Langwidge: Difference between revisions

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Langwidge is a rank-2 temperament ~~whose~~ generator is a perfect fifth~~, and it is constructed with purpose~~ of ~~spelling the minor triad wrong, as C-D~~#~~-G instead of C-Eb-G~~.

'''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]]).

The name "langwidge~~" originates~~ 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<ref>[https://www.youtube.com/watch?v=SZftrA-aCa4&t=210s&pp=ygUYSXMgQyMgdGhlIHNhbWUgbm90ZSBhcyBC Is Cb the same note as B?] by Adam Neely</ref> ~~because it's not spelled right. In addition, he goes on to mention about how the "order of spelling in Western music theory is sacrosanct".~~

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>

~~In this case,~~ the temperament's generator is [[~~3/2~~]]~~, 9 of which~~ yield [[38/1]], ~~meaning~~ [[19/16]] is ~~mapped to~~ C-D#. ~~This means~~, ~~when octave-reduced~~, ~~this would require spelling~~ the 16~~:19:24~~ triad as C-D#-E and not as C-Eb-~~E, producing this peculiar violation of standard Western music theory~~.

== Notation ==

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.

In the 5-limit, the [[~~schismic~~]] ~~temperament~~ is ~~similar~~, in ~~which~~ the ~~10:12:15~~ minor ~~triad is spelled~~ 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]], 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.

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-Langwidge is a rank-2 temperament whose generator is a perfect fifth, and it is constructed with purpose of spelling the minor triad wrong, as C-D#-G instead of C-Eb-G.
+'''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]]).
-The name "langwidge" originates 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<ref>[https://www.youtube.com/watch?v=SZftrA-aCa4&t=210s&pp=ygUYSXMgQyMgdGhlIHNhbWUgbm90ZSBhcyBC Is Cb the same note as B?] by Adam Neely</ref> because it's not spelled right. In addition, he goes on to mention about how the "order of spelling in Western music theory is sacrosanct".
+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>
-In this case, the temperament's generator is [[3/2]], 9 of which yield [[38/1]], meaning [[19/16]] is mapped to C-D#. This means, when octave-reduced, this would require spelling the 16:19:24 triad as C-D#-E and not as C-Eb-E, producing this peculiar violation of standard Western music theory.
+== Notation ==
+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.
-In the 5-limit, the [[schismic]] temperament is similar, in which the 10:12:15 minor triad is spelled 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]], 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.
 See also [[protolangwidge]].
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 : sval mapping generators: ~2, ~3
-[[Optimal tuning]] ([[CTE]]): ~3/2 = 699.752
+[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 699.7519
-[[Support]]ing [[ET]]s: {{EDOs|12, 187g, 199g, 211g, 223, 235, 247}}, ...
+{{Optimal ET sequence|legend=1| 12, 235, 247, 259b, 271b, …, 355b, 367b }}
 == References ==
 [[Category:Temperaments]]
-{{Todo| review }}