Neji: Difference between revisions
→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. |
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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''' (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 == | ||
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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 | 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 === | ||
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 == | ||
* [[Overtone scale]] | * [[Overtone scale]] | ||
* [[NEJI | * [[NEJI tables]] | ||
* [[Ringer scale]] | |||
== Notes == | == Notes == | ||