Looking at Numbers

Everyone talks about the beauty of mathematics, but almost no one observes that this beauty is largely a result of the symmetries that emerge from simple combinations of natural numbers. One sees this clearly in Looking at Numbers ._

Mathematics and music from a platonic point of view

Numbers as Pythagoras might have seen them

Numbers producing images and music too

Mathematics and music from a platonic point of view Numbers as Pythagoras might have seen them Numbers producing images and music too ? Includes supplementary material: sn.pub/extras

Autorentext

Tom Johnson (1939) is considered a minimalist, since he works with simple forms, limited scales, and generally reduced materials, but he proceeds in a more logical way than most minimalists, often using formulas, permutations, predictable sequences and various mathematical models. He is particularly well known for his operas. The Four Note Opera (1972) has been presented in 11 different languages since its premier 40 years ago. Riemannoper has been staged more than 30 times in German-speaking countries since its premier in Bremen in 1988. Often played non-operatic works include Bedtime Stories, Rational Melodies, Music and Questions, Counting Duets, Tango, Narayana's Cows, and Failing: a very difficult piece for solo string bass. His longest work is the Bonhoeffer Oratorio for four soloists, two choruses and orchestra, presented in Maastricht (1996), Berlin (1998) and New York (2000). The book Conversations avec Tom Johnson, in collaboration with Bernard Girard, was published in 2011.

Franck Jedrzejewski is a researcher in mathematical physics at the
CEA Saclay and has also a PhD in philosophy and musicology. He
teaches at the INSTN as well as in the University of Paris Sud and
Versailles-Saint-Quentin.

Inhalt
Introduction.- 1. Permutations.- 1.1 Symmetric Group.- 1.2 Bruhat Order.- 1.3 Euler Characteristic.- 1.4 Group Action.- 1.5 Permutohedra and Cayley Graphs.- 1.6 Coxeter Groups.- 1.7 Homometric Sets.- 2. Sums.- 2.1 Integer Partitions.- References.- 3. Subsets.- 3.1 Combinatorial Designs.- 4 Kirkman's Ladies, a Combinatorial Design.- 4.1 Steiner and Kirkman Systems.- 5. Twelve.- 5.1 (12,4,3).- 6. (9,4,3).- 6.1 Decomposition of Block Designs.- 7. 55 Chords.- 7.1 Chords and Designs.-8. Clarinet Trio.- 8.1 Strange Fractal Sequences.- 9. Loops.- 9.1 Self-Replicating Melodies.- 9.2 Rhythmic Canons.-10. Juggling.- 10.1 Juggling, Groups, and Braids.- 11. Unclassified.- 11.1 Some Other Designs.- A Figures.- References.