Any resources in this are welcome.
I know Pythagoras is often brought up, but where and why did he develop this?
Any resources in this are welcome.
I know Pythagoras is often brought up, but where and why did he develop this?
the pitch of a vibrating string is related to its length. if that length is shortened by a third, you get a frequency a fifth higher. shortening that by a third creates a fifth higher than that, and so forth until, 12 steps later you get a frequency that is 7 octaves above the original tone after having passed through (or stopped at) all other 11 tones. setting a reference tone at, say 440 Hz (concert A) is conventional but generating the frequencies of the remaining 11 tones is the physical consequence of the relationship between the length of strings and their relative frequencies. this sequence generates the circle of fifths and sets the relationship between the notes of the scale upon the physics of the vibration of strings.
I will partially answer the why did he bother question. The story with pythagoras is that he was passing by a blacksmith one time and noticed the sound the hammer would make banging against the anvil was different each time a different hammer was used which intrigued him and the reason for that he figured out was due to the size of the hammers.