Digital Sound & Music: Concepts, Applications, & Science, Chapter 3, last updated 6/25/2013
notes are played one after the other, it is a melodic interval. If there are at least three notes
played simultaneously, they constitute a chord. When notes are played at the same time, they
are stacked up vertically on the staff. Figure 3.24 shows a harmonic interval, melodic interval,
and chord.
harmonic interval melodic interval
Figure 3.24 Intervals and chords
Intervals are named by the number of lettered notes from the lowest to highest, inclusive.
The name of the interval can be expressed as an ordinal number. For example, if the interval
begins at F and ends in D, there are six lettered notes in the interval, F, G, A, B, C, and D. Thus,
this interval is called a sixth. If the interval begins with C and ends in E, it is called a third, as
shown in Figure 3.25 Note that in this regard the presences of sharps or flats isn’t significant.
The interval between F and D is a sixth, as is the interval between F and D#.
Figure 3.25 Intervals of different sizes: a sixth and a third
Because there are eight notes in an octave, with the last letter repeated, there are eight
intervals in an octave. These are shown in Figure 3.26, in the key of C. Each interval is
constructed in turn by starting on the key note and moving up by zero lettered notes, one lettered
note, two lettered notes, and on up to eight lettered notes. Moving up one lettered note means
moving up to the next line or space on the staff.
Figure 3.26 Intervals in an octave, key of C major
The same intervals can be created in any key. For example, to create them in the key of
D, all we have to do is move the bottom note of each interval to the key note D and move up zero
notes from D for perfect unison, one note for a major second, two notes for a major third, and so
forth, as shown in Figure 3.27. Note, however, that F and C are implicitly sharp in this key.
Figure 3.27 Intervals in key of D major
A major interval can be converted to a minor interval by lowering the higher note one
semitone. For example, in the key of C, the minor intervals are C to D♭ (minor second), C to
E♭ (minor third), C to A♭ (minor sixth), and C to B♭ (minor seventh). It isn’t possible to turn
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