Overtone scale: Difference between revisions
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Primodality emphasizes unique characters of primes, 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 prime's identity: 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 emphasizes unique characters of primes, 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 prime's identity: 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}. | ||
Approximations of [[edo]]s in certain primodalities, called ''nejis'' ("near-equal JI"), can be used to explore a prime family, while keeping the transposability, scale structures, rank-2 harmonic theory, etc. associated with that edo. | Approximations of [[edo]]s in certain primodalities, called ''nejis'' ("near-equal JI"), can be used to explore a prime family, while keeping the transposability, scale structures, rank-2 harmonic theory, notation, etc. associated with that edo. | ||
Zhea Erose's theory also deals with modulations between different prime families, and combining different prime families into one scale. | Zhea Erose's theory also deals with modulations between different prime families, and combining different prime families into one scale. | ||