Reddit reviews Mathemagical Music Production: Second Edition

Temperament describes the intervals an octave is divided into. Equal temperament takes an octave and divides it into 7 12 equal segments. Works well for melodic music, good for changing key signatures, but the math is a hot mess, full of irrational numbers. Pythagorean tuning derives these values via fractional math, aka the circle of 5ths. Start with C, multiply by 3/2 to get G, multiply that by 3/2 to get D, etc. (Handy chart.) The math is beautiful, glorious, astonishingly perfect -- and, many would say, it helps tune our bodies to work more efficiently. (You've heard of plants growing better when classical music is played; same deal for humans.)

Note that it's nearly impossible to use Pythagorean tuning on most modern instruments; equal temperament is built-in via frets, valves, or keys. Most software, which should make this trivial, even locks this out -- I'm looking at you, Ableton Live.

More info here:

https://www.amazon.com/Mathemagical-Music-Production-Derrick-Heerden-ebook/dp/B00I0YQ4OE