Corpus Analysis of Rock Music Trevor de Clercq Assistant Professor Ithaca College Department of Music Theory, History, and Composition

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Corpus Analysis of Rock MusicTrevor de
ClercqAssistant ProfessorIthaca
CollegeDepartment of Music Theory, History, and
Composition
Math, Music, and the Brain (Biology 22020) Dec.
11, 2012
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• What is corpus analysis / corpus research /
  corpus study?
• A corpus is a body of data
• the text of some collection of books
  (linguistics)
• the syllables in a collection of newspaper
  articles
• the chords in a collection of musical
  compositions
• the notes in the melodies of a collection of
  songs
• Corpus study asks questions about this data,
  e.g.
• Do composers tend to use dissonant chords in
  middle sections?
• Does music slow down at moments of rapid
  harmonic motion?
• Do melodies more often fall or rise at the end
  of phrases?

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• How can we do corpus-based music research?
• Encode music to allow searching
• humdrum (David Huron, Ohio State)
• music21 python (Michael Cuthbert, MIT)
• custom-based text encoding
• Search for patterns in encoded music
• computational analysis
• offers some level of objectivity in analysis
• statistics and probability

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• Math and music, but what about the brain?
• Corpus research can explain aspects of music
  cognition
• Our perception and conception of different
  musical styles is (at least in part) based on our
  knowledge of typical patterns in those styles.
• Corpus research helps identify those patterns
  and thus offers a window into our how we perceive
  and categorize diverse musical styles.

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• Corpus research into rock
• Rock is one of the most popular, most
  listened-to kinds of music in modern America (and
  many other countries as well).
• If we take the view that peoples music
  perception isat least partlyshaped by
  statistical regularities in the music they hear,
  then studying rock may shed interesting light on
  the music perception of modern Western listeners.

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• Our goal
• To get statistical evidence about patterns in
  rock music
• A collaborative project with David Temperley
  (Eastman)

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What is rock music? Choosing the corpus a
broad definition

• Rolling Stone magazine 500 Greatest Songs of All
  Time (2004)
• (the RS 500)
• 1 Like a Rolling Stone (Bob Dylan, 1965)
• 2 Satisfaction (The Rolling Stones, 1965)
• 3 Imagine (John Lennon, 1971)
• 4 Whats Going On (Marvin Gaye, 1971)
• 5 Respect (Aretha Franklin, 1967)
• ....
• 30 I Walk The Line (Johnny Cash, 1956)
• 44 Georgia On My Mind (Ray Charles, 1960)
• 256 Paranoid Android (Radiohead, 1997)
• 346 California Love (Dr. Dre and 2Pac, 1996)
• 399 Enter Sandman (Metallica, 1991)

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• What patterns to investigate?
• Musical patterns can exist within many domains.
• harmony, melody, rhythm, timbre
• We chose to study patterns in harmony first.
• How do harmonic patterns in rock compare or
  contrast to harmonic patterns in other styles?
• Can we expect certain patterns of harmony in
  rock music?
• Does rock music have operative harmonic
  principles at all?

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• Our work so far
• initial publication (dealing with harmony)
• de Clercq, Trevor and David Temperley. (2011).
  A corpus analysis of rock harmony. Popular
  Music 30/1 47-70.
• Popular Music article reports on a 100 song
  subset of RS 500
• 20 top songs from each decade, 50s 90s
  (RS 5x20)
• harmonic analyses (plus melodic transcriptions
  and timing data) available online at
• http//theory.esm.rochester.edu/rock_corpus/

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• Crash course in harmony
• Music theorists traditionally categorize
  harmonic entities (i.e., chords) via Roman
  numerals.
• Roman numerals describe triads built scale
  degrees.
• C major scale
• C major triads

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• Roman numerals describe classes of pitches.
• D major triads
• V chords in D major
• Diatonic and (some) non-diatonic triads in the
  key of C

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• Harmony in certain styles displays particular
  patterns.
• Common-practice music (e.g., Bach, Beethoven,
  Brahms)
• Pre-dominants (ii, IV) typically move to
  Dominants (V, viio)
• Dominants (V, viio) typically move to Tonics
  (I)
• Phrase model T (PD) D T
• e.g., The Four Seasons, Spring, mv. 1 (A.
  Vivaldi, 1725)
• e.g., String Quartet 51, menuetto (F. J.
  Haydn, 1790)
• Similar principles are found in jazz music (ii
  V I)

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• Common-practice harmonic patterns can be found in
  rock
• Twist and Shout (The Beatles, 1963)
• I IV V
• Other songs go against common-practice harmonic
  patterns
• The Lemon Song (Led Zeppelin, 1963)
• I V IV I (blues cadence)
• Louie Louie (The Kingsmen, 1963)
• I IV v IV

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• What (if any) are organizational principles of
  harmony in rock?
• Music theorists give conflicting views
• Walter Everett, 2004
• "Making Sense of Rock's Tonal Systems". Music
  Theory Online. 10/4 (December).
• gt rock as common-practice system
• Ken Stephenson, 2002
• What to Listen for in Rock A Stylistic Analysis.
  New Haven Yale University Press.
• gt rock as opposite to common-practice system
• Allan Moore, 2001
• Rock The Primary Text Developing a musicology
  of rock. Aldershot, UK Ashgate.
• gt rock as a modal system

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• Timbre and texture strongly influence our
  perception of styles
• .... but harmony (and other factors) play roles
• Ex Vitamin String Quartet
• LZT
• DDHW
• LGT

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How to encode the corpus?

• Songs individually analyzed by both authors
• Recursive notational system
• Da Doo Ron Ron (The Crystals, 1963)
• A I IV V I
• In I 4
• Vr A2 I IV I V A I 2
• So A2
• Ou A4
• S Eb 12/8 In Vr2 So Vr Ou

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• Bohemian Rhapsody
• A bVI V IV V
• B vi ii . ii42 viih7
• C IV64 I . .
• In1 Bb vi7 V7/V V7 I vi Eb V7 I
  ii/V V/V A2 Bb IV I6 viix42/V V64
• Vr1a Bb I 3 vi ii ii V I vi ii
  viih7 . . ii64
• Vr1b Eb I . . V65 B V I V6
• Vr1b1 Eb Vr1b vi iv I 2/4
• Vr1b2 Eb Vr1b B V I V6 B bVII .
  bVII/bVII vi/bVII
• Vr1 Vr1a Vr1b1
• Vr2 Vr1a Vr1b2
• Br1 A I C2 IV64 I IV64 I . . IV64 I
• Br2 A III64 V/III bIII64 V I 3 2/4 V
• Br3 Eb I A2 C2 IV I6 V/V V IV I6
  viix42/V ii7 A2
• Br4 Eb I V I . V . . I . V I V . . . I
  . V I V . . . I V . . I V bIII
• Br5 Eb bVI V/VII VII V/bIII bIII V I . V .
  . I IV I V . I IV64 V/iii iii V 4

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Recursive computer program expands harmonic
analyses

• Expanded version of Da Doo Ron Ron (The
  Crystals, 1963)
• I IV V I IV V I ....
• ... and also creates a CHORD LIST
• start end key chord chromatic relative root
• 0.00 5.00 E I 0
• 5.00 6.00 E IV 5
• 6.00 7.00 E V 7
• 7.00 9.00 E I 0
• 9.00 10.00 E IV 5
• (and so on....)
• ... So that we can then run statistics on the
  data

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Statistics show that harmonic analysis is
(somewhat) subjective

• agreement on chromatic relative root (e.g. I
  vs. IV) 92.4
• agreement on absolute root (e.g. A vs. D) 94.4
  
• (Rolling Stones, Satisfaction)
• agreement on key (or pitch center) 97.3
• (Lynyrd Skynyrd, Sweet Home Alabama)
• of songs with 100 agreement 39
• of songs where agreement was between 90-99
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• (The following statistics are averages of those
  from DT and TdC)

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• Statistics show information on harmonic palette
• (zeroth-order probabilities)
• Top five chords I, IV, V, bVII, VI. Very
  different from common-practice music, especially
  IVgtV and high freq. of bVII.

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• Statistics show information on harmonic palette
  over time
• (zeroth-order probabilities)

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• Statistics show information on harmonic syntax
• (first-order probabilities)
• Transitions from one chord (antecedent) to
  another (consequent)

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• Relationships between distribution probabilities
• Distribution of roots overall and in pre- and
  post-tonic positions
• IV chord seems to function as a preparation for
  tonic

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• Harmonic information abstracted from key or
  function
• Root motions in the RS 5x20 corpus by interval
  size
• Lots of motion (up or down) by P4 M2 next most
  common

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Root motions on a line of fifths
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• Chord vectors
• For each chromatic relative root, we created a
  vector of 99 values (one value for each song), 1
  if the song contains the chromatic relative root
  and 0 otherwise. Correlating these vectors for a
  pair of chords gives a measure of how much they
  occur together (not necessarily adjacently) in
  the same songs.

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• Chord vectors (contd)

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• Chord vectors (contd)
• Correlations above 0.350 are circled.

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Chord pairs with high correlations (above 0.350)

• IV and V
• VI, II, and III
• bIII, bVI, and bVII
• Correlations suggest some sort of modal harmonic
  organization.

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• Conclusions from harmonic data
• Rock has its own harmonic logic, very different
  from that of common-practice music
• IV is the most common non-tonic chord in rock,
  and is especially common preceding the tonic
• Rock does not show strong asymmetries in root
  motion ascending and descending 5th motions are
  roughly equally common
• Frequency of root motions corresponds strongly
  to circle-of-fifths distance
• Patterns of co-occurrence suggest flat-side
  harmonies tend to occur together, as do
  sharp-side harmonies

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What about scales in rock music? With our
melodic transcriptions, we can answer questions
about the types of pitch collections (i.e.,
scales) used in rock music. - Does rock have a
consistent scale? Can we distinguish
diatonic from chromatic scale-degrees, as we do
in classical music? - Do rock songs group into
natural categories with regard to their scalar
organization analogous to classical major and
minor?

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Theres been much speculation about these
questions. With regard to scales, a variety of
frameworks have been applied to rock -
Common-practice major and minor scales -
Pentatonic scales - Diatonic modes (Mixolydian,
etc.) - Blues scales - Scales arising from
harmonic progressions ...but theres little
consensus on this issue, and little hard evidence
has been put forth.

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Notation We devised a simple notation for
transcribing the melodies. For Hey Jude, for
example, here is a transcription of the first
main section F OCT4 ...5 3....356
v2.....23 4.1..175 6.543.........5.
6.6...6.21.7.16. 5...v1236 5..54377
1.......

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Vertical bars indicate measures. Each measure is
evenly divided into N segments, where N is a
power of 2 (assuming duple meter). If a segment
contains a note onset, that is indicated with the
scale-degree of the note, otherwise a dot is
used. F OCT4 ...5 3....356 v2.....23
4.1..175 6.543.........5. 6.6...6.21.7.16.
5...v1236 5..543.7 1....... Major-scale
degrees are assumed, unless otherwise indicated
(e.g. b7). Each pitch is assumed to be the
closest representative of that scale-degree to
the previous note, unless indicated by v (which
shifts an octave down) or (which shifts an
octave up). F indicates the tonal center
OCT4 indicates the octave of the first note
(middle C C4).

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Problems We found the task to be quite
difficulta good deal more difficult than the
harmonic analysis. - Its not always obvious
which vocal line is the melody (well see an
example in a minute) - Some notes are
indeterminate as to pitch blue notes that
fall between two pitches, or notes with gliding
pitch, or notes that are quasi-spoken - Some
notes are indeterminate as to rhythm (or seem to
require very complex rhythmic notation) (These
problems of transcription are not unique to rock
but occur with many kinds of music.)

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Problems Heres an especially complex example
a phrase from Otis Reddings Ive Been Loving
You Too Long (heres TdCs transcription, in
conventional notation) Theres a slight
scoop up to the first long note, and then a
significant glide downwards at the end of it
should these be notated or not? (TdC notates the
second, not the first.) Should the rhythm of the
next phrase be notated literally (as TdC does) or
is it just an expressively stretched rendition of
a simpler rhythm (e.g. ee e e e q. )?

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Problems Eight songs on the list were judged to
have no melody at alleither rap / hip hop songs,
or those in which the pitches of the melody were
largely indeterminate. This left a corpus of 192
songs.

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Level of agreement We both analyzed eight songs
so as to examine the level of agreement between
us. We were in agreement only 74 of the time.
(On the harmonic analyses it was much higher
92.4.) In some cases, we simply did not agree
as to which line was the melody. However, there
were also more substantive disagreements.
Generally, TdC seemed to take a literal
approach, transcribing exactly what was sung DT
seemed to go for the intended or implied notes.

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An Example Heres just one example of the kind
of disagreements that arose between usa phrase
from London Calling, by the Clash.

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ANALYSES OF THE DATA Scale-Degree
Distribution What is the overall distribution of
scale-degrees in the datathat is, pitch-classes
in relation to the tonic? Lets examine this in
comparison to some other distributions.

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Scale-degree distribution for classical music
(gathered by Temperley from a corpus of excerpts
from the Kostka-Payne theory textbook, grouping
major and minor together)

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Scale-degree distribution for classical music
(gathered by Temperley from a corpus of excerpts
from the Kostka-Payne theory textbook, grouping
major and minor together)
_ _ _ _ _ _
_ (Major-scale degrees) The seven major
degrees are most common (partly because there are
more major than minor pieces). Next are the minor
degreesb3, b6, and b7. (7 is much more common
than b7.) b2 and 4 (chromatic degrees) are
least common.

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Comparing the scale-degree distribution from our
rock harmonic analyses (counting each pitch-class
once for every chord that it occurs in), we see a
fairly similar pattern... As in
classical music, b2 and 4 are least common. 7 is
still more common than b7, but the difference is
smaller. The 6 gt b6 difference is greatly
increased.

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Now we add in the melodic rock data (blue). (We
count each note separately, not weighted for
duration.) Similar to the harmonic
rock data and classical data. But now, b7 gt 7, by
a considerable margin. Note also the very low
value for b6 (but still higher than b2 and 4).

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Our melodic data (as well as our harmonic data)
support the idea that rock as a whole reflects a
global scale collection including all 12
degrees except for b2 and 4. (Temperleys
supermode 2001). This is an important
commonality with common-practice music, where b2
and 4 are the least common degrees (chromatic in
both major and minor).

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The fact that b7 gt 7 in our melodic data is
interesting, since neither classical major
(above) nor classical minor (below) reflect this.
(Data is again from the Kostka-Payne
corpus.) Major Minor

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Our data may explain a curious feature of
Krumhansl Kesslers (1982) key-profiles. In
their probe-tone experiments, given minor-key
contexts, b7 was given a slightly higher rating
than 7, though 7 occurred in the contexts and b7
did not. The KK minor key-profile Perha
ps this reflects the influence of rock melodies.
(KKs subjects were trained classical musicians,
but undoubtedly had heard a lot of popular music
as well.)

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Scales in Rock To what extent do rock songs
reflect conventional scalesmodal, pentatonic,
etc.? As a first approach, we can represent each
song with a binary 12-valued vector, showing
which scale-degrees occur in the song and which
ones do not. A song that uses only the major
scale would therefore have this vector 1 0
1 0 1 1 0 1 0 1 0 1 (1 b2 2
b3 3 4 4 5 b6 6 b7 7)

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The most common vectors, with their frequency of
occurrence (out of 192 songs)
Num occ. 1. 101011010101 29
(major) 2. 101011010100 17 (diatonic
hexachord) 3. 101111010110 10
(bluesy?) 4. 101111010100 7 (bluesy?) 5.
101010010100 7 (major pentatonic) Not
terribly revealing because it does not consider
how often each scale-degree is used in a song.
(Note also that these 5 scales account for only
70 songs, less than 40 of the total.)

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A second approach Take a song and a scale, and
consider whether the degrees of the scale are the
most frequently occurring scale-degrees in the
song. If so, we declare that song to match that
scale. (So this allows some chromaticism in
relation to the scale.) We can then consider how
many songs match various scales.

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Examining some scales that are of particular
interest Num
matches 101011010101 42 (Major) 10101101011
0 12 (Mixolydian) 101101010110
9 (Dorian) 101101011010 6 (Aeolian
or natural minor) 101010010100 50 (major
pent) 100101010010 21 (minor pent) This data
does not give much support to the idea that rock
is largely modal. There are relatively few
songs in which the most frequent scale-degrees
form a diatonic mode (other than major). Theres
some evidence of pentatonicism, though this
matching method favors scales with fewer notes.

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Clustering Both of these approaches suggest that
there is a good deal of variability in the scale
content of songs from a purely statistical
perspective, many different scales are used. Can
we simplify this picture in any way? If we were
to cluster rock songs into a small number of
categories as to their scalar content, what would
the categories look like?

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A brute-force approach Lets classify a song
as major if 3 gt b3, minor otherwise. We
create a major distribution from all the major
songs and a minor distribution from all the
minor ones what do these distributions look like?

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Here are the results. (The major category has
121 songs, the minor has 71. Fifty-two of these
songs use both 3 and b3.) The major
distribution reflects the major scale the five
degrees of the major pentatonic are the most
common (1, 2, 3, 5, 6). In the minor
distribution, the five minor pentatonic degrees
are most frequent (1, b3, 4, 5, b7) the next
most frequent are 2 and 6, suggesting Dorian
mode. (6 gt b6, but the difference is smaller than
in major.)

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This approach simply imposes a kind of
major/minor categorization. Could we take a more
data-driven approach to sorting the songs into
clusters?

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A hill-climbing approach 1. Randomly sort the
songs into two categories. 2. For each category,
construct an aggregate scale-degree
distribution. 3. Within each category, measure
the match of each song to the categorys
distribution (here we use cross-entropy).
Combining all these values produces a measure of
the quality of that clustering. 4. Randomly
shift one song from one category to the other,
and repeat the process. If this change improves
the quality of the clustering, keep it if not,
dont. 5. Iterate this process many times.

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The result (after 800 iterations) Once
again, we get something that looks roughly like
major vs. minor (almost identical to the
brute-force approach above!). Category 1 has
higher values for b3 and b7 (and a relatively
higher value for b6) category 2 has higher
values for 3 and 7.

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Note that this method is not guaranteed to find
the optimal solution. However, the process was
repeated several times, starting with different
random sortings, and always converged on the same
solution.

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What about repeating the process, but sorting the
songs into three categories? The
result Category 1 (blue, 41 songs)
looks like major pentatonic (1, 2, 3, 5 and 6
are highest) Category 2 (red, 73 songs) looks
like major diatonic (or diatonic
hexachord) Category 3 (green, 78 songs)almost
identical to the minor category we saw before.

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Category 3the minor categoryis of particular
interest As noted earlier, the minor
pentatonic degrees are most frequent, followed
closely by 2. But both 3 and 6 are quite common.
This also resembles the blues scale, though
this is defined in different ways (4 is often
included in the blues scale). It is also the
union of the major and minor pentatonic
scales. Many of the songs in this category are
1) early (1950s) rocknroll songs, 2) songs by
hard rock or blues-based bands like the Rolling
Stones, or 3) soul songs such as Aretha
Franklins Respect.

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Conclusions 1. Rock melody, like rock harmony,
reflects a global scale in which all twelve
chromatic scale-degrees are fairly common except
for b2 and 4. (b6 is, however, a borderline
case.) 2. The biggest difference between rocks
melodic distribution and that of common-practice
music is the fact that b7 gt 7. 3. Statistical
clustering methods suggest some kind of (loosely
speaking) major/minor dichotomy in rock. One
category of songs features 3 gt b3, 7 gt b7, and 6
gtgt b6 the other category features b3 gt 3, b7 gt
7, and a smaller difference between 6 and b6.

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Conclusions (contd) 4. The rock minor is,
however, quite different from classical minor. b7
gt 7 (unlike in classical minor) 6 gt b6 (unlike
in classical minor) and 3 is quite common.
Further work is needed to determine whether this
distribution really represents a consistent
melodic practice, or perhaps several quite
different ones.

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Directions for Further Work Our work raises a
number of questions that deserve
investigation 1. How does the scale-degree
distribution of rock change over time (from 1950
to 2000)? 2. We ignored the duration of notes
in our tallies would the distributions change
significantly if notes were weighted by their
duration? 3. What is the absolute distribution
of pitch-classes in rock? Does it show a strong
preference for certain pitch-classes over others?

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Many other kinds of issues could be addressed
with our data - What are the characteristic
melodic patterns of rock? No doubt rock features
certain phenomena that are found in many other
styles, such as a preference for small intervals.
But are there characteristic melodic gestures
that are unique to rock? - To what extent is
melody in rock constrained by harmony? (Some have
suggested that these constraints are much weaker
in rock than in common-practice music.) Does our
harmonic data yield a similar clustering of
songs to the melodic data? 5. Rhythm....?! Many
questions could be asked here as well.

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Thank you for your attention!