# Primodality

Primodality (also informally called Zheanism after its originator Zhea Erose) 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. (If disambiguation is needed, one can say over-7 and 7-limit respectively for the two meanings of septimal, for instance.) Zhea's ideas are new in that she not only treats higher JI as different from close irrational tunings (as some, like Johnny Reinhard, previously have done), but also claims that each prime comes with its own unique timbral "gestalt" which is in all chords built from small multiples of p (particularly 2p) as the tonic. The gestalt aspect is critical: while individual dyads in a primodal tuning may not be recognizable for what they are (using methods like harmonic entropy), when considered as a whole, their shared relationship to /p becomes apparent.

Most importantly, primodality sees any overtone as valuable on its own, rather than relative to some fundamental. Taking a specific overtone as a tonic, even "non-xenharmonic" scales are said to gain the gestalt identity particular to the overtone, 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.

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.)

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 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 higher harmonic tuning leverages JI instead for the "harmonic cloud" effect of a shared very low (sometimes infrasonic) fundamental.

## Neji

Primodality is often used in combination with another Zhea Erose technique: neji (or Near-Equal Just Intonation) tunings, which can be used to preserve the primodal aspects while producing tunings with the benefit of near-equal intervals.