MicrotonalTheory - Revision history

Fredg999: Fix double redirect

2023-03-08T05:45:20Z

Fix double redirect

← Older revision		Revision as of 05:45, 8 March 2023
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	#REDIRECT [[~~Approaches~~ to musical tuning]]		#REDIRECT [[List of approaches to musical tuning]]

Fredg999: This page is redundant with other better developed pages. Now redirects to Approaches to musical tuning.

2023-03-05T04:24:08Z

This page is redundant with other better developed pages. Now redirects to Approaches to musical tuning.

← Older revision		Revision as of 04:24, 5 March 2023
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	~~__FORCETOC__~~		#REDIRECT [[Approaches to musical tuning]]
	~~=Theory: Inventions that shape understanding=~~

	Theories are [http://grace.evergreen.edu/%7Earunc/texts/cybernetics/heinz/disorder.pdf not discoveries but inventions] of humans, usually meant to formally describe regularities in experience, which often bring forth ''new ways of experiencing''. (The music-making itself ('practice'), if at odds with existing theories, may provoke the creation of new theories; it is thus important to recognize that theory and practice mutually and reciprocally influence each other.)

	There is a great deal of theory around the creation and/or discovering of tunings, scales, and temperaments, but whether it is useful to bother learning any of them is a matter of personal decision. (It is always possible to load up a random tuning on your retunable instrument of choice and explore it through music, without bothering to understand the theoretical considerations that led to the construction and/or discovery of said tuning.) Below you will find a partial list of currently-established theories related to alternative intonations.

	~~=Reality tunnels into microtonality=~~
	<ul><li>[[Just intonation\|Just Intonation]]: an infinite world of rational numbers and numerous models: the harmonic series, integer frequency ratios, tonality diamonds, eikosany, etc.</li><li>[[Equal-step tuning\|Equal]] tunings: each one a subtle monoculture of intervals. May be treated as temperaments, or not</li><li>In Western common practice music, the (somewhat forgotten) use of [[historical_temperaments\|historical temperaments]] (meantones, well temperaments) with 12 or more unequal notes per octave</li><li>Musical traditions of indigenous, ancient, and/or non-Western cultures<ul><li>[[Arabic,_Turkish,_Persian\|Arabic, Turkish, Persian]]</li><li>[[Indian\|Indian]] (North, South)</li><li>[[African\|African]]</li><li>Thai</li><li>[[Pre-Columbian_South_American_Music\|Pre-Columbian South American]] (e.g. Maya, Inca, Aztec..)</li><li>[[Indonesian\|Indonesian]] (Java, Bali)</li><li>Ancient Greek, [http://orthodoxwiki.org/Byzantine_Chant#~~The_scale Byzantine]</li></ul></li><li>~~[[Regular_Temperaments\|Regular Temperaments]] (including Linear Temperaments): a centuries-old practice that has recently undergone a mathematical facelift, in which Just Intonation is selectively and regularly detuned in various ways, to ~~better meet a variety of compositional desires</li><li>[[Pergen\|Pergens]], a way of classifying regular temperaments, constructing lattices for them, and determining their notation.~~
	</li><li>[[MOSScales\|Moment of Symmetry]], a means of iterating a single generative interval, modulo a period interval, to produce scales of two step-sizes. Brought to you by Erv Wilson<ul><li>[[Graham_complexity\|Graham complexity]], a complexity measure which works well with MOS scales and rank two regular temperaments.</li></ul></li><li>[[Empirical\|Empirical]] This is a form of hands-on, field research as opposed to a form of acoustical or scale engineering where tunings are specifically derived from listening and playing experiments carried out in the pitch continuum.</li><li>[[tetrachord\|Tetrachordal Scales]], which use divided fourths as building blocks for composition.</li><li>[[isoharmonic_chords\|Isoharmonic chords/scales]]</li><li>[[Pretty_Pictures\|Pretty Pictures]] that represent scales in one way or another</li><li>[[Notation\|Notation]](pretty pictures for a the purpose of writing music down)<ul><li>[[Nominal-Accidental_Chains\|Nominal-Accidental Chains]] A common approach to notation</li></ul></li><li>the notion of a [[Scalesmith\|Scalesmith]] who ''builds'' scales, with various methods, perhaps for single occasions<ul><li>Counter-intuitive, random, arbitrary scales</li><li>Numerology-based, computationally demanding scales</li><li>Scale stretching</li><li>Acoustically-based (resonant frequencies of performance space, for example)</li></ul></li><li>([[Corollaries\|Corollaries]], traces left by other reality tunnels, which by themselves are completely trivial and obvious)</li><li>[[redundancy\|Redundancy]] in a tuning ~~system</li><li>[[Composing Powerstart]]</li></ul>~~

	~~=External links=~~
	<ul><li>Tonalsoft [http://www.tonalsoft.com/enc/encyclopedia.aspx Encyclopedia of microtonal music theory] - a whole sea of information on the topic, covering both historical tuning theories and modern developments</li><li>[http://microtonalismo.com Microtonalismo] - Web microtonal</li><li>[http://www.bikexprt.com/music/tunebibl.htm A bibliography on musical tunings and temperaments], compiled by John S. Allen</li><li>[[Huygens-Fokker\|Huygens-Fokker]] Foundation's [http://www.huygens-fokker.org/docs/bibliography.html Tuning & temperament bibliography], hyperlinked and updated by Manuel op de Coul</li><li>The [http://www.untwelve.org UnTwelve] website has some pages of theoretical interest, including a [http://www.untwelve.org/what fascinating article] authored by Margo Schulter</li><li>German sister wiki [[:de:willkommen\|"Xenharmonie"]]</li></ul>
	~~[[Category:access]]~~
	~~[[Category:gate]]~~
	~~[[Category:theory]]~~
	~~[[Category:tunnels~~]]

Cmloegcmluin: /* Reality tunnels into microtonality */ I don't really know what this page is, or where to put this cool article I just discovered to make it more discoverable, but this seems like a good place

2022-01-25T18:53:12Z

Reality tunnels into microtonality: I don't really know what this page is, or where to put this cool article I just discovered to make it more discoverable, but this seems like a good place

← Older revision		Revision as of 18:53, 25 January 2022
Line 8:		Line 8:
	=Reality tunnels into microtonality=		=Reality tunnels into microtonality=
	<ul><li>[[Just intonation\|Just Intonation]]: an infinite world of rational numbers and numerous models: the harmonic series, integer frequency ratios, tonality diamonds, eikosany, etc.</li><li>[[Equal-step tuning\|Equal]] tunings: each one a subtle monoculture of intervals. May be treated as temperaments, or not</li><li>In Western common practice music, the (somewhat forgotten) use of [[historical_temperaments\|historical temperaments]] (meantones, well temperaments) with 12 or more unequal notes per octave</li><li>Musical traditions of indigenous, ancient, and/or non-Western cultures<ul><li>[[Arabic,_Turkish,_Persian\|Arabic, Turkish, Persian]]</li><li>[[Indian\|Indian]] (North, South)</li><li>[[African\|African]]</li><li>Thai</li><li>[[Pre-Columbian_South_American_Music\|Pre-Columbian South American]] (e.g. Maya, Inca, Aztec..)</li><li>[[Indonesian\|Indonesian]] (Java, Bali)</li><li>Ancient Greek, [http://orthodoxwiki.org/Byzantine_Chant#The_scale Byzantine]</li></ul></li><li>[[Regular_Temperaments\|Regular Temperaments]] (including Linear Temperaments): a centuries-old practice that has recently undergone a mathematical facelift, in which Just Intonation is selectively and regularly detuned in various ways, to better meet a variety of compositional desires</li><li>[[Pergen\|Pergens]], a way of classifying regular temperaments, constructing lattices for them, and determining their notation.		<ul><li>[[Just intonation\|Just Intonation]]: an infinite world of rational numbers and numerous models: the harmonic series, integer frequency ratios, tonality diamonds, eikosany, etc.</li><li>[[Equal-step tuning\|Equal]] tunings: each one a subtle monoculture of intervals. May be treated as temperaments, or not</li><li>In Western common practice music, the (somewhat forgotten) use of [[historical_temperaments\|historical temperaments]] (meantones, well temperaments) with 12 or more unequal notes per octave</li><li>Musical traditions of indigenous, ancient, and/or non-Western cultures<ul><li>[[Arabic,_Turkish,_Persian\|Arabic, Turkish, Persian]]</li><li>[[Indian\|Indian]] (North, South)</li><li>[[African\|African]]</li><li>Thai</li><li>[[Pre-Columbian_South_American_Music\|Pre-Columbian South American]] (e.g. Maya, Inca, Aztec..)</li><li>[[Indonesian\|Indonesian]] (Java, Bali)</li><li>Ancient Greek, [http://orthodoxwiki.org/Byzantine_Chant#The_scale Byzantine]</li></ul></li><li>[[Regular_Temperaments\|Regular Temperaments]] (including Linear Temperaments): a centuries-old practice that has recently undergone a mathematical facelift, in which Just Intonation is selectively and regularly detuned in various ways, to better meet a variety of compositional desires</li><li>[[Pergen\|Pergens]], a way of classifying regular temperaments, constructing lattices for them, and determining their notation.
	</li><li>[[MOSScales\|Moment of Symmetry]], a means of iterating a single generative interval, modulo a period interval, to produce scales of two step-sizes. Brought to you by Erv Wilson<ul><li>[[Graham_complexity\|Graham complexity]], a complexity measure which works well with MOS scales and rank two regular temperaments.</li></ul></li><li>[[Empirical\|Empirical]] This is a form of hands-on, field research as opposed to a form of acoustical or scale engineering where tunings are specifically derived from listening and playing experiments carried out in the pitch continuum.</li><li>[[tetrachord\|Tetrachordal Scales]], which use divided fourths as building blocks for composition.</li><li>[[isoharmonic_chords\|Isoharmonic chords/scales]]</li><li>[[Pretty_Pictures\|Pretty Pictures]] that represent scales in one way or another</li><li>[[Notation\|Notation]](pretty pictures for a the purpose of writing music down)<ul><li>[[Nominal-Accidental_Chains\|Nominal-Accidental Chains]] A common approach to notation</li></ul></li><li>the notion of a [[Scalesmith\|Scalesmith]] who ''builds'' scales, with various methods, perhaps for single occasions<ul><li>Counter-intuitive, random, arbitrary scales</li><li>Numerology-based, computationally demanding scales</li><li>Scale stretching</li><li>Acoustically-based (resonant frequencies of performance space, for example)</li></ul></li><li>([[Corollaries\|Corollaries]], traces left by other reality tunnels, which by themselves are completely trivial and obvious)</li><li>[[redundancy\|Redundancy]] in a tuning system</li></ul>		</li><li>[[MOSScales\|Moment of Symmetry]], a means of iterating a single generative interval, modulo a period interval, to produce scales of two step-sizes. Brought to you by Erv Wilson<ul><li>[[Graham_complexity\|Graham complexity]], a complexity measure which works well with MOS scales and rank two regular temperaments.</li></ul></li><li>[[Empirical\|Empirical]] This is a form of hands-on, field research as opposed to a form of acoustical or scale engineering where tunings are specifically derived from listening and playing experiments carried out in the pitch continuum.</li><li>[[tetrachord\|Tetrachordal Scales]], which use divided fourths as building blocks for composition.</li><li>[[isoharmonic_chords\|Isoharmonic chords/scales]]</li><li>[[Pretty_Pictures\|Pretty Pictures]] that represent scales in one way or another</li><li>[[Notation\|Notation]](pretty pictures for a the purpose of writing music down)<ul><li>[[Nominal-Accidental_Chains\|Nominal-Accidental Chains]] A common approach to notation</li></ul></li><li>the notion of a [[Scalesmith\|Scalesmith]] who ''builds'' scales, with various methods, perhaps for single occasions<ul><li>Counter-intuitive, random, arbitrary scales</li><li>Numerology-based, computationally demanding scales</li><li>Scale stretching</li><li>Acoustically-based (resonant frequencies of performance space, for example)</li></ul></li><li>([[Corollaries\|Corollaries]], traces left by other reality tunnels, which by themselves are completely trivial and obvious)</li><li>[[redundancy\|Redundancy]] in a tuning system</li><li>[[Composing Powerstart]]</li></ul>

	=External links=		=External links=

TallKite: added a link to the pergens page

2019-12-07T02:46:38Z

added a link to the pergens page

← Older revision		Revision as of 02:46, 7 December 2019
Line 7:		Line 7:

	=Reality tunnels into microtonality=		=Reality tunnels into microtonality=
	<ul><li>[[Just intonation\|Just Intonation]]: an infinite world of rational numbers and numerous models: the harmonic series, integer frequency ratios, tonality diamonds, eikosany, etc.</li><li>[[Equal-step tuning\|Equal]] tunings: each one a subtle monoculture of intervals. May be treated as temperaments, or not</li><li>In Western common practice music, the (somewhat forgotten) use of [[historical_temperaments\|historical temperaments]] (meantones, well temperaments) with 12 or more unequal notes per octave</li><li>Musical traditions of indigenous, ancient, and/or non-Western cultures<ul><li>[[Arabic,_Turkish,_Persian\|Arabic, Turkish, Persian]]</li><li>[[Indian\|Indian]] (North, South)</li><li>[[African\|African]]</li><li>Thai</li><li>[[Pre-Columbian_South_American_Music\|Pre-Columbian South American]] (e.g. Maya, Inca, Aztec..)</li><li>[[Indonesian\|Indonesian]] (Java, Bali)</li><li>Ancient Greek, [http://orthodoxwiki.org/Byzantine_Chant#The_scale Byzantine]</li></ul></li><li>[[Regular_Temperaments\|Regular Temperaments]] (including Linear Temperaments): a centuries-old practice that has recently undergone a mathematical facelift, in which Just Intonation is selectively and regularly detuned in various ways, to better meet a variety of compositional desires</li><li>[[MOSScales\|Moment of Symmetry]], a means of iterating a single generative interval, modulo a period interval, to produce scales of two step-sizes. Brought to you by Erv Wilson<ul><li>[[Graham_complexity\|Graham complexity]], a complexity measure which works well with MOS scales and rank two regular temperaments.</li></ul></li><li>[[Empirical\|Empirical]] This is a form of hands-on, field research as opposed to a form of acoustical or scale engineering where tunings are specifically derived from listening and playing experiments carried out in the pitch continuum.</li><li>[[tetrachord\|Tetrachordal Scales]], which use divided fourths as building blocks for composition.</li><li>[[isoharmonic_chords\|Isoharmonic chords/scales]]</li><li>[[Pretty_Pictures\|Pretty Pictures]] that represent scales in one way or another</li><li>[[Notation\|Notation]](pretty pictures for a the purpose of writing music down)<ul><li>[[Nominal-Accidental_Chains\|Nominal-Accidental Chains]] A common approach to notation</li></ul></li><li>the notion of a [[Scalesmith\|Scalesmith]] who ''builds'' scales, with various methods, perhaps for single occasions<ul><li>Counter-intuitive, random, arbitrary scales</li><li>Numerology-based, computationally demanding scales</li><li>Scale stretching</li><li>Acoustically-based (resonant frequencies of performance space, for example)</li></ul></li><li>([[Corollaries\|Corollaries]], traces left by other reality tunnels, which by themselves are completely trivial and obvious)</li><li>[[redundancy\|Redundancy]] in a tuning system</li></ul>		<ul><li>[[Just intonation\|Just Intonation]]: an infinite world of rational numbers and numerous models: the harmonic series, integer frequency ratios, tonality diamonds, eikosany, etc.</li><li>[[Equal-step tuning\|Equal]] tunings: each one a subtle monoculture of intervals. May be treated as temperaments, or not</li><li>In Western common practice music, the (somewhat forgotten) use of [[historical_temperaments\|historical temperaments]] (meantones, well temperaments) with 12 or more unequal notes per octave</li><li>Musical traditions of indigenous, ancient, and/or non-Western cultures<ul><li>[[Arabic,_Turkish,_Persian\|Arabic, Turkish, Persian]]</li><li>[[Indian\|Indian]] (North, South)</li><li>[[African\|African]]</li><li>Thai</li><li>[[Pre-Columbian_South_American_Music\|Pre-Columbian South American]] (e.g. Maya, Inca, Aztec..)</li><li>[[Indonesian\|Indonesian]] (Java, Bali)</li><li>Ancient Greek, [http://orthodoxwiki.org/Byzantine_Chant#The_scale Byzantine]</li></ul></li><li>[[Regular_Temperaments\|Regular Temperaments]] (including Linear Temperaments): a centuries-old practice that has recently undergone a mathematical facelift, in which Just Intonation is selectively and regularly detuned in various ways, to better meet a variety of compositional desires</li><li>[[Pergen\|Pergens]], a way of classifying regular temperaments, constructing lattices for them, and determining their notation.
			</li><li>[[MOSScales\|Moment of Symmetry]], a means of iterating a single generative interval, modulo a period interval, to produce scales of two step-sizes. Brought to you by Erv Wilson<ul><li>[[Graham_complexity\|Graham complexity]], a complexity measure which works well with MOS scales and rank two regular temperaments.</li></ul></li><li>[[Empirical\|Empirical]] This is a form of hands-on, field research as opposed to a form of acoustical or scale engineering where tunings are specifically derived from listening and playing experiments carried out in the pitch continuum.</li><li>[[tetrachord\|Tetrachordal Scales]], which use divided fourths as building blocks for composition.</li><li>[[isoharmonic_chords\|Isoharmonic chords/scales]]</li><li>[[Pretty_Pictures\|Pretty Pictures]] that represent scales in one way or another</li><li>[[Notation\|Notation]](pretty pictures for a the purpose of writing music down)<ul><li>[[Nominal-Accidental_Chains\|Nominal-Accidental Chains]] A common approach to notation</li></ul></li><li>the notion of a [[Scalesmith\|Scalesmith]] who ''builds'' scales, with various methods, perhaps for single occasions<ul><li>Counter-intuitive, random, arbitrary scales</li><li>Numerology-based, computationally demanding scales</li><li>Scale stretching</li><li>Acoustically-based (resonant frequencies of performance space, for example)</li></ul></li><li>([[Corollaries\|Corollaries]], traces left by other reality tunnels, which by themselves are completely trivial and obvious)</li><li>[[redundancy\|Redundancy]] in a tuning system</li></ul>

	=External links=		=External links=

ResonantFrequencies: links, typos

2019-01-11T04:34:20Z

links, typos

← Older revision		Revision as of 04:34, 11 January 2019
Line 7:		Line 7:

	=Reality tunnels into microtonality=		=Reality tunnels into microtonality=
	<ul><li>[[~~JustIntonation~~\|Just Intonation]]: an infinite world of rational numbers and numerous models: the harmonic series, integer frequency ratios, tonality diamonds, eikosany, etc.</li><li>[[~~Equal_Temperaments~~\|Equal]] tunings: each one a subtle monoculture of intervals. May be treated as temperaments, or not</li><li>In Western common practice music, the (somewhat forgotten) use of [[historical_temperaments\|historical temperaments]] (meantones, well temperaments) with 12 or more unequal notes per octave</li><li>Musical traditions of ~~indigienous~~, ancient, and/or non-Western cultures<ul><li>[[Arabic,_Turkish,_Persian\|Arabic, Turkish, Persian]]</li><li>[[Indian\|Indian]] (North, South)</li><li>[[African\|African]]</li><li>Thai</li><li>[[Pre-Columbian_South_American_Music\|Pre-Columbian South American]] (e.g. Maya, Inca, Aztec..)</li><li>[[Indonesian\|Indonesian]] (Java, Bali)</li><li>Ancient Greek, [http://orthodoxwiki.org/Byzantine_Chant#The_scale Byzantine]</li></ul></li><li>[[Regular_Temperaments\|Regular Temperaments]] (including Linear Temperaments): a centuries-old practice that has recently undergone a mathematical facelift, in which Just Intonation is selectively and regularly detuned in various ways, to better meet a variety of compositional desires</li><li>[[MOSScales\|Moment of Symmetry]], a means of iterating a single generative interval, modulo a period interval, to produce scales of two step-sizes. Brought to you by Erv Wilson<ul><li>[[Graham_complexity\|Graham complexity]], a complexity measure which works well with MOS scales and rank two regular temperaments.</li></ul></li><li>[[Empirical\|Empirical]] This is a form of hands-on, field research as opposed to a form of acoustical or scale engineering where tunings are specifically derived from listening and playing experiments carried out in the pitch continuum.</li><li>[[tetrachord\|Tetrachordal Scales]], which use divided fourths as building blocks for composition.</li><li>[[isoharmonic_chords\|Isoharmonic chords/scales]]</li><li>[[Pretty_Pictures\|Pretty Pictures]] that represent scales in one way or another</li><li>[[Notation\|Notation]](pretty pictures for a the purpose of writing music down)<ul><li>[[Nominal-Accidental_Chains\|Nominal-Accidental Chains]] A common approach to notation</li></ul></li><li>the notion of a [[Scalesmith\|Scalesmith]] who ''builds''scales, with various methods, perhaps for single occasions<ul><li>Counter-intuitive, random, arbitrary scales</li><li>Numerology-based, computationally demanding scales</li><li>Scale stretching</li><li>Acoustically-based (resonant frequencies of performance space, for example)</li></ul></li><li>([[Corollaries\|Corollaries]], traces left by other reality tunnels, which by themselves are completely trivial and obvious)</li><li>[[redundancy\|Redundancy]] in a tuning system</li></ul>		<ul><li>[[Just intonation\|Just Intonation]]: an infinite world of rational numbers and numerous models: the harmonic series, integer frequency ratios, tonality diamonds, eikosany, etc.</li><li>[[Equal-step tuning\|Equal]] tunings: each one a subtle monoculture of intervals. May be treated as temperaments, or not</li><li>In Western common practice music, the (somewhat forgotten) use of [[historical_temperaments\|historical temperaments]] (meantones, well temperaments) with 12 or more unequal notes per octave</li><li>Musical traditions of indigenous, ancient, and/or non-Western cultures<ul><li>[[Arabic,_Turkish,_Persian\|Arabic, Turkish, Persian]]</li><li>[[Indian\|Indian]] (North, South)</li><li>[[African\|African]]</li><li>Thai</li><li>[[Pre-Columbian_South_American_Music\|Pre-Columbian South American]] (e.g. Maya, Inca, Aztec..)</li><li>[[Indonesian\|Indonesian]] (Java, Bali)</li><li>Ancient Greek, [http://orthodoxwiki.org/Byzantine_Chant#The_scale Byzantine]</li></ul></li><li>[[Regular_Temperaments\|Regular Temperaments]] (including Linear Temperaments): a centuries-old practice that has recently undergone a mathematical facelift, in which Just Intonation is selectively and regularly detuned in various ways, to better meet a variety of compositional desires</li><li>[[MOSScales\|Moment of Symmetry]], a means of iterating a single generative interval, modulo a period interval, to produce scales of two step-sizes. Brought to you by Erv Wilson<ul><li>[[Graham_complexity\|Graham complexity]], a complexity measure which works well with MOS scales and rank two regular temperaments.</li></ul></li><li>[[Empirical\|Empirical]] This is a form of hands-on, field research as opposed to a form of acoustical or scale engineering where tunings are specifically derived from listening and playing experiments carried out in the pitch continuum.</li><li>[[tetrachord\|Tetrachordal Scales]], which use divided fourths as building blocks for composition.</li><li>[[isoharmonic_chords\|Isoharmonic chords/scales]]</li><li>[[Pretty_Pictures\|Pretty Pictures]] that represent scales in one way or another</li><li>[[Notation\|Notation]](pretty pictures for a the purpose of writing music down)<ul><li>[[Nominal-Accidental_Chains\|Nominal-Accidental Chains]] A common approach to notation</li></ul></li><li>the notion of a [[Scalesmith\|Scalesmith]] who ''builds'' scales, with various methods, perhaps for single occasions<ul><li>Counter-intuitive, random, arbitrary scales</li><li>Numerology-based, computationally demanding scales</li><li>Scale stretching</li><li>Acoustically-based (resonant frequencies of performance space, for example)</li></ul></li><li>([[Corollaries\|Corollaries]], traces left by other reality tunnels, which by themselves are completely trivial and obvious)</li><li>[[redundancy\|Redundancy]] in a tuning system</li></ul>

	=External links=		=External links=
	<ul><li>Tonalsoft [http://www.tonalsoft.com/enc/encyclopedia.aspx Encyclopedia of microtonal music theory] - a whole sea of information on the topic, covering both historical tuning theories and modern developments</li><li>[http://microtonalismo.com Microtonalismo] - Web microtonal</li><li>[http://www.bikexprt.com/music/tunebibl.htm A bibliography on musical tunings and temperaments], compiled by John S. Allen</li><li>[[Huygens-Fokker\|Huygens-Fokker]] Foundation's [http://www.huygens-fokker.org/docs/bibliography.html Tuning & temperament bibliography], hyperlinked and updated by Manuel op de Coul</li><li>The [http://www.untwelve.org UnTwelve] website has some pages of theoretical interest, including a [http://www.untwelve.org/what fascinating article] authored by Margo Schulter</li><li>German sister wiki [[:de:willkommen\|"Xenharmonie"]]</li></ul> [[Category:access]]		<ul><li>Tonalsoft [http://www.tonalsoft.com/enc/encyclopedia.aspx Encyclopedia of microtonal music theory] - a whole sea of information on the topic, covering both historical tuning theories and modern developments</li><li>[http://microtonalismo.com Microtonalismo] - Web microtonal</li><li>[http://www.bikexprt.com/music/tunebibl.htm A bibliography on musical tunings and temperaments], compiled by John S. Allen</li><li>[[Huygens-Fokker\|Huygens-Fokker]] Foundation's [http://www.huygens-fokker.org/docs/bibliography.html Tuning & temperament bibliography], hyperlinked and updated by Manuel op de Coul</li><li>The [http://www.untwelve.org UnTwelve] website has some pages of theoretical interest, including a [http://www.untwelve.org/what fascinating article] authored by Margo Schulter</li><li>German sister wiki [[:de:willkommen\|"Xenharmonie"]]</li></ul>
			[[Category:access]]
	[[Category:gate]]		[[Category:gate]]
	[[Category:theory]]		[[Category:theory]]
	[[Category:tunnels]]		[[Category:tunnels]]

Tyler Henthorn: Heading syntax fix

2018-10-03T06:05:02Z

Heading syntax fix

← Older revision		Revision as of 06:05, 3 October 2018
Line 10:		Line 10:

	=External links=		=External links=

	~~== ==~~
	<ul><li>Tonalsoft [http://www.tonalsoft.com/enc/encyclopedia.aspx Encyclopedia of microtonal music theory] - a whole sea of information on the topic, covering both historical tuning theories and modern developments</li><li>[http://microtonalismo.com Microtonalismo] - Web microtonal</li><li>[http://www.bikexprt.com/music/tunebibl.htm A bibliography on musical tunings and temperaments], compiled by John S. Allen</li><li>[[Huygens-Fokker\|Huygens-Fokker]] Foundation's [http://www.huygens-fokker.org/docs/bibliography.html Tuning & temperament bibliography], hyperlinked and updated by Manuel op de Coul</li><li>The [http://www.untwelve.org UnTwelve] website has some pages of theoretical interest, including a [http://www.untwelve.org/what fascinating article] authored by Margo Schulter</li><li>German sister wiki [[:de:willkommen\|"Xenharmonie"]]</li></ul> [[Category:access]]		<ul><li>Tonalsoft [http://www.tonalsoft.com/enc/encyclopedia.aspx Encyclopedia of microtonal music theory] - a whole sea of information on the topic, covering both historical tuning theories and modern developments</li><li>[http://microtonalismo.com Microtonalismo] - Web microtonal</li><li>[http://www.bikexprt.com/music/tunebibl.htm A bibliography on musical tunings and temperaments], compiled by John S. Allen</li><li>[[Huygens-Fokker\|Huygens-Fokker]] Foundation's [http://www.huygens-fokker.org/docs/bibliography.html Tuning & temperament bibliography], hyperlinked and updated by Manuel op de Coul</li><li>The [http://www.untwelve.org UnTwelve] website has some pages of theoretical interest, including a [http://www.untwelve.org/what fascinating article] authored by Margo Schulter</li><li>German sister wiki [[:de:willkommen\|"Xenharmonie"]]</li></ul> [[Category:access]]
	[[Category:gate]]		[[Category:gate]]
	[[Category:theory]]		[[Category:theory]]
	[[Category:tunnels]]		[[Category:tunnels]]

Avenarius: /* URI for article by Margo Schulter fixed */

2018-10-03T05:53:17Z

URI for article by Margo Schulter fixed

← Older revision		Revision as of 05:53, 3 October 2018
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	== ==		== ==
	<ul><li>Tonalsoft [http://www.tonalsoft.com/enc/encyclopedia.aspx Encyclopedia of microtonal music theory] - a whole sea of information on the topic, covering both historical tuning theories and modern developments</li><li>[http://microtonalismo.com Microtonalismo] - Web microtonal</li><li>[http://www.bikexprt.com/music/tunebibl.htm A bibliography on musical tunings and temperaments], compiled by John S. Allen</li><li>[[Huygens-Fokker\|Huygens-Fokker]] Foundation's [http://www.huygens-fokker.org/docs/bibliography.html Tuning & temperament bibliography], hyperlinked and updated by Manuel op de Coul</li><li>The [http://www.untwelve.org UnTwelve] website has some pages of theoretical interest, including a [http://www.untwelve.org/what~~.html~~ fascinating article] authored by Margo Schulter</li><li>German sister wiki [[:de:willkommen\|"Xenharmonie"]]</li></ul> [[Category:access]]		<ul><li>Tonalsoft [http://www.tonalsoft.com/enc/encyclopedia.aspx Encyclopedia of microtonal music theory] - a whole sea of information on the topic, covering both historical tuning theories and modern developments</li><li>[http://microtonalismo.com Microtonalismo] - Web microtonal</li><li>[http://www.bikexprt.com/music/tunebibl.htm A bibliography on musical tunings and temperaments], compiled by John S. Allen</li><li>[[Huygens-Fokker\|Huygens-Fokker]] Foundation's [http://www.huygens-fokker.org/docs/bibliography.html Tuning & temperament bibliography], hyperlinked and updated by Manuel op de Coul</li><li>The [http://www.untwelve.org UnTwelve] website has some pages of theoretical interest, including a [http://www.untwelve.org/what fascinating article] authored by Margo Schulter</li><li>German sister wiki [[:de:willkommen\|"Xenharmonie"]]</li></ul> [[Category:access]]
	[[Category:gate]]		[[Category:gate]]
	[[Category:theory]]		[[Category:theory]]
	[[Category:tunnels]]		[[Category:tunnels]]

Mike Battaglia: Text replacement - "(\[\[\:(dev|es|purdal|de|en):[^[:space:]\|]) (.])" to "$1|$3"

2018-09-17T00:09:14Z

Text replacement - "(\[\[\:(dev|es|purdal|de|en):[^[:space:]\|]*) (.*])" to "$1|$3"

← Older revision		Revision as of 00:09, 17 September 2018
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	== ==		== ==
	<ul><li>Tonalsoft [http://www.tonalsoft.com/enc/encyclopedia.aspx Encyclopedia of microtonal music theory] - a whole sea of information on the topic, covering both historical tuning theories and modern developments</li><li>[http://microtonalismo.com Microtonalismo] - Web microtonal</li><li>[http://www.bikexprt.com/music/tunebibl.htm A bibliography on musical tunings and temperaments], compiled by John S. Allen</li><li>[[Huygens-Fokker\|Huygens-Fokker]] Foundation's [http://www.huygens-fokker.org/docs/bibliography.html Tuning & temperament bibliography], hyperlinked and updated by Manuel op de Coul</li><li>The [http://www.untwelve.org UnTwelve] website has some pages of theoretical interest, including a [http://www.untwelve.org/what.html fascinating article] authored by Margo Schulter</li><li>German sister wiki [[:de:willkommen "Xenharmonie"]]</li></ul> [[Category:access]]		<ul><li>Tonalsoft [http://www.tonalsoft.com/enc/encyclopedia.aspx Encyclopedia of microtonal music theory] - a whole sea of information on the topic, covering both historical tuning theories and modern developments</li><li>[http://microtonalismo.com Microtonalismo] - Web microtonal</li><li>[http://www.bikexprt.com/music/tunebibl.htm A bibliography on musical tunings and temperaments], compiled by John S. Allen</li><li>[[Huygens-Fokker\|Huygens-Fokker]] Foundation's [http://www.huygens-fokker.org/docs/bibliography.html Tuning & temperament bibliography], hyperlinked and updated by Manuel op de Coul</li><li>The [http://www.untwelve.org UnTwelve] website has some pages of theoretical interest, including a [http://www.untwelve.org/what.html fascinating article] authored by Margo Schulter</li><li>German sister wiki [[:de:willkommen\|"Xenharmonie"]]</li></ul> [[Category:access]]
	[[Category:gate]]		[[Category:gate]]
	[[Category:theory]]		[[Category:theory]]
	[[Category:tunnels]]		[[Category:tunnels]]

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

Show changes

Wikispaces>xenwolf: Imported revision 431244450 - Original comment: German sister wiki (WIP) added

2013-05-13T17:00:27Z

**Imported revision 431244450 - Original comment: German sister wiki (WIP) added**

← Older revision		Revision as of 17:00, 13 May 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:~~genewardsmith~~\|~~genewardsmith~~]] and made on <tt>2013-03-30 13:32:54 UTC</tt>.<br>		: This revision was by author [[User:xenwolf\|xenwolf]] and made on <tt>2013-05-13 17:00:27 UTC</tt>.<br>
	: The original revision id was <tt>~~418939438~~</tt>.<br>		: The original revision id was <tt>431244450</tt>.<br>
	: The revision comment was: <tt>~~Reverted to May 20, 2012 11:53 pm: spam~~</tt><br>		: The revision comment was: <tt>German sister wiki (WIP) added</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>
	<h4>Original Wikitext content:</h4>		<h4>Original Wikitext content:</h4>
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	* [[http://www.bikexprt.com/music/tunebibl.htm\|A bibliography on musical tunings and temperaments]], compiled by John S. Allen		* [[http://www.bikexprt.com/music/tunebibl.htm\|A bibliography on musical tunings and temperaments]], compiled by John S. Allen
	* [[Huygens-Fokker]] Foundation's [[http://www.huygens-fokker.org/docs/bibliography.html\|Tuning & temperament bibliography]], hyperlinked and updated by Manuel op de Coul		* [[Huygens-Fokker]] Foundation's [[http://www.huygens-fokker.org/docs/bibliography.html\|Tuning & temperament bibliography]], hyperlinked and updated by Manuel op de Coul
	* The [[http://www.untwelve.org\|UnTwelve]] website has some pages of theoretical interest, including a [[http://www.untwelve.org/what.html\|fascinating article]] authored by Margo Schulter</pre></div>		* The [[http://www.untwelve.org\|UnTwelve]] website has some pages of theoretical interest, including a [[http://www.untwelve.org/what.html\|fascinating article]] authored by Margo Schulter
			* German sister wiki [[xenharmonie/willkommen\|"Xenharmonie"]]</pre></div>
	<h4>Original HTML content:</h4>		<h4>Original HTML content:</h4>
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>MicrotonalTheory</title></head><body><!-- ws:start:WikiTextTocRule:8:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:8 --><!-- ws:start:WikiTextTocRule:9: --><a href="#Theory: Inventions that shape understanding">Theory: Inventions that shape understanding</a><!-- ws:end:WikiTextTocRule:9 --><!-- ws:start:WikiTextTocRule:10: --> \| <a href="#Reality tunnels into microtonality">Reality tunnels into microtonality</a><!-- ws:end:WikiTextTocRule:10 --><!-- ws:start:WikiTextTocRule:11: --> \| <a href="#External links">External links</a><!-- ws:end:WikiTextTocRule:11 --><!-- ws:start:WikiTextTocRule:12: --><!-- ws:end:WikiTextTocRule:12 --><!-- ws:start:WikiTextTocRule:13: -->		<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>MicrotonalTheory</title></head><body><!-- ws:start:WikiTextTocRule:8:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:8 --><!-- ws:start:WikiTextTocRule:9: --><a href="#Theory: Inventions that shape understanding">Theory: Inventions that shape understanding</a><!-- ws:end:WikiTextTocRule:9 --><!-- ws:start:WikiTextTocRule:10: --> \| <a href="#Reality tunnels into microtonality">Reality tunnels into microtonality</a><!-- ws:end:WikiTextTocRule:10 --><!-- ws:start:WikiTextTocRule:11: --> \| <a href="#External links">External links</a><!-- ws:end:WikiTextTocRule:11 --><!-- ws:start:WikiTextTocRule:12: --><!-- ws:end:WikiTextTocRule:12 --><!-- ws:start:WikiTextTocRule:13: -->
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	<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="External links"></a><!-- ws:end:WikiTextHeadingRule:4 -->External links</h1>		<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="External links"></a><!-- ws:end:WikiTextHeadingRule:4 -->External links</h1>
	<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><!-- ws:end:WikiTextHeadingRule:6 --> </h2>		<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><!-- ws:end:WikiTextHeadingRule:6 --> </h2>
	<ul><li>Tonalsoft <a class="wiki_link_ext" href="http://www.tonalsoft.com/enc/encyclopedia.aspx" rel="nofollow">Encyclopedia of microtonal music theory</a> - a whole sea of information on the topic, covering both historical tuning theories and modern developments</li><li><a class="wiki_link_ext" href="http://microtonalismo.com" rel="nofollow">Microtonalismo</a> - Web microtonal</li><li><a class="wiki_link_ext" href="http://www.bikexprt.com/music/tunebibl.htm" rel="nofollow">A bibliography on musical tunings and temperaments</a>, compiled by John S. Allen</li><li><a class="wiki_link" href="/Huygens-Fokker">Huygens-Fokker</a> Foundation's <a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/bibliography.html" rel="nofollow">Tuning &amp; temperament bibliography</a>, hyperlinked and updated by Manuel op de Coul</li><li>The <a class="wiki_link_ext" href="http://www.untwelve.org" rel="nofollow">UnTwelve</a> website has some pages of theoretical interest, including a <a class="wiki_link_ext" href="http://www.untwelve.org/what.html" rel="nofollow">fascinating article</a> authored by Margo Schulter</li></ul></body></html></pre></div>		<ul><li>Tonalsoft <a class="wiki_link_ext" href="http://www.tonalsoft.com/enc/encyclopedia.aspx" rel="nofollow">Encyclopedia of microtonal music theory</a> - a whole sea of information on the topic, covering both historical tuning theories and modern developments</li><li><a class="wiki_link_ext" href="http://microtonalismo.com" rel="nofollow">Microtonalismo</a> - Web microtonal</li><li><a class="wiki_link_ext" href="http://www.bikexprt.com/music/tunebibl.htm" rel="nofollow">A bibliography on musical tunings and temperaments</a>, compiled by John S. Allen</li><li><a class="wiki_link" href="/Huygens-Fokker">Huygens-Fokker</a> Foundation's <a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/bibliography.html" rel="nofollow">Tuning &amp; temperament bibliography</a>, hyperlinked and updated by Manuel op de Coul</li><li>The <a class="wiki_link_ext" href="http://www.untwelve.org" rel="nofollow">UnTwelve</a> website has some pages of theoretical interest, including a <a class="wiki_link_ext" href="http://www.untwelve.org/what.html" rel="nofollow">fascinating article</a> authored by Margo Schulter</li><li>German sister wiki <a class="wiki_link" href="http://xenharmonie.wikispaces.com/willkommen">&quot;Xenharmonie&quot;</a></li></ul></body></html></pre></div>