Part 3 · Intervals: How Notes Relate, and How to Hear Them

Example 3.12

A pure and a tempered Major 3rd

What you hear

A3 (220 Hz) with a pure Major 3rd above it (5:4, 275 Hz), then with the piano's C#4 (277.18 Hz), each tone with its first eight harmonics, four seconds each: the first holds steady (A3's 5th harmonic and the 3rd's 4th are both 1,100 Hz); the second beats 8.73 times a second (1,100 against 1,108.73 Hz)

Every example in Part 3

• Example 3.1A melodic and a harmonic interval
• Example 3.2The thirteen simple intervals above C
• Example 3.3A Major 3rd and a Major 10th
• Example 3.4An interval and its inversion
• Example 3.5The interval listening challenge
• Example 3.6From smooth to rough
• Example 3.7Tension and release
• Example 3.8The harmonics of A4, one by one, then together
• Example 3.9Where you pluck changes the sound
• Example 3.10Waves in step and out of step
• Example 3.11The 7th harmonic
• Example 3.12A pure and a tempered Major 3rd