Langwidge: Difference between revisions

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'''Langwidge''' is a [[rank-2 temperament]] in the 2.3.17.19 [[subgroup]] [[generator|generated]] by a [[perfect fifth]]. It was found in a search for a temperament that would defy the tradition of tertian harmony (→ [[#Notation]]).

'''Langwidge''' is a [[rank-2 temperament]] in the 2.3.17.19 [[subgroup]] [[generator|generated]] by a [[perfect fifth]]. It was found in a search for a temperament that would defy the tradition of tertian harmony (→ [[#Notation]]). It is an [[extension]] of [[protolangwidge]].

The name ''langwidge'' was given by [[Eliora]] in 2023, originating from Adam Neely's video "''Is Cb The Same Note as B?''", where he mentions that there's "nothing technically incorrect about spelling the word language as "langwidge", but word structure-wise the information is different because it is not spelled right. In addition, he goes on to mention about how the "order of spelling in Western music theory is sacrosanct".<ref>[https://www.youtube.com/watch?v=SZftrA-aCa4&t=210s&pp=ygUYSXMgQyMgdGhlIHNhbWUgbm90ZSBhcyBC ''Is Cb the same note as B?''] by Adam Neely</ref>

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Since the temperament is generated by the fifth, [[chain-of-fifths notation]] can be used. Note that -17 generator steps [[octave reduction|octave-reduced]] yield [[17/16]], so that 17/16 is C–Ebbb. +9 generator steps octave-reduced yield [[19/16]], so that 19/16 is C-D#. As such, it is considered to present a challenge to the tradition of tertian harmony, since the simplest harmonic building block, the 1-19/16-3/2 triad, is C-D#-G and not C-Eb-G.

This temperament is, however, neither the first nor the most successful to raise the notational issue, and there are a number of ways to address it. First, whether 19/16 must be notated as a minor third is debatable. Western harmony mainly dealt with the [[5-limit]], and only the mapping of [[5/1|5]] is fully established. Most conceptualization systems of [[just intonation]] ([[FJS]], [[HEJI]], etc.) indeed ~~treats~~ 19/16 as a minor third, but [[Sagittal notation|Sagittal]] is a notable exception in that it is equipped with an accidental of ratio 19683/19456 besides the more common [[513/512]], so 19/16 can be an augmented second there. Otherwise, if one wants to notate 19/16 as a minor third, ~~they~~ can adopt an additional module of accidentals such as arrows to represent the comma step, allowing them to write the chord above as C-^Eb-G. There are also other temperaments known to raise the notational issue in much simpler chords, such as [[schismatic]] temperament which represents the 5-limit 10:12:15 triad as C-D#-G.

This temperament is, however, neither the first nor the most successful to raise the notational issue, and there are a number of ways to address it. First, whether 19/16 must be notated as a minor third is debatable. Western harmony mainly dealt with the [[5-limit]], and only the mapping of [[5/1|5]] is fully established. Most conceptualization systems of [[just intonation]] ([[FJS]], [[HEJI]], [[Color notation]],etc.) indeed treat 19/16 as a minor third, but [[Sagittal notation|Sagittal]] is a notable exception in that it is equipped with an accidental of ratio 19683/19456 besides the more common [[513/512]], so 19/16 can be an augmented second there. Otherwise, if one wants to notate 19/16 as a minor third, one can adopt an additional module of accidentals such as arrows to represent the comma step, allowing them to write the chord above as C-^Eb-G. (Color notation can notate 19/16 as either an ino 3rd or a noqu 2nd.) There are also other temperaments known to raise the notational issue in much simpler chords, such as [[schismatic]] temperament which represents the 5-limit 10:12:15 triad as C-D#-G.

== Temperament data ==

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[[Category:~~Temperaments~~]]

[[Category:Langwidge| ]]

[[Category:Rank-2 temperaments]]

[[Category:Subgroup temperaments]]

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-'''Langwidge''' is a [[rank-2 temperament]] in the 2.3.17.19 [[subgroup]] [[generator|generated]] by a [[perfect fifth]]. It was found in a search for a temperament that would defy the tradition of tertian harmony (→ [[#Notation]]).
+'''Langwidge''' is a [[rank-2 temperament]] in the 2.3.17.19 [[subgroup]] [[generator|generated]] by a [[perfect fifth]]. It was found in a search for a temperament that would defy the tradition of tertian harmony (→ [[#Notation]]). It is an [[extension]] of [[protolangwidge]].
 The name ''langwidge'' was given by [[Eliora]] in 2023, originating from Adam Neely's video "''Is Cb The Same Note as B?''", where he mentions that there's "nothing technically incorrect about spelling the word language as "langwidge", but word structure-wise the information is different because it is not spelled right. In addition, he goes on to mention about how the "order of spelling in Western music theory is sacrosanct".<ref>[https://www.youtube.com/watch?v=SZftrA-aCa4&t=210s&pp=ygUYSXMgQyMgdGhlIHNhbWUgbm90ZSBhcyBC ''Is Cb the same note as B?''] by Adam Neely</ref>
@@ Line 6: / Line 6: @@
 Since the temperament is generated by the fifth, [[chain-of-fifths notation]] can be used. Note that -17 generator steps [[octave reduction|octave-reduced]] yield [[17/16]], so that 17/16 is C–Ebbb. +9 generator steps octave-reduced yield [[19/16]], so that 19/16 is C-D#. As such, it is considered to present a challenge to the tradition of tertian harmony, since the simplest harmonic building block, the 1-19/16-3/2 triad, is C-D#-G and not C-Eb-G.
-This temperament is, however, neither the first nor the most successful to raise the notational issue, and there are a number of ways to address it. First, whether 19/16 must be notated as a minor third is debatable. Western harmony mainly dealt with the [[5-limit]], and only the mapping of [[5/1|5]] is fully established. Most conceptualization systems of [[just intonation]] ([[FJS]], [[HEJI]], etc.) indeed treats 19/16 as a minor third, but [[Sagittal notation|Sagittal]] is a notable exception in that it is equipped with an accidental of ratio 19683/19456 besides the more common [[513/512]], so 19/16 can be an augmented second there. Otherwise, if one wants to notate 19/16 as a minor third, they can adopt an additional module of accidentals such as arrows to represent the comma step, allowing them to write the chord above as C-^Eb-G.  There are also other temperaments known to raise the notational issue in much simpler chords, such as [[schismatic]] temperament which represents the 5-limit 10:12:15 triad as C-D#-G.
+This temperament is, however, neither the first nor the most successful to raise the notational issue, and there are a number of ways to address it. First, whether 19/16 must be notated as a minor third is debatable. Western harmony mainly dealt with the [[5-limit]], and only the mapping of [[5/1|5]] is fully established. Most conceptualization systems of [[just intonation]] ([[FJS]], [[HEJI]], [[Color notation]],etc.) indeed treat 19/16 as a minor third, but [[Sagittal notation|Sagittal]] is a notable exception in that it is equipped with an accidental of ratio 19683/19456 besides the more common [[513/512]], so 19/16 can be an augmented second there. Otherwise, if one wants to notate 19/16 as a minor third, one can adopt an additional module of accidentals such as arrows to represent the comma step, allowing them to write the chord above as C-^Eb-G. (Color notation can notate 19/16 as either an ino 3rd or a noqu 2nd.) There are also other temperaments known to raise the notational issue in much simpler chords, such as [[schismatic]] temperament which represents the 5-limit 10:12:15 triad as C-D#-G.
 == Temperament data ==
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 <references/>
-[[Category:Temperaments]]
+[[Category:Langwidge| ]] <!-- main article -->
+[[Category:Rank-2 temperaments]]
+[[Category:Subgroup temperaments]]