Just intonation: Difference between revisions
→Constrained just: “products sets” previously linked to the Wikipedia page for hexany, I have changed it so it now links to the Xen Wiki page for combination product sets |
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# ''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]].'' | # ''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]].'' | ||
# ''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.'' | # ''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.'' | ||
# ''Other theorists who, in contrast to the above, advocate the use of [[ | # ''Other theorists who, in contrast to the above, advocate the use of [[combination product sets|products sets]] of given arrays of prime numbers, such as [[Wikipedia: Erv Wilson|Ervin Wilson]], Robert Dussaut, and others.'' | ||
# ''[[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.'' | # ''[[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.'' | ||
# ''Restricting the denominator to one or very few values (the [[harmonic series]], [[overtone scale]]s or [[AFDO]]s).'' | # ''Restricting the denominator to one or very few values (the [[harmonic series]], [[overtone scale]]s or [[AFDO]]s).'' | ||