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Division of the third harmonic into 19 equal parts (19ED3) is related to 12 edo, but with the 3/1 rather than the 2/1 being just. It is also known as Stopper tuning. The octave is about 1.2347 cents stretched and the step size is about 100.1029 cents.

Division of 3/1 into 19 equal parts

Bernhard Stopper's OnlyPure tuning[dead link]

Note: 19 equal divisions of the tritave is not a "real" xenharmonic tuning; it is a slightly stretched version (with an octave of 1201.2 cents) of the normal 12-tone scale. Although it is really just the normal "harmonic" tuning framed in a tritave equivalence, the "default" approach to it is as the tritave twin of godzilla temperament (with a generator of 400.4 cents and a 3:1 ratio superdiatonic scale, weird coincidence how 17edt and 19edt tonality have the same "default" scheme with two tones more or less), which has little connection to standard 12-tone practice in spite of using the 12-tone interval set. Beyond this, it is also the tritave twin of sensi or meantone temperament (with a generator of 700.7 or 1101.1 cents and a 2:1 ratio superdiatonic scale).

See also