Half-prime subgroup: Difference between revisions

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== Harmony ==

If a [[low-complexity JI]]-based perspective is used, there is an absence of low-complexity chords with 3 or more notes that can be practically used. The chord 3:5:7, which is shared with [[Bohlen-Pierce]] and other no-twos systems, is available but it is unwieldy to manage in a 3/2-repeating system, spanning more than twice the equivalence interval of 3/2. Thus, harmony would be largely established using two notes at a time rather than three, using dyads with intervals of [[10/9]], [[25/21]], [[27/20]] or [[7/5]], as well as [[28/27]] or [[15/14]] if extreme tension is permitted. This can be compared to [[2edo]], [[3edo]] and 4edo, but with far more sophisticated types of harmonic progression. Note that in a 3/2-repeating system, tertian chords are considered voicings of a dyad–for example, the minor dyad with the interval of 25/21 is equivalent to the minor triad 1-25/21-3/2, the minor seventh chord 1-25/21-3/2-25/14, and so on.

If a [[low-complexity JI]]-based perspective is used, there is an absence of low-complexity chords with 3 or more notes that can be practically used. The chord 3:5:7, which is shared with [[Bohlen-Pierce]] and other no-twos systems, is available but it is unwieldy to manage in a 3/2-repeating system, spanning more than twice the equivalence interval of 3/2. Thus, harmony would be largely established using two notes at a time rather than three, using dyads with intervals of [[10/9]], [[25/21]], [[27/20]] or [[7/5]], as well as [[28/27]] or [[15/14]] if extreme tension is permitted. This can be compared to [[2edo]], [[3edo]] and [[4edo]], but with far more sophisticated types of harmonic progression. Note that in a 3/2-repeating system, tertian chords are considered voicings of a dyad–for example, the minor dyad with the interval of 25/21 is equivalent to the minor triad 1-25/21-3/2, the minor seventh chord 1-25/21-3/2-25/14, and so on.

There is however infiitely many high-complexity JI chords contained within half-prime subgroups, as with any just intonation system, with the diminished triad 125:147:175 (1-[[25/21]]-[[7/5]]) being of interest.

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 == Harmony ==
-If a [[low-complexity JI]]-based perspective is used, there is an absence of low-complexity chords with 3 or more notes that can be practically used. The chord 3:5:7, which is shared with [[Bohlen-Pierce]] and other no-twos systems, is available but it is unwieldy to manage in a 3/2-repeating system, spanning more than twice the equivalence interval of 3/2. Thus, harmony would be largely established using two notes at a time rather than three, using dyads with intervals of [[10/9]], [[25/21]], [[27/20]] or [[7/5]], as well as [[28/27]] or [[15/14]] if extreme tension is permitted. This can be compared to [[2edo]], [[3edo]] and 4edo, but with far more sophisticated types of harmonic progression. Note that in a 3/2-repeating system, tertian chords are considered voicings of a dyad–for example, the minor dyad with the interval of 25/21 is equivalent to the minor triad 1-25/21-3/2, the minor seventh chord 1-25/21-3/2-25/14, and so on.
+If a [[low-complexity JI]]-based perspective is used, there is an absence of low-complexity chords with 3 or more notes that can be practically used. The chord 3:5:7, which is shared with [[Bohlen-Pierce]] and other no-twos systems, is available but it is unwieldy to manage in a 3/2-repeating system, spanning more than twice the equivalence interval of 3/2. Thus, harmony would be largely established using two notes at a time rather than three, using dyads with intervals of [[10/9]], [[25/21]], [[27/20]] or [[7/5]], as well as [[28/27]] or [[15/14]] if extreme tension is permitted. This can be compared to [[2edo]], [[3edo]] and [[4edo]], but with far more sophisticated types of harmonic progression. Note that in a 3/2-repeating system, tertian chords are considered voicings of a dyad–for example, the minor dyad with the interval of 25/21 is equivalent to the minor triad 1-25/21-3/2, the minor seventh chord 1-25/21-3/2-25/14, and so on.
 There is however infiitely many high-complexity JI chords contained within half-prime subgroups, as with any just intonation system, with the diminished triad 125:147:175 (1-[[25/21]]-[[7/5]]) being of interest.