3/4-comma meantone

This page presents a topic of primarily mathematical interest. While it is derived from sound mathematical principles, its applications in terms of utility for actual music may be limited, highly contrived, or as yet unknown.

3/4-comma meantone is a tuning of meantone where the fifth is flattened by 3/4 of the syntonic comma, producing a fifth of 685.825 cents. This is approximated well by 7edo.

In terms of how just intonation intervals are mapped, 3/4-comma meantone is severely inaccurate within a meantone framework, particularly in terms of its 5/4. It might make more sense to interpret it as a different 5-limit temperament instead of meantone: deeptone. 3/4-comma’s fifth works better as a deeptone generator.

One way of extending deeptone into the 7-limit, 11-limit and 13-limit is the jamesbond temperament.