Just intonation: Difference between revisions

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=== 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):

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):

# ''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.''

# ''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.''

# ''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 [[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.''

# ''Restricting the denominator to one or very few values (the [[harmonic series]], [[isoharmonic chord]]s, [[AFDO]]s/[[overtone scale]]s).''

@@ Line 60: / Line 60: @@
 === 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):
+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):
 # ''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.''
-# ''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.''
+# ''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 [[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.''
 # ''Restricting the denominator to one or very few values (the [[harmonic series]], [[isoharmonic chord]]s, [[AFDO]]s/[[overtone scale]]s).''