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! * 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 [[octave-repeating]] scale *** the "same" pitches are available in each octave * [[equal]] divisions of some interval ** less redundant: [[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
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<html><head><title>redundancy</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><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 "Style, Grace, and Information in Primitive Art":<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 "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</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 "redundancy."</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. "a work of art", "a composition", "a tuning system") implies a network of redundancies.</li><li>We can talk about these redundancies: "less redundancy"; "more redundancy"; "no redundancy", etc.<ul><li>"Less" or "more" or "no" 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>"One thing stays the same so another thing can change."</li><li>"One thing changes so another thing can stay the same."</li></ul></li><li>"No redundancy" can be seen as redundant when the listener can predict continued lack of redundancy.<ul><li>"I know what it's going to do next - something random!"</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 "style", "meaning", "how should I listen to this?" and "is this music, anyway?"</li></ul><br /> If I look a tuning as a system, I might consider the tuning's "redundancy."<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 "see" 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: "I've heard these pitches before"</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 & 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 & 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="/octave-repeating">octave-repeating</a> scale<ul><li>the "same" 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="/quasi-equal">quasi-equal</a> divisions</li></ul></li><li>tuning lattices<ul><li>"two-dimensional", "three-dimensional", 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 & 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 "distorted" 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 "match" a stipulated tuning</li></ul></li></ul></body></html>