# 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".^{[1]}

## 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

## References

- ↑
*Is Cb the same note as B?*by Adam Neely