Tuning Systems & Interval Ratios

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

Objectives

• 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 in Indian Raga, Javanese Gamelan, and Maqam
• Student will understand the relationship between diatonic intervals and frequency ratios
• Student will be able to derive intervals from frequency calculations

Resources

• Kyle Gann, "Information on Alternate Tunings"

Class Activities

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