Half-prime subgroup: Difference between revisions

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== Harmony ==

If a [[low-complexity JI]]-based perspective is used, then harmony would be largely established using 2 notes at a time rather than three, with an absence of low-complexity triads 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 fifth-repeating system, spanning more than 2 fifths. It may be considered to use to use [[dyad]]s of [[10/9]], [[27/20]] or [[7/5]], or the 12edo-like minor and major thirds [[25/21]] and [[63/50]]. Note that in a fifth-repeating system, the dyad 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, then harmony would be largely established using 2 notes at a time rather than three, with an absence of low-complexity triads 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 fifth-repeating system, spanning more than 2 fifths. It may be considered to use to use [[dyad]]s of [[10/9]], [[27/20]], [[7/5]], or the 12edo-like minor and major thirds [[25/21]] and [[63/50]]. Note that in a fifth-repeating system, the dyad 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 an abundance of high-complexity JI chords contained within half-prime subgroups, as with any just intonation system, like 45:50:63 (1-10/9-7/5), or the diminished triad 105:125:147 (1-25/21-7/5) which is made symmetric in EDF systems where the hemimage comma is tempered out.

[[Category:Subgroup]]

[[Category:Just intonation]]

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 == Harmony ==
-If a [[low-complexity JI]]-based perspective is used, then harmony would be largely established using 2 notes at a time rather than three, with an absence of low-complexity triads 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 fifth-repeating system, spanning more than 2 fifths. It may be considered to use to use [[dyad]]s of [[10/9]], [[27/20]] or [[7/5]], or the 12edo-like minor and major thirds [[25/21]] and [[63/50]]. Note that in a fifth-repeating system, the dyad 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, then harmony would be largely established using 2 notes at a time rather than three, with an absence of low-complexity triads 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 fifth-repeating system, spanning more than 2 fifths. It may be considered to use to use [[dyad]]s of [[10/9]], [[27/20]], [[7/5]], or the 12edo-like minor and major thirds [[25/21]] and [[63/50]]. Note that in a fifth-repeating system, the dyad 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 an abundance of high-complexity JI chords contained within half-prime subgroups, as with any just intonation system, like 45:50:63 (1-10/9-7/5), or the diminished triad 105:125:147 (1-25/21-7/5) which is made symmetric in EDF systems where the hemimage comma is tempered out.
 [[Category:Subgroup]]
 [[Category:Just intonation]]