John Henckel wrote:
>
> Is "well-tempered" and "equal-tempered" the same thing? I don't think
> so. I was under the impression that equal-spaced half steps produced
> bad-sounding music. The key of E is not supposed to sound exactly like the
> key of C (except one third higher). That's why the composer dictates the
> key signature. Each key has its own peculiaritiesies because the notes are
> not equally spaced. Knowing and using the peculiarities of each key is
> part of the art of composition.
>
> One time I watched a professional piano tuner and was surprised to see that
> he didn't use any electronic pitch measuring device. He only used ONE
> tuning fork for middle C, and he tuned all the other notes from there! I
> said, "why don't you just tune each note separately to its correct
> frequency" and he said that would sound awful. He said it is impossible to
> tune any piano perfectly, but it is always a compromise of many different
> factors. In other words, it is an art.
>
> At 11:01 AM 4/4/01 +0100, Phil wrote:
>
> >We wouldn't get very far without the equal-temperament scale though
> >would we? The equally-tempered scale distributes the comma of Pythagoras
> >around all twelve intervals so all intervals are very slightly wrong.
> >It's the only way you can tune an instrument with fixed tunings and
> >have it sound reasonably OK in all keys.
>
> John Henckel alt. mailto:[EMAIL PROTECTED]
> Zumbro Falls, Minnesota, USA (507) 753-2216
>
> http://geocities.com/jdhenckel/
>
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'bad sounding music' is in the ear of the beholder. 12TET seems to be
nowhere as bad an approximation as for the diminished 7th, 1 3b 5b 7bb
(for base C in just intonation = 264, 316.8, 380.16, 456.192). That last
is a poor approximation in 12TET.
I reccommend Juan Roederer's 'The Physics and Psychophsics of Sound' and
an intoroduction to the theory of music. Practice of music is quite
advanced, but theory is primitive. On page 167 is a graph of an
experimental determination of the ratio of two frequencies judged
'consonant'. Within 75% confidence intervals anything between a minor
third (x 6/5) to a major 5th (x 3/2) work. Then things start getting
complicated.
Also it came as a surprise to me to find the Basics sound command gives
square waves at the speaker (ABC2WIN and my ABZ player). Norbeck's
AbcMus I haven't examined much, but my trials on A=440 lead to an audio
signal out as a three part sawtooth for each cycle. The ear doesn't seem
to much care how close to a sine wave it is, as far as calling it
'music' goes.
Bruce Olson
Old English, Irish and, Scots: popular songs, tunes, broadside
ballads at my website (no advs-spam, etc)- www.erols.com/olsonw
or click below <A href="http://www.erols.com/olsonw"> Click </a>
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