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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






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).






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.






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.






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.






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.






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).






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.






Kyle

Adams

~

A New

Theory

of Chromaticism

263

27

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duol,

al

mio duol mor

-

te non

sen

-

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«

i

J,J

■

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j j j h

,i

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£

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mio

duol,

™ |iiM i - > JJr - |>>rr "r'rr"^^

do

al mio

duol,

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duol,

•

ly

*r i"

it

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flptlfljfJ

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p

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Tonal

jHfl

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lit

tf

Systems

ITO

ft

j

'

j

tf

«J

Example

3. Diatonicreduction f

Gesualdo,

Ma

tu,

agion,

mm.27-34






264

JOURNAL

of

MUSIC

THEORY

31

mor

-

te non

sen

-

to,

mor

-

te non sen

-

to

A

$

J- J JJ

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Ji|J'UJ

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non sen

-

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11 i

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"

i

.

mor

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non sen

-

to

™ ¿ rr fi 'fJ » J • *"r rJ ° mB

mor

-

te non

sen

-

to

mor

-

te non sen

-

to

Stage

I '

«jr^^

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J^J

-fat

'll

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'

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Stage2

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=±rrTT-rrf

'

■ ■■

Example

3

(continued)

Diatonic reduction of

Gesualdo,

Ma

tu,

cagion.

mm.

31-34






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.






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.






Kyle

Adams

~

A

New

Theory

of Chromaticism

267

2j

e

mo-ri

'¡I I*, w ' "I

e

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*

e

mo-ri ro be

-

a

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mo-ri ro

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Systems

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e mo

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Tonal

h

ystems

lyCu

M

-

Example 4. Diatonic reduction of Luzzaschi, Lungi da te (1595), mm. 23-27






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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-

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ta

Wc

fe

r

J1J1

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(e

mo

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ri

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ro)

be

-

a

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ta)

1/

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i

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a

ro

be

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(ir

rir

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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.






Kyle

Adams

~

A New

Theory

of Chromaticism

269

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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.






270

JOURNAL

of

MUSIC

THEORY

28

per

-

che di

-

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Tonalb

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.






Kyle

Adams

~

A

New

Theory

of Chromaticism

271

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Systems

K(')

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[/

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






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.






Kyle

Adams

~

A

New

Theory

of Chromaticism 273

92

A

-

ni

-

ma me

-

a tur

-

ba

-

ta est tur

-

ba

-

ta

JL h J

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P^i

h

' JiJ-Jip ^ i^)r ^ ff

.i/JuJ.

(h)r

score

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Tonal

^£

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Systems

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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






274

JOURNAL

of

MUSIC

THEORY

Ec

-

co

O dol

-

ce^o

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life J.

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"•

ir li

r

r

r

,

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(^

■

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






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.






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

¿J

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






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.






278

JOURNAL

of

MUSIC

THEORY

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re

au

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dis

mo

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du

-

la

-

ta

te

-

no

-

re

.t. »a

Á

-*■

J

1"> I

J

,J

e

Lo =

^

i

f>

|

pò

r

*

^^

Q ,

I

i

|

| _

^? tftt1^

o

o

1

g

jg-

i

„

-

J

, ¡J

¿.

J~JßJ"JßJ

,ir-

_

*jf- rO-

-

=

«rftS-

'

O

o

1

g

jg-

'

„

-

-

I Up ¿.

'

v,ir- *jf- rO-

Stage

1

'

'

' '

('M8 p

"'

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'

rJ

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g

ln

-

I

TonaI

I

:^i

:

.'

ii

:^

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ir

^

Systems

1^)

■

'

.' .

II

Example

10.

Reduction of

Lasso,

Prologue

from

Prophetiae Sibyllarum

(1560),

mm.

1-9






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.






280

JOURNAL

of

MUSIC THEORY

l^- * i fUi ih bsVfv f"fM"|

core

(Car

-

mi

-

na)

au-dis mo

-

Car

-

mi

-

na

Chro

-

ma

-

ti

-

co

quae

au

-

dis mo

-

?»:- -'''".

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»h b

[i

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«

i¿V

iS~

i»f

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tage

1

I

«

'

_, .. J L I to ^ JL,B Lp J^ I

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






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.






282

JOURNAL

of

MUSIC

THEORY

113

Tenorl

[ TO?

-

l<h

~

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"

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■

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*

to

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Tenor2

[

TO

f

"

o

hl*'

flJ

>

J

jtjj1^1

11*'

JllftJ

*

J =

*

to.

Sol

i

-

o

per

sel

-

ve^ab-ban-do-na

te

so -le l'ar-

csr.,

v:?M.

i»

"

if

«J

if

tf

i

Tona,

fit

II

Ü

Tl

|^

"-Systems K(V) || Tl II -"- -

117

i

-

o

per

sel

-

vejib-ban-do-na

te so

-

le l'ar

-

dor

di due

be

-

T2

[

<fa

||J i^J^/'l)fJ.

«P

flJ'

l

J J

1

"

^

dor di duebe -glioc - chiel mio tor men to

¿y II il |

o^

-

^n

bc

V>'

y

o-

II

IJ

J

l

I» l l

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).






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






284

JOURNAL

of

MUSIC THEORY

Tenorl

O?

hh I

"

1"

=^j

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Tenor2

i

TO?

"

o

hfyJ

J

1jtJ_Jlil

ljl^-

JllftJ

^

J

°

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

|

fj

ttrJ I

Q-

I

f

5

ti

[$

^ * r [r~FFft'f " [r "^

i

-

o

per

sel

-

vewab-ban-do-na

te

so

-

le

T2

I

«y

K

^rx

^ ^

'^

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'*'

tr

'*

*

~=H

dor

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-

glioc

-

chiel mio tor

-

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-

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.






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.






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^^

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ig

;

^

j^j1

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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






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






288

JOURNAL

of

MUSIC

THEORY

49 i

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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.






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






290

JOURNAL

of

MUSIC THEORY

175

J

A

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A me la

yËjj?

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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.






Kyle

Adams

~

A New

Theory

of

Chromaticism

291

181

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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






292

JOURNAL

of

MUSIC

THEORY

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ITO

1

Example

20.

Reduction of

Monteforte,

Fantasie

ex

D

(1689-1700),

m.

1-10






Kyle

Adams

~

A

New

Theory

of

Chromaticism

293

69

ti i r J i == ^-^ • i-

Score

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Systems

Kff)

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-

Example

21. Reduction

of

Rossi,

Toccata

1/7/(1657),

mm.

69-74






294

JOURNAL

of

MUSIC

THEORY

75

^^

Tonal

ff

==

Systems

| W;

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in,,

^krtYn

i

rfrr^

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Example

21

(continued)

Reduction

of

Rossi,

Toccata

17/(1657),

mm. 75-83






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.






296

JOURNAL

of

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.






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.






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






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.






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.






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






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.






Kyle

Adams

™

A

New

Theory

of

Chromaticism

303

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Margaret.

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Musiktheorie:

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new theory of chromaticism

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