Question

using modular arithmetic, if you start on a (represented as 0) and move 7 semitones forward on the circle of semitones, which note do you reach? a. g b. f c. d d. e

Explanation:

Step1: Recall modular arithmetic formula

In modular arithmetic, for \(a\bmod n\), we find the remainder when \(a\) is divided by \(n\). Here, the circle of semitones has \(12\) notes (\(n = 12\)), starting from \(A=0\), and we move \(7\) semitones (\(a=7\)).

Step2: Calculate \(7\bmod 12\)

Since \(7\lt12\), \(7\bmod 12 = 7\).

Step3: Map the number to the note

The note corresponding to \(7\) in the circle of semitones is \(G\).

Answer:

a. G