Question

The lowest note on a guitar is typically tuned to an E2. The next lowest string is tuned to an A2 at 110 Hz, which is a fourth (5 half steps) higher than the E2. The next string is tuned to D3, which is a fourth higher than A2.

(a) What are the frequencies of the lowest three open strings on a guitar tuned this way?

(b) If I play the open E2 on the guitar, and then push the A2 string down at the second fret, to increase its frequency by two half steps, the two strings will make a perfect fifth interval (7 half steps). If I do this and then play the two strings, what is the dominant beat frequency I’m most likely to hear?

(c) If I play the open E2 and the open A2, the interval I get is a fourth. If I play these two opens strings together, what is the dominant beat frequency I’m most likely to hear? Hint: a “just” fourth, for which there is no beating, involves a frequency ratio of 4/3.

Answer 1

Frets are inserted on guitar neck to provide a pitch relation between musical notes usually placed a semitone apart.

frequencies of strings are given below

E4=329.6Hz

4/3

B3=246.7Hz

5/4

G3=196.0Hz

4/3

D3=146.8HZ

4/3

A2=110.0hz

4/3

E2=82.4Hz

7 th harmonic

7 x82.4hz=576.9hz11.4 hz flatter than ET D5. Low string E2 being plucked sounding E2 at 82.4hz. This will include a small amount of 7 th harmonic

If the frets of guitar are set at equal temperament the the 5 th fret is 5 semitones or equal tempered musical fourth.The frequency must be equal to the open string frequency of the next string