Neji: Difference between revisions
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=== Detempering === | === Detempering === | ||
A more structural, lattice-based approach is [[detempering]]. Detempering entails that the neji has the property of being [[epimorphic]] (obeys a mapping logic under some val) with respect to a temperament for a tempered scale, equal-division or otherwise. | A more structural, ([[JI subgroup]]) lattice-based approach is [[detempering]]. Detempering entails that the neji has the property of being [[epimorphic]] (obeys a mapping logic under some val) with respect to a temperament for a tempered scale, equal-division or otherwise. | ||
=== As harmonic segment subsets === | === As harmonic segment subsets === | ||
Revision as of 23:46, 25 February 2024
A neji or NEJI (pronounced /nɛdʒi/ "nedgy"; for "near-equal/equivalent just intonation") is a JI scale that approximates a given (usually non-JI) scale by dividing a JI equave into JI scale steps. A neji that approximates an edo is thus a circulating temperament for that edo.
History
The concept behind nejis is probably first proposed by George Secor in 2002[1], 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.
The term neji was coined by Zhea Erose.
Approaches to neji construction
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.
Detempering
A more structural, (JI subgroup) lattice-based approach is detempering. Detempering entails that the neji has the property of being epimorphic (obeys a mapping logic under some val) with respect to a temperament for a tempered scale, equal-division or otherwise.
As harmonic segment subsets
One might choose a low harmonic series segment (spanning the appropriate JI equave) and select notes therefrom in order to build a neji with extra concordance.
This distinction is more process-based than formalized, in that the pool of intervals is chosen to be a specific harmonic series segment, before notes are selected from it. This is because any JI scale occurs as some (possibly very high) harmonic series segment.
Building edo nejis
It's possible to create a working edo neji by simply approximating an edo as closely as possible with selected harmonics from a mode. However, it is sometimes preferable to build particular aesthetic choices into such 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.