History and absurdity

> I defy anyone to come up with a system suiting Quantz's requirements,
> if the 5ths on the keyboard are any tighter than 1/6 comma.

Brad is here saying that Quantz wrote a book, for publication
throughout western Europe, which only made sense if the keyboard
player used one, and only one, type of regular meantone, and only one
variety of deviation from it, within a really pretty minute region of
tolerance. (I'm not referring to Brad's cent values - just to his
'experimental' results, that seem to lead to a scheme of tuning that
is actually extremely restrictive.)

But amazingly enough Quantz never actually told his readers what this
special keyboard temperament was (that was required to make sense of
his remarks - at least as Brad interprets them), or how to set it.

What sort of author would assume a pre-existing, aurally exact notion
of temperament among practically all the German- and French-speaking
harpsichordists of the age?

The alternative is to accept that Quantz was only writing in
approximate generality, and never meant his list of 'difficult' thirds
to be taken with hairsplitting exactitude. That his meaning was
'Whenever you have set a tuning in which there are thirds which are
quite noticeably impure, as these ones often are, you might well leave
them out and let the solo instrument play them purer'. That his
keyboard-playing readers were meant to understand a general principle
of accompaniment - rather than to try and rework their own tuning
procedure, by some very roundabout method, to match the hints
supposedly given in the text.

If we actually examine Brad's sample solutions to his self-imposed
Quantz-problem, we find that the thirds F-Ab and Ab-C are in both
cases *less* pure than C-Eb and E-G# respectively. Quantz calls C-Eb
and E-G# problematic - but he *doesn't* say that F-Ab or G#-B# are
also. How could we ever believe that Quantz was being exact and
comprehensive when he mentioned C-Eb and E-G# as difficult thirds, but
not F-Ab or G#-B#?

Looking once more at Brad's intervals (or indeed, at any historically
credible modified meantone), Eb-Gb is also always worse than C-Eb: why
then did Quantz also not mention E-Gb as a difficult third?

I find Cavallo much more literally credible, when he says that every
harpsichordist tunes slightly differently to favour a slightly
different range of keys. Then the only way to understand Quantz,
without positing a Europe-wide (or even Berlin-wide) conspiracy of
harpsichord tuners, who all somehow produced the same 'bad' thirds, is
to forget the dream of being able to deduce exactly what tuning Quantz
was used to hearing by the presence or absence of this or that exact
interval in his list of undesirables.

What rings out clearly from the text is a simple principle: the desire
for purer intervals than the keyboard could provide.

Consonant with this is Quantz' insistence on the monochord:

"The best manner of escape from this ignorance
is the monochord, on which one can clearly learn the
intervals. Every singer and instrumentalist should become
familiar with its use. They would thereby learn to recognize
minor semitones much earlier as well as the fact that notes
marked with a flat must be a comma higher than those with a
sharp in front of them (...)"

Which intervals will the singer and instrumentalist find on their
monochord? Brad seems to assume that they will find *only* the
1/6-comma tempered intervals, and then strive mightily to sing and
play slightly flat fifths and slightly sharp(flat) major(minor) thirds.

But actually, the only monochords I know of (whether in theory or
practice) all have the *pure* intervals marked out first and most
prominently. Isn't it obvious that the intervals that a musician would
most likely learn from a monochord are the pure ones?

~~~T~~~

----- Original Message -----
From: "Tom Dent" <stringph@gmail.com>
To: <tuning@yahoogroups.com>
Sent: 22 Kas�m 2007 Per�embe 1:23
Subject: [tuning] History and absurdity

SNIP

>
> Consonant with this is Quantz' insistence on the monochord:
>
> "The best manner of escape from this ignorance
> is the monochord, on which one can clearly learn the
> intervals. Every singer and instrumentalist should become
> familiar with its use. They would thereby learn to recognize
> minor semitones much earlier as well as the fact that notes
> marked with a flat must be a comma higher than those with a
> sharp in front of them (...)"
>

SNIP

Tom, I can understand nought else other than 55-EDO from Quantz' statement,
a tuning which has been applied at the same age to maqam music in the
Ottoman realm by Antoine Murat.

Oz.