Corpus ID: 7468106

The Euclidean Algorithm Generates Traditional Musical Rhythms

@inproceedings{Toussaint2005TheEA,
  title={The Euclidean Algorithm Generates Traditional Musical Rhythms},
  author={Godfried T. Toussaint},
  year={2005}
}
The Euclidean algorithm (which comes down to us from Euclid’s Elements) computes the greatest common divisor of two given integers. It is shown here that the structure of the Euclidean algorithm may be used to generate, very efficiently, a large family of rhythms used as timelines (ostinatos), in sub-Saharan African music in particular, and world music in general. These rhythms, here dubbed Euclidean rhythms, have the property that their onset patterns are distributed as evenly as possible… Expand

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References

SHOWING 1-10 OF 175 REFERENCES
A Mathematical Analysis of African, Brazilian, and Cuban Clave Rhythms
TLDR
An analysis of the rhythms with several similarity measures reveals that the clave Son is most like all the other clave rhythms and perhaps provides an explanation for its worldwide popularity. Expand
The Stratification of Musical Rhythm
There are many books on counterpoint and harmony, but few indeed on the theory of rhythm. Those few approach it through its graphic notation, or in terms of metrical feet, as if it were poetry. MauryExpand
Construction and interpretation of equal-tempered scales using frequency ratios, maximally even sets, and P-cycles.
TLDR
It is shown that with an appropriate choice of nonoctave closure (6:1 in this case), determined by the formalism combined with continued fraction analysis, that this group-theoretic-generated system may be interpreted in terms of the frequency ratios 21:56:88:126. Expand
The Distance Geometry of Deep Rhythms and Scales
We characterize which sets of k points chosen from n points spaced evenly around a circle have the property that, for each i = 1, 2, . . . , k−1, there is a nonzero distance along the circle thatExpand
Rhythm and Meter in Ancient Greek Music
The resurgence of interest in ancient Greek music in the last ten years has resulted in the publication of many important monographs and articles on musical instruments, scales, particular treatises,Expand
The Rhythmic Structure of Music
In this influential book on the subject of rhythm, the authors develop a theoretical framework based essentially on a Gestalt approach, viewing rhythmic experience in terms of pattern perception orExpand
Generalized Diatonic and Pentatonic Scales: A Group-Theoretic Approach
HIS IS THE SECOND in a planned series of papers in which musical scales, tuning, and temperament are studied from a mathematical point of view.1 In the present paper, group-theoretic methods are usedExpand
THE METRICAL STRUCTURE OF MACEDONIAN DANCE
METRICAL PATTERNS In essence, the theory to be presented here states that dance forms are generated by the encoding of abstract metrical patterns into an organized sequence of movements. The theoryExpand
Periodic musical sequences and Lyndon words
When one enumerates periodic musical structures, the computation is done up to a cyclic shift. This means that two solutions which are cyclic shifts of one another are considered the same. LyndonExpand
THAI SONGS IN 7/4 METER
t became apparent during a period of research in Thailand in 1965-67 that there existed a unique group of songs, based on a rhythmic cycle of seven beats, which were practically unknown outside ofExpand
...
1
2
3
4
5
...