Question

The ascending (sharps) half-step notation for the chromatic scale is given below: C4, CH, D4, D4, E4, F4, F#, G4, GH, A4, A, B4. The pitch G4 has a frequency of 392 Hz. Using this information, determine the frequency in Hz of the pitch B4. Use two decimal place accuracy.

a) 415.30 Hz
b) 466.16 Hz
c) 523.25 Hz
d) 587.33 Hz

Answer 1

The frequency of the pitch B4 can be calculated using the twelve equal-tempered semitones from G4, resulting in a frequency of 466.16 Hz.

Step-by-step explanation:

To determine the frequency in Hz of the pitch B4 on the chromatic scale, we can use the sequence of twelve equal-tempered semitones that span from G4 to B4. Given that G4 has a frequency of 392 Hz, each semitone represents a frequency ratio of the twelfth root of two (approximately 1.05946). Since B4 is four semitones above G4, we can calculate the frequency of B4 by multiplying the frequency of G4 by this ratio four times (i.e., raising the ratio to the fourth power).

Thus, the frequency of B4 is given by:

392 Hz * (1.05946 ^ 4) = 392 Hz * 1.18921 = 466.16 Hz

Therefore, the correct answer is (b) 466.16 Hz.