Mozart's tuning

Paul Erlich and I have been having a lively exchange
off-list about my new webpage "Mozart's tuning: 55-EDO".

Paul has had many good constructive criticisms of it,
and I'll be making a lot of changes according to his
comments.

The biggest problem is that I jumped the gun and used
a 12-tone subset more-or-less attributing it to Mozart,
which is incorrect. He actually taught intonation with
a 20-tone subset of 55-EDO. And this tuning was not
used on keyboards, which were normally in well-temperament
at the time. 55-EDO mimicks 1/6-comma meantone.

One of Paul's comments to me provoked a question out
of me that really should be here on the list:

> But yes, 1/6-comma meantone, 55-tET, anything
> in-between, and all similar 18th century
> meantones would be equally difficult to tune
> by ear.

Do you know this for sure? from the literature?
from personal experience?

I'm sincerely curious, because a couple of years ago
at Johnny Reinhards I was reading Werckmeister's book
trying to learn the mathematics of his tunings. He
made diagrams of how to detune strings from a JI ratio
by fractions of a Pythagorean comma, which, without
reading much of the book or doing much of the actual
math, I took to mean that the tuner could count beats.

I wonder if there's a kind of ranking of difficulty
to tuning a piano to a variety of different tunings.
Any comments? Does Jorgenson's <sp> book have anything
to say about this idea?

I know from my own experience that simple JI systems
are the easiest to tune by ear, but beyond that I'm
not willing to make any statements yet.

-monz
http://www.monz.org
"All roads lead to n^0"

> Paul Erlich and I have been having a lively exchange
> off-list about my new webpage "Mozart's tuning: 55-EDO".

Ooops... meant to give the URL:
http://www.ixpres.com/interval/monzo/55edo/55edo.htm

-monz
http://www.monz.org
"All roads lead to n^0"

My webpage about Mozart's preferred tuning:
http://www.ixpres.com/interval/monzo/55edo/55edo.htm

now also contains analyses of close approximations
to Mozart's tuning in both 72-EDO, and (Margo, take
note!) extended Pythagorean.

-monz
http://www.monz.org
"All roads lead to n^0"

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