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Re: piano tuning etc.



****I'm hip. But, a note shouldn't beat with itself as in the case of
disparities among the three strings in the treble. In the back of
Helmholtz (*Sensations of Tone ...* ) the editor has shown how to prepare
a harmonium for true pitch. I think it will play the key, the relative
minor and the co-relative major - and maybe one more - with every
interval a ratio of small integers, as Pythagoras would have it. I have
wondered why - with computers and electric instruments - someone doesn't
build an instrument that decides what key you are modulating to and
corrects all the pitches appropriately and automatically. Back in Bach's
day, people built all sorts of marvelous monstrosities with multiple
keyboards and strings to play every key in tune, but no one could play
them. Regards / Tom ***

Dear Tom,

Was modulation employed as a musical device before the invention of equal
temperment? If so, how did other members of an ensemble cope, for example
flautists who, in the baroque, had to change joints to change keys? These
days it is not surprising to see an ensemble member with more than one
instrument, I suppose. Perhaps that was what they did. The keyboardist
would have had insuperable problems in those days, however.

I had always guessed that modulation, which seems so natural in even
temperment, was a modern development. I'm not a musician, though I have
taught the physics of music course a few times. I note your mention of
Carleen Mayley Hutchins's Catgut Acoustical Society, a noble effort on
the part of physicists to make a contribution to music, but one which,
I feel, has failed as did Galileo's effort to improve on the design of
large animals in "Two New Sciences", and for the same reason. Evolution
by natural selection is a formidable competitor.

Leigh