Tuning Systems & Interval Ratios

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This lesson is part of the Fundamentals of Sound & Music module.


  • Students will understand the concept of tuning systems and temperaments.
  • Student will understand the basis of 12-TET tuning (including definitions of cents and semitones)
  • Student will know the general differences between 12-TET and just intonation.
  • Students will be able to derive harmonic frequencies according to simple arithmetic calculations (using harmonics or interval ratios).
  • Student will have a basic understanding of tuning discrepancies based on harmonics and interval ratios
  • Student will understand the concept of beats and how they are used to tune an instrument
  • Student will be exposed to tuning variations and fluidity in Indian Raga, Javanese Gamelan, Mariachi, Tuva Throat Singing, and Maqam
  • Student will understand the relationship between diatonic intervals and frequency ratios
  • Student will be able to derive intervals from frequency calculations



teInstructor References[edit]

Listening and Videos[edit]


Class Activities[edit]

  • Demonstration of different tuning systems and temperaments
  • Demonstration of interval ratios using a monochord.
  • Calculation of intervals using just intonation ratios - discussion of tuning discrepancies
  • Demonstration of beats