User:Xenji/Redundancy - Revision history

BudjarnLambeth: BudjarnLambeth moved page Redundancy to User:Xenji/Redundancy

2025-05-19T03:48:51Z

BudjarnLambeth moved page Redundancy to User:Xenji/Redundancy

← Older revision	Revision as of 03:48, 19 May 2025
(No difference)

BudjarnLambeth at 03:48, 19 May 2025

2025-05-19T03:48:10Z

← Older revision		Revision as of 03:48, 19 May 2025
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	Redundancy is one look which makes a tuning system a tuning ~~<u>~~system~~</u>~~.		'''Redundancy''' is one look which makes a tuning system a tuning ''system''.

	{{w\|Gregory Bateson}} has this to say about redundancy in his article ''Style, Grace, and Information in Primitive Art'':		{{w\|Gregory Bateson}} has this to say about redundancy in his article ''Style, Grace, and Information in Primitive Art'':

BudjarnLambeth: Fix heading structure

2025-05-19T03:47:56Z

Fix heading structure

← Older revision		Revision as of 03:47, 19 May 2025
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	~~=Redundancy in a Tuning System=~~

	Redundancy is one look which makes a tuning system a tuning <u>system</u>.		Redundancy is one look which makes a tuning system a tuning <u>system</u>.

	Gregory Bateson has this to say about redundancy in his article "Style, Grace, and Information in Primitive Art":		{{w\|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."''		''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."''
Line 59:		Line 57:
	* matching timbre to tuning		* matching timbre to tuning
	** the reverse of the above: making a timbre (usually with a computer) to "match" a stipulated tuning		** the reverse of the above: making a timbre (usually with a computer) to "match" a stipulated tuning

	[[Category:Essays]]		[[Category:Essays]]
	[[Category:Todo:cleanup]]		[[Category:Todo:cleanup]]

BudjarnLambeth: Categorised this uncategorised page

2023-04-28T08:45:15Z

Categorised this uncategorised page

← Older revision		Revision as of 08:45, 28 April 2023
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	* matching timbre to tuning		* matching timbre to tuning
	** the reverse of the above: making a timbre (usually with a computer) to "match" a stipulated tuning		** the reverse of the above: making a timbre (usually with a computer) to "match" a stipulated tuning
			[[Category:Essays]]
			[[Category:Todo:cleanup]]

Wolftune: fixed "overtone series" vs "harmonic series"

2022-01-22T20:31:11Z

fixed "overtone series" vs "harmonic series"

Xenwolf: changed HTML lists into wiki-style lists, simplified some links

2020-06-12T20:15:25Z

changed HTML lists into wiki-style lists, simplified some links

@@ Line 7: / Line 7: @@
 ''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 (<span style="">[http://www.wikispaces.com/user/view/Andrew_Heathwaite Andrew_Heathwaite] <small>Nov 12, 2009</small></span>) assert:
+I ([http://www.wikispaces.com/user/view/Andrew_Heathwaite Andrew_Heathwaite] <small>Nov 12, 2009</small>) assert:
-<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>
+* A system (eg. "a work of art", "a composition", "a tuning system") implies a network of redundancies.
 If I look a tuning as a system, I might consider the tuning's "redundancy."
@@ Line 19: / Line 28: @@
 Here is a far from complete list of aspects of tunings systems that might indicate redundancy of some kind. Please add to it!
-<ul><li>the use of definite pitches<ul><li>instead of, or in addition to [[noise|noise]]</li></ul></li><li>a sustained pitch<ul><li>redundancy in time</li></ul></li><li>a [[Periodic_scale|scale]] (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>[[harmony|harmony]] influenced by a theory of [[consonance|consonance]]<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>[[octave_equivalence|octave equivalence]]<ul><li>B-flat considered equivalent to B-flat an octave higher...</li><li>an [[Periodic_scale|octave-repeating]] scale<ul><li>the "same" pitches are available in each octave</li></ul></li></ul></li><li>[[Equal|equal]] divisions of some interval<ul><li>less redundant: [[Maximal_evenness|maximally even]] a.k.a. "quasi-equal" 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>[[Harmonic_Limit|harmonic limit]]</li><li>building scales from/with [[tetrachord|tetrachords]]<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>[[MOSScales|moment of symmetry]] 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: [[MOS_Cradle|MOS Cradle]] or [[Second_Order_MOS|Second Order MOS]]</li></ul></li><li>matching tuning to timbre<ul><li>eg. rational intonation - selecting pitches which are copied in the [[OverToneSeries|overtone series]] 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>
+* the use of definite pitches

PreImportHandFixes>Battaglia01: Mike - removed user icon

2018-08-19T19:36:39Z

Mike - removed user icon

@@ Line 7: / Line 7: @@
 ''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 (<span style="">- [[http://www.wikispaces.com/user/view/Andrew_Heathwaite
+I (<span style="">[http://www.wikispaces.com/user/view/Andrew_Heathwaite Andrew_Heathwaite] <small>Nov 12, 2009</small></span>) assert:
 <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>

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

Show changes

Wikispaces>Osmiorisbendi: Imported revision 444543388 - Original comment:

2013-08-13T00:41:56Z

**Imported revision 444543388 - Original comment: **

← Older revision		Revision as of 00:41, 13 August 2013
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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:~~keenanpepper~~\|~~keenanpepper~~]] and made on <tt>~~2011~~-12-~~09 23~~:07:30 UTC</tt>.<br>		: This revision was by author [[User:Osmiorisbendi\|Osmiorisbendi]] and made on <tt>2013-08-13 00:41:56 UTC</tt>.<br>
	: The original revision id was <tt>~~284376846~~</tt>.<br>		: The original revision id was <tt>444543388</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)
	* [[harmony]] influenced by a theory of [[consonance]]		* [[harmony]] influenced by a theory of [[consonance]]
	** more than one pitch sounding together & their distinctness blurring		** 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		** 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]]		* [[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: [[maximal evenness\|maximally even]] a.k.a. "quasi-equal" divisions		** less redundant: [[maximal evenness\|maximally even]] a.k.a. "quasi-equal" divisions
	* tuning lattices		* tuning lattices
Line 53:		Line 53:
	** 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 & only two intervals of each class		** produces scales with only two step sizes & only two intervals of each class
	** less redundant extensions: [[MOS Cradle]] or [[Second Order MOS]]		** less redundant extensions: [[MOS Cradle]] or [[Second Order MOS]]
Line 78:		Line 78:
	<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 />		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></pre></div>		<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></pre></div>

Wikispaces>keenanpepper: Imported revision 284376846 - Original comment:

2011-12-09T23:07:30Z

**Imported revision 284376846 - Original comment: **

← Older revision		Revision as of 23:07, 9 December 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>~~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>
Line 35:		Line 35:
	* 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
Line 53:		Line 53:
	** 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 & only two intervals of each class		** produces scales with only two step sizes & only two intervals of each class
	** less redundant extensions: [[MOS Cradle]] or [[Second Order MOS]]		** less redundant extensions: [[MOS Cradle]] or [[Second Order MOS]]
Line 78:		Line 78:
	<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 />		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="/~~quasi-equal~~">~~quasi-equal~~</a> 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></pre></div>		<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></pre></div>

← Older revision		Revision as of 20:31, 22 January 2022
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	* [[harmony]] influenced by a theory of [[consonance]]		* [[harmony]] influenced by a theory of [[consonance]]
	** more than one pitch sounding together & their distinctness blurring		** 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		** if pitch 'y' appears in the harmonic 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]]		* [[octave equivalence]]
	** B-flat considered equivalent to B-flat an octave higher...		** B-flat considered equivalent to B-flat an octave higher...
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	** less redundant extensions: [[MOS Cradle]] or [[Second_Order_MOS\|Second Order MOS]]		** less redundant extensions: [[MOS Cradle]] or [[Second_Order_MOS\|Second Order MOS]]
	* matching tuning to timbre		* matching tuning to timbre
	** eg. rational intonation - selecting pitches which are copied in the [[~~overtone~~ series]] of other intervals		** eg. rational intonation - selecting pitches which are copied in the [[harmonic 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		** 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		** 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		* matching timbre to tuning
	** the reverse of the above: making a timbre (usually with a computer) to "match" a stipulated tuning		** the reverse of the above: making a timbre (usually with a computer) to "match" a stipulated tuning