Randall D. Knight — Superposition: Problem Problem_51

Western music uses a musical scale with equal temperament tuning, which means that any two adjacent notes have the same frequency ratio \( r \). That is, notes \( n \) and \( n + 1 \) are related by \( f_{n+1} = rf_n \) for all \( n \). In this system, the frequency doubles every 12 notes—an interval called an octave. a. What is the value of \( r \)? b. Orchestras tune to the note A, which has a frequency of 440 Hz. What is the frequency of the next note of the scale (called A-sharp)?