Neji: Difference between revisions

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==== Harmodal vs non-harmodal nejis ====

If the neji belongs to a "relatively not large" harmonic segment, and has a [[period]] equal to some positive integer harmonic (like the [[octave]], [[tritave]] or [[pentave]]), it is a "harmodal neji" (a contraction of "[[Harmonic mode|harmonic modal]] neji"). An octave is the most often used period.

If the neji belongs to a ''relatively not large'' harmonic segment, and has a [[period]] equal to some positive integer harmonic (like the [[octave]], [[tritave]] or [[pentave]]), it is a "harmodal neji" (a contraction of "[[Harmonic mode|harmonic modal]] neji"). An octave is the most often used period.

When the term "neji" is used, it is automatically assumed to be referring to a harmodal neji unless stated otherwise, in the same way that when "equal division" is used, it is assumed to be referring to "equal pitch division" unless otherwise stated. (That’s why there is no p in ~~edo~~, but there is an f in ~~afdo~~). So, if a neji is harmodal, this is not usually explicitly stated. It is assumed.

When the term "neji" is used, it is automatically assumed to be referring to a harmodal neji unless stated otherwise, in the same way that when "equal division" is used, it is assumed to be referring to "equal pitch division" unless otherwise stated. (That’s why there is no P in EDO, but there is an F in AFDO). So, if a neji is harmodal, this is not usually explicitly stated. It is assumed.

If a neji ~~belongs~~ to a "relatively large~~" and/or non~~-~~periodic~~ harmonic segment, then it is a "non-harmodal neji". In this case, it is advisable to explicitly name non-harmodal nejis as such, seeing as they are the exception rather than the rule.

If a neji does not belong to a ''relatively not large'', period-repeating harmonic segment, then it is a "non-harmodal neji". In this case, it is advisable to explicitly name non-harmodal nejis as such, seeing as they are the exception rather than the rule.

=== Detempering ===

A more ([[JI subgroup]]) lattice-based approach is [[detempering]]. Detempering entails that the neji has the property of being [[epimorphic]] (obeys the appropriate mapping logic) with respect to a [[regular temperament]] for a tempered scale, equal-division or otherwise.

Importantly and nontrivially, detempering is stricter than merely requiring that the target scale ''has'' a scale logic (that is, a [[mapping]]), as many nejis may approximate the target scale without following its associated mapping. Only if a neji ''obeys'' the mapping, is it a detempering.

Importantly and nontrivially, detempering is stricter than merely requiring that the target scale has a ''scale logic'' (that is, a ''[[mapping]]''), as many nejis may approximate the target scale without following its associated mapping. Only if a neji obeys the mapping, is it a detempering.

=== Building edo nejis ===

@@ Line 29: / Line 29: @@
 ==== Harmodal vs non-harmodal nejis ====
-If the neji belongs to a "relatively not large" harmonic segment, and has a [[period]] equal to some positive integer harmonic (like the [[octave]], [[tritave]] or [[pentave]]), it is a "harmodal neji" (a contraction of "[[Harmonic mode|harmonic modal]] neji"). An octave is the most often used period.
+If the neji belongs to a ''relatively not large'' harmonic segment, and has a [[period]] equal to some positive integer harmonic (like the [[octave]], [[tritave]] or [[pentave]]), it is a "harmodal neji" (a contraction of "[[Harmonic mode|harmonic modal]] neji"). An octave is the most often used period.
-When the term "neji" is used, it is automatically assumed to be referring to a harmodal neji unless stated otherwise, in the same way that when "equal division" is used, it is assumed to be referring to "equal pitch division" unless otherwise stated. (That’s why there is no p in edo, but there is an f in afdo). So, if a neji is harmodal, this is not usually explicitly stated. It is assumed.
+When the term "neji" is used, it is automatically assumed to be referring to a harmodal neji unless stated otherwise, in the same way that when "equal division" is used, it is assumed to be referring to "equal pitch division" unless otherwise stated. (That’s why there is no P in EDO, but there is an F in AFDO). So, if a neji is harmodal, this is not usually explicitly stated. It is assumed.
-If a neji belongs to a "relatively large" and/or non-periodic harmonic segment, then it is a "non-harmodal neji". In this case, it is advisable to explicitly name non-harmodal nejis as such, seeing as they are the exception rather than the rule.
+If a neji does not belong to a ''relatively not large'', period-repeating harmonic segment, then it is a "non-harmodal neji". In this case, it is advisable to explicitly name non-harmodal nejis as such, seeing as they are the exception rather than the rule.
 === Detempering ===
 A more ([[JI subgroup]]) lattice-based approach is [[detempering]]. Detempering entails that the neji has the property of being [[epimorphic]] (obeys the appropriate mapping logic) with respect to a [[regular temperament]] for a tempered scale, equal-division or otherwise.
-Importantly and nontrivially, detempering is stricter than merely requiring that the target scale ''has'' a scale logic (that is, a [[mapping]]), as many nejis may approximate the target scale without following its associated mapping. Only if a neji ''obeys'' the mapping, is it a detempering.
+Importantly and nontrivially, detempering is stricter than merely requiring that the target scale has a ''scale logic'' (that is, a ''[[mapping]]''), as many nejis may approximate the target scale without following its associated mapping. Only if a neji obeys the mapping, is it a detempering.
 === Building edo nejis ===