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

[Mike Richter <mrichter@xxxxxxx>]

Steven Barr wrote:

> 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...

Roughly, 1.06 - which is why a semitone change of pitch comes with a 6% 
speed change.

Roughly.

> 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"...?

Yes and no. (Specificity again!)

Different approximations have been used in various times and places with 
different results in the sound. In many cases, the variations are not 
subtle.

> 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?"

For each semitone.

A quick look suggests that this is a good starting point.
  http://en.wikipedia.org/wiki/Musical_temperament

Mike
--
mrichter@xxxxxxx
http://www.mrichter.com/