Re: Uruk lute (from MMM list)

--- In MakeMicroMusic@yahoogroups.com, "J.Smith" <jsmith9624@...> wrote:
>
> THE URUK LUTE: ELEMENTS OF METROLOGY
> By RICHARD DUMBRILL
>
> <snip>
>
> ... Two other gods pair to produce the ideal complement to
> the ratio of Ištar to Šakkan (15:14): these are the second
> number for Anu, 21 and the number for Šamaš, 20. Their
> ratio 21:20 gives 84.47 cents, which added to the ratio
> of 15:14 = 119,44 cents, adds up exactly to 203.91 cents.
> This is the so-called Pythagorean tone which equates to
> the Greek ratio of 9:8.
>
> <snip>
>
> It is clear, therefore that in spite of the fact that the
> Greek Pythagorean tone was a fundamental ratio in their
> harmonic series of 12:9:8:6, the structure of their semitones
> was not as simple as the Babylonian system.

I am extremely interested in all this, having done a lot of
research into (and speculation on) Sumerian and Babylonian
tuning theory. (The archives of the main tuning list can be
searched for a number of my contributions on this topic.
I had some correspondence with Dumbrill years ago too.)

What you are describing, assuming that the Babylonain limma
is the lower interval and the apotome the higher, is what the
Greeks later called "katapyknosis". In this case, the whole-tone
of ratio 9:8 has its terms multiplied by 5 so that the ratio
becomes 45:40, and a division represented by 42 is inserted
between them, to produce an upper ratio of 45:42 = 15:14
and a lower ratio of 42:40 = 21:20.

My hypothesis is that the Greek division of semitones was
indeed originally as simple as the Babylonian, and in fact
may have actually *been* the Babylonian. It was the later
theories of Pythagoras (or the pythagorians, if in fact
Pythagoras is a mythical person, which he may have been)
which mandated that all ratios be based on factors of only
2 and 3, which limited their construction of semitone division
to the now well-known pythagorean ratios.

For my own insight into the earliest known Greek
writings on tuning division, see my paper on Philolaus
in _Xenharmonikon 18_, portions of which appear in this
webpage:

http://tonalsoft.com/enc/p/philolaus.aspx

BTW, it's probably better to migrate this whole discussion
to the main tuning list, as this one is supposed to be focused
on the actual making of microtonal music. So i've cross-posted
this post to the main list, and encourages response to go there.

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
> I am extremely interested in all this, having done a lot of
> research into (and speculation on) Sumerian and Babylonian
> tuning theory. (The archives of the main tuning list can be
> searched for a number of my contributions on this topic.
> I had some correspondence with Dumbrill years ago too.)

It wasn't clear to me what the evidence for his claims were. I do think
you are correct in the powerful influence the Babylonians had on Greece.