In today’s first tutoring we looked at volumes of prisms and cubes. Then discussed why Sine, Cosine and Tangent integrate triangular geometry, curves, and sound. Then we spent most of the time exploring the nature of perception of sound and how harmonic series and pitch shifting yields musical notes, which led to an exploration of equal-tempered scales and led my student to write a javascript program that plots the differences in notes between harmonically derived and equal tempered notes – whose results we then through into Wolfram Alpha to generate a graph.

It was fun to have a session that had us using pen, paper, computer, piano and guitar at different times.

Oh yeah, we experimented with different ways of encoding binary messages into music as well, and had a really interesting conversation about why harmonic relationships appearing beauty would be an adaptive trait, and whether preference for a harmonically-based vs. even tempered scale would be more enculturated or inherent.