To all the math-geeks:

It's well-established that the Babylonians had

highly developed algebraic methods, altho they

never actually developed an algebraic notation.

There's also concrete proof that they had very good

sexagesimal approximations to both square and cube roots.

I'm investigating the possible applications some

of these methods may have had to tuning problems,

but my extremely math-challenged self needs some help.

Can someone tell me what application quadratic equations

may have to determining string-lengths? I'm interested

in possible applications for the purposes of determining

both JIs and/or temperaments.

For a reference to a modern explanation of Babylonian

algebra, please see the following, p 30-50:

Neugebauer, Otto. 1957.

_The Exact Sciences in Antiquity_.

Providence, Brown University Press, 2d ed

L.O.C.#: QA22 .N36 1957

Thanks.

love / peace / harmony ...

-monz

http://www.monz.org

"All roads lead to n^0"

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This may also be useful / helpful / interesting:

"Pythagorean Triangles and Musical Proportions"

by Martin Euser

http://www.nexusjournal.com/Euser.html

----- Original Message -----

From: monz <joemonz@yahoo.com>

To: <tuning-math@yahoogroups.com>

Sent: Monday, October 22, 2001 11:30 AM

Subject: [tuning-math] question about quadratics

> To all the math-geeks:

>

> It's well-established that the Babylonians had

> highly developed algebraic methods, altho they

> never actually developed an algebraic notation.

>

> There's also concrete proof that they had very good

> sexagesimal approximations to both square and cube roots.

>

> I'm investigating the possible applications some

> of these methods may have had to tuning problems,

> but my extremely math-challenged self needs some help.

>

> Can someone tell me what application quadratic equations

> may have to determining string-lengths? I'm interested

> in possible applications for the purposes of determining

> both JIs and/or temperaments.

>

>

> For a reference to a modern explanation of Babylonian

> algebra, please see the following, p 30-50:

>

> Neugebauer, Otto. 1957.

> _The Exact Sciences in Antiquity_.

> Providence, Brown University Press, 2d ed

> L.O.C.#: QA22 .N36 1957

>

>

> Thanks.

love / peace / harmony ...

-monz

http://www.monz.org

"All roads lead to n^0"

_________________________________________________________

Do You Yahoo!?

Get your free @yahoo.com address at http://mail.yahoo.com