Finding Alternative Musical Scales

  • J. N. HookerEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9892)


We search for alternative musical scales that share the main advantages of classical scales: pitch frequencies that bear simple ratios to each other, and multiple keys based on an underlying chromatic scale with tempered tuning. We conduct the search by formulating a constraint satisfaction problem that is well suited for solution by constraint programming. We find that certain 11-note scales on a 19-note chromatic stand out as superior to all others. These scales enjoy harmonic and structural possibilities that go significantly beyond what is available in classical scales and therefore provide a possible medium for innovative musical composition.


Frequency Ratio Constraint Programming Constraint Satisfaction Problem Simple Ratio Chromatic Scale 
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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Carnegie Mellon UniversityPittsburghUSA

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