Computational geometric aspects of rhythm, melody, and voice-leading

Toussaint, Godfried T.

doi:10.1016/j.comgeo.2007.01.003

Cited by 27 publications

(15 citation statements)

References 127 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Note that the oddity property requires that the circle is divided into an even number of units. The notion of rhythmic oddity has received different mathematical treatments; see [17] for more details.…”

Section: Introductionmentioning

confidence: 99%

Asymmetric polygons with maximum area

Barba

Caraballo

Díaz-Báñez

et al. 2016

European Journal of Operational Research

View full text Add to dashboard Cite

We say that a polygon inscribed in the circle is asymmetric if it contains no two antipodal points being the endpoints of a diameter. Given n diameters of a circle and a positive integer k < n, this paper addresses the problem of computing a maximum area asymmetric k-gon having as vertices k < n endpoints of the given diameters. The study of this type of polygons is motivated by ethnomusiciological applications.

show abstract

Section: Introductionmentioning

confidence: 99%

Asymmetric polygons with maximum area

Barba

Caraballo

Díaz-Báñez

et al. 2016

European Journal of Operational Research

View full text Add to dashboard Cite

show abstract

“…There are numerous applications based on "necklace" concept and various distances, e.g. geometry distance for music, swap distance [22,23,24], Hamming distance with shift [16], and necklace alignment distance (NAD) [5].…”

Section: Adapted Distance For Blade Design Applicationmentioning

confidence: 99%

Advanced Computational Methods for Knowledge Engineering

Nguyên

Do²,

Thi

2020

Advances in Intelligent Systems and Computing

View full text Add to dashboard Cite

Numerous optimal design applications are black-box mixed integer nonlinear optimization problems: with objective function and constraints that are outputs of a black-box simulator involving mixed continuous and integer (discrete) variables. In this paper, we address an optimal design application for bladed disks of turbo-machines in aircraft. We discuss the formulation of an appropriate distance with respect to discrete variables which can deal with the cyclic symmetry property of the system under study. The necklace concept is introduced to characterize similar blade configurations and an adapted distance is proposed for discrete space exploration of a derivative-free optimization method. The results obtained with this method on a simplified industrial application are compared with results of state-of-the-art black-box optimization methods.

show abstract

“…Mathematically, a rhythm is a partition of [0, n) into k open intervals called off-sets and k integer points called on-sets (see Refs. [1,[6][7][8][9]). Musically, we interpret the on-sets as points in time (modulo n) when a percussion instrument is to be struck.…”

Section: Introductionmentioning

confidence: 99%

Realizing partitions respecting full and partial order information

Demaine

Erickson

Kriz̧anc

et al. 2008

Journal of Discrete Algorithms

View full text Add to dashboard Cite

For n ∈ N, we consider the problem of partitioning the interval [0, n) into k subintervals of positive integer lengths 1 , . . . , k such that the lengths satisfy a set of simple constraints of the form i ij j where ij is one of <, >, or =. In the full information case, ij is given for all 1 i, j k. In the sequential information case, ij is given for all 1 < i < k and j = i ± 1. That is, only the relations between the lengths of consecutive intervals are specified. The cyclic information case is an extension of the sequential information case in which the relationship 1k between 1 and k is also given. We show that all three versions of the problem can be solved in time polynomial in k and log n.

show abstract

Computational geometric aspects of rhythm, melody, and voice-leading

Cited by 27 publications

References 127 publications

Asymmetric polygons with maximum area

Asymmetric polygons with maximum area

Advanced Computational Methods for Knowledge Engineering

Realizing partitions respecting full and partial order information

Contact Info

Product

Resources

About