**UM Math Graduate Students Seminar**

Drew Armstrong

* University of Miami *

**will present**

**Mathematics of music**

Friday, April 24, 2015, 3:30pm

Ungar Building Room 402

**Abstract: **

Yesterday I finished teaching a course on the mathematics of music. In this talk I will present some of the highlights. The mathematics of music comes in two basic flavors (1) Fourier analysis tells us that most instruments make sounds with harmonics at integer multiples of the fundamental frequency. This together with some psychoacoustics implies that small whole number frequency ratios "sound good". (2) Then, to build a music theory on small whole number ratios means we must come up with good approximate solutions to impossible problems in number theory. The first and most important such approximation is that log(3)/log(2) is very close to 19/12. This is why we divide the octave into 12 tones.

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