'The mathematics of piano tuning,' by Tony Phillips.

'Math and the Musical Offering,' by Tony Phillips.'The mathematician’s patterns, like those of the composer, must be beautiful,' by Peter Lynch, The Irish Times.Emily Howard, articles and compositions posted as Artist in Residence, Department of Mathematical Sciences, University of Liverpool.'Was Something Wrong with Beethoven’s Metronome?' by Sture Forsén, Harry B.'Music: Broken Symmetry, Geometry, and Complexity' by Gary W.'Musical Actions of Dihedral Groups,' by Alissa S.'Time-frequency Analysis of Musical Rhythm,' by Xiaowen Cheng, Jarod V.'No Static at All: Frequency modulation and music synthesis,' by David Austin.'Phase transitions: The math behind the music,', May 23, 2019.'The Smile of Math: When Categories Inspire,' by Maria Mannone.Listen to Dmitri Tymoczko (Princeton University) speak about using topology to represent musical chords as points in a space. Marcus du Sautoy (Simonyi Professor for the Public Understanding of Science and a professor of mathematics at the University of Oxford) talks to a concert audience about the connections between music and mathematics. In this podcast interview, Rob Schneiderman (Lehman College, CUNY) discusses the metaphorical connections between math and music. What Do Equations Sound Like on the Piano? Pius Wong (Austin Community College) discusses Chordinates, a web tool he created that generates melodies from the graphs of math equations.Ethan Thompson and David Hamilton explain the math behind music in a fun, concise way in this finalist entry in the 2015 Math-O-Vision contest.

Clair uses the Moonlight Sonata 'to illustrate the way Beethoven was able to convey emotion and creativity using the certainty of mathematics.' Music and math: The genius of Beethoven – Natalya St. From the constraints imposed by these rhythmic patterns, melodies emerged naturally as I composed, special to each prime.' The main theme plays in the time signature 7/4, which indicates 7 beats per measure, with an interlude that passes through the signatures 2/4, 3/4 and 5/4 as well. 'As the title indicates, the piece is written in prime-numbered time signatures which is to say, there is a prime number of beats in each measure. Robert Schneider (Apples in Stereo/Elephant 6) composed this theme for 'MSI (Math Sciences Investigation): Anatomy of Integers and Permutations,' a play by mathematician Andrew Granville and screenwriter Jennifer Granville. Robert Schneider - Reverie in Prime Time Signatures (August 2013, Banff Centre). Rickard says that he is 'passionate about mathematics, music and educating the next generation of scientists and mathematicians.' and MA and PhD degrees in applied and computational mathematics from Princeton University. Scott Rickard has degrees in mathematics, computer science, and electrical engineering from M.I.T. The world's ugliest music: Scott Rickard at TEDxMIA.

Sean Hardesty (Rice University) plays the opening of the Sibelius Violin Concerto and discusses the relationship between mathematics and music. The Science Behind the Arts: The Maths Behind Music.

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