Neji

A neji or NEJI (pronounced /nɛdʒi/ "nedgy"; for "near-equal just intonation") is a circulating temperament which approximates an equal tuning dividing a JI equave into JI scale steps. Due to the influence of Zhea Erose who originated the term, neji often specifically refers to a subset of a mode of the harmonic series. The term may also informally be used for a harmonic series approximation of any non-JI scale, e.g. "neji Lydian".

Nemi

A nemi or NEMI (near-equivalent modal intonation) is a circulating temperament which approximates some tempered scale by dividing a JI equave with a subset of a mode of the harmonic series. All NEJIs are also NEMIs, but not all NEMIs are NEJIs.

In the example above, “nemi Lydian” may be a less ambiguous way to describe said scale.

In primodality

In Zhea Erose's primodality theory, nejis can be used to explore a prime family (see primodality), while keeping the transposability, scale structures, rank-2 harmonic theory, notation, etc. associated with that edo. (The neji's denominator need not be prime but primes may be preferred for sake of minimizing lower-complexity intervals. Zhea often uses semiprimes pq.) Zhea Erose's theory also deals with modulations between different prime families, and combining different prime families into one scale.

History

The concept behind neji is probably first proposed by George Secor in 2002, where he called it a quasi-equal rational tuning.

The idea has also been suggested by Paul Erlich and a feature to produce them has existed in Scala for generating them since some time in the 1990's.

Versus detempering

Nejis are distinct from detempering. Unlike detempering, a neji need not imply a mapping. Meanwhile, detempering in general does not require the rational pitch replacements to all be part of the same harmonic series. Nejis are compatible with regular temperament theory if they are treated as working in the concrete tuning layer of temperaments.

Building nejis

It's possible to create a working neji by simply approximating an edo as closely as possible with selected harmonics. However, it is sometimes preferable to build particular aesthetic choices into a neji. One such common choice is to focus on a few intervals in the edo being "nejified" which are of particular interest. The root harmonic is then selected to approximate these intervals of interest as well as possible; the remaining harmonics to fill in the rest of the edo are chosen based on their ability to fit well with the existing notes.

See also

• Overtone scale
• NEJI Tables

External links

• Python script that generates the pareto front of n-tone nejis with given maximum harmonic by Tom Price