the real substance of the universe: ancient math/music/cosmology

>>> [Bekah, TD 690.8]
>>> I wonder if music is not the main part of the real substance
>>> of the universe?

>> [David Beardsley, TD 690.13]
>>
>> I think so. I've just been reading recently how the ancient
>> Greeks (Pythagorists?) considered ratios (proportions) part
>> of the order of the universe. Sounds good to me.

> [zHANg, TD 690.18]
>
> Well, the Hindus also believe this. As do Taoists as well.

As a complement to Dan Stearns's lengthy response to this,
I'd like to add that the earliest recorded music-theories
that still exist all posit a deep connection between numbers,
music, and cosmology.

It's evident that the Greeks got a lot of their musical,
mathematical, mythological, and cosmological ideas from
other great civilizations that preceeded them and with which
they had some contact, most notably the Egyptians, but there
is some evidence that some of their ideas came from Babylonia.

There's a great article by Ernest McClain, 'Musical Theory
and Ancient Cosmology', which is on the web at:
http://members.aol.com/markalex9/Reviews/mcclain.html
and which outlines Babylonian music-theory, mathematics, and
cosmology.

Another recent article which cites this one is Siemen Terpstra's
'A Short History of Just Intonation Tuning Culture', appearing
in _1/1_ (the Journal of the Just Intonation Network),
vol 10 no 1, Winter 1998. I believe it is available online
- check the JIN website.

McClain states that the Babylonians (who were presumably Semitic)
took over almost all of the knowledge and beliefs of the Sumerians,
who had been conquered centuries earlier by the Akkadians (also
Semitic) and whose language had died out by that time.

The Sumerians were non-Semitic, and in fact their language
has no known relatives anywhere on earth. They are justly
famous as the originators of the earliest surviving examples
of writing. I've been stimulated by McClain's article, and by
the fact that no one knows exactly who the Sumerians were,
into doing more research on Sumerian math/music/religion, and
have just gotten a copy of a book on 'Mespotamian Mathematics',
in which I hope to find out more info on Sumerian music.
I'm also giving more credence to von Danakin's (_Chariots
of the Gods_) theories these days.

Anyway, according to McClain, each Babylonian god was associated
with a number in their base-60 numbering system. The Babylonians
used a base-60 system because 60 can be divided evenly so
many different ways that they were thus able to deal with
fractions to a fair degree of accuracy, including such
quantities as:

50/60 = 5/6
48/60 = 4/5
45/60 = 3/4
40/60 = 2/3
36/60 = 3/5
30/60 = 1/2
24/60 = 2/5
20/60 = 1/3
15/60 = 1/4
12/60 = 1/5
10/60 = 1/6
6/60 = 1/10
5/60 = 1/12
4/60 = 1/15
3/60 = 1/20
2/60 = 1/30

and of course other multiples of 10ths, 12ths, 15ths, 20ths, and
30ths.

I'm not sure I agree with all of McClain's methods in reconstructing
the Babylonian scales, but there is absolutely no doubt that
if each god was associated with both a number and a musical
proportion, then their music-theory was 5-limit, because 60
factors into (2^2)*3*5.

The way I've calculated the musical proportions, which I'm
assuming were being measured on a monochord, if the basic
reference pitch of the entire string represents the whole
unit of 60 parts (I'll call it 'A' 1/1), then the whole pantheon
of gods translated into musical ratios gives the following:
(tick-marks and capital/lower-case indicate 'octaves')

god string-length = fraction frequency-ratio letter-name
Bal/Marduk 10 1/6 6:1 e'
Nergal 12 1/5 5:1 c#'
Ishtar 15 1/4 4:1 a
Shamash (sun) 20 1/3 3:1 e
Sin (moon) 30 1/2 2:1 a
Ea/Enki 40 2/3 3:2 E
Enlil 50 5/6 6:5 C
Anu/An 60 1 1:1 A'

This gives a nice symmetrical set of pitches with a 3/2
in the middle (representing the sun and moon), and with a
5-limit 'major' triad on top and 5-limit 'minor' triad on
the bottom.

McClain explains that as various rival cities assumed
the position of supremacy in Mespotamian politics, the
hierarchy in the pantheon of gods was altered so that
those cities's local gods got their turn as supreme god.

Bal/Marduk, whose cult was centered in Babylon and who is
associated with the number 10, became the 'chief god' when
Babylon became the greatest power in Mespotamia. I find this
especially interesting, because it seems (as suggested by McClain)
that this happened at just the time that Mespotamian mathematics
shifted away from a base-60 number system and to a base-10
system, and it led to the Pythagorean theory of the (base-10)
tetractys as the basis of all musical numbers:

o
o o
o o o
o o o o

-monz

Joseph L. Monzo San Diego monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
| 'I had broken thru the lattice barrier...' |
| -Erv Wilson |
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