On 27.11.2007 (13:44), Trevor Bača wrote:
> I wish I knew enough about Medieval music (or Medieval music theory anyway)
> to know if the Medieval invetors of "duplum" and "triplum" and "perfectus"
> and "imperfectus" and the like ever touched on the topic ... they'd make a
> good source to steal from ...
Oh, they did, they did... Not the medieval guys, but their
early-renaissance followers, such as Franchino Gaffurio, who, as far as I
remember, is the one who does the most thorough presentation of all the
different alternatives:
http://www.chmtl.indiana.edu/tml/15th/GAFPM4_TEXT.html
The principle is an extension of the nomenclature of sesquialtera (3:2) and
sesquitertia (4:3) etc., and particularly the names with -partiens and
-particularis. As the complexities grow, so do the names: 30:7 is called
Quadruplasuperbipartiensseptimas...
sesqui-: numerator one higher than denominator
subsesqui-: denom. one higher than num.
superpartiens: num. contains den. plus a specified part of itself, e.g.
supertripartiensquinta = 8:5, supersexcupartiensseptima=13:7, etc.
subsuperpartiens: same as the former, only upside down:
supersexcupartiensseptima=7:13
etc.
Charming system, but not very practical...
Oh, Eyolf, what a gem. Thanks so much for the beautiful reference.
And, yes: not very practical, but how fascinating ...
:-)