User:Xenji/Redundancy: Difference between revisions

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**Imported revision 176987043 - Original comment: **
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**Imported revision 284376846 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-11-05 23:24:57 UTC</tt>.<br>
: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-12-09 23:07:30 UTC</tt>.<br>
: The original revision id was <tt>176987043</tt>.<br>
: The original revision id was <tt>284376846</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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* a sustained pitch
* a sustained pitch
** redundancy in time
** redundancy in time
* a [[periodic scale|scale]] (set of definite pitches)
* a [[periodic scale|scale]](set of definite pitches)
** redundancy in time: "I've heard these pitches before"
** redundancy in time: "I've heard these pitches before"
** less redundant: a scale which changes (for instance, ascending different from descending)
** less redundant: a scale which changes (for instance, ascending different from descending)
Line 43: Line 43:
* [[octave equivalence]]
* [[octave equivalence]]
** B-flat considered equivalent to B-flat an octave higher...
** B-flat considered equivalent to B-flat an octave higher...
** an [[periodic scale|octave-repeating]] scale
** an [[periodic scale|octave-repeating]]scale
*** the "same" pitches are available in each octave
*** the "same" pitches are available in each octave
* [[equal]] divisions of some interval
* [[equal]]divisions of some interval
** less redundant: [[quasi-equal]] divisions
** less redundant: [[maximal evenness|maximally even]] a.k.a. "quasi-equal" divisions
* tuning lattices
* tuning lattices
** "two-dimensional", "three-dimensional", etc. where each axis represents iterations of a single interval
** "two-dimensional", "three-dimensional", etc. where each axis represents iterations of a single interval
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** more redundant: the same tetrachord repeated in the gamut
** more redundant: the same tetrachord repeated in the gamut
** less redundant: two (or more) different tetrachords in the gamut
** less redundant: two (or more) different tetrachords in the gamut
* [[MOSScales|moment of symmetry]] technique (making a chain of one 'generator' interval, folded within a set 'period' interval)
* [[MOSScales|moment of symmetry]]technique (making a chain of one 'generator' interval, folded within a set 'period' interval)
** produces scales with only two step sizes &amp; only two intervals of each class
** produces scales with only two step sizes &amp; only two intervals of each class
** less redundant extensions: [[MOS Cradle]] or [[Second Order MOS]]
** less redundant extensions: [[MOS Cradle]] or [[Second Order MOS]]
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&lt;br /&gt;
&lt;br /&gt;
Here is a far from complete list of aspects of tunings systems that might indicate redundancy of some kind. Please add to it!&lt;br /&gt;
Here is a far from complete list of aspects of tunings systems that might indicate redundancy of some kind. Please add to it!&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;the use of definite pitches&lt;ul&gt;&lt;li&gt;instead of, or in addition to &lt;a class="wiki_link" href="/noise"&gt;noise&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;a sustained pitch&lt;ul&gt;&lt;li&gt;redundancy in time&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;a &lt;a class="wiki_link" href="/periodic%20scale"&gt;scale&lt;/a&gt; (set of definite pitches)&lt;ul&gt;&lt;li&gt;redundancy in time: &amp;quot;I've heard these pitches before&amp;quot;&lt;/li&gt;&lt;li&gt;less redundant: a scale which changes (for instance, ascending different from descending)&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/harmony"&gt;harmony&lt;/a&gt; influenced by a theory of &lt;a class="wiki_link" href="/consonance"&gt;consonance&lt;/a&gt;&lt;ul&gt;&lt;li&gt;more than one pitch sounding together &amp;amp; their distinctness blurring&lt;/li&gt;&lt;li&gt;if pitch y appears in the overtone series of pitch x, when pitch x is sounding (on a harmonic instrument), pitch y will also sound (although might not be identifiable as a distinct pitch) - so building a scale which contains both x &amp;amp; y is redundant&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/octave%20equivalence"&gt;octave equivalence&lt;/a&gt;&lt;ul&gt;&lt;li&gt;B-flat considered equivalent to B-flat an octave higher...&lt;/li&gt;&lt;li&gt;an &lt;a class="wiki_link" href="/periodic%20scale"&gt;octave-repeating&lt;/a&gt; scale&lt;ul&gt;&lt;li&gt;the &amp;quot;same&amp;quot; pitches are available in each octave&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/equal"&gt;equal&lt;/a&gt; divisions of some interval&lt;ul&gt;&lt;li&gt;less redundant: &lt;a class="wiki_link" href="/quasi-equal"&gt;quasi-equal&lt;/a&gt; divisions&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;tuning lattices&lt;ul&gt;&lt;li&gt;&amp;quot;two-dimensional&amp;quot;, &amp;quot;three-dimensional&amp;quot;, etc. where each axis represents iterations of a single interval&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/harmonic%20limit"&gt;harmonic limit&lt;/a&gt;&lt;/li&gt;&lt;li&gt;building scales from/with &lt;a class="wiki_link" href="/tetrachord"&gt;tetrachords&lt;/a&gt;&lt;ul&gt;&lt;li&gt;more redundant: the same tetrachord repeated in the gamut&lt;/li&gt;&lt;li&gt;less redundant: two (or more) different tetrachords in the gamut&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/MOSScales"&gt;moment of symmetry&lt;/a&gt; technique (making a chain of one 'generator' interval, folded within a set 'period' interval)&lt;ul&gt;&lt;li&gt;produces scales with only two step sizes &amp;amp; only two intervals of each class&lt;/li&gt;&lt;li&gt;less redundant extensions: &lt;a class="wiki_link" href="/MOS%20Cradle"&gt;MOS Cradle&lt;/a&gt; or &lt;a class="wiki_link" href="/Second%20Order%20MOS"&gt;Second Order MOS&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;matching tuning to timbre&lt;ul&gt;&lt;li&gt;eg. rational intonation - selecting pitches which are copied in the &lt;a class="wiki_link" href="/OverToneSeries"&gt;overtone series&lt;/a&gt; of other intervals&lt;/li&gt;&lt;li&gt;eg. Indonesian gamelan tuning - the scale is made to match the inharmonic pitches of the metals used in building the instruments&lt;/li&gt;&lt;li&gt;octaves in the high range of a piano are routinely stretched to fit with the &amp;quot;distorted&amp;quot; sound of the high-tension strings&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;matching timbre to tuning&lt;ul&gt;&lt;li&gt;the reverse of the above: making a timbre (usually with a computer) to &amp;quot;match&amp;quot; a stipulated tuning&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
&lt;ul&gt;&lt;li&gt;the use of definite pitches&lt;ul&gt;&lt;li&gt;instead of, or in addition to &lt;a class="wiki_link" href="/noise"&gt;noise&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;a sustained pitch&lt;ul&gt;&lt;li&gt;redundancy in time&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;a &lt;a class="wiki_link" href="/periodic%20scale"&gt;scale&lt;/a&gt;(set of definite pitches)&lt;ul&gt;&lt;li&gt;redundancy in time: &amp;quot;I've heard these pitches before&amp;quot;&lt;/li&gt;&lt;li&gt;less redundant: a scale which changes (for instance, ascending different from descending)&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/harmony"&gt;harmony&lt;/a&gt; influenced by a theory of &lt;a class="wiki_link" href="/consonance"&gt;consonance&lt;/a&gt;&lt;ul&gt;&lt;li&gt;more than one pitch sounding together &amp;amp; their distinctness blurring&lt;/li&gt;&lt;li&gt;if pitch y appears in the overtone series of pitch x, when pitch x is sounding (on a harmonic instrument), pitch y will also sound (although might not be identifiable as a distinct pitch) - so building a scale which contains both x &amp;amp; y is redundant&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/octave%20equivalence"&gt;octave equivalence&lt;/a&gt;&lt;ul&gt;&lt;li&gt;B-flat considered equivalent to B-flat an octave higher...&lt;/li&gt;&lt;li&gt;an &lt;a class="wiki_link" href="/periodic%20scale"&gt;octave-repeating&lt;/a&gt;scale&lt;ul&gt;&lt;li&gt;the &amp;quot;same&amp;quot; pitches are available in each octave&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/equal"&gt;equal&lt;/a&gt;divisions of some interval&lt;ul&gt;&lt;li&gt;less redundant: &lt;a class="wiki_link" href="/maximal%20evenness"&gt;maximally even&lt;/a&gt; a.k.a. &amp;quot;quasi-equal&amp;quot; divisions&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;tuning lattices&lt;ul&gt;&lt;li&gt;&amp;quot;two-dimensional&amp;quot;, &amp;quot;three-dimensional&amp;quot;, etc. where each axis represents iterations of a single interval&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/harmonic%20limit"&gt;harmonic limit&lt;/a&gt;&lt;/li&gt;&lt;li&gt;building scales from/with &lt;a class="wiki_link" href="/tetrachord"&gt;tetrachords&lt;/a&gt;&lt;ul&gt;&lt;li&gt;more redundant: the same tetrachord repeated in the gamut&lt;/li&gt;&lt;li&gt;less redundant: two (or more) different tetrachords in the gamut&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/MOSScales"&gt;moment of symmetry&lt;/a&gt;technique (making a chain of one 'generator' interval, folded within a set 'period' interval)&lt;ul&gt;&lt;li&gt;produces scales with only two step sizes &amp;amp; only two intervals of each class&lt;/li&gt;&lt;li&gt;less redundant extensions: &lt;a class="wiki_link" href="/MOS%20Cradle"&gt;MOS Cradle&lt;/a&gt; or &lt;a class="wiki_link" href="/Second%20Order%20MOS"&gt;Second Order MOS&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;matching tuning to timbre&lt;ul&gt;&lt;li&gt;eg. rational intonation - selecting pitches which are copied in the &lt;a class="wiki_link" href="/OverToneSeries"&gt;overtone series&lt;/a&gt; of other intervals&lt;/li&gt;&lt;li&gt;eg. Indonesian gamelan tuning - the scale is made to match the inharmonic pitches of the metals used in building the instruments&lt;/li&gt;&lt;li&gt;octaves in the high range of a piano are routinely stretched to fit with the &amp;quot;distorted&amp;quot; sound of the high-tension strings&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;matching timbre to tuning&lt;ul&gt;&lt;li&gt;the reverse of the above: making a timbre (usually with a computer) to &amp;quot;match&amp;quot; a stipulated tuning&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 23:07, 9 December 2011

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author keenanpepper and made on 2011-12-09 23:07:30 UTC.
The original revision id was 284376846.
The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

=Redundancy in a Tuning System= 

Redundancy is one look which makes a tuning system a tuning __system__.

Gregory Bateson has this to say about redundancy in his article "Style, Grace, and Information in Primitive Art":

//Any aggregate of events or objects (e.g., a sequence of phonemes, a painting, or a frog, or a culture) shall be said to contain "redundancy" or "pattern" if the aggregate can be divided in any way by a "slash mark," such that an observer perceiving only what is on one side of the slash mark can// guess//, with better than random success, what is on the other side of the slash mark. We may say that what is on one side of the slash contains// information //or has// meaning //about what is on the other side. Or, in engineer's language, the aggregate contains "redundancy."//

I ([[user:Andrew_Heathwaite|1258062436]]) assert:
* A system (eg. "a work of art", "a composition", "a tuning system") implies a network of redundancies.
* We can talk about these redundancies: "less redundancy"; "more redundancy"; "no redundancy", etc.
** "Less" or "more" or "no" redundancy is determined by each listener (largely unconsciously) according to her structure at that moment.
* [Perceived] more redundancy in one aspect may ground a piece so that [perceived] less redundancy in another aspect can be seen as meaningful.
** "One thing stays the same so another thing can change."
** "One thing changes so another thing can stay the same."
* "No redundancy" can be seen as redundant when the listener can predict continued lack of redundancy.
** "I know what it's going to do next - something random!"
** A listener may hear or not hear (make or not make) an intended redundancy/pattern.
* Answers to questions of which redundancies (or which networks of redundancies) help us decide things like "style", "meaning", "how should I listen to this?" and "is this music, anyway?"

If I look a tuning as a system, I might consider the tuning's "redundancy."
How does this tuning system exhibit //pattern//?
I care about how a tuning system offers redundancy so that I may //choose// a different network of redundancies than th one(s) I'm familiar with (a fish attempting to "see" the water she lives in).

Here is a far from complete list of aspects of tunings systems that might indicate redundancy of some kind. Please add to it!
* the use of definite pitches
** instead of, or in addition to [[noise]]
* a sustained pitch
** redundancy in time
* a [[periodic scale|scale]](set of definite pitches)
** redundancy in time: "I've heard these pitches before"
** less redundant: a scale which changes (for instance, ascending different from descending)
* [[harmony]] influenced by a theory of [[consonance]]
** more than one pitch sounding together & their distinctness blurring
** if pitch y appears in the overtone series of pitch x, when pitch x is sounding (on a harmonic instrument), pitch y will also sound (although might not be identifiable as a distinct pitch) - so building a scale which contains both x & y is redundant
* [[octave equivalence]]
** B-flat considered equivalent to B-flat an octave higher...
** an [[periodic scale|octave-repeating]]scale
*** the "same" pitches are available in each octave
* [[equal]]divisions of some interval
** less redundant: [[maximal evenness|maximally even]] a.k.a. "quasi-equal" divisions
* tuning lattices
** "two-dimensional", "three-dimensional", etc. where each axis represents iterations of a single interval
* [[harmonic limit]]
* building scales from/with [[tetrachord|tetrachords]]
** more redundant: the same tetrachord repeated in the gamut
** less redundant: two (or more) different tetrachords in the gamut
* [[MOSScales|moment of symmetry]]technique (making a chain of one 'generator' interval, folded within a set 'period' interval)
** produces scales with only two step sizes & only two intervals of each class
** less redundant extensions: [[MOS Cradle]] or [[Second Order MOS]]
* matching tuning to timbre
** eg. rational intonation - selecting pitches which are copied in the [[OverToneSeries|overtone series]] of other intervals
** eg. Indonesian gamelan tuning - the scale is made to match the inharmonic pitches of the metals used in building the instruments
** octaves in the high range of a piano are routinely stretched to fit with the "distorted" sound of the high-tension strings
* matching timbre to tuning
** the reverse of the above: making a timbre (usually with a computer) to "match" a stipulated tuning

Original HTML content:

<html><head><title>redundancy</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Redundancy in a Tuning System"></a><!-- ws:end:WikiTextHeadingRule:0 -->Redundancy in a Tuning System</h1>
 <br />
Redundancy is one look which makes a tuning system a tuning <u>system</u>.<br />
<br />
Gregory Bateson has this to say about redundancy in his article &quot;Style, Grace, and Information in Primitive Art&quot;:<br />
<br />
<em>Any aggregate of events or objects (e.g., a sequence of phonemes, a painting, or a frog, or a culture) shall be said to contain &quot;redundancy&quot; or &quot;pattern&quot; if the aggregate can be divided in any way by a &quot;slash mark,&quot; such that an observer perceiving only what is on one side of the slash mark can</em> guess<em>, with better than random success, what is on the other side of the slash mark. We may say that what is on one side of the slash contains</em> information <em>or has</em> meaning <em>about what is on the other side. Or, in engineer's language, the aggregate contains &quot;redundancy.&quot;</em><br />
<br />
I (<!-- ws:start:WikiTextUserlinkRule:00:[[user:Andrew_Heathwaite|1258062436]] --><span class="membersnap">- <a class="userLink" href="http://www.wikispaces.com/user/view/Andrew_Heathwaite" style="outline: none;"><img src="http://www.wikispaces.com/user/pic/Andrew_Heathwaite-lg.jpg" width="16" height="16" alt="Andrew_Heathwaite" class="userPicture" /></a> <a class="userLink" href="http://www.wikispaces.com/user/view/Andrew_Heathwaite" style="outline: none;">Andrew_Heathwaite</a> <small>Nov 12, 2009</small></span><!-- ws:end:WikiTextUserlinkRule:00 -->) assert:<br />
<ul><li>A system (eg. &quot;a work of art&quot;, &quot;a composition&quot;, &quot;a tuning system&quot;) implies a network of redundancies.</li><li>We can talk about these redundancies: &quot;less redundancy&quot;; &quot;more redundancy&quot;; &quot;no redundancy&quot;, etc.<ul><li>&quot;Less&quot; or &quot;more&quot; or &quot;no&quot; redundancy is determined by each listener (largely unconsciously) according to her structure at that moment.</li></ul></li><li>[Perceived] more redundancy in one aspect may ground a piece so that [perceived] less redundancy in another aspect can be seen as meaningful.<ul><li>&quot;One thing stays the same so another thing can change.&quot;</li><li>&quot;One thing changes so another thing can stay the same.&quot;</li></ul></li><li>&quot;No redundancy&quot; can be seen as redundant when the listener can predict continued lack of redundancy.<ul><li>&quot;I know what it's going to do next - something random!&quot;</li><li>A listener may hear or not hear (make or not make) an intended redundancy/pattern.</li></ul></li><li>Answers to questions of which redundancies (or which networks of redundancies) help us decide things like &quot;style&quot;, &quot;meaning&quot;, &quot;how should I listen to this?&quot; and &quot;is this music, anyway?&quot;</li></ul><br />
If I look a tuning as a system, I might consider the tuning's &quot;redundancy.&quot;<br />
How does this tuning system exhibit <em>pattern</em>?<br />
I care about how a tuning system offers redundancy so that I may <em>choose</em> a different network of redundancies than th one(s) I'm familiar with (a fish attempting to &quot;see&quot; the water she lives in).<br />
<br />
Here is a far from complete list of aspects of tunings systems that might indicate redundancy of some kind. Please add to it!<br />
<ul><li>the use of definite pitches<ul><li>instead of, or in addition to <a class="wiki_link" href="/noise">noise</a></li></ul></li><li>a sustained pitch<ul><li>redundancy in time</li></ul></li><li>a <a class="wiki_link" href="/periodic%20scale">scale</a>(set of definite pitches)<ul><li>redundancy in time: &quot;I've heard these pitches before&quot;</li><li>less redundant: a scale which changes (for instance, ascending different from descending)</li></ul></li><li><a class="wiki_link" href="/harmony">harmony</a> influenced by a theory of <a class="wiki_link" href="/consonance">consonance</a><ul><li>more than one pitch sounding together &amp; their distinctness blurring</li><li>if pitch y appears in the overtone series of pitch x, when pitch x is sounding (on a harmonic instrument), pitch y will also sound (although might not be identifiable as a distinct pitch) - so building a scale which contains both x &amp; y is redundant</li></ul></li><li><a class="wiki_link" href="/octave%20equivalence">octave equivalence</a><ul><li>B-flat considered equivalent to B-flat an octave higher...</li><li>an <a class="wiki_link" href="/periodic%20scale">octave-repeating</a>scale<ul><li>the &quot;same&quot; pitches are available in each octave</li></ul></li></ul></li><li><a class="wiki_link" href="/equal">equal</a>divisions of some interval<ul><li>less redundant: <a class="wiki_link" href="/maximal%20evenness">maximally even</a> a.k.a. &quot;quasi-equal&quot; divisions</li></ul></li><li>tuning lattices<ul><li>&quot;two-dimensional&quot;, &quot;three-dimensional&quot;, etc. where each axis represents iterations of a single interval</li></ul></li><li><a class="wiki_link" href="/harmonic%20limit">harmonic limit</a></li><li>building scales from/with <a class="wiki_link" href="/tetrachord">tetrachords</a><ul><li>more redundant: the same tetrachord repeated in the gamut</li><li>less redundant: two (or more) different tetrachords in the gamut</li></ul></li><li><a class="wiki_link" href="/MOSScales">moment of symmetry</a>technique (making a chain of one 'generator' interval, folded within a set 'period' interval)<ul><li>produces scales with only two step sizes &amp; only two intervals of each class</li><li>less redundant extensions: <a class="wiki_link" href="/MOS%20Cradle">MOS Cradle</a> or <a class="wiki_link" href="/Second%20Order%20MOS">Second Order MOS</a></li></ul></li><li>matching tuning to timbre<ul><li>eg. rational intonation - selecting pitches which are copied in the <a class="wiki_link" href="/OverToneSeries">overtone series</a> of other intervals</li><li>eg. Indonesian gamelan tuning - the scale is made to match the inharmonic pitches of the metals used in building the instruments</li><li>octaves in the high range of a piano are routinely stretched to fit with the &quot;distorted&quot; sound of the high-tension strings</li></ul></li><li>matching timbre to tuning<ul><li>the reverse of the above: making a timbre (usually with a computer) to &quot;match&quot; a stipulated tuning</li></ul></li></ul></body></html>