Understanding Basic Music Theory, 2013a

110 CHAPTER 3. THE PHYSICAL BASIS
Solutions to Exercises in Chapter 3
Solution to Exercise 3.2.1 (p. 101)
1. The part of the string that can vibrate is shorter. The nger becomes the new "end" of the string.
2. The new sound wave is shorter, so its frequency is higher.
3. It sounds higher; it has a higher pitch.
Figure 3.15: When a nger holds the string down tightly, the nger becomes the new end of the
vibrating part of the string. The vibrating part of the string is shorter, and the whole set of sound waves
it makes is shorter.
Solution to Exercise 3.2.2 (p. 104)
There are many, but here are some of the most familiar:
• Chimes
• All xylophone-type instruments, such as marimba, vibraphone, and glockenspiel
• Handbells and other tuned bells
• Steel pan drums
Solution to Exercise 3.3.1 (p. 106)
Although trained musicians will generally agree that a particular sound is reedy, thin, or full, there are no
hard-and-fast, right-or-wrong answers to this exercise.
Solution to Exercise 3.3.2 (p. 108)
1. The eighth harmonic
2. The fth and tenth harmonics; the sixth and twelfth harmonics; the seventh and fourteenth harmonics;
and the eighth and sixteenth harmonics
3. The note that is one octave higher than a harmonic is also a harmonic, and its number in the harmonic
series is twice (2 X) the number of the rst note.
4. The eighth, sixteenth, and thirty-second harmonics will also be A's.
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