string players probably wouldn't agree

monz@juno.com wrote:

> the proper tuning of the chord in, say, a Beethoven string quartet
> (altho string players probably wouldn't agree because they
> like Pythagorean intervals).

Pythagorean? Why would you say that?

> --

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[me, monz]
>>
>> the proper tuning of the chord in, say, a Beethoven string
>> quartet (altho string players probably wouldn't agree because
>> they like Pythagorean intervals).

[Dave Beardsley, TD 180.22]
>
> Pythagorean? Why would you say that?

Orchestral string players tune the strings of their instruments
to four consecutive 3/2s. On a cello, for instance:

A 27:16 = 3^3
D 9:8 = 3^2
G 3:2 = 3^1
C 1:1 = 3^0

[ignoring powers of 2 in the prime-factoring]

In passages that many of us JI composers might think require
a 5:3 for A, that cellist is often likely to play a 27:16
to keep it in tune (a perfect 3/2 or 3/4) with his D-string.

That's a very over-simplified explanation, but studies have
corroborated this. I don't have time to look for them
right now, but I believe there's some stuff about this in
Ellis's appendices to Helmholtz. I think Paul Erlich
may have a citation or two.

The usual preference for sharpened 'leading-tones' among
musicians who play variable-pitch instruments also plays a part.
So if we're in the key of 'C', the 'leading-tone B' is much
more likely to be played as (approximately) a 243/128
[= 3^5 = ~1109.8 cents] than a 15/8 [= 1088.3 cents].
This 'B' would also be a nice Pythagorean 9/8 above the
aforementioned 'A'.

-monz

Joseph L. Monzo monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
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