Algorithmic, Geometric, and Combinatorial Problems in Computational Music Theory
نویسنده
چکیده
Computational music theory offers a wide variety of interesting geometric, combinatoric, and algorithmic problems. Some of these problems are illustrated for the special cases of rhythm and melody. In particular, several techniques useful for the teaching, analysis, generation and automated recognition of the rhythmic components of music are reviewed. A new measure of rhythm-evenness is described and shown to be better than previous measures for discriminating between rhythm timelines. It may also be more efficiently computed. Several open problems are discussed.
منابع مشابه
Towards Pedagogability of Mathematical Music Theory: Algebraic Models and Tiling Problems in computer-aided composition
The paper aims at clarifying the pedagogical relevance of an algebraic-oriented perspective in the foundation of a structural and formalized approach in contemporary computational musicology. After briefly discussing the historical emergence of the concept of algebraic structure in systematic musicology, we present some pedagogical aspects of our MathTools environment within OpenMusic graphical...
متن کاملGeometric Arrangements: Substructures and Algorithms
In this thesis we study a variety of problems in computational and combinatorial geometry, which involve arrangements of geometric objects in the plane and in higher dimensions. Some of these problems involve the design and analysis of algorithms on arrangements and related structures, while others establish combinatorial bounds on the complexity of various substructures in arrangements. Inform...
متن کاملComputational geometric aspects of rhythm, melody, and voice-leading
Many problems concerning the theory and technology of rhythm, melody, and voice-leading are fundamentally geometric in nature. It is therefore not surprising that the field of computational geometry can contribute greatly to these problems. The interaction between computational geometry and music yields new insights into the theories of rhythm, melody, and voice-leading, as well as new problems...
متن کاملThe Approximate Rank of a Matrix and its Algorithmic Applications
We study the -rank of a real matrix A, defined for any > 0 as the minimum rank over matrices that approximate every entry of A to within an additive . This parameter is connected to other notions of approximate rank and is motivated by problems from various topics including communication complexity, combinatorial optimization, game theory, computational geometry and learning theory. Here we giv...
متن کاملPERFORMANCE COMPARISON OF CBO AND ECBO FOR LOCATION FINDING PROBLEMS
The p-median problem is one of the discrete optimization problem in location theory which aims to satisfy total demand with minimum cost. A high-level algorithmic approach can be specialized to solve optimization problem. In recent years, meta-heuristic methods have been applied to support the solution of Combinatorial Optimization Problems (COP). Collision Bodies Optimization algorithm (CBO) a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003