1. What is a Pitch Class Set Calculator?

Definition: This calculator determines the pitch class (0-11) from any MIDI note number using modulo 12 arithmetic.

Purpose: It helps musicians and music theorists identify equivalent pitches across octaves in the chromatic scale.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( PCS \) — Pitch class set (0-11)
• \( n \) — MIDI note number (0-127)

Explanation: The modulo 12 operation reduces any note number to its equivalent pitch class within one octave.

3. Importance of Pitch Class Sets

Details: Pitch class sets are fundamental in music theory for analyzing atonal music, identifying chord structures, and studying musical patterns across octaves.

4. Using the Calculator

Tips: Enter any MIDI note number (0-127) to find its pitch class. The result will always be between 0 (C) and 11 (B).

5. Frequently Asked Questions (FAQ)

Q1: What does each pitch class number represent?
A: 0=C, 1=C♯/D♭, 2=D, 3=D♯/E♭, 4=E, 5=F, 6=F♯/G♭, 7=G, 8=G♯/A♭, 9=A, 10=A♯/B♭, 11=B

Q2: Why modulo 12?
A: Western music uses a 12-note chromatic scale that repeats every octave, so modulo 12 groups equivalent pitches.

Q3: How does this relate to MIDI note numbers?
A: MIDI note 60 is middle C (pitch class 0), 61 is C♯ (1), etc. The pattern repeats every 12 notes.

Q4: Can I use negative numbers?
A: While mathematically possible, standard MIDI only uses 0-127. Negative numbers would wrap around (e.g., -1 becomes 11).

Q5: How is this used in music analysis?
A: PCS helps identify equivalent pitches in different octaves, analyze chord structures, and study atonal music.