[gecode-users] random / mod

[Torsten Anders]

On 23.08.2006, at 22:01, Guido Tack wrote:
> I'll be very interested in seeing music applications [...]

BTW: the all-interval series defined as an examples for Gecode does not 
quite implement the musical concept all-interval series. The Gecode 
example constraints absolute distances between series pitches. Instead, 
an all-interval series for serial music constraints inversional 
equivalent intervals. That is, complementary intervals such a fifth 
upwards and a fourth downwards count as the same interval (namely 7). A 
typical implementation of inversional equivalent intervals uses the 
constraint modulo 12 (instead of simply computing the absolute 
distance, i.e.  | PC1-PC2 | )

	inversionalEquivalentInterval(PC1 , PC2 , Interval) := Interval = (PC2 
− PC1) mod 12

This standard all-interval series CSP for length 12 has 3856 solutions 
(cf. Morris, R. and D. Starr (1974). The Structure of All-Interval 
Series. Journal of Music Theory 18 (2)).

Best,
Torsten

PS: the problem spec at 
http://www.dcs.st-and.ac.uk/~ianm/CSPLib/prob/prob007/spec.html -- the 
source for the Gecode implementation -- shows the same 
misinterpretation of the musical concept.

--
Torsten Anders
Sonic Arts Research Centre • Queen's University Belfast
Frankstr. 49 • D-50996 Köln
Tel: +49-221-3980750
http://www.torsten-anders.de
http://strasheela.sourceforge.net