marked by silences (musical rests). Of greater interest are the boundaries at the end of the
third and fourth phrases, which are not marked by any physical discontinuity in the tone
sequence. Instead, these boundaries are marked by local durational lengthening and
lowering of pitch, cues which also serve a boundary-marking role in speech.^9
Beat and metre
A beat refers to ‘a psychological, more-or-less isochronous, pulse train—that provides the
stimulus for synchronization’.^10 K0016 readily evokes a beat: if asked to tap the beat of this
melody, listeners are likely to tap at the positions marked in Figure 21.3 by the dots at the
level labelled ‘1x’.cNote that three of these taps occur during silent intervals, showing that
the beat is not a simple marking of physically accented events. Indeed, in the sound exam-
ples all tones in K0016 have the same amplitude: there are no accents based on the intens-
ity of tones. Instead, the beat is inferred from the pattern of durations and pitches.^11
When beats are grouped into larger repeating units the result is metre, that is, periodic-
ity at multiple time scales.^12 In K0016 the beats are organized into higher-level groups of
two (as indicated by the time signature) and four (examination of Figures 21.2 and 21.3
shows that each phrase has four beats).dMelodic sequences frequently exhibit these sorts
of multiple periodicities, which can be demonstrated by asking listeners to tap at different
rates on successive listenings to a piece. Musically experienced listeners can tap at different
rates related by simple integer ratios (e.g. 1/2 or 2the basic beat), suggesting that the rate
at which one spontaneously taps the beat is simply one level (the ‘tactus’) in a hierarchy of
beats, as shown in Figure 21.3.8,13
Scale structure
The numerical ratios between the fundamental frequencies of successive musical tones define
the set of pitch intervals used in a melody. The intervals used in any given melody typically
adhere to culture-specific schemata, for example, the scales of Western tonal music.14,15
The intervals of K0016 are drawn from the major (Ionian) scale, characterized by a particular
pattern of frequency steps between adjacent tones within an octave (in semitones, step sizes
are: 2 2 1 2 2 2 1; a semitone is a ratio of approximately 1.06 in fundamental frequency).
Listeners are sensitive to the structure of pitch intervals relative to the schemata of one’s
327Figure 21.2 K0016 segmented into melodic phrases.
12 34 5cThe tempo of K0016 has been set to 120 beats per minute (bpm) in the sound examples, that is, one beat
every 500 ms. Any tempo between between ~75 and 150 bpm would likely be acceptable.
dThis helps explain why the music notation for this melody includes a rest in the final position, rather than
simply ending with the final note: this rest occurs on a beat. The psychological reality of this rest can be demon-
strated by memorizing K0016 and singing it twice in immediate succession. There will be a natural tendency to
pause after the final sung note before beginning again.