updated definition: "Pythagorean"

I've made a significant update to one of the most
important entries in the Tuning Dictionary:

http://www.ixpres.com/interval/dict/pythag.htm

Feedback, criticism, enhancements ... all most welcome.

-monz

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Like many on this list, I admire Joe Monzo for his accomplishments in
connecting the past to the present. And like Joe Pehrson, I am not a math
maven. There are 2 points, however, to make because of what seems to me
misleading to the truth.

First, the tuning Pythagorean as being a credit to Pythagorus for having had
something to do with successive 3/2 perfect fifths, especially in light of
the Babylonian and other cultures (Celts, Chinese, Turk) that use this tuning
earlier seems to compound an error. Pythagorus was most likely a
metaphorical a blank in Scrabble which the Mediterranean world credited
erroneously for a number of things. It is most likely religion determined
the tuning of the Middle Ages and not the long dead Pythagorus (see Sieman
Terpstra's chapter on religion, as yet unpublished).

And second, is the tie between Sumerian tuning and the Akkadian texts.
Please correct me if I am mistaken, but why is it assumed that the long past
civilization of the Sumerians used the tuning of the later Babylonians? The
work of Ben Hume in building exact replicas indicates just minor scales on
the Sumerian aulos.

Now, I certainly agree that these resources are unpublished as of yet, but so
is Joe Monzo's book, and so are many of the resources that we have at our
disposal. Work on Charles Ives that I have comes to mind. Can we find a way
to rassle up contemporary knowledge, regardless of its political condition
through publication? I suggest we can.

Best, Johnny Reinhard

Hi Johnny, and thanks for your comments! More below ...

> From: <Afmmjr@aol.com>
> To: <tuning@yahoogroups.com>
> Sent: Saturday, January 12, 2002 7:45 AM
> Subject: Re: [tuning] updated definition: "Pythagorean"
>
>
> Like many on this list, I admire Joe Monzo for his accomplishments in
> connecting the past to the present. And like Joe Pehrson, I am not a math
> maven. There are 2 points, however, to make because of what seems to me
> misleading to the truth.
>
> First, the tuning Pythagorean as being a credit to Pythagorus for having
had
> something to do with successive 3/2 perfect fifths, especially in light of
> the Babylonian and other cultures (Celts, Chinese, Turk) that use this
tuning
> earlier seems to compound an error. Pythagorus was most likely a
> metaphorical a blank in Scrabble which the Mediterranean world credited
> erroneously for a number of things. It is most likely religion determined
> the tuning of the Middle Ages and not the long dead Pythagorus (see Sieman
> Terpstra's chapter on religion, as yet unpublished).

Agreed. Part of the reason why I included the bit about the Sumerians
is because I want to be clear that so-called "Pythagorean" tuning is
far older than any person named Pythagoras, if he indeed ever lived at all.
So do I need to make all of this more explicit in the definition?
I guess so ...

> And second, is the tie between Sumerian tuning and the Akkadian texts.
> Please correct me if I am mistaken, but why is it assumed that the long
past
> civilization of the Sumerians used the tuning of the later Babylonians?
The
> work of Ben Hume in building exact replicas indicates just minor scales on
> the Sumerian aulos.

Johnny, please read my Sumerian page carefully. I explicitly state
that *I am assuming* that the Babylonians were retaining previous
Sumerian knowledge in their math problems because they retained the
use of the Sumerian logograms. On my webpage, I present first the
translations by Eleanor Robson of the Babylonian tablet, then I
strip out all the Akkadian (= Babylonian) words and produce another
version which uses *only* the Sumerian logograms. The gist of the
problem and the algorithm for solving it is still intact. Therefore
one must come to the conclusion that the Sumerians knew the algorithm.

Also, I state on my webpage that some Babylonian math and tuning
texts -- not to mention many of the mythology texts, if one accepts
that the Sumero-Babylonian religion was equivalent to its music-theory,
as purported by McClain and Terpstra -- seem to indicate that 5-limit
tuning may have been used by both cultures. It's just that my
emphasis here -- naturally enough, in a definition of "Pythagorean"
-- is that 3-limit tuning is far older than ancient Greece, and
I would argue *strongly* that it and its mathematics were known
to the Sumerians, as well as their conquerors.

-monz

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--- In tuning@y..., "monz" <joemonz@y...> wrote:

> > From: <Afmmjr@a...>
> > To: <tuning@y...>
> > Sent: Saturday, January 12, 2002 7:45 AM
> > Subject: Re: [tuning] updated definition: "Pythagorean"
> >
> >
> > Like many on this list, I admire Joe Monzo for his
> > And second, is the tie between Sumerian tuning and the Akkadian
> > texts.
> > Please correct me if I am mistaken, but why is it assumed that
> > the long
> > past
> > civilization of the Sumerians used the tuning of the later
> > Babylonians?
> > The
> > work of Ben Hume in building exact replicas indicates
> > just minor scales on the Sumerian aulos.

J Gill: Hello, Johnny and Joe! Do either of you fellows know
the particular scale-pitches of such "just minor scales", or
where information (of Hume's, or other's) choices resides?

Sincerely, J Gill