> Musicians and theorists struggled with this for years, coming up with various compromises that sounded good in some "keys" and awful in others, until math pro

> Musicians and theorists struggled with this for years, coming up with various compromises that sounded good in some "keys" and awful in others, until math provided the ultimate compromise: base your logarithmic scale on twelfth roots of two and every key will be exactly the same more-or-less-in-tune. This is inaccurate in two ways. First, only keyboards and those playing with them, use a fixed temperament. Everyone else, strings, voices, brass, winds, adjusts the pitch of individual notes based on vertical and horizontal context. A c does not have a fixed number of Hz throughout a piece. Second, math did not provide the ultimate compromise. Equal temperament was known as far back as the fourth century BC, and people were advocating for and composing in equal temperament in the sixteenth century. Rejecting equal temperament in favor of meantone temperings was a conscious decision, not a compromise from ignorance.