12 INTRODUCTIONby equal distances. Counting the number of degrees in a scale and comparing
the distances, or intervals, between them can tell us much about music that uses
that scale.
Of all the possible intervals between two pitches, the octave—the distance
between a pitch and another of exactly twice the frequency—has a unique fea-
ture. Our ears perceive notes an octave apart as being somehow “the same.” For
instance, when a group of men and women sing a melody together, the women
usually sing pitches an octave higher than the men, yet we perceive their melody
to be “the same.” Consequently, if two notes in a scale are an octave apart, we
can consider them to be “the same” note and count them as a single scale degree.
By no coincidence, the octave is the interval between the fi rst two partials in the
overtone series.
Most music in the Western world draws on a system in which the octave is
divided into twelve equal units, called half steps or semitones, the smallest
interval in conventional music. (In chapter 19 we’ll explore microtonal music,
which uses even smaller divisions—but for now you can disregard microtonal-
ity.) T he collection of all twelve pitches, equally spaced a semitone apart, is called
the chromatic scale. Most melodies are based on a scale of fewer than twelve
notes per octave, however. For example, the main tune of “Get Off the Track!”
(LG 17.2, 0:07–0:15) uses only fi ve pitches. That pentatonic scale is extremely
common in folk songs and is not unusual in popular songs as well. The tune of
“Lost Highway” (LG 6.4, 0:06–0:34) encompasses nine different pitches from its
nadir (the very fi rst note: “I’m a rollin’ stone”) to its apex (“When I walk by, all the
people say”). Four of those pitches, however, are octave duplicates of other notes
in the scale. If we discount those duplicate notes, there are only fi ve discrete
degrees in the scale: it’s the same pentatonic scale heard in “Get Off the Track!”
The black keys of the piano, incidentally, form a pentatonic scale.
Outside the realm of folk music, the most common scales are the two prin-
cipal diatonic scales, major and minor. Both scales encompass seven scale
degrees; the eighth note in the scale is the octave of the fi rst note—that inter-
val gets its name from the Latin word for “eight.” Diatonic scales are a mix of
whole steps and half steps (fi ve of the former and two of the latter, to be precise);
pentatonic tunes like “Lost Highway” have no half steps, only whole steps and
thirds, the latter occurring where the scale skips over a note that would be pres-
ent in a diatonic scale. Exactly where the half steps occur determines whether a
diatonic scale is major or minor. The Christmas carol “Joy to the World” begins
by working its way down a complete major scale; the interval from top to bot-
tom is an octave. Melodies in the minor are somewhat less common; “W henCDEFGABCDEFGABCDEFGABK Pentatonic scales
beginning on C and on F
sharp. If you count the half
steps between adjacent
colored keys, you will notice
that the interval pattern is
the same in both scales.172028_00b_001-017_INTRO_r3_ko.indd 12 23/01/13 9:47 AM