MicrotonalTheory: Difference between revisions

Line 8:

=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></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=

@@ Line 8: / Line 8: @@
 =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></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=