theory

Twelve feels arbitrary. An octave is a doubling of frequency, and nothing about doubling obviously suggests twelve steps rather than ten or sixteen. Is there a mathematical reason it landed on twelve, or is it purely…

A major and a minor triad differ by one semitone in the middle note, and the emotional difference is enormous. That seems out of proportion to the change. Is there an acoustic reason, or is it something we are taught…

The rule of thirds is the first thing anyone is taught about composition, and it is also the first thing more advanced people tell you to ignore. The justifications I find are either vague appeals to the golden ratio…