Primodality: Difference between revisions
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Primodality, and Zhea's microtonal theory overall, emphasize subtle timbral effects, as opposed to lower-complexity JI identities such as 4:5:6:7:9 that are more common in composite modes. Mode p and Mode 2p (called respectively the ''first'' and ''second octaves of /p'') are considered the most important for the identity of /p; those intervals are the most recognizable as distinct identities. For any prime p, the set of harmonics from p to 2p is unique in the sense that the sets {p/p, ..., 2p/p} and {n/n, ..., 2n/n} only intersect at {1/1, 2/1} for any positive integer n < p. Similarly, the second octaves of p and the second octave of any n < p only intersect at {1/1, 3/2, 2/1}. | Primodality, and Zhea's microtonal theory overall, emphasize subtle timbral effects, as opposed to lower-complexity JI identities such as 4:5:6:7:9 that are more common in composite modes. Mode p and Mode 2p (called respectively the ''first'' and ''second octaves of /p'') are considered the most important for the identity of /p; those intervals are the most recognizable as distinct identities. For any prime p, the set of harmonics from p to 2p is unique in the sense that the sets {p/p, ..., 2p/p} and {n/n, ..., 2n/n} only intersect at {1/1, 2/1} for any positive integer n < p. Similarly, the second octaves of p and the second octave of any n < p only intersect at {1/1, 3/2, 2/1}. | ||
Primodality could be understood as the use of ''prime'' [[Overtone scale|modes of the harmonic series]] (hence "prime" + "mode" + "-ality") which is of musical interest because using a prime as the mode maximizes irreducible intervals; and as an additional step away from the exhibition of obvious low-limit JI intervals, primodality suggests the use of very ''large'' modes of the harmonic series (or subsets thereof), which as in [[8th Octave Overtone Tuning|higher harmonic tuning]] leverages JI instead for the "harmonic cloud" effect of a shared very low (sometimes infrasonic) fundamental. | |||
== Neji == | == Neji == | ||