Langwidge

Langwidge is a rank-2 temperament in the 2.3.17.19 subgroup 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 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".

Notation

Since the temperament is generated by the fifth, chain-of-fifths notation can be used. Note that -17 generator steps 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 is fully established. Most conceptualization systems of just intonation (FJS, HEJI, etc.) indeed treats 19/16 as a minor third, but 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.

Temperament data

Subgroup: 2.3.17.19

Comma list: 6144/6137, 19683/19456

Sval mapping: [⟨1 0 31 -10], ⟨0 1 -17 9]]

sval mapping generators: ~2, ~3

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 699.7519

Optimal ET sequence: 12, 235, 247, 259b, 271b, …, 355b, 367b

See also

• Protolangwidge