Just intonation: Difference between revisions
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== Just Intonation in use == | == Just Intonation in use == | ||
To start off your exploration of just intonation scales, the [[ | To start off your exploration of just intonation scales, the [[Gallery of 12-tone Just Intonation Scales]] is a good place to start. | ||
Look at [[Notation|notation systems]] for Just Intonation | Look at [[Notation|notation systems]] for Just Intonation. | ||
The use of just intonation could be divided into these two flavors: | The use of just intonation could be divided into these two flavors: | ||
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=== Free Style Just === | === Free Style Just === | ||
[[ | [[Lou Harrison]] used this term; it means that you choose just-intonation pitches from the set of all possible just intervals (not from a mode or scale) as you use them in music. Dedicated page: [[FreeStyleJI|FreeStyleJI]] | ||
=== Constrained Just === | === Constrained Just === | ||
(In need of a better name maybe) Here are six ways that musicians and theorists have constrained the field of potential just ratios (from Jacques Dudon, "Differential Coherence", ''1/1'' vol. 11, no. 2: p.1): | (In need of a better name maybe) Here are six ways that musicians and theorists have constrained the field of potential just ratios (from Jacques Dudon, "Differential Coherence", ''1/1'' vol. 11, no. 2: p.1): | ||
''1. The principle of "[[ | ''1. The principle of "[[harmonic limit]]s", which sets a threshold in order to place a limit on the largest prime number in any ratio (cf: Tanner's "psycharithmes" and his ordering by complexity; Gioseffe Zarlino's five-limit "senario," and the like; Helmholtz's theory of consonance with its "blending of partials," which, like the others, results in giving priority to the lowest prime numbers). See [[3-limit]], [[5-limit]], [[7-limit]], [[11-limit]], [[13-limit]].'' | ||
''2. Restrictions on the combinations of numbers that make up the numerator and denominator of the ratios under consideration, such as the "monophonic" system of [[Wikipedia: Harry Partch|Harry Partch]]'s [[Wikipedia: Tonality diamond|tonality diamond]]. This, incidentally, is an eleven-limit system that only makes use of ratios of the form n:d, where n and d are drawn only from harmonics 1, 3, 5, 7, 9, 11, or their octaves.'' | ''2. Restrictions on the combinations of numbers that make up the numerator and denominator of the ratios under consideration, such as the "monophonic" system of [[Wikipedia: Harry Partch|Harry Partch]]'s [[Wikipedia: Tonality diamond|tonality diamond]]. This, incidentally, is an eleven-limit system that only makes use of ratios of the form n:d, where n and d are drawn only from harmonics 1, 3, 5, 7, 9, 11, or their octaves.'' | ||
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''3. Other theorists who, in contrast to the above, advocate the use of [[Wikipedia: Hexany|products sets]] of given arrays of prime numbers, such as [[Wikipedia: Erv Wilson|Ervin Wilson]], Robert Dussaut, and others.'' | ''3. Other theorists who, in contrast to the above, advocate the use of [[Wikipedia: Hexany|products sets]] of given arrays of prime numbers, such as [[Wikipedia: Erv Wilson|Ervin Wilson]], Robert Dussaut, and others.'' | ||
''4. [[ | ''4. [[Just intonation subgroups|Restrictions on the variety of prime numbers]] used within a system, for example, 3 used with only one [sic, also included is 2] other prime 7, 11, or 13.... This is quite common practice with Ptolemy, Ibn-Sina, Al-Farabi, and Saf-al-Din, and with numerous contemporary composers working in Just Intonation.'' | ||
''5. Restricting the denominator to one or very few values (the [[ | ''5. Restricting the denominator to one or very few values (the [[harmonic series]]).'' | ||
''6. Restricting the numerator to one or a very few values (the [[ | ''6. Restricting the numerator to one or a very few values (the [[subharmonic series]] or [[aliquot scales]]).'' | ||
to this can be added | to this can be added | ||