Medieval intonations

[Paul Erlich, TD 207.11]
> I hate to say it but music of 1000 years ago was totally
> different from, and probably tuned totally differently from,
> music of today. There was a "paradigm shift" at one point when
> thirds and sixths moved from dissonant to consonant, and this
> is clear in the grammar of the musical examples that
> have survived.

Of course, Paul - I know this and am not arguing this point.
Thanks anyway, because you've expressed it well here.

My point was just that a person's understanding of what
is going on harmonically (i.e., mathematically) is going
to be limited by the knowledge and understanding he already
has of mathematics and harmony.

Of course there are many musicians who are illiterate in
terms of music-theory but who still have a great understanding
and sensitivity to what's happening, purely *by ear*.

But that 'music-theory illiteracy' makes them incapable of
discussing or analyzing what they can experience, in words
or numbers, beyond what they are able to understand.

For European theorists from the time of Charlemagne (i.e.,
the rebirth of literacy altogether) to about 1200, when they
began to get re-acquainted with the ancient Greek treatises
(with their non-Pygathorean rational systems and the irrational
systems of Aristoxenus), there simply was no way to express
mathematically what *may* have been going on in practice.

My intention here is not to argue too strongly about what *was*
going on in practice; I'm just noting that theorists would have
had difficulty discussing it if it *was* more complicated than
a Pythagorean tuning, because Pythagoreanism was simply much
easier for their mathematics to handle than were other types of
harmonic measurement.

Don't forget that at this time, mathematics still used
the difficult-to-manipulate Roman numerals and had no concept
of 'zero'; this would have given music-theorists a very
different view of things that what we are accustomed to today.

My effort in this thread is directed towards keeping people's
minds open to the possibilities that may have been overlooked
by theorists of the day.

After all, we don't have any recordings from back then, and
the only way we can reconstruct what that music may have
sounded like is thru the extant manuscripts, the contemporary
theoretical descriptions, and the accumulation of knowledge
on the subject since that time. And all three of these types
of sources are less than 100% clear and accurate on the matter.

I believe that leaves room for the type of speculation in
which I like to indulge.

-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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Monzo [TD209.24]

>My point was just that a person's understanding of what
>is going on harmonically (i.e., mathematically) is going
>to be limited by the knowledge and understanding he already
>has of mathematics and harmony.

>Of course there are many musicians who are illiterate in
>terms of music-theory but who still have a great understanding
>and sensitivity to what's happening, purely *by ear*.

>But that 'music-theory illiteracy' makes them incapable of
>discussing or analyzing what they can experience, in words
>or numbers, beyond what they are able to understand.

I think that the above makes a very important point.
I am not a natural musician nor likely to be in this life. However I
believe that I have discovered some things that such folks could do
really interesting things with if we could just find a common language.

...
>Don't forget that at this time, mathematics still used
>the difficult-to-manipulate Roman numerals and had no concept
>of 'zero'; this would have given music-theorists a very
>different view of things that what we are accustomed to today.

>My effort in this thread is directed towards keeping people's
>minds open to the possibilities that may have been overlooked
>by theorists of the day.

Yes, yes.

...
>I believe that leaves room for the type of speculation in
>which I like to indulge.

I'm with you Monzo. I also enjoyed your speculation in the "Beethoven
JI tuning experiment" thread. The point about strings is well made.
It is quite legitimite to speculate about how these gents would have
presented material if they had a totally variable tunable keyboard.

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Joe Monzo wrote,

> My intention here is not to argue too strongly about what *was*
> going on in practice; I'm just noting that theorists would have
> had difficulty discussing it if it *was* more complicated than
> a Pythagorean tuning, because Pythagoreanism was simply much
> easier for their mathematics to handle than were other types of
> harmonic measurement.

As I already expressed by agreeing with Margo's post, I don't buy that. But I do appreciate the exchange of different ideas.