Mathematical explanation of music and white/black notes in a piano
The top answer on stackexchange is a superb explanation of musical science that most of the finest musicians in history could not give you. They just don't teach you these things in music class.Musical culture seems to resist illumination, perhaps fearing that the "magic" will somehow be broken. The irony is that music is, in a sense, a mathematical illusion, but revealing the trick only makes it more fascinating.I will add one important point that hasn't really been made: The purpose of equal temperament may have originally been to "change keys without retuning", but it also essentially allows you to play in 12 different keys at the same time. This has been exploited to great lengths as source of musical novelty and is absolutely fundamental to modern music.