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

Example 3.11

The 7th harmonic

What you hear

A4 (440 Hz) with the piano's G5 (783.99 Hz), then A4 with a G at 7:4 (770 Hz), each tone with its first eight harmonics, three seconds each: in the first, A4's 7th harmonic (3,080 Hz) and G5's 4th (3,135.96 Hz) roughen the sound 56 times a second; in the second they meet

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