Langwidge: Difference between revisions

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Langwidge is a rank-2 temperament whose generator is an interval close to the perfect fifth, and it is constructed with purpose of exploiting a loophole involving enharmonicity in Western music theory.
Langwidge is a rank-2 temperament whose generator is a perfect fifth, and it is constructed with purpose of spelling the minor triad wrong.


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". Therefore, langwidge temperament is constructed with the purpose of defying the Western spelling.
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".


In this case, the temperament's generator is a slightly flat fifth, 9 of which yield [[38/1]], meaning that when octave-reduced, this would require spelling root-3rd-P5 triad with 19:16 as C-D#-E and not as C-Eb-E, producing this peculiar violation of standard Western music theory.  
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.


Since [[355edo]] and [[722edo]] are good at supporting this kind of mapping, and they're also good at approximating [[17/16]], this makes 355 & 722 2.7.19 subgroup the most natural and simplest way to tune this temperament, producing a rank-2 temperament associated with the {{monzo|-109 0 0 0 0 0 9 17}} comma. This means that the generator fifth in question is mapped to [[6137/4096]], and nine of them make [[38/1]], meaning [[19/16]] is mapped to C-D#. For the purest 19th harmonic, 722edo is the best due to it being a convergent to log2(19/16). The generator fifth is flat of pure [[3/2]] by [[6144/6137]].
See also [[protolangwidge]].  
 
In the 17-limit, 17th harmonic is reached, coincidentally, 17 generators down, meaning [[17/16]] is mapped to C-Ebbb.


== Temperament data ==
== Temperament data ==
Subgroup: 2.3.17.19


Subgroup: 2.17.19
Comma list: 6144/6137, 19683/19456
 
Comma list: 2.17.19 {{monzo|-109 9 17}}
 
Sval mapping: [{{val|1 14 -1}}, {{val|0 -17 9}}]
 
Optimal tuning (CTE): ~6137/4096 = 699.712
 
{{Optimal ET sequence|legend=1|12, 271, 283, 295, 307, 319, 331, 343, 355, 367, 379 ,391, 403, 415, 722}}, ...
 
=== 23-limit langwidge ===
 
Since 355edo and 722edo are good at 2.17.19.23 subgroup, it's possible to extend this temperament into the 23-limit, although it is quite complex.
 
Subgroup: 2.17.19.23
 
Comma list: 24137569/24117248, 2.17.19.23 {{monzo|69 3 -17 -2}}


Sval mapping: [{{val|1 14 -1 64}}, {{val|0 -17 9 -102}}]
Mapping: 1 0 31 -10, 0 1 -17 9


Optimal tuning (CTE): ~6137/4096 = 699.722
Mapping generators: ~3/2 = 700...,


{{Optimal ET sequence|legend=1|12, 343, 355, 367, 379, 722, 1077, 1089, 1432}}
Supporting ETs: 12, 187g, 199g, 211g, 233, 235, 247, ..


== References ==
== References ==

Revision as of 13:10, 29 October 2023

Langwidge is a rank-2 temperament whose generator is a perfect fifth, and it is constructed with purpose of spelling the minor triad wrong.

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[1] 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".

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.

See also protolangwidge.

Temperament data

Subgroup: 2.3.17.19

Comma list: 6144/6137, 19683/19456

Mapping: 1 0 31 -10, 0 1 -17 9

Mapping generators: ~3/2 = 700...,

Supporting ETs: 12, 187g, 199g, 211g, 233, 235, 247, ..

References

  1. ↑ Is Cb the same note as B? by Adam Neely
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