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12 half-tones = 1 octave = double the frequency

1 half tone = multiply frequency by the 12th root of 2 = 1.0594631 (rounded)

'E' above 'A' is 7 half tones above 'A'.

Frequency of 'E' above = (440) x (2)7/12 = 659.3 Hz.(rounded)

'E' below 'A' is 5 half tones below 'A'.

Frequency of 'E' below = (440) divided by (2)5/12 = 329.6 Hz . (rounded)

Notice that, by golly, the frequencies we calculated for 'E' above and 'E' below

are in the ratio of 2 to 1 . . . they're an octave apart, just as we would hope.

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Q: If an A is 440 hz how many hz is an e?
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