Re Euler translation

David: I, for one, would like to see the translation of Euler's
Tentament posted. I imagine Joe Monzo, Margo, and others would also. One
might try the college or university where Smith was a student to find
his current address (if any).

The work is valuable not only for the "gradus suavitatis" consonance
function but also as the source of the Euler-Fokker genera.

Also, one might post the somewhat later texts of Euler in which he
admits the prime number 7 to music. I think at least one is in French
rather than his usual quite readable Latin.

BTW, I am reading a history of continued fractions and Pade'
approximants (anything to avoid watching more of the election debacle on
the Tube). Apparently Barbour's "mixed expansion" (in "Music and Ternary
Continued Fractions") is the division form of Brun's algorithm for
finding temperaments with good thirds and fifths (among other uses).

-- John

John Chalmers wrote,

>BTW, I am reading a history of continued fractions and Pade'
>approximants (anything to avoid watching more of the election debacle on
>the Tube). Apparently Barbour's "mixed expansion" (in "Music and Ternary
>Continued Fractions") is the division form of Brun's algorithm for
>finding temperaments with good thirds and fifths (among other uses).

John -- did you see Pierre Lamonthe post on 10/8:

>I quote first from

><http://mathworld.wolfram.com/> :

><< Although attempts were made to generalize the >>
> [ Euclidean algorithm to n >= 3 ]
><< by Hermite (1850), Jacobi (1868), Poincaré (1884), Perron (1907),
> Brun (1919, 1920, 1957), and Szekeres (1970), all such routines
> were known to fail in certain cases (Ferguson and Forcade 1979,
> Forcade 1981, Hastad et al. 1989). The first successful integer
> relation algorithm was developed by Ferguson and Forcade (1979)
> (Ferguson and Bailey 1992, Ferguson et al. 1999). >>

>Has someone here an idea on this last algorithm nature ?

John -- any ideas?