User:Xenji/Redundancy

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=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!
* definite pitches
** instead of, or in addition to [[noise]]
* sustained pitch
** redundancy in time
* a [[ScaleIndex|scale]]
** redundancy in time: "I've heard these pitches before"
** less redundant: a scale which changes (for instance, ascending different from descending)
* [[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...
* [[octave-repeating]]
** the "same" pitches are available in each octave
* [[equal]] divisions of some interval
** less redundant: [[quasi-equal]] divisions
* tuning lattices
* [[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 interval)
** produces scales with two step sizes & a finite set of intervals
** less redundant: [[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>definite pitches<ul><li>instead of, or in addition to <a class="wiki_link" href="/noise">noise</a></li></ul></li><li>sustained pitch<ul><li>redundancy in time</li></ul></li><li>a <a class="wiki_link" href="/ScaleIndex">scale</a><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="/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></ul></li><li><a class="wiki_link" href="/octave-repeating">octave-repeating</a><ul><li>the &quot;same&quot; pitches are available in each octave</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="/quasi-equal">quasi-equal</a> divisions</li></ul></li><li>tuning lattices</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 interval)<ul><li>produces scales with two step sizes &amp; a finite set of intervals</li><li>less redundant: <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>