Perfect 4ths/5ths, Diminished 5ths

Perfect fourths cover five half-steps and are highly consonant. It is easiest to confuse the perfect fourth with the perfect fifth, since both are consonant (and inverses of each other). One main difference is that in perfect fourths, the higher note tends to sound like the root note, as if the lower note is resolving to the higher note. In perfect fifths, the opposite is true: the lower note tends to sound like the root note. Try playing C → G → C (octave higher), and listen to how the C's sound like the root note of the key, and then listen to the difference when you play C → F → C. In this case, the F should sound more like it is the root. In the first example, the G → C should sound like it resolves more than the first C → G movement. Likewise, the C → F movement in the second example should sound like it resolves more than the F → C.

Perfect fifths cover seven half-steps and are also highly consonant.

Diminished fifths cover six half-steps or three whole-steps and are also referred to as "tritones." Tritones have a unique sound that is very distinct from perfect fourths and fifths. In classical music, you hear tritones most often in the context of dominant seventh chords (the interval between the third and the seventh in a dominant seventh chord is a diminished fifth). In more modern music, the tritone is sometimes actually used as a chord, as the evil twin brother of the power chord (think C5 versus C(b5)). The intro and first riff of "As I Am" illustrate a more modern use of the tritone.

Augmented fourths are equivalent to diminished fifths, and while there are some technical differences regarding voice leading and resolutions, for the purposes of these lessons, we will call all of these intervals diminished fifths. In later lessons, some diminished fifths are actually spelled as augmented fourths in the answers, but only to make certain other intervals easier to write out.

These exercises function just like the first lesson. The first six exercises cover only perfect fourths, perfect fifths, and diminished fifths. Exercises 7-18 combine all intervals from seconds to fifths. In your answers, use P4, P5, and d5 to represent the corresponding interval.