Music Theory and Math

Music and mathematics share a deep connection, from frequencies to rhythms. This article explores how numbers underpin the art of sound, revealing the science behind melody.

Frequencies

Pitch is mathematical:

  • Frequency: \( f = \frac{1}{T} \), where \( f \) is frequency and \( T \) is period.
  • Octaves: Doubling frequency (e.g., 261 Hz to 522 Hz for C4 to C5).
  • Tuning: A440 standard sets 440 Hz as A above middle C.

Sound waves are pure math in motion.

\( f = \frac{1}{T} \)

Rhythm

Rhythm is fractional:

  • Time Signatures: 4/4 means 4 beats per measure, each a quarter note.
  • Subdivision: Eighth notes split beats into \( \frac{1}{2} \).
  • Polyrhythms: Combine 3:2 ratios for complexity.

Math structures musical time.

Harmony

Harmony relies on ratios:

  • Intervals: Perfect fifth is a 3:2 frequency ratio.
  • Chords: Triads use 4:5:6 ratios for major chords.
  • Scales: Pythagorean tuning uses simple fractions.

Consonance emerges from mathematical harmony.

Applications

Math enhances music in:

  • Synthesizers: Generate waves with equations.
  • Tuning Systems: Equal temperament divides octaves into 12.
  • Composition: Algorithms create music.

Music theory and math blend art and science.