Composing with tablets - Revision history

FloraC: Fix header level and dead links. Mark with todo.

2024-10-16T10:24:29Z

Fix header level and dead links. Mark with todo.

← Older revision		Revision as of 10:24, 16 October 2024
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	__FORCETOC__		__FORCETOC__
	~~=Preface=~~		Perhaps the first thing to note about the use of [[tablet]] 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.
	Perhaps the first thing to note about the use of [[~~Tablets\|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.

	=4et tablets=		== 4et tablets ==
	Let us consider a simple [http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/fouredo.mp3 4edo piece] as a starting point:		Let us consider a simple [https://web.archive.org/web/20201127012143/http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/fouredo.mp3 4edo piece] as a starting point:

	[0 3 6 9]		[0 3 6 9]
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	[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 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 [https://web.archive.org/web/20201128050303/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 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 [https://web.archive.org/web/20201127012925/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].		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 [https://web.archive.org/web/20201127012121/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 [https://web.archive.org/web/20201127012925/http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/stella.mp3 piece].

	Because the keenanismic tablet also makes use of 4et, we can take the same 4et melodic skeleton we started with and add chords for a progression of keenanismic tablets. If we use [1 1 1], [1 1 1], [0 3 1], [1 4 0], [0 5 -1], [1 5 -3], [3 4 -4], [4 4 -6], [5 4 -8], [4 5 -9], [5 5 -11], [4 7 -11], [5 8 -12], [4 9 -13], [5 9 -15], [5 9 -15] as the sixteen keenanismic tetrads for the sixteen measures of the 4et piece, a chord progressing where each chord shares a triad with each preceeding and following, we obtain the following [http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/keenm.mp3 piece]. This in theory transposes up 2401/2400 again, but it does very little tuning damage to temper it out, leading to agni temperament. The tuning used here, 284et, tempers out both 2401/2400 and 385/384.		Because the keenanismic tablet also makes use of 4et, we can take the same 4et melodic skeleton we started with and add chords for a progression of keenanismic tablets. If we use [1 1 1], [1 1 1], [0 3 1], [1 4 0], [0 5 -1], [1 5 -3], [3 4 -4], [4 4 -6], [5 4 -8], [4 5 -9], [5 5 -11], [4 7 -11], [5 8 -12], [4 9 -13], [5 9 -15], [5 9 -15] as the sixteen keenanismic tetrads for the sixteen measures of the 4et piece, a chord progressing where each chord shares a triad with each preceeding and following, we obtain the following [https://web.archive.org/web/20201127012203/http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/keenm.mp3 piece]. This in theory transposes up 2401/2400 again, but it does very little tuning damage to temper it out, leading to agni temperament. The tuning used here, 284et, tempers out both 2401/2400 and 385/384.

	=5et tablets=		== 5et tablets ==
	We start with a 5et piece, a simple-minded one being the 62 measures of		We start with a 5et piece, a simple-minded one being the 62 measures of

	[3 0 4], [2 0 4], [2 4 3], [3 4 2], [4 3 2], [1 3 2], [3 2 0], [3 2 0], [0 3 4], [0 2 4], [4 1 3], [4 0 3], [3 1 4], [3 2 4], [2 3 0], [2 3 0], [3 2 0], [2 3 0], [1 4 0], [0 4 1], [1 4 2], [2 4 3], [3 2 4], [3 1 4], [2 3 0], [3 2 0], [4 2 0], [4 1 0], [4 1 0], [4 1 0], [2 3 0], [1 3 0], [3 4 0], [2 3 0], [2 3 0], [1 2 0], [0 2 3], [1 2 3], [3 2 4], [3 2 4], [2 3 4], [3 2 4], [3 2 4], [2 3 4], [2 4 1], [2 1 0], [2 3 0], [2 3 0], [1 0 3], [4 0 3], [4 3 1], [1 3 4], [3 1 4], [2 1 4], [1 4 0], [1 4 0], [0 1 3], [0 4 3], [3 2 1], [3 0 1], [1 2 3], [1 4 3], [4 1 0], [4 1 0], [1 4 0], [4 1 0], [2 3 0], [0 3 2], [2 3 4], [4 3 1], [1 4 3], [1 2 3], [4 1 0], [1 4 0], [3 4 0], [3 2 0], [3 2 0], [3 2 0], [4 1 0], [2 1 0], [1 3 0], [4 1 0], [4 1 0], [2 4 0], [0 4 1], [2 4 1], [1 4 3], [1 4 3], [4 1 3], [1 4 3], [1 4 3], [4 1 3], [4 3 2], [4 2 0], [4 1 0], [4 1 0], [1 0 3], [4 0 3], [4 3 1], [1 3 4], [3 1 4], [2 1 4], [1 4 0], [1 4 0], [0 1 3], [0 4 3], [3 2 1], [3 0 1], [1 2 3], [1 4 3], [4 1 0], [4 1 0], [1 4 0], [4 1 0], [2 3 0], [0 3 2], [2 3 4], [4 3 1], [1 4 3], [1 2 3], [4 1 0], [1 4 0], [3 4 0], [3 2 0], [3 2 0], [3 2 0], [4 1 0], [2 1 0], [1 3 0], [4 1 0], [4 1 0], [2 4 0], [0 4 1], [2 4 1], [1 4 3], [1 4 3], [4 1 3], [1 4 3], [1 4 3], [4 1 3], [4 3 2], [4 2 0], [4 1 0], [4 1 0], [2 0 1], [3 0 1], [3 1 2], [2 1 3], [1 2 3], [4 2 3], [2 3 0], [2 3 0], [0 2 1], [0 3 1], [1 4 2], [1 0 2], [2 4 1], [2 3 1], [3 2 0], [3 2 0], [2 3 0], [3 2 0], [4 1 0], [0 1 4], [4 1 3], [3 1 2], [2 3 1], [2 4 1], [3 2 0], [2 3 0], [1 3 0], [1 4 0], [1 4 0], [1 4 0], [3 2 0], [4 2 0], [2 1 0], [3 2 0], [3 2 0], [4 3 0], [0 3 2], [4 3 2], [2 3 1], [2 3 1], [3 2 1], [2 3 1], [2 3 1], [3 2 1], [3 1 4], [3 4 0], [3 2 0], [3 2 0], [3 0 4], [2 0 4], [2 4 3], [3 4 2], [4 3 2], [1 3 2], [3 2 0], [3 2 0], [0 3 4], [0 2 4], [4 1 3], [4 0 3], [3 1 4], [3 2 4], [2 3 0], [2 3 0], [3 2 0], [2 3 0], [1 4 0], [0 4 1], [1 4 2], [2 4 3], [3 2 4], [3 1 4], [2 3 0], [3 2 0], [4 2 0], [4 1 0], [4 1 0], [4 1 0], [2 3 0], [1 3 0], [3 4 0], [2 3 0], [2 3 0], [1 2 0], [0 2 3], [1 2 3], [3 2 4], [3 2 4], [2 3 4], [3 2 4], [3 2 4], [2 3 4], [2 4 1], [2 1 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0]		[3 0 4], [2 0 4], [2 4 3], [3 4 2], [4 3 2], [1 3 2], [3 2 0], [3 2 0], [0 3 4], [0 2 4], [4 1 3], [4 0 3], [3 1 4], [3 2 4], [2 3 0], [2 3 0], [3 2 0], [2 3 0], [1 4 0], [0 4 1], [1 4 2], [2 4 3], [3 2 4], [3 1 4], [2 3 0], [3 2 0], [4 2 0], [4 1 0], [4 1 0], [4 1 0], [2 3 0], [1 3 0], [3 4 0], [2 3 0], [2 3 0], [1 2 0], [0 2 3], [1 2 3], [3 2 4], [3 2 4], [2 3 4], [3 2 4], [3 2 4], [2 3 4], [2 4 1], [2 1 0], [2 3 0], [2 3 0], [1 0 3], [4 0 3], [4 3 1], [1 3 4], [3 1 4], [2 1 4], [1 4 0], [1 4 0], [0 1 3], [0 4 3], [3 2 1], [3 0 1], [1 2 3], [1 4 3], [4 1 0], [4 1 0], [1 4 0], [4 1 0], [2 3 0], [0 3 2], [2 3 4], [4 3 1], [1 4 3], [1 2 3], [4 1 0], [1 4 0], [3 4 0], [3 2 0], [3 2 0], [3 2 0], [4 1 0], [2 1 0], [1 3 0], [4 1 0], [4 1 0], [2 4 0], [0 4 1], [2 4 1], [1 4 3], [1 4 3], [4 1 3], [1 4 3], [1 4 3], [4 1 3], [4 3 2], [4 2 0], [4 1 0], [4 1 0], [1 0 3], [4 0 3], [4 3 1], [1 3 4], [3 1 4], [2 1 4], [1 4 0], [1 4 0], [0 1 3], [0 4 3], [3 2 1], [3 0 1], [1 2 3], [1 4 3], [4 1 0], [4 1 0], [1 4 0], [4 1 0], [2 3 0], [0 3 2], [2 3 4], [4 3 1], [1 4 3], [1 2 3], [4 1 0], [1 4 0], [3 4 0], [3 2 0], [3 2 0], [3 2 0], [4 1 0], [2 1 0], [1 3 0], [4 1 0], [4 1 0], [2 4 0], [0 4 1], [2 4 1], [1 4 3], [1 4 3], [4 1 3], [1 4 3], [1 4 3], [4 1 3], [4 3 2], [4 2 0], [4 1 0], [4 1 0], [2 0 1], [3 0 1], [3 1 2], [2 1 3], [1 2 3], [4 2 3], [2 3 0], [2 3 0], [0 2 1], [0 3 1], [1 4 2], [1 0 2], [2 4 1], [2 3 1], [3 2 0], [3 2 0], [2 3 0], [3 2 0], [4 1 0], [0 1 4], [4 1 3], [3 1 2], [2 3 1], [2 4 1], [3 2 0], [2 3 0], [1 3 0], [1 4 0], [1 4 0], [1 4 0], [3 2 0], [4 2 0], [2 1 0], [3 2 0], [3 2 0], [4 3 0], [0 3 2], [4 3 2], [2 3 1], [2 3 1], [3 2 1], [2 3 1], [2 3 1], [3 2 1], [3 1 4], [3 4 0], [3 2 0], [3 2 0], [3 0 4], [2 0 4], [2 4 3], [3 4 2], [4 3 2], [1 3 2], [3 2 0], [3 2 0], [0 3 4], [0 2 4], [4 1 3], [4 0 3], [3 1 4], [3 2 4], [2 3 0], [2 3 0], [3 2 0], [2 3 0], [1 4 0], [0 4 1], [1 4 2], [2 4 3], [3 2 4], [3 1 4], [2 3 0], [3 2 0], [4 2 0], [4 1 0], [4 1 0], [4 1 0], [2 3 0], [1 3 0], [3 4 0], [2 3 0], [2 3 0], [1 2 0], [0 2 3], [1 2 3], [3 2 4], [3 2 4], [2 3 4], [3 2 4], [3 2 4], [2 3 4], [2 4 1], [2 1 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0]

	This can be rendered [http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/penta.mp3 thusly]. We can give this more much needed pizazz by turning into a meantone piece, for instance by using chord identifiers which change every two measures from identifier 30 down to 0, tuned in 31et. This results in [http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/mean.mp3 this meantone piece]. On the other hand, we can convert it to a [http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/quint.mp3 7-limit JI piece] by chord identifiers		This can be rendered [https://web.archive.org/web/20201127014749/http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/penta.mp3 thusly]. We can give this more much needed pizazz by turning into a meantone piece, for instance by using chord identifiers which change every two measures from identifier 30 down to 0, tuned in 31et. This results in [https://web.archive.org/web/20201127014219/http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/mean.mp3 this meantone piece]. On the other hand, we can convert it to a [https://web.archive.org/web/20201127013628/http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/quint.mp3 7-limit JI piece] by chord identifiers

	[0 0 0], [-1 0 0], [-2 0 0], [-3 0 0], [-4 0 0], [-5 0 0], [-5 1 0], [-5 2 0], [-5 3 0], [-5 4 0], [-5 5 0], [-5 6 0], [-5 6 1], [-5 6 2], [-5 6 3], [-5 6 3]		[0 0 0], [-1 0 0], [-2 0 0], [-3 0 0], [-4 0 0], [-5 0 0], [-5 1 0], [-5 2 0], [-5 3 0], [-5 4 0], [-5 5 0], [-5 6 0], [-5 6 1], [-5 6 2], [-5 6 3], [-5 6 3]

	The chord [-5 6 3] has root 4374/4375 rather than 1/1, but note 0 no longer corresponds to it so we end the piece by moving the bass down 9/8.		The chord [-5 6 3] has root 4374/4375 rather than 1/1, but note 0 no longer corresponds to it so we end the piece by moving the bass down 9/8.
	[[Category:~~chords~~]]
	[[Category:~~composition~~]]		[[Category:Chords]]
	[[Category:~~notation~~]]		[[Category:Composition]]
			[[Category:Notation]]
			{{Todo\| improve readability }}

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

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Wikispaces>genewardsmith: Imported revision 260725160 - Original comment:

2011-10-02T19:52:58Z

**Imported revision 260725160 - Original comment: **

Wikispaces>genewardsmith: Imported revision 260723698 - Original comment:

2011-10-02T19:46:50Z

**Imported revision 260723698 - Original comment: **

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Wikispaces>genewardsmith: Imported revision 259428054 - Original comment:

2011-09-28T20:57:16Z

**Imported revision 259428054 - Original comment: **

← Older revision		Revision as of 20:57, 28 September 2011
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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 20:55:22 UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2011-09-28 20:57:16 UTC</tt>.<br>
	: The original revision id was <tt>~~259427566~~</tt>.<br>		: The original revision id was <tt>259428054</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 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]].		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]].

	Because the keenanismic tablet also makes use of 4et, we can take the same 4et melodic skeleton we started with and add chords for a progression of keenanismic tablets. If we use [1 1 1], [1 1 1], [0 3 1], [1 4 0], [0 5 -1], [1 5 -3], [3 4 -4], [4 4 -6], [5 4 -8], [4 5 -9], [5 5 -11], [4 7 -11], [5 8 -12], [4 9 -13], [5 9 -15], [5 9 -15] as the sixteen keenanismic tetrads for the sixteen measures of the 4et piece, we obtain the following [[http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/keenm.mp3\|piece]]. This in theory transposes up 2401/2400 again, but it does very little tuning damage to temper it out, leading to agni temperament. The tuning used here, 284et, tempers out both 2401/2400 and 385/384.		Because the keenanismic tablet also makes use of 4et, we can take the same 4et melodic skeleton we started with and add chords for a progression of keenanismic tablets. If we use [1 1 1], [1 1 1], [0 3 1], [1 4 0], [0 5 -1], [1 5 -3], [3 4 -4], [4 4 -6], [5 4 -8], [4 5 -9], [5 5 -11], [4 7 -11], [5 8 -12], [4 9 -13], [5 9 -15], [5 9 -15] as the sixteen keenanismic tetrads for the sixteen measures of the 4et piece, a chord progressing where each chord shares a triad with each preceeding and following, we obtain the following [[http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/keenm.mp3\|piece]]. This in theory transposes up 2401/2400 again, but it does very little tuning damage to temper it out, leading to agni temperament. The tuning used here, 284et, tempers out both 2401/2400 and 385/384.

	</pre></div>		</pre></div>
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	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>.<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>.<br />
	<br />		<br />
	Because the keenanismic tablet also makes use of 4et, we can take the same 4et melodic skeleton we started with and add chords for a progression of keenanismic tablets. If we use [1 1 1], [1 1 1], [0 3 1], [1 4 0], [0 5 -1], [1 5 -3], [3 4 -4], [4 4 -6], [5 4 -8], [4 5 -9], [5 5 -11], [4 7 -11], [5 8 -12], [4 9 -13], [5 9 -15], [5 9 -15] as the sixteen keenanismic tetrads for the sixteen measures of the 4et piece, we obtain the following <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/keenm.mp3" rel="nofollow">piece</a>. This in theory transposes up 2401/2400 again, but it does very little tuning damage to temper it out, leading to agni temperament. The tuning used here, 284et, tempers out both 2401/2400 and 385/384.</body></html></pre></div>		Because the keenanismic tablet also makes use of 4et, we can take the same 4et melodic skeleton we started with and add chords for a progression of keenanismic tablets. If we use [1 1 1], [1 1 1], [0 3 1], [1 4 0], [0 5 -1], [1 5 -3], [3 4 -4], [4 4 -6], [5 4 -8], [4 5 -9], [5 5 -11], [4 7 -11], [5 8 -12], [4 9 -13], [5 9 -15], [5 9 -15] as the sixteen keenanismic tetrads for the sixteen measures of the 4et piece, a chord progressing where each chord shares a triad with each preceeding and following, we obtain the following <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/keenm.mp3" rel="nofollow">piece</a>. This in theory transposes up 2401/2400 again, but it does very little tuning damage to temper it out, leading to agni temperament. The tuning used here, 284et, tempers out both 2401/2400 and 385/384.</body></html></pre></div>

Wikispaces>genewardsmith: Imported revision 259427566 - Original comment:

2011-09-28T20:55:22Z

**Imported revision 259427566 - Original comment: **

← Older revision		Revision as of 20:55, 28 September 2011
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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 20:54:02 UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2011-09-28 20:55:22 UTC</tt>.<br>
	: The original revision id was <tt>~~259427150~~</tt>.<br>		: The original revision id was <tt>259427566</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 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]].		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]].

	Because the keenanismic tablet also makes use of 4et, we can take the same 4et melodic skeleton we started with and add chords for a progression of keenanismic tablets. If we use [1 1 1], [1 1 1],		Because the keenanismic tablet also makes use of 4et, we can take the same 4et melodic skeleton we started with and add chords for a progression of keenanismic tablets. If we use [1 1 1], [1 1 1], [0 3 1], [1 4 0], [0 5 -1], [1 5 -3], [3 4 -4], [4 4 -6], [5 4 -8], [4 5 -9], [5 5 -11], [4 7 -11], [5 8 -12], [4 9 -13], [5 9 -15], [5 9 -15] as the sixteen keenanismic tetrads for the sixteen measures of the 4et piece, we obtain the following [[http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/keenm.mp3\|piece]]. This in theory transposes up 2401/2400 again, but it does very little tuning damage to temper it out, leading to agni temperament. The tuning used here, 284et, tempers out both 2401/2400 and 385/384.
	[0 3 1], [1 4 0], [0 5 -1], [1 5 -3], [3 4 -4], [4 4 -6], [5 4 -8],
	[4 5 -9], [5 5 -11], [4 7 -11], [5 8 -12], [4 9 -13], [5 9 -15],
	[5 9 -15] as the sixteen keenanismic tetrads for the sixteen measures of the 4et piece, we obtain the following [[http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/keenm.mp3\|piece]]. This in theory transposes up 2401/2400 again, but it does very little tuning damage to temper it out, leading to agni temperament. The tuning used here, 284et, tempers out both 2401/2400 and 385/384.

	</pre></div>		</pre></div>
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	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>.<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>.<br />
	<br />		<br />
	Because the keenanismic tablet also makes use of 4et, we can take the same 4et melodic skeleton we started with and add chords for a progression of keenanismic tablets. If we use [1 1 1], [1 1 1], ~~<br />~~		Because the keenanismic tablet also makes use of 4et, we can take the same 4et melodic skeleton we started with and add chords for a progression of keenanismic tablets. If we use [1 1 1], [1 1 1], [0 3 1], [1 4 0], [0 5 -1], [1 5 -3], [3 4 -4], [4 4 -6], [5 4 -8], [4 5 -9], [5 5 -11], [4 7 -11], [5 8 -12], [4 9 -13], [5 9 -15], [5 9 -15] as the sixteen keenanismic tetrads for the sixteen measures of the 4et piece, we obtain the following <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/keenm.mp3" rel="nofollow">piece</a>. This in theory transposes up 2401/2400 again, but it does very little tuning damage to temper it out, leading to agni temperament. The tuning used here, 284et, tempers out both 2401/2400 and 385/384.</body></html></pre></div>
	[0 3 1], [1 4 0], [0 5 -1], [1 5 -3], [3 4 -4], [4 4 -6], [5 4 -8], ~~<br />~~
	[4 5 -9], [5 5 -11], [4 7 -11], [5 8 -12], [4 9 -13], [5 9 -15], ~~<br />~~
	[5 9 -15] as the sixteen keenanismic tetrads for the sixteen measures of the 4et piece, we obtain the following <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/keenm.mp3" rel="nofollow">piece</a>. This in theory transposes up 2401/2400 again, but it does very little tuning damage to temper it out, leading to agni temperament. The tuning used here, 284et, tempers out both 2401/2400 and 385/384.</body></html></pre></div>

Wikispaces>genewardsmith: Imported revision 259427150 - Original comment:

2011-09-28T20:54:02Z

**Imported revision 259427150 - Original comment: **

← Older revision		Revision as of 20:54, 28 September 2011
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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 00:44:47 UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2011-09-28 20:54:02 UTC</tt>.<br>
	: The original revision id was <tt>~~258923392~~</tt>.<br>		: The original revision id was <tt>259427150</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 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]].		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]].

			Because the keenanismic tablet also makes use of 4et, we can take the same 4et melodic skeleton we started with and add chords for a progression of keenanismic tablets. If we use [1 1 1], [1 1 1],
			[0 3 1], [1 4 0], [0 5 -1], [1 5 -3], [3 4 -4], [4 4 -6], [5 4 -8],
			[4 5 -9], [5 5 -11], [4 7 -11], [5 8 -12], [4 9 -13], [5 9 -15],
			[5 9 -15] as the sixteen keenanismic tetrads for the sixteen measures of the 4et piece, we obtain the following [[http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/keenm.mp3\|piece]]. This in theory transposes up 2401/2400 again, but it does very little tuning damage to temper it out, leading to agni temperament. The tuning used here, 284et, tempers out both 2401/2400 and 385/384.

	</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 <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>		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>.<br />
			<br />
			Because the keenanismic tablet also makes use of 4et, we can take the same 4et melodic skeleton we started with and add chords for a progression of keenanismic tablets. If we use [1 1 1], [1 1 1], <br />
			[0 3 1], [1 4 0], [0 5 -1], [1 5 -3], [3 4 -4], [4 4 -6], [5 4 -8], <br />
			[4 5 -9], [5 5 -11], [4 7 -11], [5 8 -12], [4 9 -13], [5 9 -15], <br />
			[5 9 -15] as the sixteen keenanismic tetrads for the sixteen measures of the 4et piece, we obtain the following <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/keenm.mp3" rel="nofollow">piece</a>. This in theory transposes up 2401/2400 again, but it does very little tuning damage to temper it out, leading to agni temperament. The tuning used here, 284et, tempers out both 2401/2400 and 385/384.</body></html></pre></div>

Wikispaces>genewardsmith: Imported revision 258923392 - Original comment:

2011-09-28T00:44:47Z

**Imported revision 258923392 - Original comment: **

← Older revision		Revision as of 00:44, 28 September 2011
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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 00:20:20 UTC</tt>.<br>		: 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>~~258919444~~</tt>.<br>		: 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>
Line 79:		Line 79:
	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>
Line 155:		Line 155:
	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>

Wikispaces>genewardsmith: Imported revision 258919444 - Original comment:

2011-09-28T00:20:20Z

**Imported revision 258919444 - Original comment: **

Wikispaces>genewardsmith: Imported revision 258914358 - Original comment:

2011-09-27T23:52:08Z

**Imported revision 258914358 - Original comment: **

← Older revision		Revision as of 23:52, 27 September 2011
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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>2011-09-27 17:47:45 UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2011-09-27 23:52:08 UTC</tt>.<br>
	: The original revision id was <tt>~~258821548~~</tt>.<br>		: The original revision id was <tt>258914358</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 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 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.</pre></div>		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]].</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>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 />		<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>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 />
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	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 />		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 />		<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.</body></html></pre></div>		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>.</body></html></pre></div>

← Older revision		Revision as of 19:52, 2 October 2011
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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>2011-10-02 19:46:50 UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2011-10-02 19:52:58 UTC</tt>.<br>
	: The original revision id was <tt>~~260723698~~</tt>.<br>		: The original revision id was <tt>260725160</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 92:		Line 92:
	[3 0 4], [2 0 4], [2 4 3], [3 4 2], [4 3 2], [1 3 2], [3 2 0], [3 2 0], [0 3 4], [0 2 4], [4 1 3], [4 0 3], [3 1 4], [3 2 4], [2 3 0], [2 3 0], [3 2 0], [2 3 0], [1 4 0], [0 4 1], [1 4 2], [2 4 3], [3 2 4], [3 1 4], [2 3 0], [3 2 0], [4 2 0], [4 1 0], [4 1 0], [4 1 0], [2 3 0], [1 3 0], [3 4 0], [2 3 0], [2 3 0], [1 2 0], [0 2 3], [1 2 3], [3 2 4], [3 2 4], [2 3 4], [3 2 4], [3 2 4], [2 3 4], [2 4 1], [2 1 0], [2 3 0], [2 3 0], [1 0 3], [4 0 3], [4 3 1], [1 3 4], [3 1 4], [2 1 4], [1 4 0], [1 4 0], [0 1 3], [0 4 3], [3 2 1], [3 0 1], [1 2 3], [1 4 3], [4 1 0], [4 1 0], [1 4 0], [4 1 0], [2 3 0], [0 3 2], [2 3 4], [4 3 1], [1 4 3], [1 2 3], [4 1 0], [1 4 0], [3 4 0], [3 2 0], [3 2 0], [3 2 0], [4 1 0], [2 1 0], [1 3 0], [4 1 0], [4 1 0], [2 4 0], [0 4 1], [2 4 1], [1 4 3], [1 4 3], [4 1 3], [1 4 3], [1 4 3], [4 1 3], [4 3 2], [4 2 0], [4 1 0], [4 1 0], [1 0 3], [4 0 3], [4 3 1], [1 3 4], [3 1 4], [2 1 4], [1 4 0], [1 4 0], [0 1 3], [0 4 3], [3 2 1], [3 0 1], [1 2 3], [1 4 3], [4 1 0], [4 1 0], [1 4 0], [4 1 0], [2 3 0], [0 3 2], [2 3 4], [4 3 1], [1 4 3], [1 2 3], [4 1 0], [1 4 0], [3 4 0], [3 2 0], [3 2 0], [3 2 0], [4 1 0], [2 1 0], [1 3 0], [4 1 0], [4 1 0], [2 4 0], [0 4 1], [2 4 1], [1 4 3], [1 4 3], [4 1 3], [1 4 3], [1 4 3], [4 1 3], [4 3 2], [4 2 0], [4 1 0], [4 1 0], [2 0 1], [3 0 1], [3 1 2], [2 1 3], [1 2 3], [4 2 3], [2 3 0], [2 3 0], [0 2 1], [0 3 1], [1 4 2], [1 0 2], [2 4 1], [2 3 1], [3 2 0], [3 2 0], [2 3 0], [3 2 0], [4 1 0], [0 1 4], [4 1 3], [3 1 2], [2 3 1], [2 4 1], [3 2 0], [2 3 0], [1 3 0], [1 4 0], [1 4 0], [1 4 0], [3 2 0], [4 2 0], [2 1 0], [3 2 0], [3 2 0], [4 3 0], [0 3 2], [4 3 2], [2 3 1], [2 3 1], [3 2 1], [2 3 1], [2 3 1], [3 2 1], [3 1 4], [3 4 0], [3 2 0], [3 2 0], [3 0 4], [2 0 4], [2 4 3], [3 4 2], [4 3 2], [1 3 2], [3 2 0], [3 2 0], [0 3 4], [0 2 4], [4 1 3], [4 0 3], [3 1 4], [3 2 4], [2 3 0], [2 3 0], [3 2 0], [2 3 0], [1 4 0], [0 4 1], [1 4 2], [2 4 3], [3 2 4], [3 1 4], [2 3 0], [3 2 0], [4 2 0], [4 1 0], [4 1 0], [4 1 0], [2 3 0], [1 3 0], [3 4 0], [2 3 0], [2 3 0], [1 2 0], [0 2 3], [1 2 3], [3 2 4], [3 2 4], [2 3 4], [3 2 4], [3 2 4], [2 3 4], [2 4 1], [2 1 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0]		[3 0 4], [2 0 4], [2 4 3], [3 4 2], [4 3 2], [1 3 2], [3 2 0], [3 2 0], [0 3 4], [0 2 4], [4 1 3], [4 0 3], [3 1 4], [3 2 4], [2 3 0], [2 3 0], [3 2 0], [2 3 0], [1 4 0], [0 4 1], [1 4 2], [2 4 3], [3 2 4], [3 1 4], [2 3 0], [3 2 0], [4 2 0], [4 1 0], [4 1 0], [4 1 0], [2 3 0], [1 3 0], [3 4 0], [2 3 0], [2 3 0], [1 2 0], [0 2 3], [1 2 3], [3 2 4], [3 2 4], [2 3 4], [3 2 4], [3 2 4], [2 3 4], [2 4 1], [2 1 0], [2 3 0], [2 3 0], [1 0 3], [4 0 3], [4 3 1], [1 3 4], [3 1 4], [2 1 4], [1 4 0], [1 4 0], [0 1 3], [0 4 3], [3 2 1], [3 0 1], [1 2 3], [1 4 3], [4 1 0], [4 1 0], [1 4 0], [4 1 0], [2 3 0], [0 3 2], [2 3 4], [4 3 1], [1 4 3], [1 2 3], [4 1 0], [1 4 0], [3 4 0], [3 2 0], [3 2 0], [3 2 0], [4 1 0], [2 1 0], [1 3 0], [4 1 0], [4 1 0], [2 4 0], [0 4 1], [2 4 1], [1 4 3], [1 4 3], [4 1 3], [1 4 3], [1 4 3], [4 1 3], [4 3 2], [4 2 0], [4 1 0], [4 1 0], [1 0 3], [4 0 3], [4 3 1], [1 3 4], [3 1 4], [2 1 4], [1 4 0], [1 4 0], [0 1 3], [0 4 3], [3 2 1], [3 0 1], [1 2 3], [1 4 3], [4 1 0], [4 1 0], [1 4 0], [4 1 0], [2 3 0], [0 3 2], [2 3 4], [4 3 1], [1 4 3], [1 2 3], [4 1 0], [1 4 0], [3 4 0], [3 2 0], [3 2 0], [3 2 0], [4 1 0], [2 1 0], [1 3 0], [4 1 0], [4 1 0], [2 4 0], [0 4 1], [2 4 1], [1 4 3], [1 4 3], [4 1 3], [1 4 3], [1 4 3], [4 1 3], [4 3 2], [4 2 0], [4 1 0], [4 1 0], [2 0 1], [3 0 1], [3 1 2], [2 1 3], [1 2 3], [4 2 3], [2 3 0], [2 3 0], [0 2 1], [0 3 1], [1 4 2], [1 0 2], [2 4 1], [2 3 1], [3 2 0], [3 2 0], [2 3 0], [3 2 0], [4 1 0], [0 1 4], [4 1 3], [3 1 2], [2 3 1], [2 4 1], [3 2 0], [2 3 0], [1 3 0], [1 4 0], [1 4 0], [1 4 0], [3 2 0], [4 2 0], [2 1 0], [3 2 0], [3 2 0], [4 3 0], [0 3 2], [4 3 2], [2 3 1], [2 3 1], [3 2 1], [2 3 1], [2 3 1], [3 2 1], [3 1 4], [3 4 0], [3 2 0], [3 2 0], [3 0 4], [2 0 4], [2 4 3], [3 4 2], [4 3 2], [1 3 2], [3 2 0], [3 2 0], [0 3 4], [0 2 4], [4 1 3], [4 0 3], [3 1 4], [3 2 4], [2 3 0], [2 3 0], [3 2 0], [2 3 0], [1 4 0], [0 4 1], [1 4 2], [2 4 3], [3 2 4], [3 1 4], [2 3 0], [3 2 0], [4 2 0], [4 1 0], [4 1 0], [4 1 0], [2 3 0], [1 3 0], [3 4 0], [2 3 0], [2 3 0], [1 2 0], [0 2 3], [1 2 3], [3 2 4], [3 2 4], [2 3 4], [3 2 4], [3 2 4], [2 3 4], [2 4 1], [2 1 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0]

	This can be rendered [[http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/penta.mp3\|thusly]]. We can give this more much needed pizazz by turning ~~inot~~ a meantone piece, for instance by using chord identifiers which change every two measures from identifier 30 down to 0, tuned in 31et. This results in [[http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/mean.mp3\|this meantone piece]]. On the other hand, we can convert it to a [[http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/quint.mp3\|7-limit piece]] by chord identifiers		This can be rendered [[http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/penta.mp3\|thusly]]. We can give this more much needed pizazz by turning into a meantone piece, for instance by using chord identifiers which change every two measures from identifier 30 down to 0, tuned in 31et. This results in [[http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/mean.mp3\|this meantone piece]]. On the other hand, we can convert it to a [[http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/quint.mp3\|7-limit JI piece]] by chord identifiers

	[0 0 0], [-1 0 0], [-2 0 0], [-3 0 0], [-4 0 0], [-5 0 0], [-5 1 0], [-5 2 0], [-5 3 0], [-5 4 0], [-5 5 0], [-5 6 0], [-5 6 1], [-5 6 2], [-5 6 3], [-5 6 3]		[0 0 0], [-1 0 0], [-2 0 0], [-3 0 0], [-4 0 0], [-5 0 0], [-5 1 0], [-5 2 0], [-5 3 0], [-5 4 0], [-5 5 0], [-5 6 0], [-5 6 1], [-5 6 2], [-5 6 3], [-5 6 3]
Line 188:		Line 188:
	[3 0 4], [2 0 4], [2 4 3], [3 4 2], [4 3 2], [1 3 2], [3 2 0], [3 2 0], [0 3 4], [0 2 4], [4 1 3], [4 0 3], [3 1 4], [3 2 4], [2 3 0], [2 3 0], [3 2 0], [2 3 0], [1 4 0], [0 4 1], [1 4 2], [2 4 3], [3 2 4], [3 1 4], [2 3 0], [3 2 0], [4 2 0], [4 1 0], [4 1 0], [4 1 0], [2 3 0], [1 3 0], [3 4 0], [2 3 0], [2 3 0], [1 2 0], [0 2 3], [1 2 3], [3 2 4], [3 2 4], [2 3 4], [3 2 4], [3 2 4], [2 3 4], [2 4 1], [2 1 0], [2 3 0], [2 3 0], [1 0 3], [4 0 3], [4 3 1], [1 3 4], [3 1 4], [2 1 4], [1 4 0], [1 4 0], [0 1 3], [0 4 3], [3 2 1], [3 0 1], [1 2 3], [1 4 3], [4 1 0], [4 1 0], [1 4 0], [4 1 0], [2 3 0], [0 3 2], [2 3 4], [4 3 1], [1 4 3], [1 2 3], [4 1 0], [1 4 0], [3 4 0], [3 2 0], [3 2 0], [3 2 0], [4 1 0], [2 1 0], [1 3 0], [4 1 0], [4 1 0], [2 4 0], [0 4 1], [2 4 1], [1 4 3], [1 4 3], [4 1 3], [1 4 3], [1 4 3], [4 1 3], [4 3 2], [4 2 0], [4 1 0], [4 1 0], [1 0 3], [4 0 3], [4 3 1], [1 3 4], [3 1 4], [2 1 4], [1 4 0], [1 4 0], [0 1 3], [0 4 3], [3 2 1], [3 0 1], [1 2 3], [1 4 3], [4 1 0], [4 1 0], [1 4 0], [4 1 0], [2 3 0], [0 3 2], [2 3 4], [4 3 1], [1 4 3], [1 2 3], [4 1 0], [1 4 0], [3 4 0], [3 2 0], [3 2 0], [3 2 0], [4 1 0], [2 1 0], [1 3 0], [4 1 0], [4 1 0], [2 4 0], [0 4 1], [2 4 1], [1 4 3], [1 4 3], [4 1 3], [1 4 3], [1 4 3], [4 1 3], [4 3 2], [4 2 0], [4 1 0], [4 1 0], [2 0 1], [3 0 1], [3 1 2], [2 1 3], [1 2 3], [4 2 3], [2 3 0], [2 3 0], [0 2 1], [0 3 1], [1 4 2], [1 0 2], [2 4 1], [2 3 1], [3 2 0], [3 2 0], [2 3 0], [3 2 0], [4 1 0], [0 1 4], [4 1 3], [3 1 2], [2 3 1], [2 4 1], [3 2 0], [2 3 0], [1 3 0], [1 4 0], [1 4 0], [1 4 0], [3 2 0], [4 2 0], [2 1 0], [3 2 0], [3 2 0], [4 3 0], [0 3 2], [4 3 2], [2 3 1], [2 3 1], [3 2 1], [2 3 1], [2 3 1], [3 2 1], [3 1 4], [3 4 0], [3 2 0], [3 2 0], [3 0 4], [2 0 4], [2 4 3], [3 4 2], [4 3 2], [1 3 2], [3 2 0], [3 2 0], [0 3 4], [0 2 4], [4 1 3], [4 0 3], [3 1 4], [3 2 4], [2 3 0], [2 3 0], [3 2 0], [2 3 0], [1 4 0], [0 4 1], [1 4 2], [2 4 3], [3 2 4], [3 1 4], [2 3 0], [3 2 0], [4 2 0], [4 1 0], [4 1 0], [4 1 0], [2 3 0], [1 3 0], [3 4 0], [2 3 0], [2 3 0], [1 2 0], [0 2 3], [1 2 3], [3 2 4], [3 2 4], [2 3 4], [3 2 4], [3 2 4], [2 3 4], [2 4 1], [2 1 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0]<br />		[3 0 4], [2 0 4], [2 4 3], [3 4 2], [4 3 2], [1 3 2], [3 2 0], [3 2 0], [0 3 4], [0 2 4], [4 1 3], [4 0 3], [3 1 4], [3 2 4], [2 3 0], [2 3 0], [3 2 0], [2 3 0], [1 4 0], [0 4 1], [1 4 2], [2 4 3], [3 2 4], [3 1 4], [2 3 0], [3 2 0], [4 2 0], [4 1 0], [4 1 0], [4 1 0], [2 3 0], [1 3 0], [3 4 0], [2 3 0], [2 3 0], [1 2 0], [0 2 3], [1 2 3], [3 2 4], [3 2 4], [2 3 4], [3 2 4], [3 2 4], [2 3 4], [2 4 1], [2 1 0], [2 3 0], [2 3 0], [1 0 3], [4 0 3], [4 3 1], [1 3 4], [3 1 4], [2 1 4], [1 4 0], [1 4 0], [0 1 3], [0 4 3], [3 2 1], [3 0 1], [1 2 3], [1 4 3], [4 1 0], [4 1 0], [1 4 0], [4 1 0], [2 3 0], [0 3 2], [2 3 4], [4 3 1], [1 4 3], [1 2 3], [4 1 0], [1 4 0], [3 4 0], [3 2 0], [3 2 0], [3 2 0], [4 1 0], [2 1 0], [1 3 0], [4 1 0], [4 1 0], [2 4 0], [0 4 1], [2 4 1], [1 4 3], [1 4 3], [4 1 3], [1 4 3], [1 4 3], [4 1 3], [4 3 2], [4 2 0], [4 1 0], [4 1 0], [1 0 3], [4 0 3], [4 3 1], [1 3 4], [3 1 4], [2 1 4], [1 4 0], [1 4 0], [0 1 3], [0 4 3], [3 2 1], [3 0 1], [1 2 3], [1 4 3], [4 1 0], [4 1 0], [1 4 0], [4 1 0], [2 3 0], [0 3 2], [2 3 4], [4 3 1], [1 4 3], [1 2 3], [4 1 0], [1 4 0], [3 4 0], [3 2 0], [3 2 0], [3 2 0], [4 1 0], [2 1 0], [1 3 0], [4 1 0], [4 1 0], [2 4 0], [0 4 1], [2 4 1], [1 4 3], [1 4 3], [4 1 3], [1 4 3], [1 4 3], [4 1 3], [4 3 2], [4 2 0], [4 1 0], [4 1 0], [2 0 1], [3 0 1], [3 1 2], [2 1 3], [1 2 3], [4 2 3], [2 3 0], [2 3 0], [0 2 1], [0 3 1], [1 4 2], [1 0 2], [2 4 1], [2 3 1], [3 2 0], [3 2 0], [2 3 0], [3 2 0], [4 1 0], [0 1 4], [4 1 3], [3 1 2], [2 3 1], [2 4 1], [3 2 0], [2 3 0], [1 3 0], [1 4 0], [1 4 0], [1 4 0], [3 2 0], [4 2 0], [2 1 0], [3 2 0], [3 2 0], [4 3 0], [0 3 2], [4 3 2], [2 3 1], [2 3 1], [3 2 1], [2 3 1], [2 3 1], [3 2 1], [3 1 4], [3 4 0], [3 2 0], [3 2 0], [3 0 4], [2 0 4], [2 4 3], [3 4 2], [4 3 2], [1 3 2], [3 2 0], [3 2 0], [0 3 4], [0 2 4], [4 1 3], [4 0 3], [3 1 4], [3 2 4], [2 3 0], [2 3 0], [3 2 0], [2 3 0], [1 4 0], [0 4 1], [1 4 2], [2 4 3], [3 2 4], [3 1 4], [2 3 0], [3 2 0], [4 2 0], [4 1 0], [4 1 0], [4 1 0], [2 3 0], [1 3 0], [3 4 0], [2 3 0], [2 3 0], [1 2 0], [0 2 3], [1 2 3], [3 2 4], [3 2 4], [2 3 4], [3 2 4], [3 2 4], [2 3 4], [2 4 1], [2 1 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0], [2 3 0]<br />
	<br />		<br />
	This can be rendered <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/penta.mp3" rel="nofollow">thusly</a>. We can give this more much needed pizazz by turning ~~inot~~ a meantone piece, for instance by using chord identifiers which change every two measures from identifier 30 down to 0, tuned in 31et. This results in <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/mean.mp3" rel="nofollow">this meantone piece</a>. On the other hand, we can convert it to a <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/quint.mp3" rel="nofollow">7-limit piece</a> by chord identifiers <br />		This can be rendered <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/penta.mp3" rel="nofollow">thusly</a>. We can give this more much needed pizazz by turning into a meantone piece, for instance by using chord identifiers which change every two measures from identifier 30 down to 0, tuned in 31et. This results in <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/mean.mp3" rel="nofollow">this meantone piece</a>. On the other hand, we can convert it to a <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/transformers/quint.mp3" rel="nofollow">7-limit JI piece</a> by chord identifiers <br />
	<br />		<br />
	[0 0 0], [-1 0 0], [-2 0 0], [-3 0 0], [-4 0 0], [-5 0 0], [-5 1 0], [-5 2 0], [-5 3 0], [-5 4 0], [-5 5 0], [-5 6 0], [-5 6 1], [-5 6 2], [-5 6 3], [-5 6 3]<br />		[0 0 0], [-1 0 0], [-2 0 0], [-3 0 0], [-4 0 0], [-5 0 0], [-5 1 0], [-5 2 0], [-5 3 0], [-5 4 0], [-5 5 0], [-5 6 0], [-5 6 1], [-5 6 2], [-5 6 3], [-5 6 3]<br />
	<br />		<br />
	The chord [-5 6 3] has root 4374/4375 rather than 1/1, but note 0 no longer corresponds to it so we end the piece by moving the bass down 9/8.</body></html></pre></div>		The chord [-5 6 3] has root 4374/4375 rather than 1/1, but note 0 no longer corresponds to it so we end the piece by moving the bass down 9/8.</body></html></pre></div>

← Older revision		Revision as of 00:20, 28 September 2011
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>2011-09-~~27 23~~:52:08 UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2011-09-28 00:20:20 UTC</tt>.<br>
	: The original revision id was <tt>~~258914358~~</tt>.<br>		: The original revision id was <tt>258919444</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 79:		Line 79:
	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]].</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 [[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.
			</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>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 />		<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>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 />
Line 154:		Line 155:
	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>.</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 piece.</body></html></pre></div>

Composing with tablets - Revision history

FloraC: Fix header level and dead links. Mark with todo.

Wikispaces>FREEZE at 00:00, 17 July 2018

Wikispaces>genewardsmith: **Imported revision 260725160 - Original comment: **

Wikispaces>genewardsmith: **Imported revision 260723698 - Original comment: **

Wikispaces>genewardsmith: **Imported revision 259428054 - Original comment: **

Wikispaces>genewardsmith: **Imported revision 259427566 - Original comment: **

Wikispaces>genewardsmith: **Imported revision 259427150 - Original comment: **

Wikispaces>genewardsmith: **Imported revision 258923392 - Original comment: **

Wikispaces>genewardsmith: **Imported revision 258919444 - Original comment: **

Wikispaces>genewardsmith: **Imported revision 258914358 - Original comment: **