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| Mode 30 in particular is interesting because 30 is the product of the first three primes, so it's a fairly good choice if we want a tonic that isn't a power of two. It contains modes 6 and 10 as subsets. We have the classic minor triad (from 10), the subminor triad (from 6), two major triads in 30:37:45 and 30:38:45, and the Barbados triad of 30:39:45. Chords not based on the tonic include the harmonic seventh chord (32:40:48:56). A good 13-limit subset with 16 notes in it is 30:32:33:35:36:39:40:42:44:45:48:49:50:54:55:56:60. | | Mode 30 in particular is interesting because 30 is the product of the first three primes, so it's a fairly good choice if we want a tonic that isn't a power of two. It contains modes 6 and 10 as subsets. We have the classic minor triad (from 10), the subminor triad (from 6), two major triads in 30:37:45 and 30:38:45, and the Barbados triad of 30:39:45. Chords not based on the tonic include the harmonic seventh chord (32:40:48:56). A good 13-limit subset with 16 notes in it is 30:32:33:35:36:39:40:42:44:45:48:49:50:54:55:56:60. |
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| == Primodality==
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| [[Zhea Erose]] has considered over-p scales and chords where p is a prime, which she calls '''primodal scales'''. '''Primodality''' (also informally called '''Zheanism''') is an approach to JI designed to emphasize the identity of the "tonic" as the pth harmonic and places importance on the particular timbre of chords with a given tonic. Scales and chords having the identity of the prime p as the tonic are collectively called a '''prime family''', and can be denoted simply by ''/p''. Zhea also uses various adjectives for specific primodalities, such as ''septimal, undecimal, tridecimal, septendecimal, novem(decimal)'' for /7, /11, /13, /17, /19, which are not to be confused with the use of these adjectives to denote prime limits.
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| Most importantly, primodality sees any overtone as valuable on its own, rather than relative to some fundamental. Taking a specific overtone as a tonic we can get its particular scales and colors and even versions of "non-xenharmonic" scales, even when the corresponding fundamental is too low to be audible. In particular, primodality discards the concept of [[harmonic limit]], which Zhea considers an artificial way to look at JI harmony. Zhea argues that prime families are a more natural way to categorize intervals; intervals from the same prime family (intervals with a common denominator for example, all /2, all /11 or all /13) tend to blend better together. For example, it is preferable to add 21/16 to 4:5:6:7, rather than 4/3.
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| To construct a primodal scale, we fix a prime p to be the denominator and take intervals of the form n/p, where n ≥ p. Zhea often takes n to range over a certain "lineal segment" (Mode mp of the harmonic series where m is a positive integer) or a subset thereof.. For example, if we use p = 13 and take all n between 13 and 26 (inclusive), this would result in the scale 13:14:15:16:17:18:19:20:21:22:23:24:25:26. We may add a 3/2 to the scale root, which corresponds to adding 3p/p. (3/2 is a natural "halfway point" for harmonic scales, since if N is even, Mode N has a 3/2 as its N/2-th note.)
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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}.
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| === Neji ===
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| A '''neji''' (pronounced /nɛdʒi/ "nedgy"; for "near-equal JI") is an overtone series approximation of an [[EDO]].
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| Nejis can be used to explore a prime family, while keeping the transposability, scale structures, rank-2 harmonic theory, notation, etc. associated with that edo. (The neji's denominator need not be prime.)
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| Zhea Erose's theory also deals with modulations between different prime families, and combining different prime families into one scale.
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| === Music ===
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| *[https://youtu.be/ZIn6uis5duw Zhea Erose - Novemdeca (in a 12-note 19-primodal scale)]
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| *[https://youtu.be/ZSUdXVI0tO0 Zhea Erose - Pandelia (in 2*17-primodal + 3/2)]
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| *[https://youtu.be/KpiOqPr4m9M benyamind - A Story (in the Novemdeca tuning)]
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| === See also ===
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| * '''[[Primodal Archive]]''': Zhea's chord archive
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| * [[Oneirotonic#Primodal theory]]: An attempt to apply Zhea's theory to oneirotonic ([[5L 3s]] MOS) and its MODMOSes.
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| == A Solfege System == | | == A Solfege System == |