just tuning & equal temperament

[Jason Kanter]

Any historic tuning stresses some notes and relaxes others in relation to
their ET settings. It's a common practice to sacrifice A=440 in favor of
balancing out the upward and downward stresses on the notes, making the net
effect zero total stress within any octave. That's what the exam detuning
does also.
A pitch correction would tend to be uniformly south or north of the equator.
It would vary by section of the piano, not by note. That is what makes the
"pitch correction" necessary -- to balance out the sectional variations. But
even returning to ET from a zero-balanced HT, it still takes a few tunings
for the piano to feel stable. The ETD pitch correction techniques don't work
because they are designed to calculate the sectional stress by averaging out
the note-by-note offsets and compensating slightly in the other direction.
"Pitch correction" in this sense is of no use in detuning or retuning from
HT.
"Just" tuning might be referring to one of the Pythagorean tunings displayed
on rollingball.com. The extreme major thirds are 21.5 cents wide, as opposed
to the 13.7 cents wide that most of us are always listening to, and most of
the fifths are absolutely beatless.
In the opposite direction, the Meantone and Well groups favored slowing down
the most-used major thirds, and several of them (Kirnberger, Prinz) actually
make the CE third beatless. To do this, you have to narrow the fifths and
widen the fourths CG-GD-DA-AE so that the CE third is 13.7 cents contracted
from "equal". That contraction is absorbed into and divided among the above
four fourths and fifths, which then average about 5.4 cents
contracted/expanded as opposed to the 1.9+ cents we are accustomed to.
Ah well.
Jason
-----Original Message-----
From: pianotech-bounces@ptg.org [mailto:pianotech-bounces@ptg.org]On
Behalf Of Avery Todd
Sent: Tuesday, April 26, 2005 5:08 PM
To: ilvey@sbcglobal.net; Pianotech
Subject: Re: just tuning & equal temperament


David,

I may be wrong but I "believe" there are some notes on the detuning for the
PTG
exam that are at least that. I've always had a problem with that for
stability
purposes.

An article in the Journal (I believe) said that anything over 2 cents
needed to
have a pitch correction thing added to it. Well, if that's so, why is the
piano
detuning so extreme (IMHO)?

Avery

At 04:45 PM 4/26/05, you wrote:
>List,
>
>What, if any, effects does tuning a just intonation tuning on a equal
>tempered piano and then back again.   Other than how fabulous it will
>sound in Just...;-]
>I've been told there can be a 25 cent difference in some notes...it seems
>like a big change, stability, different wire moving into the speaking
length...
>
>David I.
>
>
>
>
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