited in practice since he was focused on the idea that the next step from meantone should keep some familiar features, and so was interested in tempering out 64/63. He knew 7-limit 12 and 22 had tempering out 64/63 and 50/49 in common, and 12 and 27 had tempering out 64/63 and 126/125 in common, and thought these would be logical places to progress to. While he never got around to working with augene, he did consider it. For pajara, he found tempering certain JI scales led to interesting (omnitetrachordal) results, and that there were also symmetric (MOS) scales of size 10 and 12 for pajara; he did some work with these, particularly favoring the pentachordal decatonic scale.
Gene had a basic understanding of the regular mapping paradigm during this period, but it was limited in practice since he was focused on the idea that the next step from meantone should keep some familiar features, and so was interested in tempering out 64/63. He knew 7-limit 12 and 22 had tempering out 64/63 and 50/49 in common, and 12 and 27 had tempering out 64/63 and 126/125 in common, and thought these would be logical places to progress to. While he never got around to working with augene, he did consider it. For pajara, he found tempering certain JI scales led to interesting (omnitetrachordal) results, and that there were also symmetric (MOS) scales of size 10 and 12 for pajara; he did some work with these, particularly favoring the pentachordal decatonic scale.
Line 28: Line 28:
In music theory, he introduced &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Exterior_algebra" rel="nofollow"&gt;wedge products&lt;/a&gt; as a way of classifying &lt;a class="wiki_link" href="/regular%20temperaments"&gt;regular temperaments&lt;/a&gt;.  In this system, a temperament is specified by means of a &lt;a class="wiki_link" href="/Wedgies%20and%20Multivals"&gt;wedgie&lt;/a&gt;, which may technically be identified as a point on a &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Grassmannian" rel="nofollow"&gt;Grassmannian&lt;/a&gt;.  He has long drawn attention to the relationship between &lt;a class="wiki_link" href="/Equal%20Temperaments"&gt;equal divisions of the octave&lt;/a&gt; and the &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning"&gt;Riemann zeta function&lt;/a&gt;.&lt;!-- ws:start:WikiTextRefRule:1:&amp;amp;lt;ref&amp;amp;gt;Rusin, Dave. &amp;amp;quot;Why 12 tones per octave?&amp;amp;quot; http://www.math.niu.edu/~rusin/uses-math/music/12&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-1" class="reference"&gt;&lt;a href="#cite_note-1"&gt;[1]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:1 --&gt;&lt;!-- ws:start:WikiTextRefRule:3:&amp;amp;lt;ref&amp;amp;gt;OEIS. Increasingly large peaks of the Riemann zeta function on the critical line http://oeis.org/A117536&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-2" class="reference"&gt;&lt;a href="#cite_note-2"&gt;[2]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:3 --&gt;&lt;!-- ws:start:WikiTextRefRule:5:&amp;amp;lt;ref&amp;amp;gt;OEIS. Increasingly large integrals of the Z function between zeros http://oeis.org/A117538&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-3" class="reference"&gt;&lt;a href="#cite_note-3"&gt;[3]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:5 --&gt; He &lt;a class="wiki_link_ext" href="http://www.webcitation.org/67ZUSajSK" rel="nofollow"&gt;early on&lt;/a&gt; identified and emphasized free abelian groups of finite rank and their homomorphisms, and it was from that perspective that he contributed to the creation of the &lt;a class="wiki_link_ext" href="http://x31eq.com/paradigm.html" rel="nofollow"&gt;regular mapping paradigm&lt;/a&gt;.&lt;br /&gt;
In music theory, he introduced &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Exterior_algebra" rel="nofollow"&gt;wedge products&lt;/a&gt; as a way of classifying &lt;a class="wiki_link" href="/regular%20temperaments"&gt;regular temperaments&lt;/a&gt;.  In this system, a temperament is specified by means of a &lt;a class="wiki_link" href="/Wedgies%20and%20Multivals"&gt;wedgie&lt;/a&gt;, which may technically be identified as a point on a &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Grassmannian" rel="nofollow"&gt;Grassmannian&lt;/a&gt;.  He has long drawn attention to the relationship between &lt;a class="wiki_link" href="/Equal%20Temperaments"&gt;equal divisions of the octave&lt;/a&gt; and the &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning"&gt;Riemann zeta function&lt;/a&gt;.&lt;!-- ws:start:WikiTextRefRule:1:&amp;amp;lt;ref&amp;amp;gt;Rusin, Dave. &amp;amp;quot;Why 12 tones per octave?&amp;amp;quot; http://www.math.niu.edu/~rusin/uses-math/music/12&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-1" class="reference"&gt;&lt;a href="#cite_note-1"&gt;[1]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:1 --&gt;&lt;!-- ws:start:WikiTextRefRule:3:&amp;amp;lt;ref&amp;amp;gt;OEIS. Increasingly large peaks of the Riemann zeta function on the critical line http://oeis.org/A117536&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-2" class="reference"&gt;&lt;a href="#cite_note-2"&gt;[2]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:3 --&gt;&lt;!-- ws:start:WikiTextRefRule:5:&amp;amp;lt;ref&amp;amp;gt;OEIS. Increasingly large integrals of the Z function between zeros http://oeis.org/A117538&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-3" class="reference"&gt;&lt;a href="#cite_note-3"&gt;[3]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:5 --&gt; He &lt;a class="wiki_link_ext" href="http://www.webcitation.org/67ZUSajSK" rel="nofollow"&gt;early on&lt;/a&gt; identified and emphasized free abelian groups of finite rank and their homomorphisms, and it was from that perspective that he contributed to the creation of the &lt;a class="wiki_link_ext" href="http://x31eq.com/paradigm.html" rel="nofollow"&gt;regular mapping paradigm&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In the 1970s, Gene experimented with musical compositions using a device with four square-wave voices, whose tuning was very stable and accurate, being controlled by a &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Crystal_oscillator" rel="nofollow"&gt;crystal oscillator&lt;/a&gt;. The device in turn was controlled by HP &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/HP_9800_series_desktop_computers" rel="nofollow"&gt;HP 9800 series desktop computers&lt;/a&gt;, initially the HP 9830A, programmed in HP Basic, later the 9845A. Using this, he explored both just intonation with a particular emphasis on groups of transformations, and &lt;a class="wiki_link" href="/pajara"&gt;pajara&lt;/a&gt;. &lt;br /&gt;
In the 1970s, Gene experimented with musical compositions using a device with four square-wave voices, whose tuning was very stable and accurate, being controlled by a &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Crystal_oscillator" rel="nofollow"&gt;crystal oscillator&lt;/a&gt;. The device in turn was controlled by &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/HP_9800_series_desktop_computers" rel="nofollow"&gt;HP 9800 series desktop computers&lt;/a&gt;, initially the HP 9830A, programmed in HP Basic, later the 9845A. Using this, he explored both just intonation with a particular emphasis on groups of transformations, and &lt;a class="wiki_link" href="/pajara"&gt;pajara&lt;/a&gt;. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Gene had a basic understanding of the regular mapping paradigm during this period, but it was limited in practice since he was focused on the idea that the next step from meantone should keep some familiar features, and so was interested in tempering out 64/63. He knew 7-limit 12 and 22 had tempering out 64/63 and 50/49 in common, and 12 and 27 had tempering out 64/63 and 126/125 in common, and thought these would be logical places to progress to. While he never got around to working with augene, he did consider it. For pajara, he found tempering certain JI scales led to interesting (omnitetrachordal) results, and that there were also symmetric (MOS) scales of size 10 and 12 for pajara; he did some work with these, particularly favoring the pentachordal decatonic scale.&lt;br /&gt;
Gene had a basic understanding of the regular mapping paradigm during this period, but it was limited in practice since he was focused on the idea that the next step from meantone should keep some familiar features, and so was interested in tempering out 64/63. He knew 7-limit 12 and 22 had tempering out 64/63 and 50/49 in common, and 12 and 27 had tempering out 64/63 and 126/125 in common, and thought these would be logical places to progress to. While he never got around to working with augene, he did consider it. For pajara, he found tempering certain JI scales led to interesting (omnitetrachordal) results, and that there were also symmetric (MOS) scales of size 10 and 12 for pajara; he did some work with these, particularly favoring the pentachordal decatonic scale.&lt;br /&gt;
Retrieved from "https://en.xen.wiki/w/Gene_Ward_Smith"