Neji: Difference between revisions
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Nejis are a superset of both [[detempering]] and edo nemis. Unlike detempering, a neji or a nemi need not imply a [[mapping]]. | Nejis are a superset of both [[detempering]] and edo nemis. Unlike detempering, a neji or a nemi need not imply a [[mapping]]. | ||
As noted above, nemis entail a specific process of the rational pitch replacements all being selected from a harmonic series mode that is chosen at will by the scale maker. This is not compulsory for detempered edos or nejis in general. | |||
Nejis and nemis are compatible with [[regular temperament theory]] if they are treated as working in the concrete tuning layer of temperaments. | Nejis and nemis are compatible with [[regular temperament theory]] if they are treated as working in the concrete tuning layer of temperaments. | ||
Revision as of 05:30, 25 February 2024
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, in colloquial usage neji often specifically refers to a subset of a mode of the harmonic series used to approximate an edo.
Nemi
A nemi or NEMI (near-equivalent modal intonation) is a scale which approximates some non-JI scale by dividing a JI equave with a subset of a mode of the harmonic series. The term neji may informally be used for nemis, e.g. "neji Lydian".
In primodality
In Zhea Erose's primodality theory, edo nemis 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 edo nemi'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 nemi 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. The term nemi was coined by User:Godtone; it is intended to be more faithful to the usual sense in which the term neji came to be used.
Versus detempering
Nejis are a superset of both detempering and edo nemis. Unlike detempering, a neji or a nemi need not imply a mapping.
As noted above, nemis entail a specific process of the rational pitch replacements all being selected from a harmonic series mode that is chosen at will by the scale maker. This is not compulsory for detempered edos or nejis in general.
Nejis and nemis are compatible with regular temperament theory if they are treated as working in the concrete tuning layer of temperaments.
Building edo nemis
It's possible to create a working edo nemi by simply approximating an edo as closely as possible with selected harmonics. However, it is sometimes preferable to build particular aesthetic choices into a nemi. One such common choice is to focus on a few intervals in the edo being "nemified" 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.