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Trevor de Clercq
SCSMT Conference February 29, 2020
Vanderbilt University
Lobbing for a La-Based Approach to the Minor Tonic in Popular Music Harmony
Slides available at: www.midside.com/presentations/
Slides available at: www.midside.com/presentations/
“Down Under” (Men at Work), Verse
Sing Tonic!
Slides available at: www.midside.com/presentations/
i
B‹
Tra vel lin’ in a fried
bVII
A
out com bie,
i
B‹
bVI
G A
bVII i
B‹
On a hip pie trail,
bVII
A
head full of zom
i
B‹
bie.-
bVI
G A
bVII
44&
##
0:11
‰œ œ œ œœ
œ œ œ œ œŒ Ó ‰
œœ œ œœœ œ œ œ œ œœ
Œ Ó
“Down Under” (Men at Work), Verse
Slides available at: www.midside.com/presentations/
i
B‹
Tra vel lin’ in a fried
bVII
A
out com bie,
i
B‹
bVI
G A
bVII i
B‹
On a hip pie trail,
bVII
A
head full of zom
i
B‹
bie.-
bVI
G A
bVII
44&
##
0:11
‰œ œ œ œœ
œ œ œ œ œŒ Ó ‰
œœ œ œœœ œ œ œ œ œœ
Œ Ó
“Down Under” (Men at Work), Verse
“Down Under” (Men at Work), Verse
i
B‹
Tra vel lin’ in a fried
bVII
A
out com bie,
i
B‹
bVI
G A
bVII i
B‹
On a hip pie trail,
bVII
A
head full of zom
i
B‹
bie.-
bVI
G A
bVII
44&
##
0:11
‰œ œ œ œœ
œ œ œ œ œŒ Ó ‰
œœ œ œœœ œ œ œ œ œœ
Œ Ó
“Down Under” (Men at Work), Chorus
Sing Tonic!
“Down Under” (Men at Work), Verse
i
B‹
Tra vel lin’ in a fried
bVII
A
out com bie,
i
B‹
bVI
G A
bVII i
B‹
On a hip pie trail,
bVII
A
head full of zom
i
B‹
bie.-
bVI
G A
bVII
44&
##
0:11
‰œ œ œ œœ
œ œ œ œ œŒ Ó ‰
œœ œ œœœ œ œ œ œ œœ
Œ Ó
“Down Under” (Men at Work), Chorus
I
D
Do youcome from a land
V
A
downun der?
vi
B‹
IV
G A
V I
D
Wherewo menglow
V
A
andmenplunder?
vi
B‹
IV
G A
V
44&
##
0:29
‰œ œ œ œ œ
œ œ œœ œŒ Ó ‰™
œ
rœ œ œ œ
œ œ œ œ
Œ Ó
“Down Under” (Men at Work), Verse
i
B‹
Tra vel lin’ in a fried
bVII
A
out com bie,
i
B‹
bVI
G A
bVII i
B‹
On a hip pie trail,
bVII
A
head full of zom
i
B‹
bie.-
bVI
G A
bVII
44&
##
0:11
‰œ œ œ œœ
œ œ œ œ œŒ Ó ‰
œœ œ œœœ œ œ œ œ œœ
Œ Ó
“Down Under” (Men at Work), Chorus
I
D
Do youcome from a land
V
A
downun der?
vi
B‹
IV
G A
V I
D
Wherewo menglow
V
A
andmenplunder?
vi
B‹
IV
G A
V
44&
##
0:29
‰œ œ œ œ œ
œ œ œœ œŒ Ó ‰™
œ
rœ œ œ œ
œ œ œ œ
Œ Ó
Analysis from Doll (2011)
“Down Under” (Men at Work), Verse
i
B‹
Tra vel lin’ in a fried
bVII
A
out com bie,
i
B‹
bVI
G A
bVII i
B‹
On a hip pie trail,
bVII
A
head full of zom
i
B‹
bie.-
bVI
G A
bVII
44&
##
0:11
‰œ œ œ œœ
œ œ œ œ œŒ Ó ‰
œœ œ œœœ œ œ œ œ œœ
Œ Ó
“Down Under” (Men at Work), Chorus
I
D
Do youcome from a land
V
A
downun der?
vi
B‹
IV
G A
V I
D
Wherewo menglow
V
A
andmenplunder?
vi
B‹
IV
G A
V
44&
##
0:29
‰œ œ œ œ œ
œ œ œœ œŒ Ó ‰™
œ
rœ œ œ œ
œ œ œ œ
Œ Ó
Analysis from Doll (2011)
vi
B‹
Tra vel lin’ in a fried
V
A
out com bie,
vi
B‹
IV
G A
V vi
B‹
On a hip pie trail,
V
A
head full of zom
vi
B‹
bie.-
IV
G A
V
44&
##
0:11
‰œ œ œ œœ
œ œ œ œ œŒ Ó ‰
œœ œ œœœ œ œ œ œ œœ
Œ Ó
“Down Under” (Men at Work), Verse
“Down Under” (Men at Work), Chorus
I
D
Do youcome from a land
V
A
downun der?
vi
B‹
IV
G A
V I
D
Wherewo menglow
V
A
andmenplunder?
vi
B‹
IV
G A
V
44&
##
0:29
‰œ œ œ œ œ
œ œ œœ œŒ Ó ‰™
œ
rœ œ œ œ
œ œ œ œ
Œ Ó
A “La-Based” Approach
G D F# Bm
G D Em F#
Bm F#. A E .
G D Em F#
“Hotel California” (Eagles)
Chorus
Verse
G D F# Bm
bVI bIII V iG D Em F#
bVI bIII iv V
Bm F#. A E .i V bVII IVG D Em F#
bVI bIII iv V
“Hotel California” (Eagles)
Chorus
Verse
Temperley (2013)
G D F# BmD: IV D: I V i
G D Em F#D: IV D: I iv V
Bm F#. A E .i V bVII IVG D Em F#
bVI bIII iv V
“Hotel California” (Eagles)
Chorus
Verse
de Clercq (2013)
G D F# BmD: IV D: I V i
G D Em F#D: IV D: I iv V
Bm F#. A E .i V bVII IVG D Em F#
bVI bIII iv V
“Hotel California” (Eagles)
Chorus
Verse
de Clercq (2013)
G D F# BmIV I III viG D Em F#IV I ii III
Bm F#. A E .vi III V IIG D Em F#IV I ii III
“Hotel California” (Eagles)
Chorus
Verse
Nobile (2020)
Double-Tonic Complex
Example 7: The Aeolian progression’s kinship with IV–V–I allows the possibility of combining the two, forming a double-tonic complex (a–b reproduced from Biamonte 2010, 101).
IV V I bVI bVII i
C:a:
Double-Tonic Complexes in Rock Music
Forthcoming in Music Theory Spectrum
EXAMPLES
e - v’ry move. Pri - vate eyes, they’re watching you. Pri - vate eyes
you what my head overlooks the senses will show to my heart when it’sI’m if you’re letting me in or letting me go, don’t lie when you’re
Prechorus
gon - na knowto knowgot
Example 3: Daryl Hall and John Oates, “Private Eyes” (1981): simplified transcription of verse, prechorus, and chorus
Example 3 (cont’d):
Example 5: Possible monotonal reading of “Private Eyes” in A minor.
Bridge
Ooh, why you try to put up a front for me? I’m a spy, but on your side, you see. Slip on into
starts at 2:01
Example 4: “Private Eyes,” bridge
Example 6. The double-tonic complex plotted on Gottfried Weber’s table of key relations. C minor and A major are both one step away from the A/C complex.
f
c
g
d
F
C
G
D
d
a
e
b
D
A
E
B
DTC
DTC modal mixture in “Private Eyes”
You
neve
r gi
ve
me
your
m
oney
Sun
Kin
gM
ean
Mr.
Mus
tard
Bat
hroo
m
Win
dow
“out of college,
money spent” “one sweet
dream”“all g
ood children
go to heaven”
“here comes
the Sun……King!”
Poly
then
e Pa
m
“oh yeah!”
A-C
-E-G C-m
ajor
tria
dA
-maj
or tr
iad
Alte
rnat
ion
of C
- an
dA
-maj
or tr
iads
=
com
pose
d-ou
t A-C
-E-G
four
diff
eren
t kin
ds
of to
nic
with
in D
TC
V/A
V/C
Gol
den
Slum
bers
Car
ry th
at
Wei
ght
The
End
“golden slumbers
fill your eyes”
recap of “You Never
Give Me Your M
oney”
“boy, you’re gonna
carry that weight”
clim
actic
sta
tem
ent
of A
-C-E
-G s
onor
ityA
-C-E
-G
Exam
ple
16
: The
Bea
tles,
med
ley
from
Ab
bey
Ro
ad (1
969)
, red
uctio
n. A
s in
Bai
ley’
s 19
th-c
entu
ry
exam
ples
, bot
h C
and
A a
re c
entr
al fo
r po
rtio
ns o
f the
med
ley,
but
nei
ther
em
erge
s as
the
glob
al to
nic.
One sweet dream
Example 17: Four types of tonic in “You Never Give Me Your Money”
You never give me your money You only give me your funny paper And in the middle of negotiations, you break down.
circle-of-fifths sequence in A minor
C is tonicized within sequence
Out of college, money spent See no future, pay no rent All the money’s gone, nowhere to go
descending-thirds sequence in C major
A is tonicized within sequence
a) “You never give me your money” theme (0:22): Am7 chord as tonic
b) “Out of college” theme (1:08): CM chord as tonic
c) “One sweet dream” theme (2:27): AM chord as tonic
(2:57): alternation of CM and AM chords
came true today,yes it did! Na guitar
A in melody over CM triad
Once there was a way
piano
bass
vocal
Example 18: Opening of “Golden Slumbers”
watching you, watching you, watching you, watching you You play with words
A♭
E♭
C
B♭
G
E♮
C
AThis riff continues into the next verse, but the bass note changes from A to C
Semitonal voice leading cadencing into the four-
note tonic sonority
watching for lies, wellyou can’t escape my Pri - vate eyes, they’re watching you, they see yourhurting inside, ’cause
ChorusUpper voices project C major;
bass is centered on APrechorus introduces chord structure of a major triad plus a different bass note
Chorus begins with A-C-E-G sonority
I see you, and you see me watch you blowin’ the lines, when you’re making a scene, oh girl,you play with love you can twist it around, baby that ain’t enough, cause girl,
Verse
10
Verse solidly establishes C major; most chords are triads
Chorus
a - ny disguise, I’ll still know you. Look in - to my pri - vate eyes, they’re watching you
G#Gn
Domestic animal
Pet dog
Pet cat
“I have five pets”
Petdog
Weimaraner Corgi
“I have five dogs”
Petdog
Weimaraner
“I have five Weimaraners”
???
RiverbankFinancial institution
“I am arriving at the bank”
Example 19: Cognitive engagement occurs at different conceptual levels depending on the word used in a given sentence
a) Linguistic indeterminacy: “pets” does not signify dogs and cats but rather a single abstract concept
b) Linguistic ambiguity: two potential meanings are not reconcilable into a single abstract concept
???
A minor C major
a) Tonal ambiguity
A/C complex
A minor C major
b) Double-tonic complex
Example 20: Tonal ambiguity, like linguistic ambiguity, involves two potential keys that are mutually exclusive. The double-tonic complex is analogous instead to linguistic indeterminacy, where cognitive engagement occurs at a more abstract conceptual level.
Domestic animal
Domestic animal
a) Wagner, Tristan und Isolde, “Was träumte mir von Tristans Ehre?,” Act 1, Scene 5
Example 14: Sarah McLachlan, “Building a Mystery” (1997)
Example 15: Harmonic reduction of “Building a Mystery” showing prolonged four-note chords giving rise to a double-tonic complex
Table 1: Previous tonal interpretations of “Building a Mystery”
Verse
You come out at night and the dark side’s light, and the vampires roamThat’s when the
energy comes,
etc.
0:12
Tonic
Prechorus
You’re so beautiful charm and, and so careful when I’m in your armswith anedge (and)
1:11
Subdominant Dominant
building a mys - tery Hold - ing on and hold - ing it in
Chorus
1:23Tonic
’cause you’re working,
etc.
Koozin 2008D major with “competing modal/linear pattern around B minor”
Doll 2011Verse is in B minor (although D “threatens to break through”);
choruses are in D
Richards 2017aTonal center changes from phrase to phrase in verses; choruses are in D
Attas 2011“Circular chord progression …
does not make a particular tonality clear”
de Clercq 2012,96–98
D major, with B minor an acknowledged alternative
Osborn 2017,67
D major
Example 13: The Axis progression seen as prolonging a four-note sonority with stepwise voice leading
has 6 of both A and C
has 7 and 2 of both A and C
Am F C G Am
Tonic
Subd
omin
antD
ominant
C/Am
F
Dm
(Bº)
G
(Em)
b) Mahler, Das Lied von der Erde, end
Example 1: Nineteenth-century examples of four-note sonorities functioning as tonic within a double-tonic complex. Both are built from the union of A-minor and C-major triads.
Example 2: Elliott Smith, “Everything Means Nothing to Me” (2000): a four-note sonority built from the union of two triads functions as prolonged tonic (after Schultz 2012).
melody prolongs A#
tonic sonority is union of A#m
and C#M triads
Example 8: LMFAO, “Party Rock Anthem” (2011): combination of I–V–IV and i–bVII–bVI, where the tonic chord is a four-note union of F-minor and Ab-major triads.
at 1:13
Example 9: Tina Turner, “What’s Love Got To Do With It?” (1984), prechorus into chorus: the chorus’s opening tonic contains the notes of G#m but the bass and instrumental texture hint at a B-major possibility.
Example 10: “What’s Love Got To Do With It?,” beginning of solo section (transcribed a whole step below the sounding pitch to facilitate comparison with previous example): the B-major possibility is strengthened by the solo line.
Example 11: “What’s Love Got To Do With It?,” bridge (again transcribed a whole step below the sounding pitch): this section moves away from G# minor, and when it leads back to the chorus it strongly projects B major.
Example 12: Melodic tendencies and harmonic categories within a double-tonic complex
at 0:46
Chorusend of prechorus…
Bass and guitar hint at a B chord, while e. piano plays G#m
e. guitar
e. piano
bass
After the first phrase, there is no
G# on the downbeat
at 2:02
The solo line completes aB-major triad on the first beat, forming the four-note sonority B-D#-F#-G# on the second beat
synth. harmonica
Solo
The bridge ends on a B chord, though it sounds
a bit like V of E major
etc.
When the chorus returns immediately following the bridge’s final B chord, the first chord’s B-major possibility is
especially potent
Chorus
Bridge
The bridge begins with the song’s first significant emphasis on B major
at 2:21
Example 11, cont’d
a) Non-tonic notes gravitate stepwise toward tonic notes; G and A, both members of the four-note tonic sonority, can move stepwise to one another.
b) Tonic, subdominant, and dominant functional categories are explicitly defined for diatonic triads. Songs exhibiting an Aeolian-Ionian double-tonic complex do not usually contain the chords in parentheses. (This diagram adapts Biamonte 2010’s functional diagrams, which in turn adapt those from Agmon 1996.)
iAb:
f: bVII bVII V IV
i bVII bVII V IV
at 0:29
T D S T D S
Melody outlines Ab major
(3 2 1)
Example 7: The Aeolian progression’s kinship with IV–V–I allows the possibility of combining the two, forming a double-tonic complex (a–b reproduced from Biamonte 2010, 101).
IV V I bVI bVII i
C:a:
Double-Tonic Complexes in Rock Music
Forthcoming in Music Theory Spectrum
EXAMPLES
e - v’ry move. Pri - vate eyes, they’re watching you. Pri - vate eyes
you what my head overlooks the senses will show to my heart when it’sI’m if you’re letting me in or letting me go, don’t lie when you’re
Prechorus
gon - na knowto knowgot
Example 3: Daryl Hall and John Oates, “Private Eyes” (1981): simplified transcription of verse, prechorus, and chorus
Example 3 (cont’d):
Example 5: Possible monotonal reading of “Private Eyes” in A minor.
Bridge
Ooh, why you try to put up a front for me? I’m a spy, but on your side, you see. Slip on into
starts at 2:01
Example 4: “Private Eyes,” bridge
Example 6. The double-tonic complex plotted on Gottfried Weber’s table of key relations. C minor and A major are both one step away from the A/C complex.
f
c
g
d
F
C
G
D
d
a
e
b
D
A
E
B
DTC
DTC modal mixture in “Private Eyes”
You
neve
r gi
ve
me
your
m
oney
Sun
Kin
gM
ean
Mr.
Mus
tard
Bat
hroo
m
Win
dow
“out of college,
money spent” “one sweet
dream”“all g
ood children
go to heaven”
“here comes
the Sun……King!”
Poly
then
e Pa
m
“oh yeah!”
A-C
-E-G C-m
ajor
tria
dA
-maj
or tr
iad
Alte
rnat
ion
of C
- an
dA
-maj
or tr
iads
=
com
pose
d-ou
t A-C
-E-G
four
diff
eren
t kin
ds
of to
nic
with
in D
TC
V/A
V/C
Gol
den
Slum
bers
Car
ry th
at
Wei
ght
The
End
“golden slumbers
fill your eyes”
recap of “You Never
Give Me Your M
oney”
“boy, you’re gonna
carry that weight”
clim
actic
sta
tem
ent
of A
-C-E
-G s
onor
ityA
-C-E
-G
Exam
ple
16
: The
Bea
tles,
med
ley
from
Ab
bey
Road
(196
9), r
educ
tion.
As
in B
aile
y’s
19th
-cen
tury
ex
ampl
es, b
oth
C a
nd A
are
cen
tral
for
port
ions
of t
he m
edle
y, b
ut n
eith
er e
mer
ges
as th
e gl
obal
toni
c.
One sweet dream
Example 17: Four types of tonic in “You Never Give Me Your Money”
You never give me your money You only give me your funny paper And in the middle of negotiations, you break down.
circle-of-fifths sequence in A minor
C is tonicized within sequence
Out of college, money spent See no future, pay no rent All the money’s gone, nowhere to go
descending-thirds sequence in C major
A is tonicized within sequence
a) “You never give me your money” theme (0:22): Am7 chord as tonic
b) “Out of college” theme (1:08): CM chord as tonic
c) “One sweet dream” theme (2:27): AM chord as tonic
(2:57): alternation of CM and AM chords
came true today,yes it did! Na guitar
A in melody over CM triad
Once there was a way
piano
bass
vocal
Example 18: Opening of “Golden Slumbers”
watching you, watching you, watching you, watching you You play with words
A♭
E♭
C
B♭
G
E♮
C
AThis riff continues into the next verse, but the bass note changes from A to C
Semitonal voice leading cadencing into the four-
note tonic sonority
watching for lies, wellyou can’t escape my Pri - vate eyes, they’re watching you, they see yourhurting inside, ’cause
ChorusUpper voices project C major;
bass is centered on APrechorus introduces chord structure of a major triad plus a different bass note
Chorus begins with A-C-E-G sonority
I see you, and you see me watch you blowin’ the lines, when you’re making a scene, oh girl,you play with love you can twist it around, baby that ain’t enough, cause girl,
Verse
10
Verse solidly establishes C major; most chords are triads
Chorus
a - ny disguise, I’ll still know you. Look in - to my pri - vate eyes, they’re watching you
G#Gn
Domestic animal
Pet dog
Pet cat
“I have five pets”
Petdog
Weimaraner Corgi
“I have five dogs”
Petdog
Weimaraner
“I have five Weimaraners”
???
RiverbankFinancial institution
“I am arriving at the bank”
Example 19: Cognitive engagement occurs at different conceptual levels depending on the word used in a given sentence
a) Linguistic indeterminacy: “pets” does not signify dogs and cats but rather a single abstract concept
b) Linguistic ambiguity: two potential meanings are not reconcilable into a single abstract concept
???
A minor C major
a) Tonal ambiguity
A/C complex
A minor C major
b) Double-tonic complex
Example 20: Tonal ambiguity, like linguistic ambiguity, involves two potential keys that are mutually exclusive. The double-tonic complex is analogous instead to linguistic indeterminacy, where cognitive engagement occurs at a more abstract conceptual level.
Domestic animal
Domestic animal
a) Wagner, Tristan und Isolde, “Was träumte mir von Tristans Ehre?,” Act 1, Scene 5
Example 14: Sarah McLachlan, “Building a Mystery” (1997)
Example 15: Harmonic reduction of “Building a Mystery” showing prolonged four-note chords giving rise to a double-tonic complex
Table 1: Previous tonal interpretations of “Building a Mystery”
Verse
You come out at night and the dark side’s light, and the vampires roamThat’s when the
energy comes,
etc.
0:12
Tonic
Prechorus
You’re so beautiful charm and, and so careful when I’m in your armswith anedge (and)
1:11
Subdominant Dominant
building a mys - tery Hold - ing on and hold - ing it in
Chorus
1:23Tonic
’cause you’re working,
etc.
Koozin 2008D major with “competing modal/linear pattern around B minor”
Doll 2011Verse is in B minor (although D “threatens to break through”);
choruses are in D
Richards 2017aTonal center changes from phrase to phrase in verses; choruses are in D
Attas 2011“Circular chord progression …
does not make a particular tonality clear”
de Clercq 2012,96–98
D major, with B minor an acknowledged alternative
Osborn 2017,67
D major
Example 13: The Axis progression seen as prolonging a four-note sonority with stepwise voice leading
has 6 of both A and C
has 7 and 2 of both A and C
Am F C G Am
Tonic
Subd
omin
antD
ominant
C/Am
F
Dm
(Bº)
G
(Em)
b) Mahler, Das Lied von der Erde, end
Example 1: Nineteenth-century examples of four-note sonorities functioning as tonic within a double-tonic complex. Both are built from the union of A-minor and C-major triads.
Example 2: Elliott Smith, “Everything Means Nothing to Me” (2000): a four-note sonority built from the union of two triads functions as prolonged tonic (after Schultz 2012).
melody prolongs A#
tonic sonority is union of A#m
and C#M triads
Example 8: LMFAO, “Party Rock Anthem” (2011): combination of I–V–IV and i–bVII–bVI, where the tonic chord is a four-note union of F-minor and Ab-major triads.
at 1:13
Example 9: Tina Turner, “What’s Love Got To Do With It?” (1984), prechorus into chorus: the chorus’s opening tonic contains the notes of G#m but the bass and instrumental texture hint at a B-major possibility.
Example 10: “What’s Love Got To Do With It?,” beginning of solo section (transcribed a whole step below the sounding pitch to facilitate comparison with previous example): the B-major possibility is strengthened by the solo line.
Example 11: “What’s Love Got To Do With It?,” bridge (again transcribed a whole step below the sounding pitch): this section moves away from G# minor, and when it leads back to the chorus it strongly projects B major.
Example 12: Melodic tendencies and harmonic categories within a double-tonic complex
at 0:46
Chorusend of prechorus…
Bass and guitar hint at a B chord, while e. piano plays G#m
e. guitar
e. piano
bass
After the first phrase, there is no
G# on the downbeat
at 2:02
The solo line completes aB-major triad on the first beat, forming the four-note sonority B-D#-F#-G# on the second beat
synth. harmonica
Solo
The bridge ends on a B chord, though it sounds
a bit like V of E major
etc.
When the chorus returns immediately following the bridge’s final B chord, the first chord’s B-major possibility is
especially potent
Chorus
Bridge
The bridge begins with the song’s first significant emphasis on B major
at 2:21
Example 11, cont’d
a) Non-tonic notes gravitate stepwise toward tonic notes; G and A, both members of the four-note tonic sonority, can move stepwise to one another.
b) Tonic, subdominant, and dominant functional categories are explicitly defined for diatonic triads. Songs exhibiting an Aeolian-Ionian double-tonic complex do not usually contain the chords in parentheses. (This diagram adapts Biamonte 2010’s functional diagrams, which in turn adapt those from Agmon 1996.)
iAb:
f: bVII bVII V IV
i bVII bVII V IV
at 0:29
T D S T D S
Melody outlines Ab major
(3 2 1)
Tonal Ambiguity
“Treasure” (Bruno Mars)
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IVmaj7 iii7 ii7 iii7 V vi V
IVmaj7 iii7 ii7 V9sus4
“Absent” Tonic?“Treasure” (Bruno Mars)
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IVmaj7 iii7 ii7 V9sus4
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“Rolling in the Deep” (Adele)
Nashville Chart
Williams (2017)
“Rolling in the Deep” (Adele)
Nashville Chart
Ab Bb Gm Ab
Cm Bb Ab
Williams (2017)
Cm Gm Bb
“Rolling in the Deep” (Adele)
Nashville Chart
Ab Bb Gm AbG7 !
Cm Bb Ab
Williams (2017)
Cm Gm Bb
Some Stats
(from the RS 200)
All, Do Minor (n = 200)
Root Instances % total I 6,077 33.2
IV 4,143 22.7 V 3,121 17.1
bVII 1,347 7.4 VI 1,116 6.1 II 864 4.7
bVI 662 3.6 bIII 410 2.2 III 398 2.2 bII 56 0.3
VII 52 0.3 #IV 43 0.2
Some Stats
(from the RS 200)
Major Tonic (n = 154)
Root Instances % total I 4,507 34.0
IV 3,442 26.0 V 2,502 18.9
VI 1,007 7.6 bVII 596 4.5
II 587 4.4 III 359 2.7 bIII 82 0.6 bVI 66 0.5 VII 43 0.3 #IV 31 0.2 bII 22 0.2
All, Do Minor (n = 200)
Root Instances % total I 6,077 33.2
IV 4,143 22.7 V 3,121 17.1
bVII 1,347 7.4 VI 1,116 6.1 II 864 4.7
bVI 662 3.6 bIII 410 2.2 III 398 2.2 bII 56 0.3
VII 52 0.3 #IV 43 0.2
Some Stats
Major Tonic (n = 154) Root Instances % total
I 4,507 34.0 IV 3,442 26.0 V 2,502 18.9
VI 1,007 7.6 bVII 596 4.5
II 587 4.4 III 359 2.7 bIII 82 0.6 bVI 66 0.5 VII 43 0.3 #IV 31 0.2 bII 22 0.2
Do Minor Tonic (n = 32)
Root Instances % total I 1,128 33.1
bVII 535 15.7 V 450 13.2
bVI 448 13.2 IV 441 13.0 bIII 274 8.0
II 83 2.4 bII 24 0.7 #IV 12 0.4 VI 8 0.2 III 2 0.1
VII 0 0.0
Some Stats
Major Tonic (n = 154) Root Instances % total
I 4,507 34.0 IV 3,442 26.0 V 2,502 18.9
VI 1,007 7.6 bVII 596 4.5
II 587 4.4 III 359 2.7 bIII 82 0.6 bVI 66 0.5 VII 43 0.3 #IV 31 0.2 bII 22 0.2
Do Minor Tonic (n = 32)
Root Instances % total I 1,128 33.1
bVII 535 15.7 V 450 13.2
bVI 448 13.2 IV 441 13.0 bIII 274 8.0
II 83 2.4 bII 24 0.7 #IV 12 0.4 VI 8 0.2 III 2 0.1
VII 0 0.0
Some Stats
Major Tonic (n = 154) Root Instances % total
I 4,507 34.0 IV 3,442 26.0 V 2,502 18.9
VI 1,007 7.6 bVII 596 4.5
II 587 4.4 III 359 2.7 bIII 82 0.6 bVI 66 0.5 VII 43 0.3 #IV 31 0.2 bII 22 0.2
Do Minor Tonic (n = 32)
Root Instances % total I 1,128 33.1
bVII 535 15.7 V 450 13.2
bVI 448 13.2 IV 441 13.0 bIII 274 8.0
II 83 2.4 bII 24 0.7 #IV 12 0.4 VI 8 0.2 III 2 0.1
VII 0 0.0
Chi-Squared ≈ 28,000
Some Stats
Major Tonic (n = 154) Root Instances % total
I 4,507 34.0 IV 3,442 26.0 V 2,502 18.9
VI 1,007 7.6 bVII 596 4.5
II 587 4.4 III 359 2.7 bIII 82 0.6 bVI 66 0.5 VII 43 0.3 #IV 31 0.2 bII 22 0.2
La Minor Tonic (n = 32) Root Instances % total
VI 1,128 33.1 V 535 15.7 III 450 13.2 IV 448 13.2 II 441 13.0 I 274 8.0
VII 83 2.4 bVII 24 0.7 bIII 12 0.4 #IV 8 0.2 bII 2 0.1 bVI 0 0.0
Some Stats
Major Tonic (n = 154) Root Instances % total
I 4,507 34.0 IV 3,442 26.0 V 2,502 18.9
VI 1,007 7.6 bVII 596 4.5
II 587 4.4 III 359 2.7 bIII 82 0.6 bVI 66 0.5 VII 43 0.3 #IV 31 0.2 bII 22 0.2
La Minor Tonic (n = 32) Root Instances % total
VI 1,128 33.1 V 535 15.7 III 450 13.2 IV 448 13.2 II 441 13.0 I 274 8.0
VII 83 2.4 bVII 24 0.7 bIII 12 0.4 #IV 8 0.2 bII 2 0.1 bVI 0 0.0
Chi-Squared ≈ 2,800
I ii iii IV V vi viio
Patterns of HarmonyMajor Key
I ii iii IV V vi viio
I ii iii IV V vi viio
Patterns of Harmony
All, La Minor (n = 200)
Root Instances % total I 4,781 28.7
IV 3,890 23.4 V 3,037 18.2
VI 2,135 12.8 II 1,028 6.2
III 809 4.9 bVII 620 3.7 VII 126 0.8 bIII 94 0.6 bVI 66 0.4 #IV 39 0.2 bII 24 0.1
Major KeyI ii iii IV V vi viio
I ii iii IV V vi bVII
Patterns of Harmony
All, La Minor (n = 200)
Root Instances % total I 4,781 28.7
IV 3,890 23.4 V 3,037 18.2
VI 2,135 12.8 II 1,028 6.2
III 809 4.9 bVII 620 3.7 VII 126 0.8 bIII 94 0.6 bVI 66 0.4 #IV 39 0.2 bII 24 0.1
Major KeyI ii iii IV V vi bVII
I ii iii IV V vi bVII
Patterns of Harmony
All, La Minor (n = 200)
Root Instances % total I 4,781 28.7
IV 3,890 23.4 V 3,037 18.2
VI 2,135 12.8 II 1,028 6.2
III 809 4.9 bVII 620 3.7 VII 126 0.8 bIII 94 0.6 bVI 66 0.4 #IV 39 0.2 bII 24 0.1
Major Key
i iio bIII iv v or V bVI bVIIMinor Key
I ii iii IV V vi bVII
I ii iii IV V vi bVII
Patterns of Harmony
All, La Minor (n = 200)
Root Instances % total I 4,781 28.7
IV 3,890 23.4 V 3,037 18.2
VI 2,135 12.8 II 1,028 6.2
III 809 4.9 bVII 620 3.7 VII 126 0.8 bIII 94 0.6 bVI 66 0.4 #IV 39 0.2 bII 24 0.1
Major Key
vi bVII I ii iii or III IV VMinor Key
“Axis” Progression (and rotations)
C G Am F
G Am F C
Am F C G
F C G Am
“Axis” Progression (and rotations)
C G Am FI V vi IVG Am F C
Am F C Gi bVI bIII bVIIF C G Am
Gb Db Ab Bbm.
Gb Db Ab Bbm.
“Umbrella” (Rihanna)
Bridge
Chorus
Post-Chorus
Gb Ab F Bbm.
Gb Ab F Bbm
Cb Gb Db Db .
Cb Gb F F
Gb Db Ab Bbm.IV I V viGb Db Ab Bbm.IV I V vi
“Umbrella” (Rihanna)
Bridge
Chorus
Post-Chorus
Gb Ab F Bbm.IV V III viGb Ab F BbmIV V III vi
Cb Gb Db Db .bVII IV I ICb Gb F FbVII IV III III
Works Cited:de Clercq, Trevor & David Temperley. 2011. “A Corpus Analysis of Rock
Harmony.” Popular Music 30 (1): 47-70. Doll, Christopher. 2011. “Rockin’ Out: Expressive Modulation in Verse-Chorus
Form.” Music Theory Online 17 (3). ––––––. 2017. Hearing Harmony: Toward a Tonal Theory for the Rock Era. Ann
Arbor, MI: University of Michigan Press. Nobile, Drew. 2020 (Forthcoming). “Double-Tonic Complexes in Rock Music.”
Music Theory Spectrum 42 (2). Richards, Mark. 2017a. “Tonal Ambiguity in Popular Music’s Axis
Progressions.” Music Theory Online 23 (3). Spicer, Mark. 2017. “Fragile, Emergent, and Absent Tonics in Pop and Rock
Songs.” Music Theory Online 23 (2). Temperley, David. 2007. “The Melodic-Harmonic ‘Divorce’ in Rock.” Popular
Music 26 (2): 323–42. Temperley, David and Trevor de Clercq. 2013. “Statistical Analysis of Harmony
and Melody in Rock Music.” Journal of New Music Research 42 (3): 187-204.
Williams, Chas. 2017. The Nashville Number System Gigbook. Nashville, TN: Chas Williams.
THANK YOU!