Neji - Revision history

VectorGraphics: "en ee jay eye"

2025-03-27T04:01:53Z

"en ee jay eye"

← Older revision		Revision as of 04:01, 27 March 2025
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	A '''neji''' or '''NEJI''' (pronounced /nɛdʒi/ "nedgy"; for "near-equivalent [[just intonation]]" or "near-equal 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.		A '''neji''' or '''NEJI''' (which can be pronounced /nɛdʒi/ "nedgy"; for "near-equivalent [[just intonation]]" or "near-equal 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 ==		== History ==

ArrowHead294: /* See also */

2024-11-27T14:16:01Z

BudjarnLambeth: /* See also */ add link to ringer scale

2024-11-05T18:21:01Z

BudjarnLambeth at 07:33, 18 September 2024

2024-09-18T07:33:21Z

← Older revision		Revision as of 07:33, 18 September 2024
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	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.		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.

	=== Near-equal vs near-equivalent ===		== Near-equal vs near-equivalent ==
	The term "near-equal just intonation" may refer specifically to nejis where the target scale is an [[equal-step tuning]] (i.e. the notes of the neji are near-equally spaced), or it may refer to any and all nejis (i.e. the neji's step sizes are nearly equal to the target scale's step sizes). Both uses of the term are acceptable.		The term "near-equal just intonation" may refer specifically to nejis where the target scale is an [[equal-step tuning]] (i.e. the notes of the neji are near-equally spaced), or it may refer to any and all nejis (i.e. the neji's step sizes are nearly equal to the target scale's step sizes). Both uses of the term are acceptable.

BudjarnLambeth: Added near-equal just intonation as one of the name options, and added a section explaining meanings of the names.

2024-09-18T07:32:56Z

Added near-equal just intonation as one of the name options, and added a section explaining meanings of the names.

← Older revision		Revision as of 07:32, 18 September 2024
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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). 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.		A '''neji''' or '''NEJI''' (pronounced /nɛdʒi/ "nedgy"; for "near-equivalent [[just intonation]]" or "near-equal 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 ==		== History ==
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	=== Building edo nejis ===		=== 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.		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.

			=== Near-equal vs near-equivalent ===
			The term "near-equal just intonation" may refer specifically to nejis where the target scale is an [[equal-step tuning]] (i.e. the notes of the neji are near-equally spaced), or it may refer to any and all nejis (i.e. the neji's step sizes are nearly equal to the target scale's step sizes). Both uses of the term are acceptable.

			The term "near-equivalent just intonation" refers to any and all nejis. It is interchangeable with the second reading of "near-equal".

	== See also ==		== See also ==

BudjarnLambeth: /* Detempering */

2024-03-01T04:48:30Z

Detempering

← Older revision		Revision as of 04:48, 1 March 2024
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	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.		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]]). Even in those cases ~~when~~ the target scale has a mapping, a neji ~~may~~ approximate it without following its associated mapping. A detempering, however, must ''follow'' the mapping.		Importantly and nontrivially, detempering is stricter than merely requiring that the target scale ''has'' a scale logic (that is, a [[mapping]]). Even in those cases where the target scale has a mapping, a neji might still approximate it without following its associated mapping. A detempering, however, must ''follow'' the mapping.

	=== Building edo nejis ===		=== Building edo nejis ===

BudjarnLambeth: /* Detempering */

2024-03-01T04:47:56Z

Detempering

← Older revision		Revision as of 04:47, 1 March 2024
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	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.		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]]). Even if the target scale has a mapping, a neji may approximate it without following its associated mapping. A detempering, however, must ''follow'' the mapping.		Importantly and nontrivially, detempering is stricter than merely requiring that the target scale ''has'' a scale logic (that is, a [[mapping]]). Even in those cases when the target scale has a mapping, a neji may approximate it without following its associated mapping. A detempering, however, must ''follow'' the mapping.

	=== Building edo nejis ===		=== Building edo nejis ===

BudjarnLambeth: /* Detempering */ Focused on just the “detempering” section only, since I’m already happy with how the rest of the page looks and I’m happy to leave it well enough alone. Put the emphasis on “has” instead of “scale logic”, because “has” vs “follows” is the important distinction the reader’s eye needs to be drawn to, not “scale logic” vs “scale logic”. Removed the exclamation mark because the sentence it ends does not need such intense emphasis.

2024-03-01T04:42:38Z

Detempering: Focused on just the “detempering” section only, since I’m already happy with how the rest of the page looks and I’m happy to leave it well enough alone. Put the emphasis on “has” instead of “scale logic”, because “has” vs “follows” is the important distinction the reader’s eye needs to be drawn to, not “scale logic” vs “scale logic”. Removed the exclamation mark because the sentence it ends does not need such intense emphasis.

← Older revision		Revision as of 04:42, 1 March 2024
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	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.		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~~! (And as aforementioned~~, ~~the target scale is not~~ ''~~required~~'' ~~to have a~~ mapping~~, although in many cases it does~~.)		Importantly and nontrivially, detempering is stricter than merely requiring that the target scale ''has'' a scale logic (that is, a [[mapping]]). Even if the target scale has a mapping, a neji may approximate it without following its associated mapping. A detempering, however, must ''follow'' the mapping.

	=== Building edo nejis ===		=== Building edo nejis ===

Godtone: the example used is somewhat confusing; "equal division of the octave" conveys the same information as if you added "pitch"; rather it's the way in which you divide the pitch that is of importance. also the term "target scale" for example is important in understanding the nature of the construction

2024-02-29T18:01:33Z

the example used is somewhat confusing; "equal division of the octave" conveys the same information as if you added "pitch"; rather it's the way in which you divide the pitch that is of importance. also the term "target scale" for example is important in understanding the nature of the construction

← Older revision		Revision as of 18:01, 29 February 2024
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	}}		}}
	A '''neji''' or '''NEJI''' (pronounced /nɛdʒi/ "nedgy"; for "near-equivalent [[just intonation]]~~" or "near-equal 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.		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 ==		== History ==
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	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, 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 ==		== Approaches to neji construction ==

	=== In primodality ===		=== 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 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 and maximizing unique ones specific to that prime. 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 and maximizing unique ones specific to that prime. 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 harmonic segment subsets ===		=== As harmonic segment subsets ===
	Generalizing from the primodal use case of the term "neji", one might choose any relatively low [[Glossary#H\|harmonic series segment]], not necessarily in a way associated with primodality, and select notes therefrom in order to build a neji with extra [[concordance]].		Generalizing from the primodal use case of the term "neji", one might choose any relatively low [[Glossary#H\|harmonic series segment]], ''not necessarily in a way associated with primodality'', 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:		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:

	: If you focus on choosing intervals as representing different notes of your target ''without regard'' for the growing size of the implied denominator of the scale as a single chord, then the denominator will often grow ''rapidly'' to absurd numbers, ''especially'' if you are repeatedly stacking the same interval to reach some of the notes.		: If you focus on choosing intervals as representing different notes of your target ''without regard'' for the growing size of the implied denominator of the scale as a single chord, then the denominator will often grow ''rapidly'' to absurd numbers, ''especially'' if you are repeatedly stacking the same interval to reach some of the notes.

	Technically, this is a simplification of the observation, as you can take any incomplete harmodal neji and add some intervals that are "awkward" w.r.t the denominator to complete it and thus increase the denominator massively, but the scale will overall likely still sound pretty coherent, especially if those intervals simplify w.r.t other intervals of interest to the composer, so it is rather the spirit of the observation that your notes of interest should cohere with each-other within reason and that where they don't should ideally be intentional harmonic tensions in the scale accessible for musical use. This logic also shows why the line between [[neji]]s (in the general sense) and '''harmodal nejis''' (defined below) is even more "fuzzy" than one might initially think.		Technically, this is a simplification of the observation, as you can take any incomplete harmodal neji and add some intervals that are "awkward" w.r.t the denominator to complete it and thus increase the denominator massively, but the scale will overall likely still sound pretty coherent, ''especially'' if those intervals simplify w.r.t other intervals of interest to the composer, so it is rather the spirit of the observation that your notes of interest should cohere with each-other within reason and that where they don't should ideally be intentional harmonic tensions in the scale accessible for musical use. This logic also shows why the line between [[neji]]s (in the general sense) and '''harmodal nejis''' (defined below) is even more "fuzzy" than one might initially think.

	~~==== 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.

	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 ~~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~~.		==== Harmodal nejis ====
			If the neji belongs to a (''relatively not large'') harmonic segment and the target scale 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"), meaning primodal nejis are a type of harmodal neji. This period is typically an octave, as that's the most common use case. This term has found use before by Zhea but it should be noted it was proposed as a standard way to resolve an ambiguity in the meaning of the stand-alone term "neji", therefore please see the directly below alternative, which may be preferred for consistency/backwards-compatibility.
			==== Nonharmodal nejis ====
			An alternative to using the term "harmodal nejis" is to ''assume'' that a "neji" is harmodal ''by default'', and instead specify that a neji is "''nonharmodal''" only when necessary, in order to preserve the colloquial usage of the term "neji". This is consistent with the sentiment that there does not need to be a new term "harmodal neji", while retaining clarity.

	=== Detempering ===		=== 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.		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! (And as aforementioned, the target scale is not ''required'' to have a mapping, although in many cases it does.)

	=== Building edo nejis ===		=== Building edo nejis ===

Godtone: this edit decreases clarity and inserts unnecessary quotes where italicization is sufficient for emphasis. the example used is somewhat confusing; "equal division of the octave" conveys the same information as if you added "pitch"; rather it's the way in which you divide the pitch that is of importance

2024-02-29T17:33:06Z

this edit decreases clarity and inserts unnecessary quotes where italicization is sufficient for emphasis. the example used is somewhat confusing; "equal division of the octave" conveys the same information as if you added "pitch"; rather it's the way in which you divide the pitch that is of importance

← Older revision		Revision as of 17:33, 29 February 2024
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	==== Harmodal vs non-harmodal nejis ====		==== 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 ===		=== 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.		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 ===		=== Building edo nejis ===

← Older revision		Revision as of 14:16, 27 November 2024
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	== See also ==		== See also ==
	* [[Overtone scale]]		* [[Overtone scale]]
	* [[NEJI ~~Tables~~]]		* [[NEJI tables]]
	* [[Ringer scale]]		* [[Ringer scale]]

← Older revision		Revision as of 18:21, 5 November 2024
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	* [[Overtone scale]]		* [[Overtone scale]]
	* [[NEJI Tables]]		* [[NEJI Tables]]
			* [[Ringer scale]]

	== Notes ==		== Notes ==