Alternate tuning systems

[daveyarwood]

For equal-temperament tuning with a reference pitch other than A440, we can just bind *reference-pitch* to the frequency of A4. We can provide a tune! function that will use alter-var-root to change the *reference-pitch*, and a with-reference-pitch function/macro that executes the body, binding *reference-pitch* to a particular value. (EDIT 10/28: done)

Will have to think a little more about how to handle other kinds of tunings (just, well, Pythagorean, etc.) It would be nice to have them built-in, so you can do something like (with-tuning :pythagorean (note->hz "A4")), but currently all the formulas are for equal-temperament tuning. Maybe we could add a *tuning-system* var that the *->hz functions will consider, and add logic to the functions so that they use the right formula for the current tuning.

[daveyarwood]

with-tuning-system, *tuning-system* etc. are all set up so that we can add other tunings with relative ease. For each tuning, we just need to add its formula to the case statements in hz->midi and midi->hz.

TODO:

• Werckmeister III
• just (a.k.a. harmonic tuning, Helmholtz's scale)
• La Monte Young's tuning from The Well-Tuned Piano
• mean-tone (seems like there are a lot of variations on this -- quarter-comma meantone, etc.)
• Pythagorean
• schismatic
• implement reverse function for ratio-based tunings

[daveyarwood]

Hmm... so, at least for well-tempered tunings (and possibly for others), the tuning happens relative to what key you're in. So when using these tuning systems, the key will need to be set, and an error should be thrown if there is not at least a *tonic* set in the environment (we can assume major is the type of scale, when not specified otherwise).

Will first add the mechanism for setting the key, then can proceed with implementing the tuning systems that need to know what key you're in.

EDIT: done