Alan Marsden
ISBN 9026516355 (hardback)
No.4 of the series Studies on New Music Research
Published in 2000 in Lisse (Netherlands) by Swets & Zeitlinger, 68.00 euro. [Link to Further Publisher's details, including ordering]
Representing Musical Time examines a crucial issue in processing music by computer and in other abstract and formal approaches to music. The relations of time specified in musical scores and found in bodies of musical performances have a complex and sometimes indeterminate structure, and even the nature of musical time can be in question. Complicating factors such as partially determined ordering of events are found not only in music of the twentieth century, when composers explicitly employed such indeterminacy, but also in music where the indeterminacy is only implicit in the interpretation of the notation. This book analyses in detail the essential issues of the nature of musical time, possible formulations of musical temporal relations, taking account of indeterminacy, and systems for the measurement of musical time. Representations are classified according to their expressive power and computational complexity. Existing systems of musical representation are related to these formulations, and some generic representations of music are proposed and analysed. The most expressively powerful representations are shown to be computationally intractable, while those of least computational complexity are shown to be incapable of representing some music. A perfect system of representation is therefore impossible, and different representations are appropriate for different purposes.
p.182-183. Algorithms 17 and 18 only apply to tables of relations which are consistent. Otherwise the events as represented do not necessarily form a partial order, and so the normalisation is meaningless.
p.183. Step 3.3.2 in Algorithm 18 should refer to order[i] and order[j] instead of simply i and j. Step 4, line 3 should read '... count2[x, z] is more than count2[y, z] ...'.
p.185. Step 5.8 in Algorithm 20 should also specify that the inverse relation be set for the cell diagonally opposite c1 in the case of square tables. Step 3 of the function propagate(r1, r2, r3) [period-relation version] should make clear that 'corresponding components' means that each component of p4 must be set to the intersection of propagate(c1, c2, c3) for each of the four tuples <c1, c2, c3> drawn from the components named SS, SE, ES and EE of p1, p2, and p3 respectively, such that the first letter of the name of c1 is the same as the first letter of the name of the required component of p4, the first letter of the name of c2 is the same as the last letter of the name of c1, similarly for c3 and c2, and the last letter of the name of c3 is the same as the last letter of the name of the required component of p4 (e.g., <SS, SS, SS>, <SS, SE, ES>, <SE, ES, SS> and <SE, EE, ES> for the SS component of p4).
Applets and software implementing the algorithms in Appendix 1 of the book can be found here.