Neji: Difference between revisions

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A '''neji''' or '''NEJI''' (pronounced /nɛdʒi/ "nedgy"; for "near-equal [[just intonation]]") is a ~~[[circulating temperament]] which~~ approximates ~~an [[Equal~~-~~step tuning|equal tuning]]~~ dividing a JI [[equave]] into JI scale steps.

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.

~~Due to the influence of Zhea Erose who originated the term, in colloquial usage ''~~neji~~'' often specifically refers to a subset of a chosen mode of the [[harmonic series]] used to approximate~~ an edo or another non-JI scale. To express this sense more literally, the following term has been coined: 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 chosen beforehand. The term ''neji'' may informally be used for nemis, e.g. "neji Lydian".

~~Nejis and nemis are both defined via intention rather than (wholly) via mathematical definition. For both nejis and nemis, "near-equal/equivalent" is fuzzy; for nemis, any periodic JI scale~~ is a ~~subset of some (possibly very high) harmonic series segment, making "subset of some harmonic segment" mathematically trivial.~~

~~== 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<ref>[http://www.anaphoria.com/secor-blarney.html GEORGE SECOR - A BIT O' BLARNEY]</ref>, where he called it a '''quasi-equal rational tuning'''.

The concept behind nejis is probably first proposed by [[George Secor]] in 2002<ref>[http://www.anaphoria.com/secor-blarney.html GEORGE SECOR - A BIT O' BLARNEY]</ref>, 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~~.

The term ''neji'' was coined by Zhea Erose.

== ~~Versus detempering~~ ==

== Approaches to neji construction ==

~~Nejis are~~ a ~~superset of both~~ [[~~detempering~~]] ~~and~~ edo ~~nemis~~. ~~Unlike detempering, a~~ neji ~~or a nemi~~ need not ~~imply a [[mapping]]~~.

=== 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.

~~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~~.

=== 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.

~~Nejis~~ and ~~nemis are compatible~~ with ~~[[regular temperament theory]] if they are treated~~ as ~~working in the concrete tuning layer of temperaments~~.

=== Harmodal nejis ===

One might choose a low harmonic series mode and selecg notes therefrom in order to build an edo neji with extra concordance. Such a neji can be described as a "harmodal neji", from "harmonic mode".

== Building edo ~~nemis~~ ==

This distinction is more process-based than formalized, in that the pool of intervals is chosen to be some mode m::2m, before notes are selected from it. This is hecause any JI scale occurs as some (possibly very high) harmonic series segment.

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.

=== Building edo nejis ===

It's possible to create a working harmodal 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.

== See also ==

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-A '''neji''' or '''NEJI''' (pronounced /nɛdʒi/ "nedgy"; for "near-equal [[just intonation]]") is a [[circulating temperament]] which approximates an [[Equal-step tuning|equal tuning]] dividing a JI [[equave]] into JI scale steps.
+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.
-Due to the influence of Zhea Erose who originated the term, in colloquial usage ''neji'' often specifically refers to a subset of a chosen mode of the [[harmonic series]] used to approximate an edo or another non-JI scale. To express this sense more literally, the following term has been coined: 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 chosen beforehand. The term ''neji'' may informally be used for nemis, e.g. "neji Lydian".
-Nejis and nemis are both defined via intention rather than (wholly) via mathematical definition. For both nejis and nemis, "near-equal/equivalent" is fuzzy; for nemis, any periodic JI scale is a subset of some (possibly very high) harmonic series segment, making "subset of some harmonic segment" mathematically trivial.
-== 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<ref>[http://www.anaphoria.com/secor-blarney.html GEORGE SECOR - A BIT O' BLARNEY]</ref>, where he called it a '''quasi-equal rational tuning'''.
+The concept behind nejis is probably first proposed by [[George Secor]] in 2002<ref>[http://www.anaphoria.com/secor-blarney.html GEORGE SECOR - A BIT O' BLARNEY]</ref>, 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.
+The term ''neji'' was coined by Zhea Erose.
-== Versus detempering ==
+== Approaches to neji construction ==
-Nejis are a superset of both [[detempering]] and edo nemis. Unlike detempering, a neji or a nemi need not imply a [[mapping]].
+=== 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.
-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.
+=== 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.
-Nejis and nemis are compatible with [[regular temperament theory]] if they are treated as working in the concrete tuning layer of temperaments.
+=== Harmodal nejis ===
+One might choose a low harmonic series mode and selecg notes therefrom in order to build an edo neji with extra concordance. Such a neji can be described as a "harmodal neji", from "harmonic mode".
-== Building edo nemis ==
+This distinction is more process-based than formalized, in that the pool of intervals is chosen to be some mode m::2m, before notes are selected from it. This is hecause any JI scale occurs as some (possibly very high) harmonic series segment.
-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.
+=== Building edo nejis ===
+It's possible to create a working harmodal 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.
 == See also ==