Geometric Series in Music?

📌 CONCEPT: A geometric series in music is a sequence of notes with frequencies that follow a geometric progression, where each note's frequency is a fixed constant multiple of the previous note's frequency.

📐 RULE / FORMULA: The frequency of each note in a geometric series can be calculated using the formula: f_n = f_1 * r^(n-1), where f_n is the frequency of the nth note, f_1 is the frequency of the first note, and r is the common ratio.

💡 WORKED EXAMPLE: Given the frequency of the first note (f_1) as 330 Hz, and assuming a common ratio of 1.1, we can find the frequency of the sixth note: f_6 = 330 * (1.1)^(6-1) = 330 * (1.1)^5 = 540.522 Hz.

⚠️ COMMON MISTAKE: Students often forget to subtract 1 from the note number (n) in the formula f_n = f_1 * r^(n-1), leading to incorrect calculations.