BasisTakts

BasisTakts is a theoretical framework and practical toolkit for representing and manipulating rhythmic structure in digital music systems. It treats rhythms as linear combinations of elementary rhythmic units, called basis takts, enabling compact representation, analysis, and synthesis of complex patterns. The approach combines ideas from linear algebra with tempo- and takt-based timing to produce tempo-normalized representations that can be mapped across meters and tempi.

Origin and motivation: BasisTakts emerged from work on rhythm representation for algorithmic composition and music-information retrieval. By decomposing a rhythm into basis takts, it becomes possible to compare patterns across different tempi, interpolate between patterns, and perform efficient coding.

Core concepts: A basis takt is an elementary rhythmic unit aligned to a tempo grid. A rhythm is represented by a vector of coefficients that weight basis takts; a tempo lattice defines how basis takts scale when tempo changes. The representation supports operations such as projection, decomposition, and recombination. The framework emphasizes phase-consistent alignment, so beats line up under tempo variation.

Technical implementation: Common implementations use matrix factorization or sparse coding to fit a target rhythm as a nonnegative combination of basis takts. Time alignment is achieved via warping and phase-shift invariant modeling. The approach is compatible with digital-audio workstations and algorithmic composition pipelines, enabling real-time or offline processing.

Applications and variants: BasisTakts supports rhythm analysis, similarity search in large music corpora, adaptive scoring for multimedia, and generative rhythm construction. Variants differ by the choice of basis set, tempo normalization scheme, and sparsity constraints.

See also: Rhythm analysis, beat tracking, basis functions, rhythm decomposition, tempo normalization.