Neji: Difference between revisions

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A '''neji''' or '''NEJI''' (pronounced /nɛdʒi/ "nedgy"; for "near-equivalent [[just intonation]]") is a [[JI]] scale that is "nearly-equivalent" to an associated ''target scale'' (or ''target'' for short). ~~This target is often (but not always!) equipped with a ''scale logic'' (that is, a [[mapping]]); ''in that case only'', a neji is a type of [[detempering]].~~ Nejis are designed with a focus on the harmonic resonance of the pitches in mind w.r.t their foreseen musical use. If the target scale is an [[edo]], a neji is ~~therefore~~ technically also a type of [[well temperament]] for that edo.

A '''neji''' or '''NEJI''' (pronounced /nɛdʒi/ "nedgy"; for "near-equivalent [[just intonation]]") is a [[JI]] scale that is "nearly-equivalent" to an associated ''target scale'' (or ''target'' for short). Nejis are designed with a focus on the harmonic resonance of the pitches in mind w.r.t their foreseen musical use. If the target scale is an [[edo]], a neji is technically also a type of [[well temperament]] for that edo.

== History ==

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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 ''neji'' was coined by [[Zhea Erose]].

Due to the influence of Zhea Erose who originated the term~~, in colloquial usage~~, the term "neji" has often been used in connection with naming [[#Harmodal nejis|harmodal nejis]] specifically, with other types of nejis being less common.

Due to the influence of Zhea Erose who originated the term, the term "neji" has often been used in connection with naming [[#Harmodal nejis|harmodal nejis]] specifically, with other types of nejis being less common.

== 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.

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 the target scale (usually an [[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 ===

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=== As harmonic segment subsets ===

One might choose a low harmonic series segment and select notes therefrom in order to build a neji with extra concordance.

One might choose a low harmonic series segment and select notes therefrom in order to build a neji with extra [[concordance]].

This distinction is more process-based than formalized (because any JI scale trivially occurs as some (possibly very high) harmonic series segment subset); sometimes the pool of intervals is chosen to be a specific "relatively not large" harmonic series segment before notes are selected from it while other times it is guessed at in some "relatively not large" range and then later revised based on what fits (or other considerations). The "relatively not large" focuses on the following key observation of Zhea's that others have agreed with as a valuable observation in the design of JI scales:

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==== Harmodal nejis ====

If the target scale has a [[period]] equal to some positive integer harmonic (like the [[octave]], [[tritave]] or [[pentave]]), a fitting name for this type of neji is a "harmodal neji", a contraction of "harmonic modal neji". ~~By default, this refers to a~~ period of an octave, as that's the most common usecase.

:If the target scale has a [[period]] equal to some positive integer harmonic (like the [[octave]], [[tritave]] or [[pentave]]), a fitting name for this type of neji is a "harmodal neji", a contraction of "harmonic modal neji". This period is typically an octave, as that's the most common usecase.

=== Building edo nejis ===

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-A '''neji''' or '''NEJI''' (pronounced /nɛdʒi/ "nedgy"; for "near-equivalent [[just intonation]]") is a [[JI]] scale that is "nearly-equivalent" to an associated ''target scale'' (or ''target'' for short). This target is often (but not always!) equipped with a ''scale logic'' (that is, a [[mapping]]); ''in that case only'', a neji is a type of [[detempering]]. Nejis are designed with a focus on the harmonic resonance of the pitches in mind w.r.t their foreseen musical use. If the target scale is an [[edo]], a neji is therefore technically also a type of [[well temperament]] for that edo.
+A '''neji''' or '''NEJI''' (pronounced /nɛdʒi/ "nedgy"; for "near-equivalent [[just intonation]]") is a [[JI]] scale that is "nearly-equivalent" to an associated ''target scale'' (or ''target'' for short).  Nejis are designed with a focus on the harmonic resonance of the pitches in mind w.r.t their foreseen musical use. If the target scale is an [[edo]], a neji is technically also a type of [[well temperament]] for that edo.
 == History ==
@@ Line 12: / Line 12: @@
 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 ''neji'' was coined by [[Zhea Erose]].
-Due to the influence of Zhea Erose who originated the term, in colloquial usage, the term "neji" has often been used in connection with naming [[#Harmodal nejis|harmodal nejis]] specifically, with other types of nejis being less common.
+Due to the influence of Zhea Erose who originated the term, the term "neji" has often been used in connection with naming [[#Harmodal nejis|harmodal nejis]] specifically, with other types of nejis being less common.
 == 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.
+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 the target scale (usually an [[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 ===
@@ Line 24: / Line 24: @@
 === As harmonic segment subsets ===
-One might choose a low harmonic series segment and select notes therefrom in order to build a neji with extra concordance.
+One might choose a low harmonic series segment and select notes therefrom in order to build a neji with extra [[concordance]].
 This distinction is more process-based than formalized (because any JI scale trivially occurs as some (possibly very high) harmonic series segment subset); sometimes the pool of intervals is chosen to be a specific "relatively not large" harmonic series segment before notes are selected from it while other times it is guessed at in some "relatively not large" range and then later revised based on what fits (or other considerations). The "relatively not large" focuses on the following key observation of Zhea's that others have agreed with as a valuable observation in the design of JI scales:
@@ Line 33: / Line 33: @@
 ==== Harmodal nejis ====
-If the target scale has a [[period]] equal to some positive integer harmonic (like the [[octave]], [[tritave]] or [[pentave]]), a fitting name for this type of neji is a "harmodal neji", a contraction of "harmonic modal neji". By default, this refers to a period of an octave, as that's the most common usecase.
+:If the target scale has a [[period]] equal to some positive integer harmonic (like the [[octave]], [[tritave]] or [[pentave]]), a fitting name for this type of neji is a "harmodal neji", a contraction of "harmonic modal neji". This period is typically an octave, as that's the most common usecase.
 === Building edo nejis ===