Pretty Pictures - Revision history

BudjarnLambeth at 08:51, 27 September 2025

2025-09-27T08:51:46Z

← Older revision		Revision as of 08:51, 27 September 2025
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	===Audio sculpture===		===Audio sculpture===
	If you have a visual environment whose contents can translate directly into the audio domain in some way, this is one way of doing audio sculpture. Unlike the quantized grids of piano rolls, there usually is no grid (or the grid is so fine as to be invisible). Iannis Xenakis developed an interface called [https://en.wikipedia.org/wiki/UPIC UPIC], which recently inspired the program [http://www.highc.org HighC]. In three-dimensional space, [http://audiosculptures.com/ Andy Fillebrown] has done some work, as well as...well, gosh, he's surely not the only one!= =		If you have a visual environment whose contents can translate directly into the audio domain in some way, this is one way of doing audio sculpture. Unlike the quantized grids of piano rolls, there usually is no grid (or the grid is so fine as to be invisible). [[Iannis Xenakis]] developed an interface called [https://en.wikipedia.org/wiki/UPIC UPIC], which recently inspired the program [http://www.highc.org HighC]. In three-dimensional space, [http://audiosculptures.com/ Andy Fillebrown] has done some work, as well as...well, gosh, he's surely not the only one!= =

	=Aids to understanding=		=Aids to understanding=

BudjarnLambeth: /* JI, temperament Lattices */

2024-12-05T08:40:25Z

JI, temperament Lattices

← Older revision		Revision as of 08:40, 5 December 2024
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	===JI, temperament Lattices===		===JI, temperament Lattices===
	Tonalsoft's Tonescape makes it possible to compose with scales that are represented by two- or three-dimensional lattices. Tempering a comma out of a lattice turns it into a closed structure...		Tonalsoft's [[Tonescape]] makes it possible to compose with scales that are represented by two- or three-dimensional lattices. Tempering a comma out of a lattice turns it into a closed structure...
	[[Category:Overview]]		[[Category:Overview]]
	[[Category:Lists]]		[[Category:Lists]]

Fredg999: Notation moved to Musical notation

2023-10-04T03:16:53Z

Notation moved to Musical notation

← Older revision		Revision as of 03:16, 4 October 2023
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	===Microtonal Notation===		===Microtonal Notation===
	Usually, a ghastly extension of the five-line sharps-n-flats Western tradition, sometimes with more and/or differently-spaced lines, or fancy new squiggles for accidentals. See dedicated page on [[~~Notation\|~~notation]].		Usually, a ghastly extension of the five-line sharps-n-flats Western tradition, sometimes with more and/or differently-spaced lines, or fancy new squiggles for accidentals. See dedicated page on [[musical notation]].

	===Piano-roll===		===Piano-roll===

BudjarnLambeth: Categorised this uncategorised page

2023-04-26T01:01:24Z

Categorised this uncategorised page

← Older revision		Revision as of 01:01, 26 April 2023
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	=Connections between sound and vision=		=Connections between sound and vision=
	<ul><li>Pictures can facilitate understanding a particular concept of tuning, especially for visual learners.</li><li>Cross-pollinating aims: thinking visually or spatially may lead you to ideas for new tunings, and thinking about tunings may lead you to new ways to see.</li><li>Some listeners report having [[~~visions\|~~visions]]when in the presence of a particular tuning or piece of music.<ul><li>Moreover, a small percent of people experience [[synaesthesia\|synaesthesia]] (seeing certain colors when they hear certain sounds, for example)</li></ul></li></ul>		<ul><li>Pictures can facilitate understanding a particular concept of tuning, especially for visual learners.</li><li>Cross-pollinating aims: thinking visually or spatially may lead you to ideas for new tunings, and thinking about tunings may lead you to new ways to see.</li><li>Some listeners report having [[visions]]when in the presence of a particular tuning or piece of music.<ul><li>Moreover, a small percent of people experience [[synaesthesia\|synaesthesia]] (seeing certain colors when they hear certain sounds, for example)</li></ul></li></ul>
	=Aids to composing=		=Aids to composing=

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	===Audio sculpture===		===Audio sculpture===
	If you have a visual environment whose contents can translate directly into the audio domain in some way, this is one way of doing audio sculpture. Unlike the quantized grids of piano rolls, there usually is no grid (or the grid is so fine as to be invisible). Iannis Xenakis developed an interface called [~~http~~://en.wikipedia.org/wiki/UPIC UPIC], which recently inspired the program [http://www.highc.org HighC]. In three-dimensional space, [http://audiosculptures.com/ Andy Fillebrown] has done some work, as well as...well, gosh, he's surely not the only one!= =		If you have a visual environment whose contents can translate directly into the audio domain in some way, this is one way of doing audio sculpture. Unlike the quantized grids of piano rolls, there usually is no grid (or the grid is so fine as to be invisible). Iannis Xenakis developed an interface called [https://en.wikipedia.org/wiki/UPIC UPIC], which recently inspired the program [http://www.highc.org HighC]. In three-dimensional space, [http://audiosculptures.com/ Andy Fillebrown] has done some work, as well as...well, gosh, he's surely not the only one!= =

	=Aids to understanding=		=Aids to understanding=
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	===JI, temperament Lattices===		===JI, temperament Lattices===
	Tonalsoft's Tonescape makes it possible to compose with scales that are represented by two- or three-dimensional lattices. Tempering a comma out of a lattice turns it into a closed structure...		Tonalsoft's Tonescape makes it possible to compose with scales that are represented by two- or three-dimensional lattices. Tempering a comma out of a lattice turns it into a closed structure...
			[[Category:Overview]]
			[[Category:Lists]]

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

Show changes

Wikispaces>spt3125: Imported revision 616005221 - Original comment: added link (deorphaning)

2017-07-30T15:51:21Z

**Imported revision 616005221 - Original comment: added link (deorphaning)**

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Wikispaces>JosephRuhf: Imported revision 385637366 - Original comment:

2012-11-24T23:03:57Z

**Imported revision 385637366 - Original comment: **

Wikispaces>JosephRuhf: Imported revision 385637072 - Original comment:

2012-11-24T23:01:34Z

**Imported revision 385637072 - Original comment: **

Wikispaces>JosephRuhf: Imported revision 385634152 - Original comment:

2012-11-24T22:40:44Z

**Imported revision 385634152 - Original comment: **

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	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:~~mbattaglia1~~\|~~mbattaglia1~~]] and made on <tt>2012-11-22 01:25:27 UTC</tt>.<br>		: This revision was by author [[User:JosephRuhf\|JosephRuhf]] and made on <tt>2012-11-24 22:40:44 UTC</tt>.<br>
	: The original revision id was <tt>~~384946906~~</tt>.<br>		: The original revision id was <tt>385634152</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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	=Aids to understanding=		=Aids to understanding=
	===The rulers metaphor for microtonality===		===The rulers metaphor for microtonality===
	Imagine a ruler with 12 inches on it. Now imagine one where, in the space of 12 inches, 13 equally spaced lines are drawn. Although these new lines are each only a little less than an inch apart from each other, they are clearly not "inches" and it would be silly to use them as such. If you used these 13ths of a foot to measure and estimate lengths frequently, you would ~~soonyourself~~ rounding to this new set of lengths which before you would have rounded to inches. You might soon find yourself rounding something exactly 6 inches long to either 6 or 7 of these. My, what a crazy you must be!		Imagine a ruler with 12 inches on it. Now imagine one where, in the space of 12 inches, 13 equally spaced lines are drawn. Although these new lines are each only a little less than an inch apart from each other, they are clearly not "inches" and it would be silly to use them as such. If you used these 13ths of a foot to measure and estimate lengths frequently, you would soon find yourself rounding to this new set of lengths which before you would have rounded to inches. You might soon find yourself rounding something exactly 6 inches long to either 6 or 7 of these. My, what a crazy you must be!

	===The colors metaphor for microtonality===		===The colors metaphor for microtonality===
	Imagine you're a painter. All your life, you have been told that there are only ~~twelve~~ colors, that any shade between two of the colors is just an out-of-tune version of ~~one~~ of the ~~'real'~~ colors...		Imagine you're a painter. All your life, you have been told that there are only //n// 'real' colors, that any shade between two of the colors is just an out-of-tune version of of the colors...

	===Equal divisions burst===		===Equal divisions burst===
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	<!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><a name="Aids to understanding--The rulers metaphor for microtonality"></a><!-- ws:end:WikiTextHeadingRule:14 -->The rulers metaphor for microtonality</h3>		<!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><a name="Aids to understanding--The rulers metaphor for microtonality"></a><!-- ws:end:WikiTextHeadingRule:14 -->The rulers metaphor for microtonality</h3>
	Imagine a ruler with 12 inches on it. Now imagine one where, in the space of 12 inches, 13 equally spaced lines are drawn. Although these new lines are each only a little less than an inch apart from each other, they are clearly not &quot;inches&quot; and it would be silly to use them as such. If you used these 13ths of a foot to measure and estimate lengths frequently, you would ~~soonyourself~~ rounding to this new set of lengths which before you would have rounded to inches. You might soon find yourself rounding something exactly 6 inches long to either 6 or 7 of these. My, what a crazy you must be!<br />		Imagine a ruler with 12 inches on it. Now imagine one where, in the space of 12 inches, 13 equally spaced lines are drawn. Although these new lines are each only a little less than an inch apart from each other, they are clearly not &quot;inches&quot; and it would be silly to use them as such. If you used these 13ths of a foot to measure and estimate lengths frequently, you would soon find yourself rounding to this new set of lengths which before you would have rounded to inches. You might soon find yourself rounding something exactly 6 inches long to either 6 or 7 of these. My, what a crazy you must be!<br />
	<br />		<br />
	<!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name="Aids to understanding--The colors metaphor for microtonality"></a><!-- ws:end:WikiTextHeadingRule:16 -->The colors metaphor for microtonality</h3>		<!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name="Aids to understanding--The colors metaphor for microtonality"></a><!-- ws:end:WikiTextHeadingRule:16 -->The colors metaphor for microtonality</h3>
	Imagine you're a painter. All your life, you have been told that there are only ~~twelve~~ colors, that any shade between two of the colors is just an out-of-tune version of ~~one~~ of the ~~'real'~~ colors...<br />		Imagine you're a painter. All your life, you have been told that there are only <em>n</em> 'real' colors, that any shade between two of the colors is just an out-of-tune version of of the colors...<br />
	<br />		<br />
	<!-- ws:start:WikiTextHeadingRule:18:&lt;h3&gt; --><h3 id="toc9"><a name="Aids to understanding--Equal divisions burst"></a><!-- ws:end:WikiTextHeadingRule:18 -->Equal divisions burst</h3>		<!-- ws:start:WikiTextHeadingRule:18:&lt;h3&gt; --><h3 id="toc9"><a name="Aids to understanding--Equal divisions burst"></a><!-- ws:end:WikiTextHeadingRule:18 -->Equal divisions burst</h3>

Wikispaces>mbattaglia1: Imported revision 384946906 - Original comment:

2012-11-22T01:25:27Z

**Imported revision 384946906 - Original comment: **

← Older revision		Revision as of 01:25, 22 November 2012
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	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:~~xenjacob~~\|~~xenjacob~~]] and made on <tt>2012-11-~~21 19~~:15:13 UTC</tt>.<br>		: This revision was by author [[User:mbattaglia1\|mbattaglia1]] and made on <tt>2012-11-22 01:25:27 UTC</tt>.<br>
	: The original revision id was <tt>~~384878112~~</tt>.<br>		: The original revision id was <tt>384946906</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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	</span>		</span>
	This is a polar graph of the values of all the fractions between 0 and 1 with ~~numerator~~ less than 32. The top represents both 0 and 1 (modulo 1); the fractions' values sweep clockwise; the closer to the center, the smaller the denominator. This graph accompanies the chart [[edo anatomy\|Anatomy of an Equally Divided Octave]].		This is a polar graph of the values of all the fractions between 0 and 1 with denominator less than 32. The top represents both 0 and 1 (modulo 1); the fractions' values sweep clockwise; the closer to the center, the smaller the denominator. This graph accompanies the chart [[edo anatomy\|Anatomy of an Equally Divided Octave]].

	===JI, temperament Lattices===		===JI, temperament Lattices===
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	<br />		<br />
	</span><br />		</span><br />
	This is a polar graph of the values of all the fractions between 0 and 1 with ~~numerator~~ less than 32. The top represents both 0 and 1 (modulo 1); the fractions' values sweep clockwise; the closer to the center, the smaller the denominator. This graph accompanies the chart <a class="wiki_link" href="/edo%20anatomy">Anatomy of an Equally Divided Octave</a>.<br />		This is a polar graph of the values of all the fractions between 0 and 1 with denominator less than 32. The top represents both 0 and 1 (modulo 1); the fractions' values sweep clockwise; the closer to the center, the smaller the denominator. This graph accompanies the chart <a class="wiki_link" href="/edo%20anatomy">Anatomy of an Equally Divided Octave</a>.<br />
	<br />		<br />
	<!-- ws:start:WikiTextHeadingRule:20:&lt;h3&gt; --><h3 id="toc10"><a name="Aids to understanding--JI, temperament Lattices"></a><!-- ws:end:WikiTextHeadingRule:20 -->JI, temperament Lattices</h3>		<!-- ws:start:WikiTextHeadingRule:20:&lt;h3&gt; --><h3 id="toc10"><a name="Aids to understanding--JI, temperament Lattices"></a><!-- ws:end:WikiTextHeadingRule:20 -->JI, temperament Lattices</h3>
	Tonalsoft's Tonescape makes it possible to compose with scales that are represented by two- or three-dimensional lattices. Tempering a comma out of a lattice turns it into a closed structure...</body></html></pre></div>		Tonalsoft's Tonescape makes it possible to compose with scales that are represented by two- or three-dimensional lattices. Tempering a comma out of a lattice turns it into a closed structure...</body></html></pre></div>

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	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:JosephRuhf\|JosephRuhf]] and made on <tt>2012-11-24 23:01:34 UTC</tt>.<br>		: This revision was by author [[User:JosephRuhf\|JosephRuhf]] and made on <tt>2012-11-24 23:03:57 UTC</tt>.<br>
	: The original revision id was <tt>~~385637072~~</tt>.<br>		: The original revision id was <tt>385637366</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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	=Aids to understanding=		=Aids to understanding=
	===The rulers metaphor for microtonality===		===The rulers metaphor for microtonality===
	Imagine a ruler with 12 inches on it. Now imagine one where, in the space of 12 inches, 13 equally spaced lines are drawn. Although these new lines are each only a little less than an inch apart from each other, they are clearly not "inches" and it would be silly to use them as such. If you used these 13ths of a foot to measure and estimate lengths frequently, you would soon find yourself rounding to this new set of lengths which before you would have rounded to inches. You might soon find yourself rounding something exactly inches long to ~~either~~ 6 ~~or 7~~ of these. My, what a crazy you must be!		Imagine a ruler with 12 inches on it. Now imagine one where, in the space of 12 inches, 13 equally spaced lines are drawn. Although these new lines are each only a little less than an inch apart from each other, they are clearly not "inches" and it would be silly to use them as such. If you used these 13ths of a foot to measure and estimate lengths frequently, you would soon find yourself rounding to this new set of lengths which before you would have rounded to inches. You might soon find yourself rounding something exactly 7 inches long to 7.6 of these. My, what a crazy you must be!

	===The colors metaphor for microtonality===		===The colors metaphor for microtonality===
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	Imagine a ruler with 12 inches on it. Now imagine one where, in the space of 12 inches, 13 equally spaced lines are drawn. Although these new lines are each only a little less than an inch apart from each other, they are clearly not &quot;inches&quot; and it would be silly to use them as such. If you used these 13ths of a foot to measure and estimate lengths frequently, you would soon find yourself rounding to this new set of lengths which before you would have rounded to inches. You might soon find yourself rounding something exactly inches long to ~~either~~ 6 ~~or 7~~ of these. My, what a crazy you must be!<br />		Imagine a ruler with 12 inches on it. Now imagine one where, in the space of 12 inches, 13 equally spaced lines are drawn. Although these new lines are each only a little less than an inch apart from each other, they are clearly not &quot;inches&quot; and it would be silly to use them as such. If you used these 13ths of a foot to measure and estimate lengths frequently, you would soon find yourself rounding to this new set of lengths which before you would have rounded to inches. You might soon find yourself rounding something exactly 7 inches long to 7.6 of these. My, what a crazy you must be!<br />
	<br />		<br />
	<!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name="Aids to understanding--The colors metaphor for microtonality"></a><!-- ws:end:WikiTextHeadingRule:16 -->The colors metaphor for microtonality</h3>		<!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name="Aids to understanding--The colors metaphor for microtonality"></a><!-- ws:end:WikiTextHeadingRule:16 -->The colors metaphor for microtonality</h3>

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	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:JosephRuhf\|JosephRuhf]] and made on <tt>2012-11-24 22:40:44 UTC</tt>.<br>		: This revision was by author [[User:JosephRuhf\|JosephRuhf]] and made on <tt>2012-11-24 23:01:34 UTC</tt>.<br>
	: The original revision id was <tt>~~385634152~~</tt>.<br>		: The original revision id was <tt>385637072</tt>.<br>
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	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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	===Audio sculpture===		===Audio sculpture===
	If you have a visual environment whose contents can translate directly into the audio domain in some way, this is one way of doing audio sculpture. Unlike the quantized grids of piano rolls, there usually //is// no grid (or the grid is so fine as to be invisible). Iannis Xenakis developed an interface called [[http://en.wikipedia.org/wiki/UPIC\|UPIC]], which recently inspired the program [[http://www.highc.org\|HighC]]. In three-dimensional space, [[http://audiosculptures.com/\|Andy Fillebrown]] has done some work, as well as...well, gosh, he's surely not the only one!		If you have a visual environment whose contents can translate directly into the audio domain in some way, this is one way of doing audio sculpture. Unlike the quantized grids of piano rolls, there usually is no grid (or the grid is so fine as to be invisible). Iannis Xenakis developed an interface called [[http://en.wikipedia.org/wiki/UPIC\|UPIC]], which recently inspired the program [[http://www.highc.org\|HighC]]. In three-dimensional space, [[http://audiosculptures.com/\|Andy Fillebrown]] has done some work, as well as...well, gosh, he's surely not the only one!
	= =		= =
	=Aids to understanding=		=Aids to understanding=
	===The rulers metaphor for microtonality===		===The rulers metaphor for microtonality===
	Imagine a ruler with 12 inches on it. Now imagine one where, in the space of 12 inches, 13 equally spaced lines are drawn. Although these new lines are each only a little less than an inch apart from each other, they are clearly not "inches" and it would be silly to use them as such. If you used these 13ths of a foot to measure and estimate lengths frequently, you would soon find yourself rounding to this new set of lengths which before you would have rounded to inches. You might soon find yourself rounding something exactly 6 inches long to either 6 or 7 of these. My, what a crazy you must be!		Imagine a ruler with 12 inches on it. Now imagine one where, in the space of 12 inches, 13 equally spaced lines are drawn. Although these new lines are each only a little less than an inch apart from each other, they are clearly not "inches" and it would be silly to use them as such. If you used these 13ths of a foot to measure and estimate lengths frequently, you would soon find yourself rounding to this new set of lengths which before you would have rounded to inches. You might soon find yourself rounding something exactly inches long to either 6 or 7 of these. My, what a crazy you must be!

	===The colors metaphor for microtonality===		===The colors metaphor for microtonality===
	Imagine you're a painter. All your life, you have been told that there are only //n// 'real' colors, that any shade between two of the colors is just an out-of-tune version of of ~~the~~ colors...		Imagine you're a painter. All your life, you have been told that there are only //n// 'real' colors, that any shade between two of the colors is just a to-some-degree-out-of-tune version of each of these colors...

	===Equal divisions burst===		===Equal divisions burst===
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	<br />		<br />
	<!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="Aids to composing--Audio sculpture"></a><!-- ws:end:WikiTextHeadingRule:8 -->Audio sculpture</h3>		<!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="Aids to composing--Audio sculpture"></a><!-- ws:end:WikiTextHeadingRule:8 -->Audio sculpture</h3>
	If you have a visual environment whose contents can translate directly into the audio domain in some way, this is one way of doing audio sculpture. Unlike the quantized grids of piano rolls, there usually ~~<em>~~is~~</em>~~ no grid (or the grid is so fine as to be invisible). Iannis Xenakis developed an interface called <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/UPIC" rel="nofollow">UPIC</a>, which recently inspired the program <a class="wiki_link_ext" href="http://www.highc.org" rel="nofollow">HighC</a>. In three-dimensional space, <a class="wiki_link_ext" href="http://audiosculptures.com/" rel="nofollow">Andy Fillebrown</a> has done some work, as well as...well, gosh, he's surely not the only one!<br />		If you have a visual environment whose contents can translate directly into the audio domain in some way, this is one way of doing audio sculpture. Unlike the quantized grids of piano rolls, there usually is no grid (or the grid is so fine as to be invisible). Iannis Xenakis developed an interface called <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/UPIC" rel="nofollow">UPIC</a>, which recently inspired the program <a class="wiki_link_ext" href="http://www.highc.org" rel="nofollow">HighC</a>. In three-dimensional space, <a class="wiki_link_ext" href="http://audiosculptures.com/" rel="nofollow">Andy Fillebrown</a> has done some work, as well as...well, gosh, he's surely not the only one!<br />
	<!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><!-- ws:end:WikiTextHeadingRule:10 --> </h1>		<!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><!-- ws:end:WikiTextHeadingRule:10 --> </h1>
	<!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Aids to understanding"></a><!-- ws:end:WikiTextHeadingRule:12 -->Aids to understanding</h1>		<!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Aids to understanding"></a><!-- ws:end:WikiTextHeadingRule:12 -->Aids to understanding</h1>
	<!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><a name="Aids to understanding--The rulers metaphor for microtonality"></a><!-- ws:end:WikiTextHeadingRule:14 -->The rulers metaphor for microtonality</h3>		<!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><a name="Aids to understanding--The rulers metaphor for microtonality"></a><!-- ws:end:WikiTextHeadingRule:14 -->The rulers metaphor for microtonality</h3>
	Imagine a ruler with 12 inches on it. Now imagine one where, in the space of 12 inches, 13 equally spaced lines are drawn. Although these new lines are each only a little less than an inch apart from each other, they are clearly not &quot;inches&quot; and it would be silly to use them as such. If you used these 13ths of a foot to measure and estimate lengths frequently, you would soon find yourself rounding to this new set of lengths which before you would have rounded to inches. You might soon find yourself rounding something exactly 6 inches long to either 6 or 7 of these. My, what a crazy you must be!<br />		Imagine a ruler with 12 inches on it. Now imagine one where, in the space of 12 inches, 13 equally spaced lines are drawn. Although these new lines are each only a little less than an inch apart from each other, they are clearly not &quot;inches&quot; and it would be silly to use them as such. If you used these 13ths of a foot to measure and estimate lengths frequently, you would soon find yourself rounding to this new set of lengths which before you would have rounded to inches. You might soon find yourself rounding something exactly inches long to either 6 or 7 of these. My, what a crazy you must be!<br />
	<br />		<br />
	<!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name="Aids to understanding--The colors metaphor for microtonality"></a><!-- ws:end:WikiTextHeadingRule:16 -->The colors metaphor for microtonality</h3>		<!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name="Aids to understanding--The colors metaphor for microtonality"></a><!-- ws:end:WikiTextHeadingRule:16 -->The colors metaphor for microtonality</h3>
	Imagine you're a painter. All your life, you have been told that there are only <em>n</em> 'real' colors, that any shade between two of the colors is just an out-of-tune version of of ~~the~~ colors...<br />		Imagine you're a painter. All your life, you have been told that there are only <em>n</em> 'real' colors, that any shade between two of the colors is just a to-some-degree-out-of-tune version of each of these colors...<br />
	<br />		<br />
	<!-- ws:start:WikiTextHeadingRule:18:&lt;h3&gt; --><h3 id="toc9"><a name="Aids to understanding--Equal divisions burst"></a><!-- ws:end:WikiTextHeadingRule:18 -->Equal divisions burst</h3>		<!-- ws:start:WikiTextHeadingRule:18:&lt;h3&gt; --><h3 id="toc9"><a name="Aids to understanding--Equal divisions burst"></a><!-- ws:end:WikiTextHeadingRule:18 -->Equal divisions burst</h3>

Pretty Pictures - Revision history

BudjarnLambeth at 08:51, 27 September 2025

BudjarnLambeth: /* JI, temperament Lattices */

Fredg999: Notation moved to Musical notation

BudjarnLambeth: Categorised this uncategorised page

Wikispaces>FREEZE at 00:00, 17 July 2018

Wikispaces>spt3125: **Imported revision 616005221 - Original comment: added link (deorphaning)**

Wikispaces>JosephRuhf: **Imported revision 385637366 - Original comment: **

Wikispaces>JosephRuhf: **Imported revision 385637072 - Original comment: **

Wikispaces>JosephRuhf: **Imported revision 385634152 - Original comment: **

Wikispaces>mbattaglia1: **Imported revision 384946906 - Original comment: **

Wikispaces>spt3125: Imported revision 616005221 - Original comment: added link (deorphaning)

Wikispaces>JosephRuhf: Imported revision 385637366 - Original comment:

Wikispaces>JosephRuhf: Imported revision 385637072 - Original comment:

Wikispaces>JosephRuhf: Imported revision 385634152 - Original comment:

Wikispaces>mbattaglia1: Imported revision 384946906 - Original comment: