Methods for Learning Tunes

[alistair]

Yes it is the same Ian Stewart of Warwick University. (I also got his "Cabinet of Mathematical Curioisities" for Christmas last year, but have not dared yet to do more than flip through it, for fear of jeopardising all other activities.)

I had vowed not to get drawn into this, but can you really tell the difference, aurally that is, with what you call "compromise build" instruments? The wonderful irony of the underlying mathematics is that if you want to be able to play a chromatic instrument in any key (and be equally "wrong" in all), you have to give up any attempt to produce exactly those beautiful Pythagorean rational frequency ratios, like 3/2 or 4/3, and try instead to get as close as possible to an irrational semitone frequency ratio of the 12th root of 2 (roughly 1.0595). [That's what Ian Stewart shows in his article the Strahle method achieves extremely well.] If you do that well enough you get still pretty close to the magic ratios: at least close enough that most people (I am told) can't tell the difference. But I guess you know all that.

Maybe we should go back to using instruments which are correct only in a few compatible keys (or to using a separate instrument for each different required key, as moothie and whistle players to some extent already do).