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Duke University Press and Yale University Department of Music are collaborating with JSTOR to digitize, preserve and
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http://www.jstor.org
Yale University epartment of Music
A New Theory of Chromaticism from the Late Sixteenth to the Early Eighteenth CenturyAuthor(s): Kyle Adams
Source: Journal of Music Theory, Vol. 53, No. 2 (Fall 2009), pp. 255-304Published by: on behalf of theDuke University Press Yale University Department of MusicStable URL: http://www.jstor.org/stable/40925745Accessed: 01-11-2015 23:31 UTC
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ANewTheory fChromaticism
from
he
Late
Sixteenth o
the
Early ighteenth
entury
Kyle
Adams
Abstract This rticle s
intended s a
solution o a
perceived roblem
ith
xisting
heories f
pretonal
hro-
matic
music:
Many
modem heories f
this
repertoire
ave
made anachronistic
ses of models from
major/
minor
onality,
nd
contemporaneous
heorieswere not
broad
nough
o
adequately epresent
he
phenomena
that,
o
my
wn
and, believe,
many
thermodern isteners'
ears,
gave
chromatic usic ts
unique
ound.
Both
roups
f
theoriesmissed he mark
y
reating
ll
chromaticvents
n
this
repertoirequally.
his rticle
therefore
egins
by
uggesting
hat,
ust
s in
onal
music,
hromaticism
n
his
period
omprises
many
ifferent
phenomena.
therefore
rovide
model or
eparating
hromatic
ones
ccording
o
their tructural
unctionnd
an
analytical
method or
educing
hromatic
orks o their iatonic
oundations.
present
xamples
of
each of
the chromatic
echniques
hat
describe nd
give
detailed
riteria or
dentifying
ach
technique.
n
doing
o,
I
provide
new
vocabulary y
which cholars nd
analysts
an
model he
way
n
which
hey
ear
hromatic usic
from
his
period.
Introduction
the
theory
presented in
this
article is
best
ntroduced
y
n
analogy
o
tonal music.
present
he
two
progressions
iven
n
Example
1 in
order to
explain
their
elevance o
the
present ubject.
Each
example
uses
the same
chromatic
onority,
heBl?
major
hord
n
the
econd
half fm.
2,
n
different
ways.
n
Example
a,
the
chromatic
onority
s
folded nto he
overall
D-major
tonality
nd
is
understood s
a
substitute or
diatonic
onority.
n
analyst
would
thereforeabel it
bVI,
n
orderto
indicate
ts
origins
n
the
diatonicvi
chord. nExample b, the ame chordfunctionss a chromatic ivot ousher
in
a new
tonality
nd
would
ikely
eceive
wo
abels,
bVTn D
and
IV in
F,
to
indicate ts
dual
function.
he
point
of
this
xample
s
twofold:
irst,
ur
per-
ception
of
the
function f
the
chromatic
onority
s
dependent
on
context.
This article s
a
condensed
version of the
theorypresented
in
my
dissertation
Adams
2006),
which
I
encourage
readers
to consult
for more
comprehensive
reatment f this
opic,
ncluding
complete
list
of
the
repertoire
examined
in
my
research. I
express my
gratitude
o William
Rothstein,
Ruth
DeFord,
David
Gagne, Nancy
Nguyen-Adams,
nd
Linda
Pearse,
as
well as
the
anonymous
readers,
for
heir
help
in
developing
nd
focusing
his rticle.
Journal
f
Music
Theory
3:2,
Fall
2009
DOI 10.1215/00222909-2010-004 2010
by
Yale
University
255
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256
JOURNAL
of
MUSIC
THEORY
The istenernderstandshe hord
nly
n
ight
fthe
following
onorities,
since
oth
rogressions
egin
he ame
way.1
econd,
onalmusic heorists
re
comfortableith he ame hromaticonorityaving ifferentunctionsn
different
ontexts,
ith
he seofdifferentabels or uch
onorities,
nd
with
the xistence
f
different
arietiesf hromaticism
n
general.
(a) (b)
ziMuJ
j
|J ,j
|j
j
|o n
j
|j .J |i|,j g=F^=Ti
' ...
J
J J U U
J o
J J J U J
j
,
Vl " r r rT y r r f ~ ? "i r v "
Example
1.
Chromaticism
in
two tonal
progressions,
(a)
and
(b)
I
bring p
these
wo
points
ecause,
while onal
heory
eems
o be
completely
t ease with hese
oncepts,retonal
heory
oes
not eem obe.
Part
fwhat ashindered heorists'
nderstanding
fchromaticism
n
early
musicsthe nsistencen a
single onception
f
hromaticism,
rom
heorists
both f his ime
eriod
nd
of ur wn.
hus,
he
resent
rticle
egins
rom
the remisehathromaticonoritiesanhave ifferentunctionsnpretonal
music,2
ust
s
they
an ntonal
music,
nd
that ontextan
help
odetermine
the
ype
f hromaticismt
play
n a
given
assage.
Background
Analystspproaching
hromatic
usic
romhis
eriod
ave uffered
romn
overreliance
n a
single
heoretical
odel.3 heorists
rom he
period
nder
discussionubscribed
o
one of two
views f the
chromatic
enus.
Those
adhering
o therelative
onception
onsidered
he
hromatic
enus
o
reside
inthe seof givenntervalr ntervallicrogression,ypicallyhe hromatic
semitone.4
hishas lsobeen
he
onception
ut
orth
y
modern
historicist"
1
In
fact,
he
very
xistence
of chromaticism
n
his
passage
is
contextual.Out
of
context,
he
Bb
major
hord s
diatonic,
unlike,
or
xample,
an
augmented
sixth
hord,
which
can-
not
be taken
from
ny
diatonic cale
and is therefore
hro-
matic
regardless
of ts context.
2
I
am aware
of the
strong
differences
f
opinion
on the
appropriate
erm
formusic from
his
period.
Some scholars
consider
"pretonal"
overly eleological,
nd others
consider
"early
music"
overly ague.
Since this
article
learly
delin-
eates
the historical
eriod
with which
it
deals,
I use both
terms interchangeablyo describe music from hatperiod
and do not
enter nto he
controversy
ver
terminology.
3 What follows
s a
highly
ondensed
version of
my
sum-
mary
f earlier
onceptions
of chromaticism
n
Adams
2007,
15-25,
and of
my xplication
f modern
onceptions
of
early
chromaticism,
s well
as
problems
with both
conceptions,
in Adams
2006,
53-79.
Space
does not
permit
me
to thor-
oughly
xplore
those
subjects
here,
but
I
directreaders
to
those works
for
much more
comprehensive
reatment.
4 These include
Vicentino
[1555] 1996),
Lusitano
([1561]
1989),
Burmeister
[1606] 1993),
and Printz
1679).
Even
Rameau
([1737]
1966)
describes
the
origin
of "this
new
genus of Harmony" n the semitone producedbythe over-
tones
of two notes
a third
part
171).
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Kyle
Adams
~
A New
Theory
of Chromaticism 257
scholars,5
otablyMargaret
ent
ndjames
Haar,
both fwhom
mphasize
he
melodic
nature fchromaticism
n
early
music,
specially
heuse of melodies
involvinghechromaticemitone.6 n the otherhand,theoristsubscribing
to the absolute
onception
f chromaticismefine he chromatic
enus by
ts
use
of
pitches
utsideof an established iatonic ollection.7
n
the sixteenth
century,
his collectionwas
typically
he
gamut
of musica
ecta,
ut
moving
intothe
eighteenth entury,
twasconceived f as whatever iatonic cale
(in
the
modern
ense)
was
operational
n a
givenpassage.
Since this
onception
of
chromaticisms
basically
he one used
in
tonal
theory,
t s not
surprising
that he
more
"presentisi"nalyses
f
early
hromaticism se it as a
starting
point.
Presentist
pproaches
takevarious
orms,
nd mosthave focused n a
single
work,
he
Prologue
to Orlando di Lasso's
Prophetiaeibyllarum
1560).
Among heapproachesto thiswork re WilliamMitchell's1970) Schenker-
ian
analysis,
nd Karol
Berger
s
(1976)
and WilliamEastmanLake's
(1991)
hierarchical
rrangements
f
Roman numerals.
All
three
ttempt
o
explain
Lasso's chromaticism uch as one
would
n
a tonal
piece,
by
describing
he
chromatic onorities s
they
elate o diatonic onorities.
In
brief,
o
single
ne of
these
pproachesproves atisfactory
ormod-
eling
the
wealth f
works,
assages,
nd
techniques
rom his
period
that an
reasonably
e
called "chromatic." elianceon thechromatic
emitone reates
two
problems.
irst,
t does not accountfor ll of
the
ntentionally
hromatic
passages
from his
period. Example
2
is
from asso's
Sibylla
immeria.asso's
owntext o thePrologueof thiswork ellsus that t s intended o be chro-
matic,
nd
yet
this
brief uccessionof
chords,
triking
s it
is,
contains
no
chromatic emitones.
Second,
one also finds
assages
n
whichnotated
hromatic emitones
occur
in
completely
iatonic
progressions.
he best known f
these comes
from uca
Marenzio's
madrigal
O voi he
ospirate
miglior
ote 1581
,
n which
a dense
umble
of
notated hromatic emitones an
be renotated o reveal
simple
hain
of
descending
ifths.8
I/l (K 1 I
flP^dflfl ,xi-- r) J .H - -
iJaLs
L_
tfc
I-*- II
Example
2.
Lasso,
Sibylla
Cimmeria
5 For
explanations
of the
historicist nd
presentist
posi-
tions,
ee
Christensen
1993).
6
Haar's view
(1977,
392)
is more
temperate
than
Bent's,
who
asserts that
"for
Zarlino,
only
melodic
progressions
that ound chromatic ecause theyuse the chromatic emi-
tone
qualified
s
chromatic"
2002,
129).
7
These include Zarlino
([1558]
1968),
Bottrigari
[1594]
1962),
Morley
[1597]
1973),
Mersenne
([1627]
2003),
and
Werckmeister
[1707] 1970).
8
This
passage
is
discussed
in
Fétis
1879.
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258
JOURNAL
of
MUSIC THEORY
The
presentist,
absolute"
onception
of
chromaticismikewise
as its
weaknesses. oth the Schenkerian nd Roman-numeral
nalyses
uffer
rom
attemptsofit asso'sprologue nto n overall tonality"fG. Mitchellgnores
surface
eatures f themusic hat ontradict
is
Schenkerian
pproach,
while
Berger
uses Roman numeralswithout
egard
or
he
hierarchy
f functional
relationships
hat uch
usage
traditionallymplies.
Thus,
n
Berger's
hart f
Roman
numerals,
ne finds
rogressions
uch as V-VI-I without
ny xplana-
tory
ote.
The
present heory
oes not
pretend
o olve
very roblem
n
the
nalysis
of
early
hromaticmusic.
However,
s
I
stated
bove,
begin
from
he
premise
that
hromaticonorities
n
early
music an havedifferentunctions
n
different
contexts nd that chromaticism"s
applied
to
early
music
does
not
describe
single echnique nymore han tdoes ntonalmusic. assert hatnot ll chro-
matic
ones xist
or
he
ame reason r at the ame evel
f
tructure
nd that
differentevels f these ones an be
separated
rom ne another
ccording
o
their tructuralunctions. n one
hand,
approach
hemusic rom
present-
ist
point
of
view
y ttempting
o describe
my
wn
and, believe,
he
typical
modern istener's
perception
f chromaticmusic.9 use
historical exts s
informantsut do not
try
o divine
he
composer's
onception
f chromatic
music r to describe he ixteenth-
r
seventeenth-century
istener's
erception
of
t. On the other
hand,
take
historicist
oint
of view
by pproaching
he
musicwithout
sing
the Procrustean
ed of
major/minor
onality. attempt
toprovide n accuratemodelfor hisrepertoirey usingprinciples
erived
from hemusical exts.
My
heory
herefore
ries o
converge
he
presentist
nd
historicist
ositions
yusing
oth
he
oncepts
vailable
o earlier heorists
nd
appropriate
oncepts
rom he
present
ay
o describe s
accurately
s
possible
the
objective
henomena
hat,
o a modern
istener,
istinguish
his
epertoire
from ther
ypes
f ixteenth-
nd
seventeenth-century
usic.
Repertoire
nd
time
period
The
theory
hat
follows s based
on a
study
f all available
chromatic
music
published
roughly
ithin he
time
period
1555-1737.
This
period
s
demar-
catedbythepublication f NicolaVicentino'sAncient usicAdaptedoMod-
ernPracticend
Jean-Philippe
ameau
s Génération
armonique,
hich
were,
respectively,
he
firstnd last
works fter lassical
ntiquity
oth
to discuss
he
chromatic
s a
separategenus
and to
apply
tsuse
to
contemporary
usic.10
Works
rom his
ime
period
were
ncluded
n the
tudy
f
hey
ell
ntoone
or
more
of the
following
lasses:
9
I
use the term
listener" to mean
someone familiar
ith
the norms
ofWestern art
music.
10
Even
the use
of these
fairly bjective
criteria
o choose
a time
period
ed to some
absurdities: Can
one
really ay
that Bach used a different arietyof chromaticism fter
1737
than he used
before?
Nevertheless,
t was
necessary
to
have some
boundary
dates for
he musical
examples
in
order o
keep
their
numbersfrom
ecoming
unmanageably
large.
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Kyle
Adams
~
A
New
Theory
of Chromaticism 259
•
Pieces whose title
r
text ontains he word
chromatic,
r some var-
iation
of it. This
category
ncludes
pieces
identified s
durezze,
seventeenth-centuryeyboard enre haracterizedy multitude f
harshdissonances nd
unusually esolvinguspensions.
•
Pieces withfeatures hat onformed o
contemporaneous
r earlier
theoretical
onceptions
f
chromaticism,
ncluding
a)
conspicuous
uses of theancientGreek
hromatic etrachord
two
emitones
nd
a
minor
hird);11b)
widespread
se of
"black-key"
i.e.,
chromatically
altered)
ones;12
nd
(c)
employment
f
thechromatic ourth
i.e.,
ix
consecutive emitones
illing
he
nterval f a
perfect
ourth).13
•
Pieces
featuring
idespread
se
of
what modernmusician
would
call chromatic
iguration.
• Piecesfrom wo angentiallyelated ategories:hosewhose itles on-
tain the term
enharmonic"
as
opposed
to
"chromatic"),
nd others
that
very
learly
make use of
enharmonic
elationships
o
uxtapose
distantly
elated
onorities;
nd
"labyrinth"
r "circle"
pieces
that,
through
equential repetition,
ravel o
very
distant onalities nd
eventually
eturn o their
tarting
onalities.
I.
Explanation
of
the
theory
Components
f the
theory
nd
definitions
This theory as twocomponents: theoreticalmodel forclassifyingiffer-
ent
types
f
chromaticismnd an
analytical
method
that uses that model
to
separate
different
ypes
f
chromatic ones
according
o
their
tructural
functions.
Definitions.
his
theory
ses the
following
efinitions:
(
1
Tonal
ystem:
collection f
pitch
lasses
quivalent
o
the modern
diatonic cale
but without
ny
hierarchy
mong
them.The
tonal
system
s
named
for
the
number
of
accidentals t
contains; hus,
the
one-sharp ystem
ould be
equivalent
o the modern
G-major
scale but
without center n
G. When
passage
of
musicuses
only
tones from singletonalsystem,hat ystems said togovernhe
passage.14
(2)
Diatonic:
diatonic
one s one
that
elongs
o the
governing
onal
system.
diatonic
onority
s
one that
ontains
nly
uch
tones.
11 In
this
article,
chromatic
etrachord"
lways
refers o
this melodic
succession.
12
Bottrigari
1594]
1962 defines
the
chromatic
enus
as
the
use of
these tones
(see
33-34).
13
In
my
research,
examined more
than
1,400
examples
of the chromatic ourth. ince mydissertationdevotes an
entire
chapter
to
my analytical
indings egarding
his
pro-
gression,
examples
containing
t are
not treated in
this
article.
14
See
Appendix
A
for
further
iscussion
of
my concep-
tion
of tonal
system.
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260
JOURNAL
of
MUSIC
THEORY
(3)
Chromatic.
chromatic one s
one that alls
utside he
governing
tonal
system.
chromatic
onority
s one that ontains
ny
such
tones.
(4)
Essential
hromaticism:he use of chromatic lterations o correct
an
unacceptable onority
n
a
given epertoire.
n
the
period
under
consideration
ere,
uch
alterations
ypically
orrect he ntervals
excluded
by
he mi ontra
a prohibition,
hat
s,
mperfect
nisons,
fourths,ifths,
nd
octaves,
whether ertical r horizontal.15
(5)
Nonessential
hromaticism:
he use of eitherof the
following
wo
types
f chromatic lterations:
(a)
Type
A: Alterations hat erveto correct onorities hat re
contextually
ncorrect. or
example,
n the ixteenth
entury,
a minor ixth sbyno meansprohibitedutcan become so if
it
progresses
o an octave t a final adence.
Typically,ype
A
alterationsnvolve ither adential
eading
tones or
Picardy
thirds
which
hemselves
ecome less
structurallymportant
throughout
his
eriod);16
owever,
heymay
lso be used to
preserve
trictmitation
f a motive.17
(b)
Type
: Alterationshat erve
nly xpressive urposes.
hey
may
xist or ffectiver
text-painting
easons utdo notcor-
rect
ny
ype
f ncorrect
onority.
Indirect Direct
Diatonicism
chromaticism
chromaticism
Pure Nonessential Essential
Juxtaposed Suspended
diatonicism chromaticism chromaticism
diatonicism diatonicism
Figure
1.
A continuum of chromaticism
The heoreticalodel: continuum
f
hromaticism.
igure
1
presents
con-
tinuum
ontaining
arious
ategories
f
chromaticism.
he
techniques
n
Fig-
ure
1
are isted
n
order
f
ncreasing
hromaticism.
he
top
of
he
ontinuum
isdivided nto three argecategories. iatonicismefers opassagesgoverned
by
a
single
tonal
system.
ndirect
hromaticismefers o
passages
n which
ny
two
uccessive
onorities
elong
to a
single
onal
ystem
ut the
passage
con-
taining
hemdoes not. Direct hromaticism
efers o
passages
containing
wo
successive onorities
hat o not
belong
to
the ame tonal
ystem.
nderneath
the
continuum re several maller-scale
echniques.
At the two nds
are
pure
15
The status
of
chromatic lterations
hat correct cross-
relations
epends
on the
composer
and time
period,
ince
cross-relations
enerally
became
more
acceptable
as this
period
went
on.
16
Following
he distinctionsmade in
Berger
2004, 137, I
consider cadences to be more
structurallyignificant
han
other
places
inwhich
composer
or
performer
ight
hoose
to create
directed motion
via a chromatic
nflection.
17
See
Appendix
B for further iscussion
of the terms
essential
and nonessential.
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Kyle
Adams
~
A
New
Theory
of Chromaticism
261
diatonicism,
hich efers o
any
passage
that ses
only
diatonic
onorities,
nd
suspended
iatonicism,
hich onsists
f
ny
passage
forwhich
t s
mpossible
o
determine hegoverningonalsystem.he latter sually ccursbecause the
accumulation f
emitones
makes t
mpossible
o
arrive t a diatonic
basisfor
the
passage.
These
endpoints
re whatCarl
Dahlhaus,
following
Max
Weber,
refers o as ideal
types;18
hat
s,
they
re
categories
hat
exist n
principle
but
may
have no
occurrences n actual music.Pure
diatonicism,
or
xample,
rarely
xists or
ong spans
of
time,
espite
he fact hat
single
Renaissance
work
may
e notated
without ccidentals rom
eginning
o end.
Ifunnotated
musica
ictais
onsidered o be
a
given
eature
f
themusical
urface,
s
I
argue
it hould
see
Appendix
B)
,
then
here s
hardly
Renaissancework hat oes
not exhibit
hromaticisms
I
have
defined t.
Likewise,
lthoughmany
musi-
cal examplesvergeon suspendeddiatonicism,his deal type oes not seem
to
exist
n
practice.
Every assage
have
examined,
no matter ow
densely
chromatic,
as features hat
give
t some diatonic
ontext.
Between
pure
diatonicism
nd
suspended
diatonicism re threeother
chromatic
echniques
dentifiable
n music rom his
eriod.
Nonessential
hro-
maticism
as
already
been defined.
Note that t
appears
under
the
general
category
f diatonicism ecause
nonessential
hromatic ones re alterations
of
diatonic
ones nd can be removed
o reveal
passage
of
pure
diatonicism.
Essential hromaticismas also
already
een
defined,
nd
it s the first
ype
f
chromaticism
long
the continuum.
Essentialchromatic ones will
nearly
always ignal move nto a tonalsystemnwhichthey re diatonic.Unlike
true
diatonic
ones,however,
hey
re chromatic
n relation o the
ystem
hat
came before.
uxtaposed
iatonicismonsists f the
placement
f
twodifferent
tonal
ystemslongside
ne another
using
direct hromaticism.
Figure
1
is not a line
n
which
very
hromatic orkhas a
position
ela-
tive o
every
ther nd one can
plot precisely
he relative
egree
of
chromati-
cism f
ny
work. he
categories
nd
techniques
f
chromaticism
epresented
on it can coexist n the
same
work,
r even in a
single passage.
Nor
is
the
continuum he most ccurate
possiblegraphicrepresentation
f the
catego-
ries t
contains;
or
xample,
nonessential hromaticisman
existwithin
ux-
taposed
diatonicism.
onetheless,
t
s
a useful
way
o schematize
hromatic
techniques
nthe
repertoire
nderconsideration.
The
analytical
method:
Diatonic eduction
Diatonic
reduction
s
a method f
distinguishingmong
various
evels fchro-
maticismn a
given
passage.
t consists f the
removal
f
nonessential hro-
matic
alterations o reveal
the tonal
system
s)
underlying
given passage.
18
Weber,
as
quoted
in
Gossett
1989,
describes an "¡deal
type"
as follows: An
deal
type
s
formed
..
by
the
synthe-
sis of a
great
many
diffuse,
iscrete,
more or less
present
and occasionally absent concrete individual
phenomena,
which are
arranged ccording
to those
one-sidedly mpha-
sized
viewpoints
into a unified
nalytical
onstruct.
n
its
conceptual
purity,
his mental
construct cannot
be found
empirically nywhere
n
reality"
51).
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262
JOURNAL
of
MUSIC THEORY
I
explain
diatonic eduction
hrough
eference
o an
example.
The
guidelines
for
reating
diatonic eduction re also
given
n list orm
n
Appendix
C.
Example3 presents diatonicreduction f the asteightmeasures f
Carlo Gesualdo's Ma
tu,
agion,
he second
part
f Poiché'avida
ete,
rom he
fifthook of
madrigals.
ecause
my
ocus t this
tage
s on the
meaning
f he
analytical
otation
nd
not
on
the
composition
tself,
do notmakeextensive
arguments
or he
analytical
hoices the notation ommunicates.
A
typical
iatonic
reduction,
ike the one in
Example
3,
has four
om-
ponents.
he
top system eproduces
he
core.The lowest
taff,
abeled
"tonal
systems,"
racks
he
governing
onal
ystem
t each
moment
n themusic.The
ways
n
which
key ignatures
nd barlines re used on this taffre
explained
below.Between hese wo
ystems
re two uccessive
tages
f
reduction.
tage
1
ofthe reduction eproduces he score withoutny typeB alterationsthose
that xist
nly
for
xpressive urposes) Stage
2
reduces
tage
1
even further
byremoving
ype
alterations
those
hat orrect
tructurally
ncorrectonor-
ities).
f
a
givenpassage
contains
nly
ne
type
f nonessential
lteration,
r
none at
all,
either
tage
1
or
2
or
both
may
be omitted.
he
lowest
ystem
f
music
n
thereductionwill
lways
ontain hediatonic ramework
pon
which
a
given
hromatic
assage
s
built,
nd the "tonal
ystem"
taff elow
thatwill
show ts
governing
onal
ystem.
Example
3
may
be read as follows: he
passage begins
n the
two-sharp
system,
s shownon the lowest taff.
onal
systems
n this taff
ill
always
be notated s modernkey ignatures,19ith wo xceptions: assagesofsus-
pended
diatonicism
illhave
no
key ignature,
nd
passages
n thenatural
ys-
temwill
e written ith
signature
f
B^.20
he
two-sharpignature
means
hat
any
tones
n
the
original assage
not
belonging
o the
two-sharpystem
re
chromatic lterations
nd have been
removed ither
n
stage
1
or
in
stage
2
ofthereduction.
y omparing
he corewith
he
tages
f
reduction,
eaders
can see which
ypes
f chromatic
lterations
ave been
removed;
hus,
n
the
first
measure
f
the
example,
he
soprano
Dtt
as
been removed
n
stage
2
of
the reduction
ince
t s a
type
A
alteration,
roviding
irected
motion
o the
followingonority.
On the tonal
ystem"
taff,
hanges
f
ystem
rought
bout
by
ndirect
chromaticismre
represented
ith otted arlines, ollowed ywhatevercci-
dentalhas
been
added,
or a natural
ign
n the
position
where
n accidental
has been removed.
Any
ccidentals
efore he
dottedbarline
re assumed
o
still e
in
effect fter
t.
n the
middle
of m.
28,
Cft
s introduced
ia
ndirect
chromaticism
the
eaps
from
G to
C in alto and
tenor
1).
The
musicthere-
fore
briefly
oves
nto
the
one-sharp
ystem.
t the end
of the
bar,
he
pas-
sage
returns o the
two-sharp
ystem,gain
via indirect
hromaticism.
Ctt
s
19 These
signatures
are not intended
to be
equivalent
to
modern
key signatures;
they represent
only
the
sharps
or
flats
used
in
the
tonal
system,
which
I
notate
in
the
tradi-
tionalpositionsfor larity.
20 I chose B^
mainly
ecause
of ts
position
n
the
middleof
the staff
nd because
of the
special
significance
f the
Bty
B'?
relationship
n
early
music.
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Kyle
Adams
~
A New
Theory
of Chromaticism
263
27
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Tonal
jHfl
ft
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tf
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ITO
ft
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tf
«J
Example
3. Diatonicreduction f
Gesualdo,
Ma
tu,
agion,
mm.27-34
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264
JOURNAL
of
MUSIC
THEORY
31
mor
-
te non
sen
-
to,
mor
-
te non sen
-
to
A
$
J- J JJ
1^
o^L,JitJ
Ji|J'UJ
J
mor
-
te
non sen
-
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™
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r
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i'
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r 1
11 i
"i
*
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i"
"
i
.
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-
te
non sen
-
to
™ ¿ rr fi 'fJ » J • *"r rJ ° mB
mor
-
te non
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-
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mor
-
te non sen
-
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Stage
I '
«jr^^
/2
J^J
-fat
'll
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=±rrTT-rrf
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■ ■■
Example
3
(continued)
Diatonic reduction of
Gesualdo,
Ma
tu,
cagion.
mm.
31-34
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Kyle
Adams
~
A New
Theory
of
Chromaticism 265
reintroduced
n
the
soprano
to form
perfect
ifth ith he
upcoming
bass
Ft.)
The
two-sharp
ystem
overns
he
passage through
he middle of m.
31,
withinwhich ne can see the removal f two ypeB alterationsCflndGitn
mm.
29-30)
in
stage
1,
nd two
ype
A
alterations
the
tenor
Dtt
n m. 30 and
the
bass
Gtt
n m.
31)
in
stage
2.
The
passage
returns o the
one-sharp ystem
n
the middle of
m.
31,
again
via indirect
hromaticism,
s indicated
by
the dottedbarline nd can-
cellation f
Ctt
y
Ö on the owest taff.
The
Fit
nd
Ctt
t the
beginning
f
the owest taff
n m. 31 are
courtesy
ccidentals nd do
not
represent
ny
change.)
Within his
ystem,
he
eading
tone
Gtt
n
tenor has been removed
in
stage
2
of the
reduction,
ince t s a
type
A
alteration. t the end of m.
32
is
a double
barline,
ollowed
y signature
f
three
harps.
his
signifiesux-
taposeddiatonicism, hich stheuxtaposition ftwo onal ystemsia direct
chromaticism.21
ere,
the music
bruptly
moves nto
the
three-sharp
ystem
via the ntroduction
f
Ctt
nd
Gtt
n thedownbeat
f
m. 33.
Typically,
s in this
example,
the two tonal
systems articipating
n
uxtaposed
diatonicismwill
differ
y
more than one accidental.The
only
hromatic
henomenon
from
Figure
1
not
occurring
n
this
assage
s
suspended
diatonicism,
hichwould
be indicated ia a double barline ollowed
y
no
signature.
Just
s in the
tonal
progressions iven
n
Example
1,
thismethod llows
for
the same
phenomenon
to be
analyzed
n
different
ays, epending
on
context r function.
hus,
n m.
32,
the
eading
tone
Gtt
n
tenor
2
has
been
removed ecause t s chromatic ithinhegoverning ne-sharp ystem. ow-
ever,
n
the final
measure,
he
alto
eading
tone
Gtt
emains n the reduction
because t s
diatonicwithin he
governing
hree-sharpystem.
There are
two
guidingprinciples
f
diatonic
reduction.The
principle
of referred
iatonicismtates
hat
he
governing
onal
system
f a
passage
will
always
e
the
one
in
which he
greatest ossible
number f onorities re dia-
tonic.
Preference illbe
given
o a tonal
ystem
n
which he first
onority
f
a
passage
s
diatonic;however,
s we shall
ee,
many assages
begin
with hro-
matic onorities. he
principlefgreater
implicity
tates hat he
stages
of
the
reductionmust
become
successively
ore diatonic.The reduction
may
not
create
chromaticismhatwas not
present
n
the
originalpassage.
illustrate
bothofthese
principles
nthe
examples
hat ollow.
Diatonic
reductions an be
used
in
conjunction
with he continuum f
Figure
1
to describe
he
types
f
chromaticismt
play
n
a
givenpassage. By
examining
he
single
taff t
the bottom f a
reduction,
reader can deter-
mine
whether
givenpassage
s
diatonic
r
uses
ndirect r
direct hromati-
cism.
f
a
givenpoint
on
the lowest
taff as no
barline
which
will be the
majority
f the
staff)
nd
is
preceded by
a
key ignature,
he
passage
above
21
This is an
important
istinction,
o which
return urther
below:
Juxtaposed
diatonicism
requires
the
placement
alongside
one
another of two
incompatible
onal
systems,
not usttwo incompatible onorities.
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266
JOURNAL
of
MUSIC
THEORY
it s diatonic
n
the tonal
ystem epresented y
the
signature,
nd
any
chro-
matic ones
ppearing
n
the score at that
point
re
nonessential
lterations.
Theywillhave been removed n either tage1 or stage2 of the reduction.
Rightward
motionson the continuum re
represented
y
barlines
n
the
reduction.Dotted barlines
ignal
the use
of
indirect
hromaticism,
ouble
barlines
ollowed
y
key ignature ignifyuxtaposed
diatonicism,
nd dou-
ble barlines
ollowed
y
no
key ignature ignifyuspended
diatonicism.
n all
cases,
the owest
ystem
f
music
n the diatonicreductionwill ontain
only
tones hat re diatonic
n
the tonal
ystem
hown n the bottom taff.
II.
Analyses
Essential
nd nonessential hromaticism
Nonessential hromaticism.
xample
4
presents
a diatonic reduction
of
mm.
23-29
from uzzasco
Luzzaschi's
madrigal ungi
da te.
All but
two
f the
semitones
n the
passage
re
type
nonessential
lterations,
ince
they
o not
serveto correct
ny potential
rrors
n
part
writing.
hese alterations
ave
therefore een removed o
create he
tage
1
reduction
n the econd
system.
Notice that wo
penultimate
it's
n the cantus
remain,
ince
they
re
type
A
alterations:
oth erve s
leading
tones o the
following
,
and the
A
between
them s
only
decoration.
he third
ystem
emoves hese
lterations
s well.
The
single
taff
nderneath he
example
has
only
B*1,
ndicating
hatthe
entire
assage
s n
the
natural
ystem.
One
could
argue
that he distinctionetween
ype
A and B alterations
is false.Almost
very
nonessential
lteration
nvolves
aising
pitch,
which
automatically
reatesdirected
motion to
the
following
onority,
r at
least
the
expectation
f it.
In
Example
4,
all
of the chromatic
lterations
n the
original
reate directed
motionto the
following
onority,
nd
it
may
eem
arbitrary
o
single
out the
final lteration s
more
significant.
owever,
ais-
ing
the
penultimate
one
t thefinal adence
s a
syntactical
equirement,
nd
Luzzaschi's
notation
f the alteration
as
more a reflection
f
contemporary
performance ractice
han n
expressive
hromatic
esture. y
contrast,
he
other
hromatic lterations
n
the
passage
can be removed
without
reating
anyviolationsfmusical yntax.heydo notbelongtothefundamentaloice
leading
because,
motivic
onsiderations
side,
the
istener
as no reason
to
expect
hem.
Rather,
hecontinual
aising
f
pitches
y
emitone
nd the
uc-
cessively igher
tatements
fthe
hromatic
etrachord
re
probably
ntended
to
portray
he
rising
f
the oul
to heaven
during
heblessed
death
described
in
the
text.
The diatonic
version
f a
tone does not
always
ave
to
appear
before
its
orresponding
hromatic
ersion;
requently,
nonessential
lteration
ill
appear
before
the tone
that
s altered.
Example
5
presents
reduction
f
mm.
25-30
from nother
f Luzzaschi's
madrigals,
e
parti
V
moro.
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Kyle
Adams
~
A
New
Theory
of Chromaticism
267
2j
e
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Tonal
h
ystems
lyCu
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-
Example 4. Diatonic reduction of Luzzaschi, Lungi da te (1595), mm. 23-27
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268
JOURNAL
of
MUSIC
THEORY
28
a
-
ta,)
e
mo
-
ri
-
ro
be
-
a
-
ta
i-r ft jl . »r [¿¡J' 'J'uim »
_
mo
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ri
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ta
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fe
r
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p
p
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(e
mo
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be
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a
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ta
ta)
1/
p
iiç
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i
»
a
ro
be
-
a
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ta)
(ir
rir
'r i**
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J'
k Iti
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r e
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-1
. . L I. I I II
U r r í r r ijiJi
.
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Tonal 9
L
Systems
KC')
1
Example
4
(continued)
Diatonic reduction of
Luzzaschi,
Lungida
te
(1595),
mm. 28-29
In a situation hat
s
almost
he exact
reverse f
Example
4,
we
find
seriesof
descending
tatements
f the chromatic
etrachord.22
s indicated
on the lowest
taff,
his
passage
is
governedby
the natural
ystem,
hich
means hat
n
each statement
fthe
hromatic
etrachord,
he hromatic
one
22
Since this
passage
is based on the chromatic
etrachord,
one
might argue
that the "chromatic"
tones are
in fact
equivalent
o diatonic
ones.
Vicentino,
or
xample,
viewed
the tones of
the chromatic etrachord s
substitutesfor he
tones of the diatonic
etrachord,
o
one
might
herefore
ay
that
hese
tones are "diatonic"
n
he
chromatic
enus.
This,
inturn,would
imply
hat the tones I have reduced out as
"chromatic"
were
not,
n
fact,
utside
of the
tonal
system,
since
those would be
the
only
tones
available
in
the
tonal
system.
There
may
be works
forwhich
his s
true,
but since
Se
parti
/'
moro
contains
passages
that re
clearly
iatonic,
it eems fair
o
say
that he
chromatic ones
in
this
passage
are
not conceived of
as
structurally
quivalent
to diatonic
tones.
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Kyle
Adams
~
A New
Theory
of Chromaticism
269
lL.J
J
J J.
-
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tJ
1
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v
h . hJ
"-"
fi)*'j w
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tJ v i
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it .
Quei
che
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r 0/
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JJ J J
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d d rJ» d li Ti I
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che
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per
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di
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sej'.
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per
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ul- J
h
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che
cor-giun
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che
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rJ
f
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Tonal
^
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Systems
| W)
1
-
Example
5.
Reduction of
Luzzaschi,
Se
partì
/'
moro
(1595),
mm.
25-27
precedes
the diatonic
one.
Stage
1 of the reduction hows hat
nearly
ll of
the chromatic lterations re
type
B;
only
the
Gtt
n m.
25,
which
provides
directedmotion o a
cadence,
and the
Picardy
hirds n mm.
26
and 30 are
type
A
alterations.
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270
JOURNAL
of
MUSIC
THEORY
28
per
-
che di
-
vi
-
di?
^S^
ft 1
rJ
j,
ZI
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di,
per
-
che
di
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di
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Score
fe
It
II
-
rJ rJ.
J
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O
=
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vi
-
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per
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che
di
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tage
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2
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ystems
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H
Example
5
(continued)
Reduction of
Luzzaschi,
Se
parti
i'
moro
(1595),
mm. 28-30
Essentialhromaticism.
xample
6
presents
reduction
f hefirstixmea-
sures f Lasso's
madrigal
Anna,
mihi ilecta.25his
excerpt
ontains
xamples
of essential hromaticism.
he
El?'s
n
thebass and
tenor f m. 3 are
essential
23 Note Lasso's use of the chromatic tetrachord n the
soprano part
of mm. 3-4.
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Kyle
Adams
~
A
New
Theory
of Chromaticism
271
ÈIA"
o^"*Vg go
i
Jl
io
_^-k l___/'r^f._ II
%):==E^ »"^J,^ tf^OD" 'p p 100^
g,
b8^J^8 -o^-o- Uw"
(An
-
na)
(eta)
An
-
na,
mi
-
hi
di
-
le
-
eta,
ve
-
ni,
me
-
. i .
'J:l£
o I?
p 'pì>rj
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i I "II
[>bg.
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If
[
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k'V^J,"
"II
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J n |o
^
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K ^1
Stage
1
i I
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^=Ha
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Tonal
XV
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Systems
K(')
"
;
;
[/
Example
6.
Reduction
of
Lasso, Anna,
mihi
dilecta
(1579),
mm. 1-6
chromatic itches, ecessaryo avoid a diminished ifthgainst hesoprano
Bk
In m.
5,
the
Al?
n
the bass
is
also
an essential hromatic
itch,
ince it
avoids melodicdiminished
ifth rom he
previous
ass Ek
The first
tage
of the reduction
hows hat he
Fit
n
m.
1
and the B4
n
mm.3 and
4
are the
only
nonessential hromatic
itches.
t
may
eem coun-
terintuitiveo call the
Fit
f the
opening onority
hromatic,
ut the
principle
of
preferred
iatonicism
uggests
his
reading.
After
he
opening sonority,
subsequent
ventsmake
t
clear that he
Fit
was chromatic.
More of the tones
in thefirst ourmeasures
elong
to theone-flat
ystem
han o
any ystem
hat
wouldcontain he
D-major
onority;
lso,
this s a case
in
whichwe can claim
withnearcertaintyo knowwhatLasso intended, ince he wrote he one-flat
signature.
ad
he
conceived he
opening onority
s
diatonic,
he could have
notated he
piece
a whole
step
owerwithno
signature,making
he
opening
chord "diatonic"
-major onority,
nd the
following
ne an
Al?-major
onor-
ity,
hichwould
certainlyppear
chromatic.
Unlike
Examples
2
and
3, however,
he
passage
fromAnna cannot be
explained
n
terms f a
singlegoverning
onal
system,
ince the
Ab
n m. 5
is
incompatible
with he A^ of the
opening sonority.
his
passage
therefore
contains ndirect hromaticism:
ince the
Ab-major
onority
nd the
opening
D-major
onority
annot
belong
to the same
tonal
system,
heremustbe
a
change
omewhere.
utone cannot
point
o a
single
moment s
signaling
he
change,because
any
wo
djacent
onoritiesn
stage
1are diatonic elative o
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272
JOURNAL
of
MUSIC
THEORY
one
another.One
can
only ay
that he
passage
begins
n the one-flat
ystem
and ends n thethree-flat
ystem.
he lowest
taff
n
thereduction racks hese
changes ntonal ystem ith otted arlines ollowed y henewflats. he dot-
tedbarlines ndicate hat heessential
hromatic ones
n
stage
1 of
the
reduc-
tion
bring
bout
changes
f tonal
ystem
ithout
ny
direct
hromaticism.
Most
xamples
f ssential hromaticismre created
y
descending-fifth
motion n
the
bass,
as in m. 5 of the
previous xample.
Although
t s much
less
common,
ssential hromatic ones an
also be created
by scending-fifth
motion.Vicentino sed this
echnique
n several f his works.
n
the
excerpt
fromAnimamea
resented
s
Example
7,
he uses the
technique uite
beauti-
fully
o balance a
previous
escent
by
fifth.
As the reduction
hows,
he
passagebegins
n theone-flat
ystem,
hich
changes o the three-flatystem hrough series fdescending-fifthotions,
only
to cancel the
newly
dded
accidentals n the
subsequent
measures.
Although
he chord
progression
n mm.97-98 mirrors he
progression
rom
mm.
94-95,
the
systems
o not
change accordingly
ecause the sonorities
n
mm.
97-98
still
elong
to thethree-flat
ystem,
hichhas
not
yet
een contra-
dicted.
Only
with
he
reappearance
fPÁdo thetonal
ystemsegin
o
change
again.
Also,
because the
passage
contains
nly
ssential hromatic
lterations,
both
tages
and
2
ofthereduction ave
been
omitted,
eaving nly
he
ingle
staff o track he
changes
of tonal
ystem.
Chromatic
onesn the
pening
onority.
n
Example
6,
the
opening
onority
ofa piececontained chromatic one.There
are
many
uch
cases, ncluding
ones where
t s
quite
difficulto
distinguish
hromatic
rom iatonic ones.
Example
is a
reduction fthefirst ourmeasures
f
Pomponio
Nenna's
motet
cco, dolce,
gradita.
venwithout
he
Bb
ignature,
he
Y&
f the
open-
ing onority
ould
oon be revealed s a
chromatic onerather
han diatonic
tone.
The
soprano eap
in m.
2
ensures or he
istener hat
Bb
s at
leastan
essential
hromatic
one,24
f
not a diatonic
one,
and
the
persistence
f
Bl?
throughout
he measuredefines
he B^ at
the end of the
bar as a chromatic
alteration.
espite
the
one-flat
ignature
n
the
music,
consider
mm. 1-3 to
be
in the
wo-flat
ystem,
ince heEl?
n thebass nd alto
arise s essential
hro-
matic
ones,
gainst
he
background
fwhich he lto
E^
n m.
3
becomes
type
A alteration.The one-flatystemhatgovernsmost f thepiece isnotfirmly
established
ntil he adence
at the
nd ofm.
4.)
Analyzed
his
way,
he
triking
Eb
sonority
nder
"dolce" becomes
a
sweetly
elaxing
move nto the
govern-
ing
tonal
ystem,
ather han
striking
hromatic
vent
gainst
he
opening
G-major onority,
reading
hat
findmore
consistent ith
hetext.25
24 At this
point
n music
history,
with the innovations
f
the
secunda
prattica,
he distinction
etween essential
and
nonessential
pitches
starts
to blur.Nenna does
use a verti-
cal diminished
ifth etween the
soprano
and alto
in
m. 4.
However,
his
diminished ifths
between two
upper
voices,
bothof which re consonant
with he
bass,
and is not
nearly
as harsh
as a
leap
of a diminished ifthn the
soprano
of
m.
2 would be.
25 It s true
that "dolce" was
oftenused
ironically y
com-
posers
of this
period
and
therefore
was often set
using
harsh-sounding
onorities.
However,
I
do not
believe
that
Nenna
intended uch
a
setting
here.
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Kyle
Adams
~
A
New
Theory
of Chromaticism 273
92
A
-
ni
-
ma me
-
a tur
-
ba
-
ta est tur
-
ba
-
ta
JL h J
J
J J lJ(l»)Jl»)JJ ^.J .i/JuJ.
P^i
h
' JiJ-Jip ^ i^)r ^ ff
.i/JuJ.
(h)r
score
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r
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i
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^£
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97
est val
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sed tu do
-
mi
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ne
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;: r "t ,ir r ■ r .r ■ ,M
1^^
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^n,
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H
1
Example
7.
Reduction of
Vicentino,
Anima mea
(1572),
mm.
92-101
Nonessential hromatic oneswith characteristics
f
essential hromatic ones.
Occasionally,
chromatic one that s nonessential
n
originmay
lso serve o
correct n unallowabledissonance.
Example
9
presents
reduction f mm.
44-47
fromHeinrich cheidemanns Praembulumrom he Anders onDüben
Tablature.
The Praembulum
llustrates
he
frequent
mbiguity
etween he natural
and one-flat
ystems
n
pieces
with D final:
Bl? nd B^ will ach be diatonic
at various
imes,
epending
on whether
particular
oice
moves
upward
r
downward,
nd most uch
pieces
will hift
requently
etween he two
ystems.
Thispiece s n thenaturalystem ith final nD, and B^ s theprimaryorm
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274
JOURNAL
of
MUSIC
THEORY
Ec
-
co
O dol
-
ce^o
_
gra
-
Score
y
t
o* J
*
J
.o |J
^
c
-
co O dol
-
ce,
Ina
•••
r i
r
r
f
'It. }(BB. °
(B|.
life J.
**'
a: ¿ ¿
i~
¿
,
'm
"•
ir li
r
r
r
,
*
(^
■
i
Stage
2 <
(■^« ■ I
Tonal
^
ystems
|TO
Example
8.
Reduction
of
Nenna, Ecco,
ò
dolce,
ò
gradita
(1607),
mm. 1-2
ofB
throughout
he
iece.
The measures
n
question
ontain
chromaticized
variantf n
ascending
-6
sequence,
ne that reates ome
ignificant
na-
lyticalroblems.
Consider he
Ft
n the eft
and f
m. 44. s this
one ssential
r
non-
essential? iven
he
ontext,
t s
clearly
n alteration
f
diatonic
and
s
perceived
s such
fone follows
nly
hevoice
eading
f the
various
arts.
However,
t s a nonessential
lteration
hat asthe dded
ffect
f
orrecting
what
ould therwise
ave
een diminished
riad,
sonority
hat
omposers
still id not
generally
se
n
root
osition
nd that
ertainly
ould
othave
had
place
n
this
equence.
fweread
he
t
s an essential
hromatic
one,
it hould
ignal
t east
temporary
hange
f
onal
ystem,
ccording
o
the
principlesfdiatoniceductionutlinedbove.But feel tmost ccurately
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Kyle
Adams
~
A
New
Theory
of Chromaticism 275
kv ■.» à ' J"-/3J J .1 ...i^ -frr f Pri-Tf - ff ]tr^
i
-
ta Vi ta del
-
a mia
vi
-
ta
o
gra
-
di
-
ta Vi
-
ta del
-
a mia
vi
-
ta
(^^Y
r
i
rlrr"
r
r
r^
'g rrr r r-^uf - rr f
a
mt
fi flrrr
~
r
r^^
Tonai
V^^
ji[
=
Systems
'CV)
;
Example
8
(continued)
Reduction of
Nenna, Ecco,
ò
dolce,
ò
gradita
(1607),
mm.
3-4
represents
he istener's
erception
f hemusic o
ay
hat,
hile he
Fit
s
an
essentialhromatic
itch,
t s a rare ssentialhromatic
itch
hat
oes not
signal change
f
tonal
ystem.
he
nonessentialature fthe
Ftt
s
clearly
defined
y
hemotion
-Ftt-G
n the enor oice
nd
the
equential
ature f
the
passage.
n
this
equence,
he hords n the econd nd fourtheats re
clearly
ubordinateo those n the irstnd third
eats,
ince he ormerre
what ewould all
pplied
ominants.
ne
might
herefore
ay
hat hile he
Ff
s
"essential"
n
order o reate
perfect
ifth ith he
ass,
t s
nonessential
in
the
arger
enseof
beingpart
f
a
nonessential
onority.
herefore,
he
reductionhows he irst easure eing overnedy henaturalystem.
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276
JOURNAL
of
MUSIC THEORY
44
gWü' IT i i i I
l^^É
i'
I
1/
V
V
I
Tonal
^£b |,
=
Systems
K(V)
1
j
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Example
9.
Reduction of
Scheidemann,
Praembulum
(early
seventeenth
century),
mm.
44-45
As
I
have shown n
the
reduction,
owever,
he music
does
change
to
the one-flat
ystem
eginning
with he
G-minor
onority
n
m. 45.
This sonor-
ity
erves s the
goal
of
directedmotionrather
han a
sonority
hat
provides
such
motion.An
analysis
onsistent ith
whathas come
beforewould read
the tones ofthis onoritys diatonic.Just s in theprevious enorprogres-
sion
F-Ftt-G,
he
Fit
was a
chromatic
lteration, o,
in
this enor
progression
Bt-B^-C,
heB^ s read as a
chromatic
lteration,
lbeit nother
ssential hro-
matic lteration hat
does not
signal change
of
system.
he
corresponding
change
to the
one-flat
ystem
lso
accountsforthe
Bl?-majoronority
n
the
following
ar.The final
hromatic one
n
the
passage,
Ctt,
emains n
stage
1
of
the reduction
ecause t s
syntacticallyequired
t the
cadence.
Juxtaposed
iatonicism
Juxtaposed
iatonicisms
perhaps
he
most
difficult
ype
f
chromaticismo
identify,ince tsuse is often ndependent f thechromaticemitone, nd
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Kyle
Adams
~
A New
Theory
of Chromaticism
277
""
t | f | f i 1* |
Tonal
V
I
Systems
yfy)
Example
9
(continued)
Reduction of
Scheidemann,
Praembulum
(early
seventeenth
century),
mm.
46-47
since
ts
dentificationften elies n
subjective
udgment.
Unlike
xamples
f
essential
nd nonessential
hromaticism,
t has little r no
basis
n
sixteenth-
or
seventeenth-century
usic
heory.
Example
10
presents
diatonicreduction f the
first ine bars of the
celebrated rologuetoLasso'sProphetiaeibyllarum.26he piece begins n the
natural
ystem,
hich
Lasso
uxtaposes gainst
he
four-sharpystem
n m.
3.
This
system
emains
n
effect ntil he
econd chordof m.
6,
whoseD^
signals
a
change
to
the
three-sharpystem.
he
following
eries fbass motions own
by
fifth
arries
change
of
system
ith ach chord
change
until
he arrival f
the one-flat
ystem,
hich s
uxtaposed against
he
one-sharp
ystem
n
the
downbeat f m. 8.
Stage
2
has been
omitted rom he
reduction
ecause the
passage
contains
no
type
A
alterations o
remove. ven
though
he two
final
26 As
I
noted
above,
the
presentist/historicist
ebate
regarding arly
hromaticism
as
played
out
almost
entirely
inreference o this piece; see Mitchell1970, Berger1976,
Lake
1991,
and Bent
2002.
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278
JOURNAL
of
MUSIC
THEORY
(fr'- * I fU I IW u£V |'° £ i
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II
Example
10.
Reduction of
Lasso,
Prologue
from
Prophetiae Sibyllarum
(1560),
mm.
1-9
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Kyle
Adams
~
A New
Theory
of
Chromaticism
279
Fit's
n
the can us erve o createdirectedmotion o the
following
,
they
re
diatonic ones rather han chromatic
lterations,
ince the
one-sharp ystem
governshis rogression.nfact, heonlynonessential lterationn theentire
passage
s the
type
alteration f E1 o
El?
n thebass of m. 8.
Example
10 also demonstrateshe
application
f the
principles
f
pre-
ferred iatonicism nd
greater implicity.
he
B-major
onority
n m.
3
ush-
ers
n a
new,
four-sharpystem ccording
o the
principle
f
preferred
ia-
tonicism.Without his
rinciple,
ne
is
forced o somehow
ntegrate
he
next
four onoritiesnto the
natural
ystem
s chromatic
lterations
f
underlying
diatonic onorities.
owever,
hileLasso's triads n
B, Ctt, ,
and
Fit
re chro-
matic
n
relation o the G
harmony
hat ame
immediately
efore,
hey
re
certainly
otchromatic
n
relation o one another.
n
fact,
f he
ntire
assage
were ransposeds inExample11,theopeningwould ppearchromatic hile
mm.3-5 would
ppear
diatonic.
'JLt
■
, i
=
t^imi.
i
iJ
lu
H °;
'' w
8
=
Example
11.
Transposition
of the
first
five bars of the
Prologue
This
suggests
hatLasso's chromaticismoes not have
a
single
diatonic
foundation,
ut
rather tems rom he
side-by-side
lacement
f two ncom-
patible
iatonic
assages.
The
advantage
f
readinguxtaposed
diatonicism
n
this nd other uch
examples
s that t
highlights
he
fact hat
many
onorities
belong
to the
ame diatonic
ystem,
ithout
ttempting
o create
functional
hierarchy
etween he sonorities r the
systems.
One
might rgue
that
he
B-major
onority
n
m. 3 is
an alteration
f
an
underlying-minor riad, nd thattheDf serves o createdirectedmotion
to the
next
onority
n
the manner f an
evaded cadence. This
would ead to
the diatonicreduction
resented
n
Example
12.
(I
present nly
he first
ix
measures,
ince the remainder
f the reduction
wouldbe the
same.)
Here,
the
relevant
uxtaposition
would occur in m. 3
between the
one-sharp
nd
three-sharp
ystems.
ut this
eading gnores
he
very
moment
that
ives
he
passage
ts hromatic
ound,
namely,
he
hange
rom he
G-major
to the
B-major
armony.
Recall
that he"
rinciple
f
preferred
iatonicism
gives reference
o a
tonal
ystem
n
which hefirst
onority
f a
group
s dia-
tonic.)
Example
10 is
therefore much
simpler
nterpretation,
nd one
that
corresponds
more
closely
o the
istener's
xperience
f the music.
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280
JOURNAL
of
MUSIC THEORY
l^- * i fUi ih bsVfv f"fM"|
core
(Car
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Example
12.
Alternate
reduction,
first ix bars of the
Prologue
One final oint boutExample 0: The presence fonly our itch-
classes
n
mm.
-2
means hat hosemeasuresouldbe
interpreted
n either
thenatural r the
one-sharpystem.
have
nterpreted
hem
n
thenatural
system
n
accordance ith
he
bsence
f
Fit
n the
amut.
While his ituation
doesnot rise ften
nough
owarrantts
nclusions a
principle,
he educ-
tions ill how
preference
or
nterpreting
ones
elonging
o the
gamut
f
musicaectas diatonic.
Distinguishinguxtaposed
diatonicism
rom
nonessential
hromaticism.
ne
defining
haracteristic
f
uxtaposed
iatonicism
s the
placement
f two
incompatible
onal
ystems
longside
ne
another,
ot
ust
two
ncompatible
sonorities.fLasso'sPrologueontinueds inExample 3,the oprano tt
would
imply
e a
type
nonessential
lterationnd
couldbe removed
o
reveal n
underlyingne-sharp
ystem.
Instead,
uxtaposed
iatonicism
s
created
y
he ontinuation
f
sys-
tem
n
which
he
Dt
and ts
orresponding
-major
riad ecome
diatonic.
The
reading iven
n
Example
0
recognizes
hat,
while heharmonies
n
mm.
-6
may
e chromatic
n
relation
othe
harmonies
n mm.
-2,
hey
re
diatonic
n relationo each
other;
t
s the
ystem
o
which
hey elong
hat
is
chromatic.
Notice hat
mm. -7
of
he
Prologue
ontain
chromatic
ircle-of-fifths
progression,
ne
of hemost ommon
ays
hat
omposers
especially
asso
introducedhromaticismn this eriod. he differentaysf nalyzinguch
progressions
ear
heavily
n the
oncept
f
uxtaposed
iatonicism
ecause
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Kyle
Adams
~
A New
Theory
of Chromaticism
281
I
flpfr Q. , j ..
Ih.
,j gi^JjjjJ
M
1
>j:t"~
-
rj
"
_ _ »a r <>
"
Example
13.
Prologue
with lternate ontinuation
most
examples
of it are
either
preceded
or followed
y
such
progressions.
Often,
uxtaposition
s
followed
y descending
ircle-of-fifths
rogression
that eturns
o the
original ystem.
laus
Hübler
1976),
in his
analysis
f the
Prophetiaeibyllarum,xplained
Lasso's chromaticismn
ust
this
way,
s con-
sisting
f a
Sprung,
r
leap
to a distant
armony,
ollowed
y
motion round
the circle f fifths.
lternatively,
descending
ircle-of-fifths
rogression
hat
has
"gone
too far"
nd left he
original
ystem
s
followed
y
a
uxtaposition
to
bring
he
original ystem
ack. The
following
llustrates
ow this
theory
accounts
or
uch
progressions.
Consider
mm.
113-28
fromClaudio Monteverdi'swell-knownanzo-
netta
Zéfiro,
orna,
resented
s
Example
14. This
passage
could be read as a
series
of
nonessential
hromatic lterationswithin he
one-sharp ystem.
n
such a
reading,
he
chromatically
lteredtones
n
mm. 114-16 and
parallel
passages ould be seen as typeB alterationsreating irectedmotion o the
following
onorities.
Nevertheless,
he reduction howsthis uccession s
a
true nstance
f
uxtaposed
diatonicism. he differenceies
n
context. he
fourthmeasure of the
excerpt
does indeed return o a
sonority
elonging
to
the
one-sharp ystem
hathas
governed
he
piece
so
far, ut,
fter
m.
113,
there s never
sonority
hat
belongs exclusively
o the
one-sharp
ystem.
f
the
passage proceeded
as
in
Example
15,
the
E-major
nd
A-major
onorities
wouldbe
perceived
n
retrospect
s chromatic lterations.
Not
only
does
Monteverdi ot return o the
one-sharp
ystem,
ut he
introduces second
uxtaposition
o the
four-sharpystem.
his
time,
he
succeedingcircle-of-fifthsrogression eturns o the one-sharp ystem,ut
Monteverdi
pends nough
time n the
new
ystem
hatm. 117 s
perceived
n
retrospect
s motion o a
newtonal
ystem
ather
han
s
a series fchromatic
alterations.27
This
theory
must llowfor
certain mount f
subjectivity
n determin-
ing
whether
hromatic
uxtapositions
willbe
perceived
s
nonessential hro-
maticism r a
move o an
entirely
ew
ystem.
actors ther han
harmony
an
27
Example
14
would seem an ¡deal
place
to
apply
Hübler's
concept
of
Sprung
o a distant
harmony
ollowed
by
motion
around the circle of
fifths;
ne
might
wonder whether t s
appropriate
o
describeMonteverdi's hromaticismnterms
of
Sprünge.
While the idea
of a
Sprung
would
accurately
describe the
juxtapositions
in
mm.
113-14, 116-17,
and
122-23 of this
example,
Hübler's
concept
does not
provide
a
complete
picture
of a
passage
such as this one.
In
par-
ticular,
t does
not address the
issue of the
relationship
f
the Sprüngeto the underlyingonalsystems. Sprünge, ike
single
chromatic
ones,
do not
always
exist for
the same
reason or serve the
same
purpose.
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282
JOURNAL
of
MUSIC
THEORY
113
Tenorl
[ TO?
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TO
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11*'
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to.
Sol
i
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-
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te
so -le l'ar-
csr.,
v:?M.
i»
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if
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tf
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Tona,
fit
II
Ü
Tl
|^
"-Systems K(V) || Tl II -"- -
117
i
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sel
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vejib-ban-do-na
te so
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di due
be
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T2
[
<fa
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«P
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l
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dor di duebe -glioc - chiel mio tor men to
¿y II il |
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bc
V>'
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II
IJ
J
l
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tt
Tonal y
ffi*tf||
fí
Systems
|((')
fí
«T
Example
14. Reduction
of
Monteverdi,
Zeftro,
orna
(1632),
mm. 113-20
influencene's
hearing
f
passage;
n
Example
4,
he
hange
fmeter
nd
the
hange
rom dancelike
haracter
o a
recitative
einforce
he
ense
f
juxtaposed
iatonicism.28
evertheless,
rom he
preceding
xamples
e
can
induce
ome riteria
hat erve
o
separate
xamples
f
uxtaposed
iaton-
icism
rom ther
ypes
fchromaticism.
irst,
he istener
s much
ess
ikely
28 Gioseffo
Zarlino
himself
mphasized
that chromaticism
was
as much
a
stylistic
henomenon
as a
structural
ne:
"There
cannot be
a difference
n
genus
between
compo-
sitions that
do not
sound different
n melodic idiom.
. .
Conversely,
difference
f
genus
may
be
assumed
when
a notable
divergence
nmelodicstyle s heard,withrhythm
and
words
suitably
ccommodated
to it"
[1558] 1968,
277).
Dahlhaus
(1967)
makes a similar
point,
noting
that
chro-
maticism
rises
not
only
rom
he
uxtaposition
f unrelated
harmonies,
but also
from
he
rhythmic
solation,
metrical
relationship,
nd
position
i.e.,
inversion)
f
those
harmo-
nies (78-79).
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Kyle
Adams
~
A
New
Theory
of Chromaticism
283
121
T1ifeïr g f Í
--
r f í J 1 flJ t Jk^_J]l]ê
^-
i r -- i i
glioc
chiel
mio tor
-
men to
sol
i
-
o
per
sel
-
veab-ban-do
"
U
i"
'
r r r r r PCpM
sol
i
-
o
per
sel
-
ve_ab-ban-do
B.C.
'*f[
tf
|
"
|
"
|
"
^
tt
Ton, I ¡|| jl ||tt|[tt
l
systems
Ken
j
;
II
jl =
tJ
725
°
na
-
te so
-
le
l'ar
-
dor
de
due
be-gl'oc
chiel mio
tor-men to
na - te sol - le la'r - dor de due be-gl'oc chiel mio tor-mento
™
¿¥
^
ni
Systems
K(')
^
n
Example
14
continued)
Reduction
f
Monteverdi, éfiro,
oma
1632),
mm.121-28
to
perceive
change
n
ystem
f,
ollowingpotential
uxtaposition,
he om-
poser
ntroduces
sonority
hatwasdiatonic
n the
riginal
ystem
utwould
notbe
in
the
new ne. Such
sonority
ill
robably
ot ound hromatic
n
a new
ystem
utwill
erve s a reminder
f he
riginal
onal
ystem,gainst
which
revious
hromatic
vents ill tand
ut as nonessentiallterations.
Second,
he ikelihoodhat he
istener ill
erceive
change
o a different
tonal
ystem
ncreases ith he
numbernddurationf onoritieshat
elong
to that
ystem
nd not he
previous
ne.
Juxtaposed
iatonicism
rising
rom
onessentialhromaticism.
xample
16,
mm. 0-26from enryurcell's loriaatri,llustratesow chromaticone
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284
JOURNAL
of
MUSIC THEORY
Tenorl
O?
hh I
"
1"
=^j
* Sol
Tenor2
i
TO?
"
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hfyJ
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1jtJ_Jlil
ljl^-
JllftJ
^
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°
to
Sol
i
-
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per
sel
-
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ab-ban-do-na te so
-
le l'ar-
(Basso
lj/
;:y
ï
'fa
I"'
II
I
fj
ttrJ
j
I
Q-
'-'
Iontinuo)
j/ ï
|q|.
I"' I
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fj
ttrJ I
Q-
I
f
5
ti
[$
^ * r [r~FFft'f " [r "^
i
-
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per
sel
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te
so
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le
T2
I
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K
^rx
^ ^
'^
*
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tr
'*
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~=H
dor
di due be
-
glioc
-
chiel mio tor
-
men
-
to
b.c.
j:^v
^
h°^
r°
m
"ii
Example
15.
Alternate version of
Zéfiro,
torna
that
was
originally
onessential an introduce
uxtaposition
o a
new
tonal
system.
he
passage begins
n the three-flat
ystem
hat
governs
most
of
the
piece,
as indicated
by
Purcell's
ignature.
Within his
ystem,
he
soprano
B^
in m.
22
is a
type
A
alteration
hat,
long
with
he alto
F,
creates
expecta-
tion of directedmotionto a C-minor
onority.
It
is a
type
A rather han a
type
B
alteration ince
coming
o rest n a minor eventh hordwould have
been
syntactically
ncorrect
n this
repertoire.)
Nothing
rom
m.
22
resolves
as expected:The F,a chordal eventh,eaps to D and then G beforeresolv-
ing,
and when t does
resolve,
t moves
to
E^
insteadof Ek29
Moreover,
he
B^ remains
n the chord nsteadof
resolving
o C.30 he harmonies hat
fol-
low are diatonic
n
relation
o the E-minor
onority,reating
he
uxtaposi-
tionof the three-flatnd
natural
ystems
hown
n the reduction. he B4
has
therefore
hanged
from nonessential
hromatic
itch
nto diatonic
pitch.
29
I
consider the motion o
E in m. 23 a
resolution
f the
F
from
m.
22,
albeit
highly
ecorated one.
30 None
of the voice
parts
in m.
23 contains
a literal ar-
ryover
f
B*lfrom one
sonority
o the
next.
However,
I
have included the editorialrealization f the figuredbass
by
Anthony
ewis
and
Nigel
Fortune,
which shows thatthe
retention f
B^ is
part
of the
underlying
oice
leading.
The
claim that B^ "remains"
in
the chord
s not invalidated
y
the fact that this voice
leading
s not
literally
xpressed by
any
one
part.
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Kyle
Adams
~
A New
Theory
of Chromaticism
285
Si
-
cut
e
-
rat
in
prin
-
ci
-
pi
-
o
et
nunc,
¿
f
I
r
¿
f
~
f
F
(Continuo)
'I
Stage
2 <
Tonal
0
X
-
Systems
ITO
"
[/
Example
16. Reduction
of
Purcell,
Gloria
Patri
late
seventeenth
century),
mm.
20-21
The reduction
ppears
oviolate
he
principle
f
greater implicity
y
ntroduc-
ing
cross-relationb
o E^ in m.
23
thatwas
not
present
efore,
utthe
reduc-
tion s ntended
o track he istener's
xpectations
nd
perceptions,
ccording
to which l?would
till e the
xpected
diatonic one
n thethree-flat
ystem
f
m.
22
and would
only
be
supplanted y
B^ with he
E-minor
onority
n m.
23.
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286
JOURNAL
of
MUSIC THEORY
et nunc et sem
per
si
-
cut e
-
rat
in
prin
ci
-
pi
-
0 ,
L
^J ^^ ,
L-
._|
J J
^F.i j Ir y V_j«
'>a
j
r
t
r-H' i' i1 '
y
i^^
?A
ig
;
^
j^j1
*r
iJ"ii J'J'J' .
>
. J-
;.
i
ig
;
r- f
*r
r^^ ^ ¿
.
y
>
T
^
Tonal
| fo
?^|
F
'^
MU
||H
=
Systems
fo
F
'^
||H
=
Example
16
(continued)
Reduction of
Purcell,
Gloria
Patri
late
seventeenth
century),
mm. 22-24
Suspended
diatonicism
Pretonal usic
lways
ontains iatonic
eatures,
lthough
n some nstances
one sunable o rrivet
definite
overning
onal
ystem
or
passage.
itu-
ations hat
pproach
uspended
iatonicism
re
rare;
his
ection xamines
few
ypes
nd the riteria
y
which ne can
dentify
hem.
Suspended
iatonicism
rising
rom
imultaneoushromatic
ones.
uspended
diatonicisman be created ytheuse of severalones imultaneouslyhat
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Kyle
Adams
~
A
New
Theory
of
Chromaticism
287
25
o
et
nunc,
et nunc et sem
-
per
i.
Oik
i
,
ki
'
i
?
li^
J),
K
hi hi. I 1
¿ r * 7 ^ F
^
qP ? r r »r
lSf r I'r p r li,.,
Stage
1
r
i
k
L
Stage
2
r l
k L
Tonal
£b
ystems
|W)
1
-
Example
16
(continued)
Reduction of
Purcell,
Gloria Patri
late
seventeenth
century),
mm.
25-26
cannot
elong
othe ame
ystem.xample
7
presents
m.
9-53
from er-
nardo
Storaces
Passagagli
sic].
This s a
very
riefmoment f
suspended
iatonicism
n
an other-
wise lear
passage.
he natural
ystem
as
governed
he
piece
thus ar nd
is
strengthened
ith
ach
repetition
f the
ground
ass
pattern
-G-F-E.
Withinhis
ystem,
he
onority
n
the econd eat fm.
50 s
seeminglyasy
to
explain:
he Bl? nd the
Gtt
reboth
ype
alterations.
ut he
triking
is-
sonance f he hord it ontains diminishedhird,diminishedifth,nd
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288
JOURNAL
of
MUSIC
THEORY
49 i
Hhr-
J ilJ-JiiJ
.j/J
^
i
J À
„J
i... =fl
Score
;ü-
i.
r-ií
r
r
i
:<>
'■- "
>«
■
|
■
|J,'I
J
I -I I,J I
■
||
Stage
1
■"i
■
I
•
Ir r1 ' I
•
I
h
*)
-
i
■
i
-
i
u
I
¿ i^^i
)
I
Stage
2
3q^
-
I
-
I
-
I
"•
1
■
I
Tonal/£ b II lib
Systems
KCV)
1
H
111
Example
17. Reduction
of
Storace,
Passagagli
(1664),
mm. 49-53
an
augmented
ctave,
s well s
a
leap
of n
augmented
econd
o the
next
chord
makes
t
extremely
ifficult
or
he istener
o
distinguish
hromatic
tones
rom iatonic
ones
n real
time nd
therefore
reates
situation
n
which he
music ould
continue
n one
of everal
ifferent
onal
ystems.31
For
xample,
he
passage
ould
proceed
s
in
Example
8,
with
change
o
the hree-sharpystem.
In
this
ase,
here
ould
e
no
single
moment
f
uxtaposition
etween
systems,
nly passage
n the
natural
ystem,
ollowed
y
an
ambiguous
sonority
the
moment
f
uspended
iatonicism
and a
continuation
n the
three-sharp
ystem.
he
passage's
ontinuation
n the ame
ystem
nwhich
t
began
oes
not
hange
hemoment
f
uspended
iatonicism.
31 This
sonority
s
analogous
to
the
sonority
hat
François-
Joseph
Fétis
(1879)
used
to
illustrate
he omnitonic
rder,
a
sonority
hat
did
not
belong
clearly
o
any
one
key
and
therefore ould resolveto virtuallyny key.
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Kyle
Adams
~
A
New
Theory
of
Chromaticism 289
^^g^-
-
f
-
i
r
'^
-e-
IJ "
Example
18. Alternate version of
Passagagli
Suspended
iatonicism
rising rom
onsecutiveemitones. he most
frequent
case of
suspended
diatonicism ccurswhen there s a
buildup
of
consecutive
semitones
n
more than one
voice,
which
can blur
the distinction etween
diatonic and chromatic emitones nd make the identificationf a single
tonal
systemmpossible.
As
with
uxtaposed
diatonicism,
he
perception
f
suspended
diatonicism
epends argely
n
context.
xample
19,
fromCuore
che
reprime
lle
lingua
di
manifestare
l nomedella sua cara
by
Barbara
Strozzi,
is
not an
example
of
suspended
diatonicism,
lthough
t contains
onsecutive
semitones
n
bothvoices.
The bass
progression
n mm.
175-77,
which
hromatically
ills
n
a
per-
fect
fifth,
as an
audible distinction etween
diatonic nd chromatic ones
because the
precedingpassages
have been
governed
xclusively y
the natu-
ral
system.
he
Dt,
Cf
and Bl? re therefore
ype
B
alterations,nd,
having
beenperceived s type alterationsnthebass, heywill lso be perceived s
such
n
the
soprano
n
m. 176ff. he
cadence
on A in
the natural
ystem
n
mm.
178-79 contextualizes
he chromatic ones n
the bass of the
following
bars as
type
B
alterations,nd,
having
been
chromatic
n
the
bass,
they
re
chromaticn the
soprano.
In
Example
20,
on
the other
hand,
suspended
diatonicism oes occur
because there
havenotbeen
enough
tones
ounding
o
establish
single
onal
system.
he
example
gives
reduction
f
thefirst
en measures f
theFantasie
ex
D
by
Claudio de
Monteforte.
Stages
1
and
2
of
the reduction
have been
omitted or
the first our
measures. his sbecause the nature fsuspendeddiatonicisms a lack of an
audible distinction
etween
iatonic nd
chromatic
ones;
t
s
impossible
n
such
circumstanceso
distinguish
mong
different
ypes
f
chromatic ones.
Instead,
he
single
taff
elow the score
carriesno
signature
t all untilm.
5,
whenthe
analysis
roceeds
s usual.
In
the
first our
bars,
only
the
tones D
and A
can be
perceived
s
dia-
tonic,
nd
this s
only
because
they
ach
have
twice he
value of the
other
tones.D
begins
he
piece,
nd A is
thefirst
mportant
metrical
oint
f
rrival.
It s safeto
assume, herefore,
hat he
istener
would
perceive
hesetones s
diatonic,
r at
east
more table
han he
others.
ut two
diatonic
onesdo
not
constitute tonal
ystem.
rue,
he istener
ill
most
ikely erceive
heD as
a
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290
JOURNAL
of
MUSIC THEORY
175
J
A
lj__i_^
■ ■
|
■
fejj?
■
'' r^r^fipY
lj__i_^
r*l<t*l7*'rrrr"^
|
"
I**hPS(ore
sor-te
A me la
lin-gua^e
ol
ca-gion
di mor te
A me la
yËjj?
■
'j
r
r
rirr
H^7^^
~
^^^
Stage
1
7:'T rrlJJJJl^'i r Jjfrrlrrrr
^
■
I
-
I
-
N%r'J|
-
I
-
Stage
2
:;:"
I I
I
rr
j
I M
Tonal 0 L
Systems
| y(V)
1
~
•J
Example
19. Reduction
of
Strozzi,
Cuore
che
reprime
alle
lingua
di manifestare
il
nome
della
sua
cara
(1654)
final nd
the
A
as
its
ifth,
ut
that
oes not
necessarily
etermine
he
tatus
f
the
other ones.
n
particular,
t s still ncertain
whether
^
or
Ft
s diatonic.32
By
m.
5,
however,
he
diatonic
ontext
ecomes
much
clearer:
E^
is another
point
of arrival
nd
thusdiatonic
for he same
reasons
s
D and
A,
and the
four ixteenthotes ttheendofthebar establish ^and F^ as diatonic ones
as well.
Only
he one
B
is eft
ndecided,
nd, here,
he
principle
f
preferred
diatonicism,
hichwould
take
heBb
s diatonic
ince
t
ppears
first,
s
super-
seded
by
motivic
onsiderations.33
ince FA
has
become
clearly
stablished
s
diatonic
n the
downbeat
f
m.
5,
the
istener
ecomes
ware
hat
heEl?
t the
32
Although
he
R fallson
a downbeat
and
might
herefore
be more
easily perceived
as
diatonic,
he meter
does
not
become
clear until t
least
m.
3,
so
for he
listener
he met-
rical tatus
of both
R and
Ft
remains
ambiguous.
Nothing
in the first wo
bars indicates
that the
piece
is not
in
triple
meter,with he E*) allingn the second downbeat.
33
This
piece,
like
Example
9,
illustrates
he
difficulty
f
determining
onal
systems
in
pieces
with
D final.
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Kyle
Adams
~
A New
Theory
of
Chromaticism
291
181
|>)tJii^Ji.Jij<rjt>i.j>ij7^J]J]ji
"
i
"
i
'
ii
Score
lin-gua,
me la
lin-gua
e sol
ca-gion
di mor
-
te
hi*
m'?m
#«
_
, m "Ttti^i*"
m'?0
+ r_, „
■
r
tti*
T
ir
T
f[T|fr
«
_
,
r
j i
p
r
T|iTr ji°
_,
i
(pJ
J~3J
Jlj^Jilj^JJJjl
"
1
"
|"l
tage
1
<
(^ rr|rrr'iHrr ]lrfrni^H
(^ iJjJiii
i
"
i
•
ri
Stage
2 <
'^=- |rr r'Pi
-
I
-
1 H
Tonal
V
L
Systems
Vl')
H
Example
19
(continued)
Reduction of
Strozzi,
Cuore che
reprime
alle
lingua
di
manifestare
il
nome della sua cara
(1654)
beginning
f he
ubject
as
chromatic
one,
n
accordance ith
hich he
parallel
b
nm.5 s
lso hromatic.n m.
7,
where
ither l? rB^would
atisfy
the
grammatical
nd
syntactical
equirements
f he
group
ffour ixteenth
notes,
he
omposer ptsforB^, llowingor consistenteadingwith hefour ixteenthst the nd ofm.5. J& urns ut obethedominantorm fB
throughout
he
piece;
Monteforteses t
consistently
nstead fBl?whenever
either
onewould e
satisfactory.
tsuse establishes
henatural
ystem
s the
governing
onal
ystem
or he
piece.
Again,
hedifference
etween
xamples
9 and
20
is
one
of
context.
Although
hebassof
Example
9
s almost he xact
everse
f
the
opening
subject
rom
xample
0,
t
does not
represent
uspended
iatonicism.
n
Example
0
from
Monteforte,
o
context
ad
been
stablished
gainst
hich
chromaticlterations
ould tand
ut s
such,
whereasn
Example
9 from
Strozzi,
everal
adenceshave
trongly
stablishedhe natural
ystem.
ur-
thermore,nmm. 79-82 fStrozziswork,hebass hromaticallyillsnan
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292
JOURNAL
of
MUSIC
THEORY
rihr-^.
,,i i I. n I yJiJdJdJi
J
*
^1772^=1
Score
I I
I I
-f-
,
j )
J333,jrnJ=,
(fs)yj
-
-
_ _
•
Stage
I
I I
I
^^
I
r
rr
I
Systems
| yCv)
1
7
_
Score
'
'
^^^
LJ- L-J
I I
I
g^^- 1 ■ 1 ■ Lj v^à
Stage
'
'
^^a*'
' ' ' '
'
'
I
>■■ 1
I Ll ^
srage2
t
r
r
^^
Lj Jj|
Tonal
h
ystems
ITO
1
Example
20.
Reduction of
Monteforte,
Fantasie
ex
D
(1689-1700),
m.
1-10
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Kyle
Adams
~
A
New
Theory
of
Chromaticism
293
69
ti i r J i == ^-^ • i-
Score
^»^^fc ■^^^■^^■m ^bb^^b^mh F^T^T^^H
V'
r
*
^-^=^^^
^
F
#
a
b
i* i^ F ^ Z 'rrilirri
0
I
I
■]
.
i
,
m
m _, _,
i 1
f- i , ,
- -
i
Tonal
V L
Systems
((V)
H
-
72
_
i'm^ytt
J
^^
I
^JT"3
J||J
pj
1
J
J
J
j||J
J
sc<>re1^ -r^^=i^V^^i ,JpJi,. SVP^o
/'
_^^^^^n ^^^^^^n ^^^^^^^^
(fai
^^^^^n
J
J
J
JqJ
J
I
*^
J
J
J J
J
J
:ST7^
j
j
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rr r
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t:.
v
1u
r
r
1
i i i
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^^
Tonal
jj
L
II
Systems
Kff)
1
||
-
Example
21. Reduction
of
Rossi,
Toccata
1/7/(1657),
mm.
69-74
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294
JOURNAL
of
MUSIC
THEORY
75
^^
Tonal
ff
==
Systems
| W;
~
7*
in,,
^krtYn
i
rfrr^
J
U
J
III
I I-- I
core
I
i
U
J
U
J
III
I I-- I
Tonal V
Systems
ytT)
~
"
'■i^iWJl¿,Ti;gij,gg2,JiJ3
fr
I
JTJj|jiijJ.J^
-na,
¿
lit,
=
Systems
KCv)
II
Example
21
(continued)
Reduction
of
Rossi,
Toccata
17/(1657),
mm. 75-83
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Kyle
Adams
~
A
New
Theory
of
Chromaticism 295
84
__
Score
^^^^^^^
III I
Stage
1
^^^^^^^
III I
Tonal
y^
Systems
[y(v)
Example
21
(continued)
Reduction of
Rossi,
Toccata
17/(1657),
mm. 84-87
octave
albeit
with
change
of
register),
ith durational ccenton thefifth
step
down,
whichwillbe the
final f the
piece.
This
gives
trozzis
passage
a
much
tronger
iatonic ontext han
Monteforte's,
hich
hromatically
illed
in
the
space
of a ninth.
An even more
striking xample
of
suspended
diatonicism ccursin
Example
21,
mm.
69-87
of
Michelangelo
Rossi's Toccata IL
Beginning
n
the
sixth
measure,
he accretion f
chromatic emitones
n
all of
the voices
and
the ackofclear
cadences,
r even the
expectation
f
them,
makes
discerning
a
governing
ystem
mpossible.34
his ack of a
single
discernible onal
ystem
is
the
primary
eature hat
distinguishes
uspended
diatonicism
rom ll of
theother
hromatic
henomena
discussedhere.For
nstance,
onsider
gain
Example
10,
thefirst ine
barsofLasso's
Prologue.
n
mm.
6-7,
thereduction
34 Note
that he
example
does
begin
n
the natural
ystem,
despite the one-flat ignature.
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296
JOURNAL
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MUSIC THEORY
shows he tonal
systems
hanging
with ach
sonority,eginning
n the four-
sharp ystem
nd
ending
n theone-flat
ystem.
his, oo,
could be seen as an
instance fsuspendeddiatonicism,ince the tonal ystemshangeso rapidly
and come to rest
n
a
system
o farremoved
rom he one in
which
he
pas-
sage
started. ut the crucialdifference etween asso's
passage
and Rossi's
s
that
n
the
Prologue,
hemusic ould come to rest
n
any
of
the
onoritiesn
mm.
5-7,
and the
governing
iatonic
ystem
t that
point
would be
clear. n
Rossi's
passage,
on the other
hand,
f
the musicwere to
stop
on
any
of the
sonorities romm. 74 to m. 81 even
f the
sonority
ere
a
major
or minor
triad therewould
notbe a clear
enough
context o determine he
governing
tonal
ystem
r
the status
diatonic
r
chromatic)
f the chord
n
question.
There are features hat
make certain ones tandout as
more
stable,
f
not diatonic.Mostof the chromatic scents nd descents ill n the nterval
fromG to
D or
from
to
A,
bothofwhich re
significant
ntervals ithin he
natural
r one-flat
ystems.
ote,
n
Example
21,
the
oprano's
scent
n m.
72,
the bass's ascentfromm.
73 to m.
75,
and the
soprano's
scent
beginning
n
m.
77.
Furthermore,
ll of the
quarter
notes nd most
f the
repeated
ighth
notes
n
the
passage
belong
to the one-flat
ystem,
nd
many
tand
out as the
goals
ofchromatic scents
r descents
especially
he
oprano
A^
n
m. 74 and
D^
in m.
75).
Certain
progressions
may
lso be
interpreted
s cadential:
The
motion rom
major
o
F
major
mm.73-74)
can
be
interpreted
s an evaded
cadence to
A minor. n m.
75,
the
oprano
nd bass
move
uite
forcefully
rom
an augmented ixth, b-Ctt,35o an octaveD, although n actual cadenceto
D
minor s evaded
by
hemiddle oice'smotion
o
Bk
Finally,
he
motion rom
m. 79 to m. 80 could
be seen as a
plagal-type
adence to
D
major, nticipating
thefinal adence.
Nevertheless,
verall
he
passage
remains n
example
of
uspended
dia-
tonicism.
f all the
potential
adences,
ery
ew all n
strong
eats,
nd
most
are
evaded,
whichweakens
heir
bility
o define
tonal
system.
here are
many
ituationswhere
the use
of several
hromatic ones
n
succession
n
multiple
oices creates
mbiguous
onorities nd
progressions.
ne of the
most ommon
ways
ossi
reates hese
ituations
s
byhaving
wo oices
move
by
consecutive
emitone
n
parallel
motion,
herefore
maintaining
he same
intervalize.36 he
complex
of tones reatedby his ype f motion annever
belong
to a
single
onal
ystem,
t
least
not
by
the
third onsecutive
nterval.
Nearly
ll
of the music
from he
middle
of m. 73 to
m. 80 contains
his
ype
of motionbetween
t least
two f
thevoices.
On the
second half
f the
third
beat
of m.
73,
the
oprano
nd
bass rise
n
parallel
major
hirds rom
-Ft
to
35
This
ugmented
sixth
ctually
as two
conflicting
ffects:
On
the one
hand,
it intensifies
motion to the
octave
D,
which ould
highlight
he status
of
D
as
a diatonic
one,
and
on
the other
hand,
t destabilizes
any
sense of
diatonicism
by
virtue f
the fact that E'> and
Ct
cannot
belong
to the
same tonalsystem.
36 Strozzi
lso used
this
technique
in
Example
19,
but the
governing
onal
ystems
were clear
for he reasons
outlined
above.
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Kyle
Adams
<^>
A
New
Theory
of Chromaticism 297
F-A.
(The
fact hat he
bass
continues
moving
p by
emitone s the mainfac-
tor hatdestabilizes he sense of evaded cadence on the
downbeat
f
m.
74.)
Immediatelyfter hedownbeat fm.74,thebass and middlevoicesbeginto
move n
parallel
minor
hirds,
ontinuing
ntil he second halfof the third
beat.
At this
point
omes the most
onally
estabilizing
vent f all the con-
secutive
ugmented
riads rom he
third
o
thefourth eat of m.
74,
eading
to another
ugmented
riad
n
the downbeat f m. 75. The
augmented
riad
is
already
n
ambiguous onority;
ne
augmented
riad
annot
belong
to a
single
onal
ystem,
nd two f
them
n
a row
ompletely egate ny
ense of
diatonicism.n
mm.
76, 77,
and
78,
the middlevoice
and
soprano
move n
parallelperfect
ourths,
reating
he
onority
-B-E
on the econd half fthe
third eat of m.
77,
a
sonority
ifficulto
explain by
the
voice-leading rin-
ciplesoftonalorpretonalmusic.Manymore nstances fthis ype fmotion
occur betweenmm.79
and 81.
The
passage
n
Example
21
also
contains
many
uccessions f
sonori-
ties thatdo not
follow
ny
kind of standard
oice-leading attern
n
either
the
soprano
or the bass
(e.g.,
a
descending-fifth
attern),
much ess exist n
any
kind of
functional
elationship
o one
another.Considerthe
succession
of
chords
beginning
n
beat 3 of m. 77 and
continuing
o the downbeat f
m. 78.
This is not a
succession f sonorities
hat reates
predictable
et of
expectations.
ince it s not
sequential,
t
does not
even create the
expecta-
tion hat t
will ontinue
n
the ame
fashion.Until he
rrival f the
bass
G in
m.
82,
t s
difficulto
distinguish
tablefrom
nstable
ones nd therefore o
differentiateones
belonging
o the
governing
ystem
rom
hromatic lter-
ations f
those ones.
Conclusion
Concerning
ixteenth-century
usic,
ames
Haar has
written:
There
ppears
to have
been no
regularly
sed term or
music ull f
harps
nd
flats,
utwith-
out
directmelodic
hromaticism.
ieces to which
his
escription pplies
may
nonetheless ound
quite
chromatic,
t east n the
enseof
being
harmonically
colorful,
o our
ears"
(1977,
393).
This article
was
ntendedto
address
pre-
cisely his henomenon.Thistheoryecognizes,s Haarseemsto,that chro-
matic"
had
many
ifferent
eanings
o
earlier
musicians,
ot all of
which re
accountedfor
by
either
ontemporaneous
r
modern
heories.
t also serves
to blur
the
distinction
etween
diatonic
nd chromatic
y
howing
hat
onori-
ties are
not
always
ne or
the
other.
Rather,
here
re
shades of
chromatic
tones,
ome of
which
xist t
much
deeper
evels
f
structure
hando
others.
Some
represent
urface
xpressive
evices,
while
thers
epresent
undamen-
tal
hiftsn
diatonic
ollections.
he
methodology resented
ere
ims
o
give
analysts
oncrete
riteria or
differentiating
mong
these
types
f
tones
nd,
in
doing
so,
to
provide
vocabulary
ithwhich
heorists
an
discuss he
ways
inwhich hey erceive ifferenthromatic henomenafrom hisperiod.
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298
JOURNAL
of
MUSIC THEORY
Reading
n earlier raft f
this
rticle,
ne scholar
ointed
ut that
some f he riteria
present
or
making
nalyticaludgments
un he
isk f
openinghe oor o ounterarguments.view his s a strength,atherhan
weakness,
f his
heory.
n none f he
xamples
or
his rticle o intend
o
assert hat have ncovered
bjective
ruthsbout he
music.
ather,
or
ach
example,my
rgument
uns s follows:
1)
This
passage
an
egitimately
e
called hromatic.
2)
Chromaticism,
n
this
eriod,
onsistsf ome ombina-
tion f he
echniquesresented
n
Figure
.
3)
Theobservations
ade
n
my
discussionf he
xample epresent
he
est
way
f
pplying
y
methodology
to this
assage,
hat
s,
f
using
he
ocabularyresented
erein
omodel
my
own
hearing
fthe
piece.
Without
doubt,
ther
nalysts
ill
hear
many
f
these
xamples
ifferently,
nd,
fortunately,
heboundariesetween
ach
of
thechromaticechniquesdiscuss ere reblurrynough hat hetheory
allows
ach
nalyst
oaccount
or is r
her wn
hearing.
n that
ense,
very
category
have
resented
ere
s an "ideal
ype."
oneof
hem s a
category
with
ixed
oundaries,
uch
hat
passage
must e
placed
ither
nside r
outside he
ategory.
Of
the
many
spects
fthis
heory
hat re
ripe
or
xpansion,
wo re
worth
entioning
ere:
ts ntersection
ith
enre,
nd ts
elationship
othe
crystallization
f
major/
inor
onality.
oncerningenre,
twould e
worth
studying
he
degree
o which
hevarious
echniques
describe
re used
n
various
enres.
oth
xamples
f
suspended
iatonicism,
or
xample,
re
fromeventeenth-centuryeyboardorks,o doubt ecause uch ortuously
chromatic
assages
ould
e much
more ifficult
o
sing
han o
play.
he
amount f hromaticism
n
acred
nd
ecular
enres
ould
ikewisee
worth
exploring.
o the best
of
my
knowledge,
uxtaposed
iatonicism
ppears
rarely,
f
ver,
n scaredmusic.
uch
striking
egree
f hromaticism
eems
usually
obe
reserved
or ecular
music,
here
tcan
more
ffectively
irror
the
hanges
n textualffect.
evertheless,
twould e
interesting
o
see
f,
and
how,
he
more
ighly
harged
hromatic
echniques
hat have
escribed
areused
n
sacred
music
rom his
eriod.
The
question
f hromaticism
s trelates
o he
evelopment
f
major/
minor
onality
s
more ifficult.
present
ere
single
nalytical
odel
hat
attemptso account or ll ofthechromatic usicwrittenn a period or
which
cholars
till
isagree
n the
best
way
o
modeldiatonic
music.
s
of
this
riting,
here
sno
universallyccepted
model
or iatonicism
n
pretonal
music,
nd
perhaps
his
s
appropriate,
ince
he
meaning
f
"diatonic"
t
the
nd of
this
eriod
s so
far emoved
rom
ts
meaning
t the
beginning.
It seems
nlikely,
hen,
hat
single
heory
r
analytical
ethod
ould
fully
account
or
hromaticism
n
early
music ither.
he
change
rom
retonal
to tonal
music
ndoubtedly
ffected
hromaticism
n
subtler,
ore
ntricate
ways
han
re,
r can
be,
dealt
with
ere.
he
change
rom
retonal
o
tonal
music
satbest
ncompletely
nderstood.
evertheless,
fascinating
nd
use-
ful tudyouldbe made f hedifferenceetweenhe tructuralunctionf
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Kyle
Adams
~
A
New
Theory
of Chromaticism 299
chromaticism
n tonal nd
pretonal
music,
sing
raditionalmusic heories s
modelsfor heformer nd the
theory resented
ere s
a
model
for he atter.
Furthertudywould no doubt ead towelcomechangesand refinementsn
the
present
heory.
hese,
in
turn,
ould
expand my heory
o that t
might
better ddress he tremendous
hanges
n
tonalityhroughout
he
sixteenth,
seventeenth,
nd
eighteenth
enturies.
Whether
r not this omes to
pass,
t s
myhope
that he term chromatic" illbe
applied
differently
o music f this
period
than t has been
previously,
o describenot a
singlenarrowly
efined
technique,
ut a
rich
ource
of
compositional rocedures
nd
possibilities.
Appendix
A:
Further iscussion
of
tonal
systems
My onception f tonal ystems asoriginallyased on thehexachordalmod-
els of
Dahlhaus
(1990)
and
Eric
Chafe
1992).
Chafe defines onal
system
s
"the
aggregate
f
pitches excluding
ccidentals)
that
may
occur"
(23),
in
other
words,
he set of
pitches
hat he
istenerwould
perceive
s
belonging
together
t
anygivenpoint
n
a
piece, usually
ased on some
previously
stab-
lished
context. t
is like a
key
n
that t describes he unordered
pitch-class
content f all thevoices
n
a
polyphonic
exture not
ust
the ordered
et
of
pitches
n
a
particular
oice and
yet
differs rom
key
n
thatno one
pitch
necessarily
erves s a tonalcenter o which ll the others re
subordinate.
Dahlhaus'smodel of tonal
ystem
onsists
f
single
hexachord,
ither
on
Bb,F,C,
or
G,
and the triads hat an be built
upon
its
ones,
with
he
pro-viso hatminor riads an be altered o
major
for
urposes
f
creating
irected
motion.
he tonal
ystem
s
ndependent
f thefinal f the
piece.
The
lowest
tone of the hexachordon whichthe
system
s based will not
necessarily
e
the
final;rather,
he final an be
any
of the
tones
of
the hexachord.Chafe
expands
his tonal
ystems
o ncludethreehexachords nd
their
orrespond-
ing
triads.
hafe'snatural
ystem
onsists f
hexachords uilt n
F,
C,
and
G;
his
one-flat
ystem
onsists
f
hexachords n
Bb,F,
and C.
(Chafe
uses
only
these two
ystems
ince Monteverdi'smusic
uses
only
these
two
ignatures.)
Each of
his tonal
ystems
herefore
orresponds
o
the modern
diatonic cale
plus
the raised
fourth cale
degree.
I have used Dahlhaus'ssingle-hexachord odel as a starting oint,but
mine differs rom
his in several
respects.
irst,
allow for the
existence,
n
theory,
f
hexachords o be
built
n
any
one.
Thus,
s stated n the
rticle,
he
tonal
ystem
an
comprise ny
transposition
f the
tonesof the modern
dia-
tonic cale.
Allowing
onal
ystems
o be built
n tones ther
han
Bt,F,
C,
and
G
enables me to
accurately
escribe ll of
the different
iatonic
progressions
in
a
given
passage
or
work.
econd,
do not
necessarily
llowminor
riads o
be
alteredwithout
change
of
ystem,
s
Dahlhaus does. I
prefer
o treat
uch
alterations n
a
case-by-case
asis ince
believe
hatnot all of
them xist or
the ame
reasonor
at the same
evelof
structure.
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300
JOURNAL
of
MUSIC THEORY
Third,
nd most
mportant,
have divorced
my
onception
f
tonal
ys-
tem
from ts
hexachordal
rigins,
ince the
concept
of
hexachord
does
not
ultimatelylay role inmy heory. hus,although hepitches fthe tonal
system
ere
originally
enerated y single
hexachord,
hat
eneration
oes
not factor n
to how the tonal
systems
re used.
The hexachordal
rigins
f
the tonal
ystems
sed in
this
heory
re
only
mportant
nsofar s
they
oint
to
the reasons
for he nclusion f
certain ccidentals
t the
expense
of oth-
ers.
Each tonal
ystem
as
generated
rom he triads
hat ould be built
using
only
the tones of a
given
hexachord nd the tone a
perfect
ifthbove the
third
hexachordal
tep.
Thus,
the
one-sharp
ystem
ncludes
Fit
instead
of,
e.g.,
Ctt
r
Gf
because it
was
generated
rom he triads uilton
the tonesof
the G
hexachord.
Appendix
B:
Further
iscussion of the terms essential and
nonessential
Many
cholarswill
undoubtedly
ake
xception
oth to
my
se of
these
erms
and to
the
way
n
which
apply
hem.The
following
iscussion heds some
light
n the
specificways
n
which
propose
to use them.
Clearly,
he terms
havebeen
adopted
from
ohannKirnberge
,
butthat oes notmean that
hey
shouldbe construed o have
ny
relationship
o his terms.
ather,
hey
hould
be
taken s
literally
s
possible:
Nonessential" hromatic lterations
ither
are
unnecessary iven
he
compositional tyle
r could
become so
in
a differ-
ent
context,
nd "essential" hromatic
lterationsre those hat re
necessaryno matterwhatthe context.Readers of earlierversions f this rticlehave
pointed
me to
many ossibleproblems temming
rom
heuse ofthese
erms,
and I
address he threemost
ignificant
f these.
First,
nd
perhaps
most
ignificant,
s the
objection
hat ccidentals hat
serve o create
adential
eading
tones hould not be called chromatic t all.
Margaret
ent has
amply
laborated n this
point
of view
n
"DiatonicFicta"
and
elsewhere,
nd
it
s
necessary
orme to
clarifymyposition
with
espect
to this
point.
do not
deny
hat he
progressions y
which hese ccidentals
arise
are,
in
many
ases,
entirely
iatonic,
n that
they
an be understood
and solmized
ntirely
ithin he extended
gamut.
However,
consider
hese
accidentalshromatic,na sense closer o themodern ne, n that hepitches
arising
rom heir se lie outsidethe
governing
onal
system
see
my
defini-
tions n
p.
260).
37
Note the
underlyingssumption,
n this
rticle,
hat he ear will
xpect
the continuation f the
governing
onal
ystem
nless
xplicitly
irected th-
erwise.
Thus,
whether
chromatically
lteredcadential
eading
tone arises
from iatonic r chromatic
melodic
uccessions,
twillbe marked
s a differ-
entform
f
given
etter
ame than hatwhich
ne would
xpect.38
his s the
sense of the term chromatic"
hatmodernmusicians
se,
and the one
that
37 This view
is,
in
fact,
onsistent with hat
of
many
ate-
sixteenth-centuryheorists; ee Adams 2007.
38
Berger
2004,
45-46)
makes a similar
oint.
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Kyle
Adams
~
A
New
Theory
of Chromaticism 301
use here.
n
fact,
lthough
would
nticipate trong
bjections
rom ent nd
others
n
my
use
of "chromatic"
o describe hese
tones,
can
only
magine
that he amescholarswould greewithmy onclusions: hat nce such tones
are reduced
out
of
themusical
urface,
passage
containing
hem s revealed
to be
exclusively
iatonic.
The second
objection
s that adential
eading
tones nd
Picardy
hirds,
even
f
hey
an
legitimately
e called
chromatic
ccording
o
my
efinitions,
are
hardly
nonessential,"
specially
n the sixteenth
entury.
do
notwish o
imply
ere that he
use of these
toneswas
n
some
way ptional,
but rather
that he
music
ould,
n
principle,
ontinue
n the same tonal
ystem
ithout
them.While
cadential
eading
tones and
Picardy
hirds
may
be essential
n
terms
f
the
style,
he circumstances
hat
give
rise to them re
not. To illus-
trate, willborrow wo xamples rom ietroAronsAggiuntao the Toscanello
in musica.
il-
J
j .. ,... h.
M =n
l-
$■„■
^r*^"
.. ,... h.
r^
M
¡rw^
=n
Example B1. Two examples fromAron,Aggiunta to the Toscanello in musica ([1529] 1970, 22)
Arons
examples
are intended
to illustrate
he sorts f circumstances
under
which
composer
hould notate
ccidentals,
ather
han
eaving
hem
to
the discretion
f the
performer.
owever,
hey
lso illustrate
ather
icely
my
easonsfor
allingPicardy
hirds
nonessential."
he first
onority
f the
example
shownon
the
right
s intended
to substitute orthe
third
onority
of the
example
shownon
the eft.Aron's
point
s
that he
composer
hould
notate he
oprano
Git
hown
n the eft
n
Example
Bl,
because
if he music
continued s on the
right,
he G would better
e left naltered.
My
reasons
for
alling
such a Gtt onessentialre similar. f course the
Picardy
hirdn
the eft
xample
s an "essential"
spect
of
the
tyle,
utthefact hat hemusic
happens
to end there
s
not.
If the music continued s on the
right,
here
would be no need for
GÌ;
in
fact,
t
would
be incorrect o add one.
Thus,
the
Picardy
hird
Gtt
n the eft s
nonessential,
nsofar s
a
different
usical
context ould render t
unnecessary.
ne can
easily magine
imilar ituations
with adential
eading
tones,
ncluding
he familiar
inganno"
adence.
Finally,
he
theory
makes no distinction etween ccidentals ncluded
by
the
composer
n
the score and those
mplied
by
the
proper application
of musica
icta.
Here,
I
would
agree
with
Berger
(2004)
that
accidentals
stemmingrom heproper pplication f musicaictare as much part fthe
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302
JOURNAL
of
MUSIC THEORY
musical ext s those
pecifically
otateci
y
he
composer
see l70ff.).
n
fact,
Example
Bl
illustrateshis
oint
s well. n the
progression
n
the
right,
ron
hasnot ndicated cadentialCttnthe lto, venthough nyperformerfhis
day
urely
would
have ncludedone.
Thus,
any nalysis
f this
passage
would
have to treat he
ltovoice as
though
t contained
notated
Ci
While would
still
onsider his chromatic
itch,
or
he reasons
given
bove,
wouldcon-
sider
t "essential" o
my nalysis,
f
not to the musical
urface.
Thus,
all of
my nalyses
reat
mplicit
ut
necessary
ccidentals s
equivalent
o
notated
accidentals.
Appendix
C: Guidelines for diatonic
reduction
The followings a more succinct resentationf theprinciples f diatonic
reduction
iven
n Section .
(1)
The
top system eproduces
he core.
(2)
Underneath he
op
ystem,
nd
aligned
with
t,
tage
1
of hereduc-
tion
copies
the score without
ny type
B alterations.
have taken
out these alterations irst ecause
they
re the furthest
emoved
from he
underlying
oice
leading; they
xistfor
expressive ur-
poses
rather hanfor
easons
f
musical
yntax
r
grammar. tage
1
therefore
ontains iatonic
ones,
ssential
hromatic
ones,
nd
type
A
chromatic lterations.
(3) Underneath he econd ystem,ndalignedwith heothers,tage
reproduces tage
1
without
ny ype
alterations.
tage
2
therefore
contains
nly
diatonic ones nd essential
hromatic ones.
(4)
Underneath he hird
ystem,
single
taffracks he onal
ystem(s)
governing
he
passage by notating
ach
new
tonal
system
nder-
neath he
point
n
stage
at which t
ppears.
The
tonal
ystems
re
shown s
key
ignatures.
or
example, signature
f
Ft
would
rep-
resent he
one-sharp ystem.
here are
two
exceptions: assages
containing uspended
diatonicism re
given
no
signature
t
all,
and
passages
n the natural
ystem
re
given signature
f
Y& o
distinguish
hemfrom
uspended
diatonicism.
hanges
of
system
brought
bout
by
direct hromaticism
re
represented y
double
barlines,
ollowed
y
he
ignature
f the new
ystem.
(5)
The
principlef referred
iatonicismtates hat
he
governing
onal
system
f
passage
will
lways
e
the
one in which he
greatest
os-
sible
number
f onorities re diatonic. reference
illbe
given
o
a tonal
system
n which
he
first
onority
f a
passage
s
diatonic;
however,
many assages
do
begin
with hromatic
onorities.
(6)
The
principle
f reaterimplicity
tates hat he
tages
fthereduction
mustbecome
successively
ore
diatonic.The
reduction
may
not
create hromaticism
hatwas not
present
n the
original assage.
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Kyle
Adams
™
A
New
Theory
of
Chromaticism
303
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7/24/2019 New Theory of Chromaticism
http://slidepdf.com/reader/full/new-theory-of-chromaticism 51/51
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Werckmeister,
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ildesheim,
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Translated
yGuy
A.
Marco and
Claude V. Palisca. New Haven: Yale
University
ress.
Kyle
Adams is assistant
professor
f music
theory
nd
aural skills
oordinator t Indiana
University.
n
2009,
he
presented
work on
sixteenth-century
usic at the
Society
forMusic
Theory
nnual
meeting
and was invited
o
speak
on the
analysis
of
rap
music at the biannual
Stop. Spot
festival
n
Linz,
Austria.