© 2019 Taylor & Francis

Chapter 2 Answer Key

Applications

Exercises

1. Provide the proper label to indicate the size and quality of each interval.

2. Provide the correct note above the given note to form the requested interval.

Chapter 2 Answer Key2

© 2019 Taylor & Francis

3. Provide the correct note below the given note to form the requested interval.

Brain Teasers

1. If an interval and its inversion complete a perfect octave (P8), why do their sizes add up to 9? In other words, why do the sizes of complementary inter-vals (such as the M3 and m6 in Example 2-4) add up to 9 instead of 8?Answer: Refer to the complementary intervals in Example 2-4. The note C gets counted twice: first as the bottom note of the M3 C–E, and second as the top note of the m6 E–C. (When counting up from E4 to E5, the space for C5 should only be counted once, leading to P8.)

2. Identify and label the harmonic interval below. Is there more than one op-tion for classifying this interval?

Answer: Although it might be tempting to label this interval as a dimin-ished unison (O1), an interval cannot be smaller than the unison, so this can only be considered an +1.

3. Identify and label the harmonic interval below.

Chapter 2 Answer Key 3

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Thinking Critically

1. Why is an +4 or O5 called the “tritone?”Answer: It consists of three whole steps. Whole steps are sometimes referred to as “whole tones.” “Three tones” = “tritone.”

2. Perfect consonances sound stable because the frequencies of their two pitches are in a simple ratio. For instance, the ratio for a P8 is 2:1, so if the upper note is vibrating at 440 Hz, the lower note is vibrating at 220 Hz. The ratio for the P5 is 3:2. At what frequency will the lower note of a P5 be vibrating if the upper note vibrates at 780 Hz?Answer: 520 Hz.