temper / temperament

[Tom Kysilko]

Any scale (or instrument so tuned) whose intervals deviate from the Pythagorean
ratios (octave=2/1, fifth=3/2, fourth=4/3, etc) is said to be "tempered".  The
title of J. S. Bach's set of preludes and fugues in all 24 keys to be played on
a single instrument is usually translated into English as "The Well-tempered
Clavier".  The system by which these ratios are adjusted is called
the "temperament".  Modern pianos are tuned using "equal temperament" in which
all half-steps have a ratio of the twelfth root of two to one.  When
tuners "lay the temperament" they tune 12 notes in the middle of the piano.
After that, they tune octaves going up and down from the middle.  Other
temperaments are sometimes used on organs, harpsichords, or when requested by
early music performers.

Background:  the problem is that the Pythagorean ratios don't add up.  If you
start at A-27.5Hz and double the frequency seven times, you will get a
different frequency (3520Hz) from the one you get if you go up by fifths (A-E-B-
F#-...-G-D-A) using a 3/2 ratio (3568Hz).  This was one of Pythagorus' dirty
little secrets.  A temperament is a fudging of ratios to deal with that
difference.

--Tom "married to a piano tuner" Kysilko

Quoting "Arnold M. Zwicky" <zwicky at CSLI.STANFORD.EDU>:

> ---------------------- Information from the mail header
> -----------------------
> Sender:       American Dialect Society <ADS-L at LISTSERV.UGA.EDU>
> Poster:       "Arnold M. Zwicky" <zwicky at CSLI.STANFORD.EDU>
> Subject:      Re: Antedating of "Musicologist"
> ------------------------------------------------------------------------------
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>
> On Friday, October 10, 2003, at 06:04 AM, James A. Landau wrote:
>
> > I find it interesting that the quote uses the word "temperament" to
> > refer to
> > the selection of notes used in the scale, because TTBOMK (to the best
> > of my
> > knowledge) the correct word is "temper" and the word "temperament" is
> > used in
> > music only to refer to the emotional stability of musicians.
>
> this is exactly backwards.  the musicological term is "temperament",
> and "temper" refers only to an emotional state.
>
> randel's New Harvard Dictionary of Music has an entry for "temperament"
> and doesn't mention "temper".  meanwhile, isacoff's 2002 book about
> selecting the tones of a musical scale is entitled Temperament.
>
> arnold (zwicky at csli.stanford.edu)