Still assuming that A4 = 426.7Hz, what is the frequency for E5? Information from

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Still assuming that A4 = 426.7Hz, what is the frequency for E5?

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In this homework we will find frequencies for notes of an A major scale. The note names for this scale are A, B, C#, D, E, F#, G#, A. The # symbol means "sharp." (C# is the black key just above the white C key on the piano keyboard.) If we start at A4 = 440 Hz, then the pitch of B4 can be found by multiplying 440 by the square of the twelfth root of two, since B is two half steps above A and each half step raises the pitch by the 12th root of 2. Do this calculation and see if you get the frequency given in the Appendix E of the online textbook. Now, suppose you are trying to reproduce an A major scale from the early 18th or 19th century, when A4 was perhaps tuned to 426.7Hz. What is the correct frequency (in Hz) for C#5 (assuming we want an equal tempered scale)?

Explanation / Answer

given A4 = 440 Hz
then, B4 = 440*(2^1/12)^2 = 493.8833 Hz
C#4 = B4*(2^1/6) = 554.365261 Hz
D4 = C#4*(2^1/12) = 587.32953 Hz
E4 = D4*(2^1/6) = 659.255113 Hz
F#4 = E4*(2^1/6) = 739.9888454 Hz
G#4 = F#4(2^1/6) = 830.6093 Hz
A5 = G#4*(2^1/12) = 880 Hz

for A4 = 426.7 Hz
C#5 = 2A4*(2^4/12) = 1075.2166239 Hz

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