Bjorklund's algorithm has identical structure to Euclidean algorithm

Key theoretical insight: both algorithms use repeated subtraction (division) to recursively partition sequences; this structural identity justifies the term 'Euclidean rhythm'.

Source paper

extracted_from

The Euclidean Algorithm Generates Traditional Musical Rhythms

(2021) · Toussaint, Godfried

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Communities (2)

community

Manifold-aware concept steering in neural representations
members_of
Explores geometry of activation/behavior manifolds to enable selective, non-destructive concept interventions.
Euclidean rhythms in world music
members_of
Mathematical structure underlying diverse musical traditions via Bjorklund's algorithm, correlating Euclidean string distributions with cultural preferences.

Frameworks (1)

framework

Euclidean Rhythms
supports
Family of musical rhythms generated via Bjorklund's algorithm, where k onsets are distributed evenly across n time units; denoted E(k,n).

Related by similarity (8)

cosine ≥ 0.65 · no typed edge

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

Bjorklund's Algorithmconcept0.856
Algorithm developed for timing systems in neutron accelerators; generates binary sequences where pulses are distributed as evenly as possible among intervals.
Many rhythms used in world music are Euclidean rhythms generated by Bjorklund's algorithm.finding0.762
Euclidean Algorithmconcept0.756
Ancient algorithm from Euclid's Elements (circa 300 B.C.) that computes greatest common divisor; shown to structurally parallel Bjorklund's rhythm generation algorithm.
The degree of similarities which exist in a structure must correspond exactly to the degree of similarity of the conditions there, and the degrees of differences which exist in a structure must also correspond to the degrees of difference in the conditions there.claim0.739
The profound principle that underlies all living structure; symmetry as the mathematical trace of necessity.
Representation-computation mismatch (Feucht: cyclic concepts computed in base-10, not circular geometry) will force About Blank to decouple 'representational geometry' from 'operational structure' in prediction0.730
We hypothesize that a similar 'brutal' and purely geometric process always occurs somewhere in other kinds of unfolding that generate living order — in poetry, dance, social structure, planning, and family relationships.hypothesis0.726
Extends the brutal geometry thesis beyond architecture into all creative and social domains; acknowledged as not yet confirmed with certainty
There is a bidirectional relationship between the geometry of representation and behavior across tasks and modalities.claim0.723
Author’s interpretive claim that the shared geometry is general and robust.
Circular representational structure does not imply that the model computes using the corresponding modular arithmeticclaim0.722
The paper's primary interpretive claim, directly answering the central question

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same_concept_as · Nomic cosine

External markdown files that talk about the same concept as this entity.

alexander
**The Euclidean Algorithm Generates Traditional Musical Rhythms**papers/extracted/2021-11-17_Stefan-Lesser_banff.pdf_a9e313.md0.793