Digital Sound & Music: Concepts, Applications, & Science, Chapter 3, last updated 6/25/2013
to G5#, a span of 10 notes. 10 mod 7 = 3, so this is a compound third. However, because the G
is raised to G#, this is, more precisely, a compound augmented third.
Figure 3.29 Compound intervals
Intervals can be characterized as either consonant or dissonant. Giving an oversimplified
definition, we can say that sounds that are pleasing to the ear are called consonant, and those
that are not are called dissonant. Of course, these qualities are subjective. Throughout the
history of music, the terms consonant and dissonant have undergone much discussion. Some
music theorists would define consonance as a state when things are in accord with each other,
and dissonance as a state of instability or tension that calls for resolution. In Section 3.3.2, we’ll
look more closely at a physical and mathematical explanation for the subjective perception of
consonance as it relates to harmony.
Intervals help us to characterize the patterns of notes in a musical composition. The
musical conventions from different cultures vary not only in their basic scales but also in the
intervals that are agreed upon as pleasing to the ear. In Western music the perfect intervals,
major and minor thirds, and major and minor sixths are generally considered consonant, while
the seconds, sevenths, augmented, and diminished intervals are considered
dissonant. The consonant intervals come to be used frequently in musical
compositions of a culture, and the listener’s enjoyment is enhanced by a sense
of recognition. This is not to say that dissonant intervals are simply ugly and
never used. It is the combination of intervals that makes a composition. The
combination of consonant and dissonant intervals gives the listener an
alternating sense of tension and resolution, expectation and completion in a
A chord is three or more notes played at the same time. We will look at the most basic chords
here – triads, which consist of three notes.
Triads can be major, minor, diminished, or augmented. The lowest note of a triad is its
root. In a major triad, the second note is a major third above the root, and the third note is a
perfect fifth above the root. In the root position of a triad in a given key, the tonic note of the
key is the root of the triad. (Refer to Table 3.2 for the names of the notes in a diatonic scale.)
The major triads for the keys of C, F, and A are shown in root position in Figure 3.30.
Figure 3.30 Major triads in root position