Re: [ARSCLIST] Temperament--was: Are we at the end of the road musically??

[Steven Barr <stevenc@xxxxxxxxxxxxxx>]

----- Original Message ----- 
From: "Don Cox" <doncox@xxxxxxxxxxxxxx>
> Certainly. You can start from any note, such as A=440Hz, and then apply
> a constant ratio of the 12th root of 2 from note to note. 
> 
> It doesn't give the exact ratios for any chord, but is considered near
> enough for practical purposes on pianos, which go out of tune so quickly
> that the ratios are never likely to be exact.
> 
1) What is the numerical value of this "twelfth root of two?" I don't
think I have either a sufficiently advanced calculator (or program),
or sufficient calculation skills, to figure that out...

2) Just a thought...if, as you say, "It doesn't give the exact ratios
for any chord"...is it not, then, a practical approximation...or, as
we used to say back in my USAF days, "Close enough for government
work"...?

3) Does "from note to note" allow for the fact that some notes in
the major scale differ by full tones, while others differ by
half-tones (i.e. there is no C-flat!)...or were you speaking of
the series in a twelve-tone "scale?"

I'm not challenging you...I'm just trying to get as full an
understanding as possible of how...and why...western-world
music "works!"

Steven C. Barr