Composing with tablets: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 258919444 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 258923392 - 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:genewardsmith|genewardsmith]] and made on <tt>2011-09-28 00: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-28 00:44:47 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>258923392</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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This traverses all eight tetrads of the 7-limit tonality diamond, a scale of thirteen notes. But since we have the piece in tablet form, it is easy to transform it in a variety of ways. For instance, we may add [1 1 1] to each chord identifier. This makes for a [[http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/stella.mp3|piece]] which traverses the stellated hexany, a scale of fourteen notes. The rather surprising increase from thirteen to fourteen notes is possible since each scale has 32 tablets to each octave, but more than one tablet corresponds to each note. The 32 tablets of the diamond, corresponding to thirteen notes, transform to the 32 tablets of the stellated hexany, corresponding to fourteen notes. | This traverses all eight tetrads of the 7-limit tonality diamond, a scale of thirteen notes. But since we have the piece in tablet form, it is easy to transform it in a variety of ways. For instance, we may add [1 1 1] to each chord identifier. This makes for a [[http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/stella.mp3|piece]] which traverses the stellated hexany, a scale of fourteen notes. The rather surprising increase from thirteen to fourteen notes is possible since each scale has 32 tablets to each octave, but more than one tablet corresponds to each note. The 32 tablets of the diamond, corresponding to thirteen notes, transform to the 32 tablets of the stellated hexany, corresponding to fourteen notes. | ||
This is not, of course, the only way to transform the original tonality diamond piece into one in the stellated hexany. More or less at random we could try converting the chord identifier [a b c] to [-a -c -b]; this sort of transformation will send two related chords to another pair of related chords. Doing this leads to the following [[http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/rella.mp3|piece]]. But we have perfect freedom to choose our chord identifiers however we like; we could for example use [0 0 0], [0 1 -1], [0 2 -1], [0 2 -2], [0 3 -2], [0 3 -3], [1 3 -3], [2 3 -3]. This modulates upwards by 2401/2400, and leads to the following piece. | This is not, of course, the only way to transform the original tonality diamond piece into one in the stellated hexany. More or less at random we could try converting the chord identifier [a b c] to [-a -c -b]; this sort of transformation will send two related chords to another pair of related chords. Doing this leads to the following [[http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/rella.mp3|piece]]. But we have perfect freedom to choose our chord identifiers however we like; we could for example use [0 0 0], [0 1 -1], [0 2 -1], [0 2 -2], [0 3 -2], [0 3 -3], [1 3 -3], [2 3 -3]. This modulates upwards by 2401/2400, and leads to the following [[http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/stella.mp3|piece]]. | ||
</pre></div> | </pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
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This traverses all eight tetrads of the 7-limit tonality diamond, a scale of thirteen notes. But since we have the piece in tablet form, it is easy to transform it in a variety of ways. For instance, we may add [1 1 1] to each chord identifier. This makes for a <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/stella.mp3" rel="nofollow">piece</a> which traverses the stellated hexany, a scale of fourteen notes. The rather surprising increase from thirteen to fourteen notes is possible since each scale has 32 tablets to each octave, but more than one tablet corresponds to each note. The 32 tablets of the diamond, corresponding to thirteen notes, transform to the 32 tablets of the stellated hexany, corresponding to fourteen notes.<br /> | This traverses all eight tetrads of the 7-limit tonality diamond, a scale of thirteen notes. But since we have the piece in tablet form, it is easy to transform it in a variety of ways. For instance, we may add [1 1 1] to each chord identifier. This makes for a <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/stella.mp3" rel="nofollow">piece</a> which traverses the stellated hexany, a scale of fourteen notes. The rather surprising increase from thirteen to fourteen notes is possible since each scale has 32 tablets to each octave, but more than one tablet corresponds to each note. The 32 tablets of the diamond, corresponding to thirteen notes, transform to the 32 tablets of the stellated hexany, corresponding to fourteen notes.<br /> | ||
<br /> | <br /> | ||
This is not, of course, the only way to transform the original tonality diamond piece into one in the stellated hexany. More or less at random we could try converting the chord identifier [a b c] to [-a -c -b]; this sort of transformation will send two related chords to another pair of related chords. Doing this leads to the following <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/rella.mp3" rel="nofollow">piece</a>. But we have perfect freedom to choose our chord identifiers however we like; we could for example use [0 0 0], [0 1 -1], [0 2 -1], [0 2 -2], [0 3 -2], [0 3 -3], [1 3 -3], [2 3 -3]. This modulates upwards by 2401/2400, and leads to the following piece.</body></html></pre></div> | This is not, of course, the only way to transform the original tonality diamond piece into one in the stellated hexany. More or less at random we could try converting the chord identifier [a b c] to [-a -c -b]; this sort of transformation will send two related chords to another pair of related chords. Doing this leads to the following <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/rella.mp3" rel="nofollow">piece</a>. But we have perfect freedom to choose our chord identifiers however we like; we could for example use [0 0 0], [0 1 -1], [0 2 -1], [0 2 -2], [0 3 -2], [0 3 -3], [1 3 -3], [2 3 -3]. This modulates upwards by 2401/2400, and leads to the following <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/stella.mp3" rel="nofollow">piece</a>.</body></html></pre></div> | ||
Revision as of 00:44, 28 September 2011
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2011-09-28 00:44:47 UTC.
- The original revision id was 258923392.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
Perhaps the first thing to note about the use of [[tablets]] as an aid to composition is that while the tablet for a given note is always non-unique, it can become unique if we require all of the notes sounding in a particular chord to share the same chord identifier, and this is the most basic of ways to make use of tablets. In other words, if c is a chord identifier in a tablet, a chord can often be notated as the set of notes {note(n1, c), note(n2, c), ..., note(nk, c)}, all with the same chord identifier c. If a piece of music uses chords sharing the same note identifier exclusively, we can completely separate the numbers n, the note skeleton, from the sequence of chord identifers, and change each around at will completely independently.
Let us consider a simple [[http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/fouredo.mp3|4edo piece]] as a starting point:
[0 3 6 9]
[0 3 5 10]
[0 2 5 11]
[0 2 5 12]
[0 3 6 13]
[0 3 5 14]
[0 2 5 15]
[0 2 5 16]
[0 3 6 9]
[0 3 5 10]
[0 2 5 11]
[0 2 5 12]
[0 3 6 13]
[0 3 5 14]
[0 2 5 15]
[0 2 5 16]
[0 3 6 9]
[0 3 5 10]
[0 2 5 11]
[0 2 5 12]
[0 3 6 9]
[0 3 5 10]
[0 2 5 11]
[0 2 5 12]
[0 3 6 9]
[0 3 5 10]
[0 2 5 11]
[0 2 5 12]
[0 3 6 9]
[0 3 5 10]
[0 2 5 11]
[0 2 5 12]
[0 2 5 11]
[0 2 5 11]
[0 3 6 9]
[0 3 6 9]
[0 2 5 11]
[0 2 5 11]
[0 3 6 9]
[0 3 6 9]
[0 2 5 11]
[0 2 5 11]
[0 3 6 9]
[0 3 6 9]
[0 2 5 11]
[0 2 5 11]
[0 3 6 9]
[0 3 6 9]
[0 2 5 16]
[0 2 5 15]
[0 3 5 14]
[0 3 6 13]
[0 2 5 12]
[0 2 5 11]
[0 3 5 10]
[0 3 6 9]
[0 3 6 8]
[0 3 6 8]
[0 3 6 8]
[0 3 6 8]
[0 2 5 8]
[0 2 5 8]
[0 2 5 8]
[0 2 5 8]
This has sixteen measures of four notes each. If to each two measures we attach the chord identifier of a 7-limit 4et tablet, then we may convert all of the 4et notes into 7-limit JI notes by means of the associated chord identifier and therefore by the assoicated tablet. For instance, from the sequence of chords [-1 -1 -1], [0 -1 -1], [0 0 -1], [0 -1 0], [-1 -1 0], [-1 0 -1], [-1 0 0], [0 0 0] we obtain [[http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/diamond.mp3|this piece]].
This traverses all eight tetrads of the 7-limit tonality diamond, a scale of thirteen notes. But since we have the piece in tablet form, it is easy to transform it in a variety of ways. For instance, we may add [1 1 1] to each chord identifier. This makes for a [[http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/stella.mp3|piece]] which traverses the stellated hexany, a scale of fourteen notes. The rather surprising increase from thirteen to fourteen notes is possible since each scale has 32 tablets to each octave, but more than one tablet corresponds to each note. The 32 tablets of the diamond, corresponding to thirteen notes, transform to the 32 tablets of the stellated hexany, corresponding to fourteen notes.
This is not, of course, the only way to transform the original tonality diamond piece into one in the stellated hexany. More or less at random we could try converting the chord identifier [a b c] to [-a -c -b]; this sort of transformation will send two related chords to another pair of related chords. Doing this leads to the following [[http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/rella.mp3|piece]]. But we have perfect freedom to choose our chord identifiers however we like; we could for example use [0 0 0], [0 1 -1], [0 2 -1], [0 2 -2], [0 3 -2], [0 3 -3], [1 3 -3], [2 3 -3]. This modulates upwards by 2401/2400, and leads to the following [[http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/stella.mp3|piece]].
Original HTML content:
<html><head><title>Composing with tablets</title></head><body>Perhaps the first thing to note about the use of <a class="wiki_link" href="/tablets">tablets</a> as an aid to composition is that while the tablet for a given note is always non-unique, it can become unique if we require all of the notes sounding in a particular chord to share the same chord identifier, and this is the most basic of ways to make use of tablets. In other words, if c is a chord identifier in a tablet, a chord can often be notated as the set of notes {note(n1, c), note(n2, c), ..., note(nk, c)}, all with the same chord identifier c. If a piece of music uses chords sharing the same note identifier exclusively, we can completely separate the numbers n, the note skeleton, from the sequence of chord identifers, and change each around at will completely independently.<br />
<br />
Let us consider a simple <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/fouredo.mp3" rel="nofollow">4edo piece</a> as a starting point:<br />
<br />
[0 3 6 9]<br />
[0 3 5 10]<br />
[0 2 5 11]<br />
[0 2 5 12]<br />
[0 3 6 13]<br />
[0 3 5 14]<br />
[0 2 5 15]<br />
[0 2 5 16]<br />
[0 3 6 9]<br />
[0 3 5 10]<br />
[0 2 5 11]<br />
[0 2 5 12]<br />
[0 3 6 13]<br />
[0 3 5 14]<br />
[0 2 5 15]<br />
[0 2 5 16]<br />
[0 3 6 9]<br />
[0 3 5 10]<br />
[0 2 5 11]<br />
[0 2 5 12]<br />
[0 3 6 9]<br />
[0 3 5 10]<br />
[0 2 5 11]<br />
[0 2 5 12]<br />
[0 3 6 9]<br />
[0 3 5 10]<br />
[0 2 5 11]<br />
[0 2 5 12]<br />
[0 3 6 9]<br />
[0 3 5 10]<br />
[0 2 5 11]<br />
[0 2 5 12]<br />
[0 2 5 11]<br />
[0 2 5 11]<br />
[0 3 6 9]<br />
[0 3 6 9]<br />
[0 2 5 11]<br />
[0 2 5 11]<br />
[0 3 6 9]<br />
[0 3 6 9]<br />
[0 2 5 11]<br />
[0 2 5 11]<br />
[0 3 6 9]<br />
[0 3 6 9]<br />
[0 2 5 11]<br />
[0 2 5 11]<br />
[0 3 6 9]<br />
[0 3 6 9]<br />
[0 2 5 16]<br />
[0 2 5 15]<br />
[0 3 5 14]<br />
[0 3 6 13]<br />
[0 2 5 12]<br />
[0 2 5 11]<br />
[0 3 5 10]<br />
[0 3 6 9]<br />
[0 3 6 8]<br />
[0 3 6 8]<br />
[0 3 6 8]<br />
[0 3 6 8]<br />
[0 2 5 8]<br />
[0 2 5 8]<br />
[0 2 5 8]<br />
[0 2 5 8]<br />
<br />
This has sixteen measures of four notes each. If to each two measures we attach the chord identifier of a 7-limit 4et tablet, then we may convert all of the 4et notes into 7-limit JI notes by means of the associated chord identifier and therefore by the assoicated tablet. For instance, from the sequence of chords [-1 -1 -1], [0 -1 -1], [0 0 -1], [0 -1 0], [-1 -1 0], [-1 0 -1], [-1 0 0], [0 0 0] we obtain <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/diamond.mp3" rel="nofollow">this piece</a>.<br />
<br />
This traverses all eight tetrads of the 7-limit tonality diamond, a scale of thirteen notes. But since we have the piece in tablet form, it is easy to transform it in a variety of ways. For instance, we may add [1 1 1] to each chord identifier. This makes for a <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/stella.mp3" rel="nofollow">piece</a> which traverses the stellated hexany, a scale of fourteen notes. The rather surprising increase from thirteen to fourteen notes is possible since each scale has 32 tablets to each octave, but more than one tablet corresponds to each note. The 32 tablets of the diamond, corresponding to thirteen notes, transform to the 32 tablets of the stellated hexany, corresponding to fourteen notes.<br />
<br />
This is not, of course, the only way to transform the original tonality diamond piece into one in the stellated hexany. More or less at random we could try converting the chord identifier [a b c] to [-a -c -b]; this sort of transformation will send two related chords to another pair of related chords. Doing this leads to the following <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/rella.mp3" rel="nofollow">piece</a>. But we have perfect freedom to choose our chord identifiers however we like; we could for example use [0 0 0], [0 1 -1], [0 2 -1], [0 2 -2], [0 3 -2], [0 3 -3], [1 3 -3], [2 3 -3]. This modulates upwards by 2401/2400, and leads to the following <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/stella.mp3" rel="nofollow">piece</a>.</body></html>