Numbering from the bottom, if the 1st string is tuned A_4 (440 Hertz), the secon
ID: 1517447 • Letter: N
Question
Numbering from the bottom, if the 1st string is tuned A_4 (440 Hertz), the second string E4 can be tuned to be a perfect 4 interval (3:4 ratio) hence frequency: f = 440 times 3/4 = 330 Hertz. This is about 0.1% lower than the 329.6 Hertz of equal temperament piano key, but we'd only hear a 0.4 Hertz beat (i.e. 1/0.4=2.5 seconds between beats) Suppose the next string C_4 is tuned to be a M3 (4:5 ratio) below 330 Hertz. What would be its frequency? What would be the "beat" frequency with the piano C_4 key? Suppose the next string G_4 is tuned to be a P5 (2:3 ratio) above the C_4 string. What would be its frequency? What would be the "beat" frequency with the piano G_4 key? Would this method give a reasonably close tuning for the Ukulele?Explanation / Answer
a) f = 4/5 * 330 = 264 Hz
Beat freq = 264 - 261.626 = 2.374 Hz
b) f = 3/2 * 261.626 = 392.439 Hz
Beat = 392.439 - 391.995 = 0.444 Hz
c) Yes, as tuning string is already giving close beat frequencied for piano, and ukulele is a stringed instrument
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