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=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=

Revision as of 18:53, 25 January 2022

Theory: Inventions that shape understanding

Theories are 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

  • Just Intonation: an infinite world of rational numbers and numerous models: the harmonic series, integer frequency ratios, tonality diamonds, eikosany, etc.
  • Equal tunings: each one a subtle monoculture of intervals. May be treated as temperaments, or not
  • In Western common practice music, the (somewhat forgotten) use of historical temperaments (meantones, well temperaments) with 12 or more unequal notes per octave
  • Musical traditions of indigenous, ancient, and/or non-Western cultures
  • 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
  • Pergens, a way of classifying regular temperaments, constructing lattices for them, and determining their notation.
  • 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
    • Graham complexity, a complexity measure which works well with MOS scales and rank two regular temperaments.
  • 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.
  • Tetrachordal Scales, which use divided fourths as building blocks for composition.
  • Isoharmonic chords/scales
  • Pretty Pictures that represent scales in one way or another
  • Notation(pretty pictures for a the purpose of writing music down)
  • the notion of a Scalesmith who builds scales, with various methods, perhaps for single occasions
    • Counter-intuitive, random, arbitrary scales
    • Numerology-based, computationally demanding scales
    • Scale stretching
    • Acoustically-based (resonant frequencies of performance space, for example)
  • (Corollaries, traces left by other reality tunnels, which by themselves are completely trivial and obvious)
  • Redundancy in a tuning system
  • Composing Powerstart

External links

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