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#rhythm

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Stewart Russell

I had fun making this pattern. It was worth the time I spent balancing the areas of all the parts. Is it a weave of horizontal squares with diagonal decoration, or a weave of diagonal squares with horizontal decoration?

For a non-visual metaphor for the ways these patterns can flip, it's a little like polyrhythms in music. You can be bopping along to one rhythm, then suddenly the other one resolves. For the rest of the piece, your focus can flip between the rhythms

a staggered interwoven array of squares, each made up of four kites arranged nose to tail. The kites don't completely fill each square: there's an angled four-sided space in the centre, and it has the same area as one of the kites. This same four-sided space also makes an appearance as a horizontal spacer between the squares.
#pattern#rhythm#geometry
Public
Constraints Journal

Happy Monday everyone!

Here's something to brighten up the start of your week: a paper about solving mathemusical problems with ILP and SAT, from our latest issue:

Computing aperiodic tiling rhythmic canons via SAT models
link.springer.com/article/10.1

To make this Monday extra sweet: the authors use MapleSAT!

#Mathematics
#Music
#ConstraintProgramming
#AI
#Rhythm
#AcademicMastodon
#BooleanSatisfiability
#AperiodicTiling
#MapleSAT
#ILP
#CombinatorialAlgorithms
#ArtificialIntelligence

SpringerLinkComputing aperiodic tiling rhythmic canons via SAT models - ConstraintsIn Mathematical Music theory, the Aperiodic Tiling Complements Problem consists in finding all the possible aperiodic complements of a given rhythm A. The complexity of this problem depends on the size of the period n of the canon and on the cardinality of the given rhythm A. The current state-of-the-art algorithms can solve instances with n smaller than $$\varvec{180}$$ 180 . In this paper, we propose an ILP formulation and a SAT Encoding to solve this mathemusical problem, and we use the Maplesat solver to enumerate all the aperiodic complements. We then enhance the SAT model in two different ways. First, we enforce the SAT model with a set of clauses that retrieves the solutions up to translation. Second, we propose a decomposition of the solution space that allows to parallelize the resolution of the problem. We validate our different models using several different periods and rhythms and we compute for the first time the complete list of aperiodic tiling complements of standard Vuza rhythms for canons with period $$\varvec{n} = \varvec{\left\{ 180, 420, 900 \right\} }$$ n = 180 , 420 , 900 .
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Erik L. Midtsveen 🏴🏳️‍🌈

"We have come more and more under the dominance of mechanics and sacrificed living humanity to the dead rhythm of the machine without most of us even being conscious of the monstrosity of the procedure. Hence we frequently deal with such matters with indifference and in cold blood as if we handled dead things and not the destinies of men."

— Rudolf Rocker

Image depicting a quote by Rudolf Rocker: "We have come more and more under the dominance of mechanics and sacrificed living humanity to the dead rhythm of the machine without most of us even being conscious of the monstrosity of the procedure. Hence we frequently deal with such matters with indifference and in cold blood as if we handled dead things and not the destinies of men." — Rudolf Rocker
#RudolfRocker#AnarchoSyndicalist#AnarchoSyndicalism
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cernejpudink.cz

V roce 2001 RCA/Private Records nahráli prosincové vystoupení vynikající bluesové zpěvačky Etty James v losangelském klubu House Of Blues. Záznam vyšel o několik měsíců později na DVD i CD pod názvem Etta James and The Roots Band: Burnin‘ Down The House.
#10YearsOfPuddingRevisited #EttaJames #Music #Blues #Rhythm'n'blues #Soul
cernejpudink.cz/2016/07/03/ett

Obal alba Etta James and The Roots Band: Burnin‘ Down The House
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