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I know Pythagoras is often brought up, but where and why did he develop this?

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marked as duplicate by Tim, Dom♦ theory Jan 3 '17 at 15:30

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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.

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    It should be pointed out that twelve perfect fifths do not add up exactly to seven octaves. Even God can't change that, if She's logical. – Scott Wallace Jan 3 '17 at 10:41
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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.

cite: https://en.wikipedia.org/wiki/Pythagorean_hammers

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  • It might be pointed out that this nice story about Pythagoras and the anvils doesn't appear until the Middle Ages, and the scholarly opinion is that it's spurious. Not only that, but it doesn't work acoustically: it's the anvils that ring far more audibly than the hammers, and the ratio of frequency to weight is not the same as string lengths. But it's a good story. – Scott Wallace Jan 3 '17 at 10:34

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