Technical Notes for Newbeams: Difference between revisions
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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>2012-03-17 21: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-03-17 21:59:33 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>312001628</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">Technical notes for Newbeams, a xenharmonic album by [[Andrew Heathwaite]]: | <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">[[toc]] | ||
Technical notes for Newbeams, a xenharmonic album by [[Andrew Heathwaite]]: | |||
I created [[@http://andrewheathwaite.bandcamp.com/|Newbeams]] in February 2012 for the [[@http://www.rpmchallenge.com|RPM Challenge]]. I wanted to create a thoroughly xenharmonic album that was full of interesting-to-me stuff using some newly-acquired hardware and software, pursuing relatively new-to-me scales, temperaments, and rhythmic ideas, that would be exciting and interesting to open-minded, adventurous listeners. | I created [[@http://andrewheathwaite.bandcamp.com/|Newbeams]] in February 2012 for the [[@http://www.rpmchallenge.com|RPM Challenge]]. I wanted to create a thoroughly xenharmonic album that was full of interesting-to-me stuff using some newly-acquired hardware and software, pursuing relatively new-to-me scales, temperaments, and rhythmic ideas, that would be exciting and interesting to open-minded, adventurous listeners. | ||
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The scale here is a [[MODMOS Scales|MODMOS]] of Sensi[8] in 46edo. Ordinary ol' Sensi[8] has scale pattern ssLssLsL, with L = 7\46edo ~ 182.6¢, and s = 5\46edo ~ 130.4¢. The difference between L and s is the "chroma", "c", and here it's 2\46edo ~ 52.2¢. Sensi[8]'s "s" is the same as Sensi[11]'s "L", and its "c" is the same as Sensi[11]'s "s". This is to be expected (see Tumbledown Stew above). Anyway, if you add c to L you get "A", an augmented step, and if you subtract c from s you get "d", a diminished step. The form of the MODMOS used in this hyperimprovisation is sssLsssA. Since A is 7\46 + 2\46 = 9\46edo ~ 234.8¢, an approximate 8/7, we have a harmonic seventh above the bottom note in this scale. We also have three intervals of a perfect fifth available, instead of just one, as you'd get in the standard Sensi[8] MOS scale. This improvisation wanders around a lot, but mostly moves between three main chords, each with a perfect fifth above the bass note.</pre></div> | The scale here is a [[MODMOS Scales|MODMOS]] of Sensi[8] in 46edo. Ordinary ol' Sensi[8] has scale pattern ssLssLsL, with L = 7\46edo ~ 182.6¢, and s = 5\46edo ~ 130.4¢. The difference between L and s is the "chroma", "c", and here it's 2\46edo ~ 52.2¢. Sensi[8]'s "s" is the same as Sensi[11]'s "L", and its "c" is the same as Sensi[11]'s "s". This is to be expected (see Tumbledown Stew above). Anyway, if you add c to L you get "A", an augmented step, and if you subtract c from s you get "d", a diminished step. The form of the MODMOS used in this hyperimprovisation is sssLsssA. Since A is 7\46 + 2\46 = 9\46edo ~ 234.8¢, an approximate 8/7, we have a harmonic seventh above the bottom note in this scale. We also have three intervals of a perfect fifth available, instead of just one, as you'd get in the standard Sensi[8] MOS scale. This improvisation wanders around a lot, but mostly moves between three main chords, each with a perfect fifth above the bass note.</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>Technical Notes for Newbeams</title></head><body>Technical notes for Newbeams, a xenharmonic album by <a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a>:<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>Technical Notes for Newbeams</title></head><body><!-- ws:start:WikiTextTocRule:30:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><div style="margin-left: 1em;"><a href="#Some tuning background">Some tuning background</a></div> | ||
<!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><div style="margin-left: 1em;"><a href="#Track notes:">Track notes:</a></div> | |||
<!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><div style="margin-left: 2em;"><a href="#Track notes:-Rats">Rats</a></div> | |||
<!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><div style="margin-left: 2em;"><a href="#Track notes:-Shorn Brown">Shorn Brown</a></div> | |||
<!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --><div style="margin-left: 2em;"><a href="#Track notes:-Jellybear">Jellybear</a></div> | |||
<!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><div style="margin-left: 2em;"><a href="#Track notes:-Hypnocloudsmack 1">Hypnocloudsmack 1</a></div> | |||
<!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><div style="margin-left: 2em;"><a href="#Track notes:-Elf Dine on Ho Ho">Elf Dine on Ho Ho</a></div> | |||
<!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><div style="margin-left: 2em;"><a href="#Track notes:-Undernova">Undernova</a></div> | |||
<!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><div style="margin-left: 2em;"><a href="#Track notes:-Pentaswing">Pentaswing</a></div> | |||
<!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --><div style="margin-left: 2em;"><a href="#Track notes:-Spun">Spun</a></div> | |||
<!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><div style="margin-left: 2em;"><a href="#Track notes:-Hypnocloudsmack 2">Hypnocloudsmack 2</a></div> | |||
<!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --><div style="margin-left: 2em;"><a href="#Track notes:-Shimmerwing">Shimmerwing</a></div> | |||
<!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><div style="margin-left: 2em;"><a href="#Track notes:-Cardinal">Cardinal</a></div> | |||
<!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --><div style="margin-left: 2em;"><a href="#Track notes:-Tumbledown Stew">Tumbledown Stew</a></div> | |||
<!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --><div style="margin-left: 2em;"><a href="#Track notes:-Hypnocloudsmack 3">Hypnocloudsmack 3</a></div> | |||
<!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --></div> | |||
<!-- ws:end:WikiTextTocRule:46 --><br /> | |||
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Technical notes for Newbeams, a xenharmonic album by <a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a>:<br /> | |||
<br /> | <br /> | ||
I created <a class="wiki_link_ext" href="http://andrewheathwaite.bandcamp.com/" rel="nofollow" target="_blank">Newbeams</a> in February 2012 for the <a class="wiki_link_ext" href="http://www.rpmchallenge.com" rel="nofollow" target="_blank">RPM Challenge</a>. I wanted to create a thoroughly xenharmonic album that was full of interesting-to-me stuff using some newly-acquired hardware and software, pursuing relatively new-to-me scales, temperaments, and rhythmic ideas, that would be exciting and interesting to open-minded, adventurous listeners.<br /> | I created <a class="wiki_link_ext" href="http://andrewheathwaite.bandcamp.com/" rel="nofollow" target="_blank">Newbeams</a> in February 2012 for the <a class="wiki_link_ext" href="http://www.rpmchallenge.com" rel="nofollow" target="_blank">RPM Challenge</a>. I wanted to create a thoroughly xenharmonic album that was full of interesting-to-me stuff using some newly-acquired hardware and software, pursuing relatively new-to-me scales, temperaments, and rhythmic ideas, that would be exciting and interesting to open-minded, adventurous listeners.<br /> | ||
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This is one of several pieces in <a class="wiki_link" href="/46edo">46edo</a> that I wrote using an Axis-49 key mapping for <a class="wiki_link" href="/Sensi">Sensi</a> Temperament. Sensi offers 8-, 11-, and 19-tone <a class="wiki_link" href="/MOSScales">MOS scales</a>, but for Rats, I explored the keyboard freely, without concern for staying &quot;in&quot; a particular key or scale. To my ears, this piece has a tonal center and patterns of tension and release that you might associate with &quot;tonality&quot;. It obviously does not take a tour of all 98 keys on the Axis-49, and so somebody could of course analyze it and say, &quot;This is the scale.&quot; Although this sort of analysis may be informative, I have not done this and don't plan to.<br /> | This is one of several pieces in <a class="wiki_link" href="/46edo">46edo</a> that I wrote using an Axis-49 key mapping for <a class="wiki_link" href="/Sensi">Sensi</a> Temperament. Sensi offers 8-, 11-, and 19-tone <a class="wiki_link" href="/MOSScales">MOS scales</a>, but for Rats, I explored the keyboard freely, without concern for staying &quot;in&quot; a particular key or scale. To my ears, this piece has a tonal center and patterns of tension and release that you might associate with &quot;tonality&quot;. It obviously does not take a tour of all 98 keys on the Axis-49, and so somebody could of course analyze it and say, &quot;This is the scale.&quot; Although this sort of analysis may be informative, I have not done this and don't plan to.<br /> | ||
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<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:65:&lt;img src=&quot;/file/view/some_melodic_mappings.png/311610976/some_melodic_mappings.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/some_melodic_mappings.png/311610976/some_melodic_mappings.png" alt="some_melodic_mappings.png" title="some_melodic_mappings.png" /><!-- ws:end:WikiTextLocalImageRule:65 --><br /> | ||
The mapping I used for this and all other tracks on this album in 46edo Sensi temperament is the one on the right in the diagram above. Likewise, the mapping I used for the two tracks in Orwell temperament is the one on the left. Both of them make MOS scales easy to play by bunching all the tones together in a zig-zag pattern.<br /> | The mapping I used for this and all other tracks on this album in 46edo Sensi temperament is the one on the right in the diagram above. Likewise, the mapping I used for the two tracks in Orwell temperament is the one on the left. Both of them make MOS scales easy to play by bunching all the tones together in a zig-zag pattern.<br /> | ||
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This piece takes a walk in <a class="wiki_link" href="/37edo">37edo</a> through the keyboard in a mapping for <a class="wiki_link" href="/Orgone">Orgone</a> (or Orpheus) temperament. I was playing with 37edo as a 2.5.7.9.11.13 system, that is, a <a class="wiki_link" href="/13-limit">13-limit</a> system with no <a class="wiki_link" href="/perfect%20fifth">perfect fifths</a>. I hear this piece going on a journey to harmonically distant places and then suddenly returning, and would consider it as &quot;tonal&quot; as Rats. It is the only &quot;pop song&quot; on the album.<br /> | This piece takes a walk in <a class="wiki_link" href="/37edo">37edo</a> through the keyboard in a mapping for <a class="wiki_link" href="/Orgone">Orgone</a> (or Orpheus) temperament. I was playing with 37edo as a 2.5.7.9.11.13 system, that is, a <a class="wiki_link" href="/13-limit">13-limit</a> system with no <a class="wiki_link" href="/perfect%20fifth">perfect fifths</a>. I hear this piece going on a journey to harmonically distant places and then suddenly returning, and would consider it as &quot;tonal&quot; as Rats. It is the only &quot;pop song&quot; on the album.<br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:66:&lt;img src=&quot;/file/view/shorn_brown_keyboard.png/311618904/shorn_brown_keyboard.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/shorn_brown_keyboard.png/311618904/shorn_brown_keyboard.png" alt="shorn_brown_keyboard.png" title="shorn_brown_keyboard.png" /><!-- ws:end:WikiTextLocalImageRule:66 --><br /> | ||
In March, I relearned Shorn Brown to perform live, so I took an opportunity to figure out exactly what tones I happened to use. I was just curious. It turns out that the complete chain of orgone generators looks like:<br /> | In March, I relearned Shorn Brown to perform live, so I took an opportunity to figure out exactly what tones I happened to use. I was just curious. It turns out that the complete chain of orgone generators looks like:<br /> | ||
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As I mentioned in the description for Elf Dine on Ho Ho, Pentaswing uses a meter I call 7x5 with extension 7x5x2. This means seven beats per measure, each beat divided into five subdivisions (and, in the case of the extension, each subdivision divided further into two smaller subdivisions). The basic idea of the pentaswing rhythm is to generalize the &quot;swing&quot; or &quot;shuffle&quot; rhythm of jazz and other styles, which features each beat divided into a long first duration and a short second duration, usually with a 2:1 ratio between the durations, allowing for a triplet grid. If the triplet is further divided, it's divided in half. That gives us at most six subdivisions of a beat (3x2). So if we happened to have seven beats in a measure with a standard triplet swing, I'd call that meter 7x3x2 or 7x6. Compare this with 7x5, the basic &quot;pentaswing&quot; meter. In pentaswing, the &quot;swing&quot; grouping is 3+2, rather than 2+1 or equivalently 4+2. Pentaswing is slightly closer to even than standard swing, giving it a &quot;lazier&quot; or &quot;looser&quot; quality. The subdivisions are slower, too: 5 subdivisions in a beat instead of 6. The pentaswing cannot do an even triplet. Uneven triplets with 5 subdivisions are 2+2+1, 2+1+2, and 1+2+2. When the 5's are divided into 3's (5x2 -- decaswing, perhaps), we have more even triplets available: 3+3+4, 4+3+4, and 4+3+3. (Of course, standard triplet swing has the same problem approximating quintuplets. Uneven quintuplets with 6 subdivisions include 2+1+1+1+1, 1+2+1+1+1, 1+1+2+1+1, 1+1+1+2+1, and 1+1+1+1+2; none of those really sound like quintuplets. With twelve subdivisions, we can do better of course: 3+2+2+3+2, 2+2+3+2+3, 2+3+2+3+2, 3+2+3+2+2, and 2+3+2+2+3. These rhythms are exactly analogous to the modes of the black-key pentatonic scale in 12edo. In addition to being MOS rhythms, they are maximally-even and thus also Euclidean rhythms.) Pentaswing (the song) uses both 7x5 and 7x5x2 in different measures. The tuning is 23edo, obviously not all of it, but not a specific intentional subset, either, but something that emerged out of purely melodic and rhythmic considerations.<br /> | As I mentioned in the description for Elf Dine on Ho Ho, Pentaswing uses a meter I call 7x5 with extension 7x5x2. This means seven beats per measure, each beat divided into five subdivisions (and, in the case of the extension, each subdivision divided further into two smaller subdivisions). The basic idea of the pentaswing rhythm is to generalize the &quot;swing&quot; or &quot;shuffle&quot; rhythm of jazz and other styles, which features each beat divided into a long first duration and a short second duration, usually with a 2:1 ratio between the durations, allowing for a triplet grid. If the triplet is further divided, it's divided in half. That gives us at most six subdivisions of a beat (3x2). So if we happened to have seven beats in a measure with a standard triplet swing, I'd call that meter 7x3x2 or 7x6. Compare this with 7x5, the basic &quot;pentaswing&quot; meter. In pentaswing, the &quot;swing&quot; grouping is 3+2, rather than 2+1 or equivalently 4+2. Pentaswing is slightly closer to even than standard swing, giving it a &quot;lazier&quot; or &quot;looser&quot; quality. The subdivisions are slower, too: 5 subdivisions in a beat instead of 6. The pentaswing cannot do an even triplet. Uneven triplets with 5 subdivisions are 2+2+1, 2+1+2, and 1+2+2. When the 5's are divided into 3's (5x2 -- decaswing, perhaps), we have more even triplets available: 3+3+4, 4+3+4, and 4+3+3. (Of course, standard triplet swing has the same problem approximating quintuplets. Uneven quintuplets with 6 subdivisions include 2+1+1+1+1, 1+2+1+1+1, 1+1+2+1+1, 1+1+1+2+1, and 1+1+1+1+2; none of those really sound like quintuplets. With twelve subdivisions, we can do better of course: 3+2+2+3+2, 2+2+3+2+3, 2+3+2+3+2, 3+2+3+2+2, and 2+3+2+2+3. These rhythms are exactly analogous to the modes of the black-key pentatonic scale in 12edo. In addition to being MOS rhythms, they are maximally-even and thus also Euclidean rhythms.) Pentaswing (the song) uses both 7x5 and 7x5x2 in different measures. The tuning is 23edo, obviously not all of it, but not a specific intentional subset, either, but something that emerged out of purely melodic and rhythmic considerations.<br /> | ||
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<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:67:&lt;img src=&quot;/file/view/pentaswing.png/311612002/pentaswing.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/pentaswing.png/311612002/pentaswing.png" alt="pentaswing.png" title="pentaswing.png" /><!-- ws:end:WikiTextLocalImageRule:67 --><br /> | ||
I created the diagram above to compare triplet swing and pentaswing. I didn't use it as a reference for the album, but it might be useful in future projects that use these types of rhythms. I think the pentaswing rhythm is worth returning to.<br /> | I created the diagram above to compare triplet swing and pentaswing. I didn't use it as a reference for the album, but it might be useful in future projects that use these types of rhythms. I think the pentaswing rhythm is worth returning to.<br /> | ||
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