Re: Gis major key signature; Lily's key signature algorithm

[David Kastrup]

"N. Andrew Walsh" <address@hidden> writes:

> It is entirely acceptable to be a music hobbyist who enjoys a passing
> familiarity with the classical tradition and is largely uninterested
> in more … esoteric discussions of theory. It is absolutely *not* all
> right to be spreading historical inaccuracies of this sort. The WTC is
> extensively researched and discussed in musicological and historical
> circles, sometimes heatedly, but the idea that Bach wrote it to prove
> that Well Temperament sounded "awful" (or the much worse assertion,
> that he wrote it to demonstrate *equal* temperament, a technological
> and historical impossibility in the 18th century)

Don't be silly.  Equal temperament most certainly is not
"technologically impossible".  Tuners of organs and accordions versed in
their art work by tuning a circle of fifths in a reference octave by
getting the proper sequence of beatings corresponding to the desired
temperament, then tune the other octaves in reference.

Meantone temperament is a bit different in that you walk a "circle of
major thirds" and distribute the tuning error across certain thirds
instead of across certain fifths like most well-tempered tunings do, or
even across _all_ fifths like equal temperant does.

Electronic tuners have been around for much much shorter times and are
usually not employed by experts since they waste the tuner's precision
on _absolute_ pitch references rather than the _relative_ references
important to hearing because they cause the beat frequencies.

If you get a fifth off by 0.5cent, the beating to one of its neighboring
fifths will be almost double (5/3) the beatings to its other neighboring
fifths, assuming those are totally accurate.

-- 
David Kastrup