Voice Leading: The Science Behind a Musical Art

269 Pages·2016·2.58 MB·English

by  David Huron

Voice Leading
The Science behind a Musical Art
David Huron

The MIT Press
Cambridge, Massachusetts
London, England
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Library of Congress Cataloging-in-Publication Data Names: Huron, David Brian.
Title: Voice leading : the science behind a musical art / David Huron.
Description: Cambridge, MA : MIT Press, [2016] | Includes bibliographical references and index.
Identifiers: LCCN 2016004808 | ISBN 9780262034852 (hardcover : alk. paper) eISBN 9780262335430
Subjects: LCSH: Harmony. | Music--Psychological aspects. | Music perception.
Classification: LCC ML3836 .H87 2016 | DDC 781.4/2--dc23 LC record available at
http://lccn.loc.gov/2016004808
ePub Version 1.0
Table of Contents
Title page
Copyright page
Preface
1 Introduction
2 The Canon
3 Sources and Images
4 Principles of Image Formation
5 Auditory Masking
6 Connecting the Dots
7 Preference Rules
8 Types of Part-Writing
9 Embellishing Tones
10 The Feeling of Leading
11 Chordal-Tone Doubling
12 Direct Intervals Revisited
13 Hierarchical Streams
14 Scene Setting
15 The Cultural Connection
16 Ear Teasers
17 Conclusion
Afterword
Acknowledgments
References
Index
List of Tables
List of Tables
Table 10.1 Probabilities of successive diatonic pitches (major mode only)
List of Illustrations
Figure 4.1 Changes of toneness versus pitch for complex tones from various
natural and artificial sources, calculated according to the method described in
Terhardt, Stoll, and Seewann (1982a, 1982b). Solid line: pitch weight for
standardized electronic tones from C1 to C7. Dotted lines: toneness for
recorded tones spanning the entire ranges for harp, violin, flute, trumpet,
cello, and contrabassoon.
Figure 5.1 Relationship between input frequency and place of maximum
stimulation on the basilar membrane.
Figure 5.2 Approximate size of critical bands represented using musical
notation. Successive notes are separated by approximately one critical
bandwidth—roughly 1 millimeter separation along the basilar membrane.
Notated pitches represent pure tones rather than complex tones. Note: The
internote distances plotted in this figure have been calculated according to
the equivalent rectangular bandwidth-rate (ERB) scale devised by Moore and
Glasberg (1983; revised Glasberg & Moore, 1990).
Figure 5.3 The approximate position of the first sixteen harmonics for a
single complex tone with a fundamental of C2 (roughly 65 Hz). Compare the
distances between successive harmonics with the size of critical bands shown
in figure 5.2. Successive lower harmonics are separated by more than a
critical band and so will be individually resolved by the cochlea. Beyond the
sixth harmonic, the distances separating successive partials are smaller than a
critical band, so neighboring harmonics will tend to interfere with each other.
Notated pitches represent pure tones rather than complex tones.
Figure 5.4 Average spacing of tones for sonorities having various bass
pitches from C4 to C2. Calculated from over ten thousand four-note
sonorities extracted from Haydn string quartets and Bach keyboard works.
Bass pitches are fixed. For each bass pitch, the average tenor, alto, and
soprano pitches are plotted to the nearest semitone. (Readers should not be
distracted by the specific sonorities notated; only the approximate spacing of
voices is of interest.) Note the wider spacing between the lower voices for
chords having a low average tessitura. Notated pitches represent complex
tones rather than pure tones. Source: Huron (2001; see also Huron, 1993c).
Figure 5.5 Masking effect of a 1,000 Hz pure tone with an 80 dB intensity
level. Complete masking is represented by the triangular region under the
masking skirt. The lower tone (950 Hz with an intensity level of 60 dB) is
completely masked. The higher tone (1,050 Hz with an intensity level of 70
dB) is only partially masked. Asymmetrical spread of masking with
frequency is not illustrated. After Egan and Hake (1950).
Figure 5.6 Masking skirts for seven harmonics of a complex tone with a
fundamental frequency of 230 Hz. Note: When masking skirts are plotted
with respect to position along the basilar membrane (rather than with respect
to frequency), they are symmetrical.
Figure 5.7 Masking skirts for two complex tones, both containing seven
harmonics with identical intensities or amplitudes. The lower tone has a
fundamental of 100 Hz (dashed lines); the upper tone has a fundamental of
230 Hz (solid lines). Significant mutual masking is evident. Notice that the
lower partials of the higher tone mask the upper partials of the lower tone
more than the other way around.
Figure 5.8 Four potential masking situations: (a) no masking, (b) moderate
masking, (c) significant masking, (d) complete masking.
Figure 5.9 Reported consonance for complex tones from Kaestner (1909).
Figure 5.10 Comparison of sensory consonance for complex tones (line)
from Kaestner (1909) with interval prevalence (bars) from a sample of music
by J. S. Bach. Notice especially the discrepancies for P1 and P8. Source:
Adapted from Huron (1991b).
Figure 6.1 Schematic illustration of auditory induction. A faint tone (line)
alternates with a series of noise bursts (blocks). Listeners report hearing the
faint tone as continuing throughout the noise bursts even though the tone is
physically absent.
Figure 6.2 Effect of pitch separation on the sense of auditory motion. (a)
Neighboring pitches evoke the perception of a single undulating line. (b)
Distant pitches evoke the perception of two static beeping tones with no
sense of movement between the pitches.
Figure 6.3 Influence of interval size and tone duration on the perception of
alternating tones. In region 1, listeners always hear one stream (small
interval sizes and slow tempos). In region 2, listeners always hear two
streams (large interval sizes and fast tempos). In the large region between the
two boundaries listeners may hear either one or two streams depending on
the context and the listener’s mental disposition. Source: After van Noorden
(1975, p. 15).
Figure 6.4 Frequency of occurrence of melodic intervals in notated sources
for folk and popular melodies from several cultures. Interval sizes have been
rounded to the nearest equally tempered semitone. Source: Huron (2001).
Figure 6.5 Illustration of pitch competition. Four auditory interpretations are
illustrated for the stimulus shown in example (a). Ensuing pitches commonly
stream to the nearest preceding pitch, as in example (b). Other stream
organizations (c–e) are less likely to be heard.
Figure 6.6 Illustration of part-crossing. Listeners tend to hear the two lines as
bouncing away from each other (b) rather than crossing (a).
Figure 6.7 Schematic illustration of two possible perceptions of intersecting
pitch trajectories. Bounced perceptions (right) are more common for stimuli
consisting of discrete pitch sequences, when the timbres are identical.
Figure 6.8 Illustration of rhythmic discontinuity caused by crossing parts.
When passage (a) is performed, listeners have a strong tendency to hear
passage (b). The upper stream becomes syncopated at the point of pitch
crossover, whereas the lower stream ceases to be syncopated at the point of
crossover.
Figure 6.9 Two pairs of circular targets illustrating Fitts’s law. Participants
were asked to alternate the point of a stylus back and forth as rapidly as
possible between two targets. The minimum duration of movement between
targets depends on the distance separating the targets as well as target size.
The movement is more rapid between the lower pair of targets. Fitts’s law
applies to all muscle motions, including the motions of the vocal muscles.
Musically, the distance separating the targets can be regarded as the pitch
distance between two tones, whereas the size of the targets represents pitch
accuracy or intonation. Fitts’s law predicts that if the intonation remains
fixed, vocalists will be unable to execute wide intervals as rapidly as small
intervals.
Figure 6.10 Passage from Maurice Ravel’s Bolero (three measures after
rehearsal marking “8”) showing the use of parallel motion in the piccolos,
horn, and celeste. The pitch co-modulation in this orchestration causes an
“emergent” or virtual instrument.
Figure 8.1 Onset synchrony autophase functions for a random selection of
ten of Bach’s two-part keyboard Inventions (BWVs 772–786) (Huron,
1993a). Values plotted at zero degrees indicate the proportion of onset
synchrony for the actual works. All other phase values indicate the
proportion of onset synchrony for rearranged music, controlling for duration,
rhythmic order, and meter, etc. The dips at zero degrees are consistent with
the hypothesis that Bach avoided synchronous note onsets between the parts.
The solid line plots an average onset synchrony function for all ten works.
Figure 8.2 Three-dimensional onset synchrony autophase graphs comparing
polyphonic and homophonic works: (a) three-part Sinfonia no. 1 (BWV 787)
by J. S. Bach; (b) four-part hymn “Adeste Fideles.” The vertical axis
indicates the onset synchrony (measured according to method 3 described in
Huron, 1989a). The horizontal axes indicate measure-by-measure shifts of
two of the voices with respect to the remaining voice(s). Figure 8.2a shows a
marked dip at the origin (front), whereas figure 8.2b shows a marked peak at
the origin (back). The horizontal axes in the two graphs have been reversed
to preserve visual clarity. The graphs formally demonstrate that any
realignment of the parts in Bach’s Sinfonia no. 1 would result in greater
onset synchrony, whereas any realignment of the parts in “Adeste Fideles”
would result in less onset synchrony.
Figure 8.3 Three passages illustrating (a) synchronous movement to a
nonfused interval, (b) synchronous movement to a harmonically fused
interval, and (c) asynchronous preparation of a tonally fused interval.
Figure 8.4 Comparison of harmonically fused intervals in chorales and
fugues by J. S. Bach. Only perfect harmonic intervals are plotted (e.g.,
unisons, fourths, fifths, octaves, twelfths). In the more homophonic chorale
repertoire, most perfect intervals are formed synchronously; that is, both
notes tend to begin sounding at the same moment. But in polyphonic
textures, most perfect intervals are approached with asynchronous onsets
(one note sounding before the onset of the second note of the interval). The
two repertoires show no differences when approaching imperfect and
dissonant intervals.
Figure 8.5 Voice-tracking errors while listening to polyphonic music. Black
columns: average estimation errors for textural density (number of
polyphonic voices). Gray columns: unrecognized single-voice entries in
polyphonic listening. The data show that tracking confusions for listeners to
polyphonic textures employing relatively homogeneous timbres are common
when more than three voices are present. Source: Huron (1989b).
Figure 8.6 Relationship between nominal number of voices or parts and
mean number of estimated auditory streams in 108 polyphonic works by J. S.
Bach. Plotted points indicate average values for each repertoire; vertical bars
indicate data ranges. The dotted line shows a relation of unity slope, where
an N-voice polyphonic work maintains an average of N auditory streams.
The graph shows evidence consistent with a preferred textural density of
three auditory streams. Note: Average stream density for each work was
calculated according to a method described and tested experimentally in
Huron (1989a, chap. 14).
Figure 8.7 Illustration of the “frustrated leading tone.” In the key of C, the
leading tone (B) does not resolve upward to the tonic, but instead drops
down to the dominant in order to allow the tonic chord to be spelled with all
three chord factors (root, third, and fifth). This not uncommon harmonization
suggests that in many circumstances, musicians deem full triadic harmony to
be a more important goal than optimum voice leading.
Figure 8.8 Schematic illustration of Wessel’s (1979) illusion. A sequence of
three rising pitches is constructed using two contrasting timbres (marked
with open and closed noteheads). As the tempo of presentation increases, the
perception of an ascending pitch figure is replaced by two independent
streams of descending pitch, each distinguished by a unique timbre.
Figure 9.1 Illustrations of various embellishing tones. Examples are drawn
from Bach chorale harmonizations.
Figure 9.2 Illustration of two different ways of deploying embellishing tones.
In both examples (a) and (b), the pitch C is doubled between the bass and
alto voices. In example (a), the passing tone is assigned to a voice that does
not double a pitch class. In example (b), the passing tone is assigned to a
voice that does double a pitch class. The second example is more
characteristic of J. S. Bach’s musical practice and is consistent with efforts to
minimize tonal fusion.
Figure 9.3 Frequency of occurrence of embellishing tones in chorale
harmonizations by J. S. Bach. Embellishing tones occur with nearly identical
frequency in the bass, tenor, and alto voices. Relatively few embellishments
are found in the soprano. Source: Huron (2007).
Figure 10.1 Two interleaved melodies: the odd-numbered pitches form the
melody “Frère Jacques.” The even-numbered pitches form the melody
“Twinkle, Twinkle, Little Star.” Source: After Dowling (1967).
Figure 10.2 The same interleaved melodies as in figure 10.1 transposed.
“Frère Jacques” (odd-numbered pitches) has been transposed upward, while
“Twinkle, Twinkle, Little Star” (even-numbered pitches) has been
transposed downward, increasing the likelihood of hearing out the two
melodies.
Figure 10.3 Final two phrases of the four-part hymn “St. Flavian”: (a)
normal; (b) same passage played backward. Are any part-writing rules
transgressed in the backward version?
Figure 10.4 Schematic illustration of scale-degree successions for major-
mode melodies from Huron (2006b). The thickness of each connecting line is
proportional to the probability of melodic succession. The quarter-rest
symbol signifies any rest or the end of a phrase. Lines have been drawn only
for transitions that occur more than 1.5 percent of the time.
Figure 10.5 Schematic illustration of scale-degree successions for , ♯ , and ♯
for major-key melodies. The thickness of each connecting line is
proportional to the probability of melodic succession. The quarter-rest
symbol signifies any rest or the end of a phrase.
Figure 10.6
Figure 10.7
Figure 12.1
Figure 12.2
Figure 13.1
Figure 13.2
Figure 13.3
Figure 13.4
Figure 13.5
Figure 13.6
Figure 14.1