#Nyu music math series#

This is great intuitive preparation for the concepts of discrete vs continuous generally. Keyboards, fretted string instruments and saxophones produce discrete pitches. The voice, fretless stringed instruments and trombones produce continuous pitches. The pitch continuum is, well, continuous, but tuning systems and scales are discrete.

Seventeenth-century European bellringing introduced one of the earliest nontrivial results in graph theory, change or method ringing. Generating diatonic chords from a scale is an exercise in combinatorics. See this delightful paper by Vi Hart about symmetry and transformations in the musical plane.

Music is really just a way of applying symmetry to events in time. You also need logarithms to understand decibels and loudness perception. The relationship between absolute pitches and pitch classes is an excellent doorway into logarithms generally. Octave equivalency is really just your brain’s ability to detect frequencies related by powers of two. I wasn’t at all surprised to learn that Einstein conceptualized wave mechanics in musical terms as well. The concept of orbitals in quantum mechanics made zero sense to me until I finally found out that they’re just harmonics of the electron field’s vibrations.

#Nyu music math series#

There’s a strong case to be made that overlapping overtone series is the basis of all of western music theory. If two pitches share a lot of overtones, we tend to hear them as consonant, at least here in the western world. We can’t necessarily consciously compare the partials of a sound, but we certainly do it unconsciously - that’s how we’re able to distinguish different timbres, and is probably the basis for our sense of consonance and dissonance. The brain turns out to be adept at decomposing sinusoids into their component frequencies. Placing rhythms on a circle gives a good multisensory window into ratios and angles. My masters thesis is devoted in part to a method for teaching math concepts using a drum machine organized on a radial grid. Music is richly mathematical, and an understanding of one subject can be a great help in understanding the other.