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Heinichen, Rameau, and the Italian Thoroughbass Tradition: Concepts of Tonality and Chord inthe Rule of the Octave

Author(s): Ludwig HoltmeierSource: Journal of Music Theory, Vol. 51, No. 1, Partimenti (Spring, 2007), pp. 5-49Published by: on behalf of theDuke University Press Yale University Department of MusicStable URL: http://www.jstor.org/stable/40283107Accessed: 01-11-2015 23:33 UTC

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Heinichen, Rameau,

and the

Italian

Thoroughbass

Tradition

Concepts

of

Tonality

and Chord

in the

Rule

of

the

Octave

Ludwig

Holtmeier

Abstract

This

essay explores

the

understanding

of

tonality

and

in

particular

he

concept

of

chord,

as demon-

strated

in the Italian

horoughbass

tradition,

especially

in

the

didactic tradition

of

partimenti.

Fora

long

time

this

tradition

was

entirely

overlooked

because

of the dominance

of the neo-Ramellian

Harmonielehre

radition.

The

differences

are

exemplified

by comparing

Rameau's

basse fondamentalewWh

Heinichen's

luctuating

understand-

ing

of

tonality.

Itwas Heinichen

who,

at the

start of the

eighteenth

century,

attempted

most

thoroughly

o

concep-

tualize

Italian

music

theory.

Like

Rameau, he,

too,

developed

an

overarching

explanatory

model

of

harmony

hat

involves coherent

concepts

of

harmonic

unctionality

and chord

morphology.

Heinichen'sand

Rameau's

"systems,"

however,

rest

on

opposing

assumptions.

However

many speculative

aspects

it

may

embrace,

Heinichen'smusic

theory

nonetheless

remains

directly

indebted

to

musical

practice

and

consistently rejects

that

esprit

du

système

that is so

characteristic

of Rameau's

theory.

While

Rameau,

acting

in

the

modern,

scientific

spirit

of the

early

Enlightenment, ttempts to derive all aspects of his theoryfrom a few fundamentalprinciples,Heinichenworks

through

he

many

tensions

and contradictions

between

the modern

Klangprogression,

as formalized

n

the Rule

of the

Octave,

and

the old

legacy

of traditional

counterpoint

nstruction.

A blind

spot

in

the

history

of music

theory

in the

last

few

years,

with the

strengthening

of that

movement

within music

theory

commonly

known as

historische

atzlehre

r

"historically

nformed

music

theory,"

t seems

as

if an

awareness

of

a

forgotten

"culture"

of music

theory

has

been

given

new

life.

The

nineteenth-century

German

Harmonielehre

radition

occupied,1

well

into

the

twenty-first

century,

such

an

unquestioned,

nearly

1 The

bourgeois

tradition

of

the Harmonielehre

(meaning

both

"the

theory

of

harmony"

and "the

harmony

textbook")

is "German"

in view

of the

fact that

those treatises

that

later

served

as

models

were

nearly

all

published

in Ger-

many.

During

the

course

of the

nineteenth

century,

these

treatises

were translated

into several

languages,

and

many

of

the texts

originating

outside

of

Germany-

particularly

those

in the

English-speaking

world follow

those

models

in

their

organization.

It is not

asserted,

however,

that the

Harmonielehre

tradition was the

only

one,

or that

there was

a lack of

relevant national differences.

Journal

of

Music

Theory

51:1,

Spring

2007

DOI

10.1215/00222909-2008-022

©

2009

by

Yale

University

5






6

JOURNAL

of

MUSIC THEORY

monopolistic position

that one must first come to terms

with the notion

that,

existing

alongside

the theoretical

lineage

of

Jean-Philippe

Rameau,

there was

yet another music-theoretical culture no less significant in music historyand

the

history

of music

theory.

It is this

forgotten

culture and its

renaissance

that

are the focus of this

essay.

The fixation of the Harmonielehreradition

on the

late,

"abstract"

writ-

ings

of Rameau2

and

his

successors has led

to one of the

largest

omissions

of

music-theoretical

historiography:

he

nearly complete neglect

of

Italian

music

theory,

its

concept

of

tonality,

and

particularly

the so-called

partimento

radi-

tion,

which contributed so much to the true

face of

European

composition

teaching

from the seventeenth to the

early

nineteenth

century.3

There can be

little

doubt,

for

instance,

that the

thoroughbass

teachings

of

"Viennese classi-

cism"were at their core a Ramellian reshaping of an Italian music theory,4 ust

as the

prevailing

music

theory

at

the Paris

Conservatory

was likewise

minted

in

Italy.5

n

Europe,

the Ramellian and neo-Ramellian

tradition was

an essential

music-theoretical

current,

but until the mid-nineteenth

century

it was

by

no

means the one with the

greatest practical impact.

In terms

of

reception history,

there are

many

reasons

why

the

partimento

tradition could never

step

out from the shadow of

Rameau s

theory.

Here it

is sufficient to note

only

the most obvious: the

textbooks of the

partimento

tradition

usually

consisted

mainly

of music notation.

In these

books,

"theory"

is

not,

in the

common

meaning

of the

word,

presented

and

developed

"sci-

entifically."

In

general, nineteenth-century

music theorists

could no

longer

take this tradition

to

be,

strictly speaking, "theory,"

et alone take it

seriously

(Weber 1826).

Viewed

in

retrospect,

it

decayed

into Generalbasslehre

thor-

oughbass

teaching),

to

"pure

practice,"

and

simply

fell outside the

concept

of

theory.6

The

sharp

and

often

polemical

delimitation of

eighteenth-century

thoroughbass teaching,

which

continues

beyond

Hugo

Riemann

up

to Carl

Dahlhaus,

is a

precondition

for the rise of the

nineteenth-century

Harmonie-

lehre

radition.7

2

Meaning

those

writings

produced

after the

Traité de

l'Harmonie

(1722).

3

Regarding

the

history

of the

Neapolitan

conservatories,

see Florimo

1882/83.

In

this

connection,

the

works of

Rosa Cafiero

1993,

1999,

2001,

2005

and

Giorgio Sangui-

netti

1999,

2005

merit

special

mention.

After Carl Gustav

Fellerer's

early

studies

(1939),

Florian

Grampp

gave

a first

larger

overview of

the

topic

(2004/2005).

In

2007,

Robert 0.

Gjerdingen presented

his

comprehensive

study

(Gjerdingen

2007).

Bruno

Gingras

2008

followed with a

study

on the

German

partimento

fugue.

See also

Aerts

(2006).

Holtmeier

and

Diergarten

2008

offers a

general

overview.

4

On

this

point,

see

especially

Budday

2002,

Holtmeier

2008,

2009,

Grandjean

2006,

Kaiser

2007a,

and

Diergar-

ten 2008. The harmony and thoroughbass text of Bruck-

ner's

teacher

Durrnberger

(1841)

is written in

the

spirit

of

the

partimento

tradition,

and one can still

clearly

detect

this

provenance

in

Simon Sechter's

already unequivocally

Ramellian Practische Generalbass-Schule (1830). Only the

neo-Ramellian turn taken

in

Sechter's Grundsâtze

(1852/54)

represents

a real break.

5

On the

reception

of

partimenti

in

France,

see the article

by

Rosa Cafiero

in

this issue.

6 On

this

point, compare

the

disparaging

remarks of Fétis

quoted

by

Rosa Cafiero

in

her

article

in

this issue

(150).

7

Even a

cursory glance

at

the

leading

music

journals

in

the

first half of the

nineteenth

century

shows that

"thorough-

bass

bashing"

was

pervasive.

Gottfried

Weber

speaks

of a

"jumble

of note

numbers and other

symbols

that one calls

thoroughbass" (1824,

55).

In

the

context of his discussion

of

Johann Bernhard

Logier's System

der

Musikwissen-






Ludwig

Holtmeier

~

Heinichen,

Rameau,

and Italian

Thoroughbass

A

digression

on

partimento

reception

Alexandre-Etienne

Choron

's

Principes 'accompagnement

esÉcoles 'Italie

1804)

and his

monumental

Principes

e

composition

es écolesd'Italie

1808)

together represent

what

is

surely

the most

obvious source

for the French

reception

of the

partimento

tradition,

and

the influence

of Choron

on

François-Joseph

Fétis is of central

importance

for

French music

theory

(Simms

1975).

But Choron

's direct influence on the

teaching

of

composition

at the

Conservatoire

emained limited.

"Italian"

nfluence, however,

goes

far

beyond

these

explicit

documents.

The structure

of Charles-Simon Catel's

popular

Traité

d'harmonie,

or

example,

shows

clear

vestiges

of "Italian"

practice

(1802).

But it

was first

and foremost

Luigi

Cherubini's

teaching

method

(1847)

that stood

completely

within this

tradition.

Even the basses

données nd

chantsdonnés xercises

found

in

text-

books

like Henri

Reber's

Traité 'harmonie

1862)

and

François

Bazin s Coursd'harmonie

théorique

t

pratique

1875)

-

both

texts

already

clearly

marked

as Ramellian- document

the

continuing

influence of the Italian

partimento

tradition.

While

for a

long

time

partimento

practice

remained

a

living

tradition

in Pari-

sian

conservatories

and

in

Italy

(Vidal

and

Boulanger

2006),

its decline

in

Germany

was

accelerated

by

the

collapse

of

the old

bourgeois

and clerical

institutions

of music

education.

With

the establishment

of the

Leipzig

Conservatory

(1843),

the

training

of

musicians

in

Germany

was

reprofessionalized.

The Italian

partimento

tradition could

find

only sporadic

admission

into this

new civil

institution.

Nevertheless,

the tradition

reshaped

by

other

music-theoretical

tendencies

-

did survive

at other

conservatories,

especially

in Munich.

There

Josef

Gabriel

Rheinberger

taught "high-Romantic"

parti-

men ti

(both

figured

and

unfigured;

Rheinberger

2001;

Irmen

1974),

and the exercises

provided

in the

influential

Harmonielehre

1907)

of Rudolf

Louis and

Ludwig

Thuille

also remain in this tradition. In Germany,however,the partimento tradition and, in

particular,

he

practice

of

the Rule

of the Octave

survived

best

in

the

"lower"

music

pedagogy

of

teacher

seminars

with

a

practical

orientation

(Piel

1887).

Their

complete

abolition

with the

general

program

of the

Kestenberg

reforms

in

1925

(Leo

Kesten-

berg

was an

influential

music educator

in the Weimar

Republic)

sealed

the fate

of the

partimento

tradition

in

Germany.

From

thoroughbass

to

Harmonielehre

The

purely

performance-practice

term

thoroughbass

Gen:

Generaibass,

t.:

basso

continuo),

which

underlies

the above-mentioned

polemic,

oversimplifies

the facts. In 1873, the Beethoven researcher GustavNottebohm had

already

pointed

out that

in Beethoven's

time

one understood

a

"twofold"

meaning

by

the

term

thoroughbass

Nottebohm

1873,

5): "(1)

the

embodiment

of

the rules

for

accompanying

a

figured

bass,

and

(2)

the

science

of the

combination

and

connection

of

intervals

and

chords,

with

or without

consideration

of thor-

oughbass

performance."

Johann

David

Heinichen

grounded

his

thoroughbass

schaften

(1827),

Adolf

Bemhard

Marx

speaks

of the

"anti-

musical

sloppiness

of

thoroughbass"

(1830,

414).

As late as

1860,

Heinrich

Josef

Vincent titled

his text

on the

basics of

music theory Kein Generalbass mehr (No More Thorough-

bass;

Vincent

1830).






8

JOURNAL

of

MUSIC THEORY

method on the

categorical

distinction between

Accompagnisten

and

Componis-

ten

(Heinichen

1728,

preface).

In

the

eighteenth

century,

Heinichen's

distinc-

tion became

part

of common sense and led to music theory differentiating

between a

"theory"

and a

"practice"

of

thoroughbass,

as

Johann

Friedrich

Daube described it

(Daube

1756,

vii).

Johann

Georg

Sulzer even

speaks

of

a "science of

thoroughbass"

(1771/74, 456).

Although

the

borders between

theory

and

practice

were

fluid,

their

relationship

was

nevertheless

subject

to

a

clear hierarchical order. As declared

in

Sulzer's

Allgemeine

Théorieder

schônen

Kunste

(1771/74, 456),

"Without a

complete

understanding

of

harmony

it is

impossible

to

play

thoroughbass

correctly."

Daube

defined the

relationship

between the

theory

and

practice

of

thoroughbass

as

follows

(1756,

viii):

To it

[thoroughbass performance] belongs,

besides

a skill

in the

practical

exer-

cise, a theoretical cognisance so that one knows: (1) from whence most chords

originate,

(2)

to where

they may

be

connected,

and

(3)

how,

from the first

chord,

one can deduce the

subsequent

ones. ...

In addition to the

practice

of

thoroughbass,

an

accompanist

should also understand

the

theory,

so that

he

can know how the rules

of

composition

derive

from

it. A well

grounded

com-

poser

could

even

dispense

with the

practice

of

thoroughbass

if he

only pos-

sessed a

complete

command of the

theory.

Nevertheless

having

both

together

is better still. A

complete

understanding

of

thoroughbass

always

remains the

foundation for

the

melodic structures

that can be built

upon

it.8

Thus,

in the

eighteenth century,

the term

thoroughbass

covered

exactly

the

subject matter that, in the nineteenth century, would fall under the jurisdic-

tion of a

Harmonielehre.

Riemann

spoke

of

thoroughbass

as a

"simple

tool of

performance

prac-

tice."

Equally problematical

is the

overgeneralizing

discourse of "the" thor-

oughbass,

which

implicitly

assumes a

single two-hundred-yearperiod

embrac-

ing

a

broadly

static,

self-contained

historical and theoretical

entity.

But what

one

comprehends

by thoroughbass

around the

year

1600

is

entirely

different

from

what the

term

implies

around 1700 or even 1800. Notions of an

"Age

of

Thoroughbass"

(Generalbasszeitalter)

r of

"Thoroughbass Harmony"

(Dahl-

haus

1990,

125)

provide

little

help.

In

particular,

the

typical

German Harmo-

nielehre

radition,

which

attained

international

prevalence

in

the second half

of the nineteenth

century,

had an undifferentiated and

markedly

one-sided

understanding

of

thoroughbass.

In

the

process, nearly

all Harmonielehreheo-

reticians

developed

an

almost manic

fixation on the

numerical

shorthand,

on

the

"figures"

of

"figured

bass."

They

read

the

figures

as

representatives

of

8 Hierzu

gehôrt,

neben der der

praktischen

Ausubung

auch

eine

theoretische

Kenntnifc,

dafc man

wisse:

(1)

woher die

meisten

Accorde

entspringen.

(2)

Wohin

sie sich lenken

las-

sen.

(3)

Und wie

man aus

dem ersten

Accorde den

darauf-

folgenden

errathen

solle.

. . .

Ein

Accompagnist

soil

neben

der

Praxis auch die

Théorie

des

General-Basses

verstehen,

damit er wisse: wie die Regeln der Composition daraus

entspringen.

Ein

grundlicher Componist

kann

noch eher

die

Praxis des

General-Basses

entbehren,

wenn er

nur die

Théorie

vollkommen

besitzet. Doch ist

beydes

beisammen

noch besser.

Die

vôllige

Kenntnift

des General-Basses bleibt

jederzeit

der

Grund des darauf zu

bauenden melodischen

Gebaudes.






Ludwig

Holtmeier

~

Heinichen,

Rameau,

and Italian

Thoroughbass

9

chords,

understood

them almost

exclusively

vertically,

built

"stacks" f thirds

over the

respective

bass

notes,

and thus

unconsciously

transferred their own

understandingof chord, harmonic progression,and, aboveall, harmonic anal-

ysis

to the music

of the

past.

For

the

Harmonielehre

radition,

whether oriented

toward theories

of scalar

degrees

(Roman

numerals,

Stufentheorie)

r func-

tional

theory

(Funktionstheorie)

harmonic

progression

meant the

leap

from

chord to

chord,

and

it was

in

this

sense that even

thoroughbass

was under-

stood and

its

figures

read.9

In

this

purely

vertical

reading,

the

figures

can be

read

off

clearly.

Hence,

the Harmonielehre

heorists were unable

to

engage

with

thoroughbass

appropriately

because

the

separation

of

Harmonielehrend Kon-

trapunkt

ad

already

been

completely

internalized

and

transferred

to the

past

as

something

self-evident.

The

opposition

between

"harmony"

and

"melody,"

and the resultantdivisionbetween the teaching of harmonyand counterpoint,

is the

starting point

for

the neo-Ramellian

German

Harmonielehre.

he more

the

Harmonielehre

heorists

decried,

wrote

against,

and tried to

surmount this

"artificial"

eparation,

the

more it

became solidified

and,

as

it

were,

a natural

law.

They

attempted

to

resolve

a self-inflicted

problem.

The reconciliation

of

harmony

and

melody,

of line and

Klang

(i.e.,

a

sonority perceived

as a

chord),

is ^central

theme

of

the

entire

Harmonielehre

radition

(Kuhn

1994).

In the seventeenth

and

eighteenth

centuries,

considering

the

typical

case,

thoroughbass

figures

had

not

only

vertical

but also

linear

significance.

One

is often

unable

to draw

a

line between

the

contrapuntal

and harmonic

sense

of

the

figures.10

The

recurring

formulation

in Italian

lesson

books,

where one

learns

counterpoint

through

thoroughbass

or

partimento,

should

be taken

seriously

and

understood

quite

concretely

by contrapunto

ne

had

in mind

not

just

the

"special

disciplines"

of

counterpoint

but above all

the

correct

disposizione

Sanguinetti

2005,

496f.),

that

is,

"diebeste

Lage"

the cor-

rect

voice

leading

above

the

thoroughbass

(Fôrster

1818, 1;

Holtmeier

2009).

The

trio

sonatas

of

Arcangelo

Corelli

became the

unquestioned

pedagogi-

cal

models

for this

ideal

voice

leading.

They

embodied

a

compositional

ideal

valid

from

the seventeenth

century

to the

mid-eighteenth

century.

That

is,

a

four-voice

texture

was

considered

a

three-voice

texture

supplemented

by

the

presence

of an

added

voice

(ad

libitum),

which

could

as

easily

be

missing.

For the Ramellian and neo-Ramellian Harmonielehre,owever, a three-voice

texture

is an

idealized

four-voice

texture

missing

one

voice.

I

return

later

to

the substantial

difference

between

these

concepts

of chord.

9

Hugo

Riemann

also understood

the

figures

as

pure

"instruc-

tions

for

hand

positions"

{Griffanweisung)

to

which

no func-

tional

harmonic

or

contrapuntal

significance

is attached.

Characteristically

he

put

not

only

his

notorious

Klangschlùs-

sel

but

also

his

symbols

for

harmonic

function

under

all the

exercises

in

his

Anleitung

zum

Generalba&Spielen

(Rie-

mann

1889).

10 One is

tempted

to

say

-

with all due

caution

-

that at

the

beginning

of the

eighteenth

century

the linear

significance

still

predominates,

and

that

thoroughbass

or the

under-

standing

of

thoroughbass

becomes

increasingly

"vertical-

ized"

during

the course

of the

century

under

the influence

of

Ramellian

thinking.

The one-sided

vertical

reading

of the

German

Harmonielehre

is

only

a

(radical)

consequence

of

this development.






10

JOURNAL

of

MUSIC THEORY

A

digression

on Corelli

reception

Withoutexaggeration, can one assert thatfor the stilontoderno,

orelli

had

as authorita-

tive a stature as that of Palestrina

for

stilo

antico.

He

was,

in terms of

the

reception

of

his

style

and the diffusion of his

works,

a

composer

of

European

importance.

Angelo

Berardi had

already

called him the "new

Orfeo of

our time"

("nuovo

Orfeo

nostri

giorni";

Berardi

1689,

45).

For

Johann

Mattheson

he was

"the

prince

of

all

composers"

(Mattheson

1739,

326).

And Michel de

Saint Lambert

referred

to him as

the "famous

Corelli,

so celebrated

now in all

Europe,

and

for several

years

so

fashionable

among

us"

("fameux

Corelli,

si célèbre maintenant

dans

l'Europe,

& si à la mode

parmi

nous

depuis quelques

années";

Saint Lambert

1707,

41).

Corelli s

music was so

popular

that

Denis Arnold

spoke

of a "Corellian

cult"

(Arnold

1978).

In

1681,

the

Pasquini pupil

George

Muffat became

personally

acquainted

with

Corelli

in

Rome. One

could

point

to

Muffat's

Regulae

oncentuum

artiturae

1699)

as

f/œ heoretical document for the modern

(Corellian)

trio-sonata

style

of

composition.

Here

composition

in

four or more

voices is

consistently

presented

as an

extension

of three-voice

composition.

Mattheson

stressed,

"If one can deal

with three

voices

properly,

singably,

and with full

sonority,

then all will

go happily

even

with

twenty-four

voices"

(1739, 344).

Even in

Joseph Riepel's

dialogues,

the

Teacher

explains

to

his Stu-

dent that one must

"patch

n"

the

fourth voice

(Riepel

1996,

571).

This

procedure

can

still be seen

clearly

n Stanislao Mattei's

our-voice

settings

of bassi

numerati

1850)

-

the

viola

part

is an

optional

filler

voice.

The

single

voice of the

thoroughbass

stood as

representative

of an

essen-

tially

three-voice,

contrapuntal

constellation

of

voices,

whose

contrapuntal

topoi

had

already

been

practiced during

instruction

in

composition.11

Given

a schematic

excerpt

of the bass

and/or

the

figures,

one

assigned

it a two-voice

accompaniment.

By

no

means could

the harmonic "content"

of a bass be

logi-

cally

derived,

as it

were,

in

the abstract from the

figures

themselves.

Thus one

knew that the two-voice

2-6-7-3

model for the

upper

voices

(bracket

"a"

in

Example

lb)

was

assigned

to a

rising

fifth with the

figures

4-3

(Example

1,

Ledbetter

1990, 12;

Fenaroli

1978,

bk.

3,

9).

Likewise,

one knew

which

upper

voices

corresponded

to the clausula of the cadenza

composta

(slur

"b"

in Exam-

ple

lb).

One

recognized larger

contexts and allocated

the

missing

voices,

but

on no account

was the

point

to be

"counting

outM

chord tones from the bass.

11

Particularly

n

recent

German music

theory,

the

discus-

sion of

compositional

models

represents

its own

strong

tradition.

In

this

regard,

Ernst

Seidel's article on the

"devil's

mill"

{Teufelsmûhle;

1969)

is

of

special

significance

(see

also

Holtmeier

2008,

s.v.

"Teufelsmûhle";

Dietrich

2007;

Yellin

1998).

Furthermore,

one

should

mention,

on

the

one

hand,

the

teaching

methods and the

less

historically

than

systematically

oriented

works of the "Berlin

school"

centered

around Hartmut

Fladt

(2005,

2007),

which found

its most

powerful

expression

in

Ulrich

Kaiser's influential

two-volume

Gehôrbildung

{Ear

Training-,

000)

and,

on

the

other

hand,

the works

developed

in

the environment of

the

so-called "historical

composition

training"

{historische

Satzlehre).

Here the

teaching

methods

and the

writings

of

Markus Jans have been

exemplary

(Jans

1987, 1993;

see

also Holtmeier

2002,

2008,

s.v.

"Satzmodelle";

Dodds

2006;

Froebe

2007;

Menke

2008;

Schwenkreis

2008).

See

also the current discussions

around these models:

Aerts

2007,

Kaiser

2007b,

and Schwab-Felisch 2007.






Ludwig

Holtmeier

~

Heinichen, Rameau,

and Italian

Thoroughbass

11

434343436

43

' I ' T

c _ T

Example

1a.

A

typical

series

of

bass tones and

figures

H T 7 p

V f

n y r

' U » r

u t

l < i

Example

1b. A

realization of the bass of

Example

1

using

preferred voice-leading

models

Toward a

history

and

theory

of the

Rule

of

the

Octave

At the

beginning

of the

eighteenth

century,

the

splitting

of

thoroughbass

into

"science"and

"practice,"along

with the "invention"of the Rule of

the Octave

around

1700,

was a

pivotal turning point

in

the

history

of both

thoroughbass

and harmonic

tonality.

It

is a still

widespread

misunderstanding

that

the Rule

of the Octave is only a "modelharmonization,"one among severalpossibilities

for

furnishing major

and minor scales with chords. But that

view

recognizes

only

the most extrinsic

aspect

of

the

Rule of the Octave and overlooks

its intrin-,

sic

significance

for

music

history

and the

history

of music

theory.

At heart the

Rule of the Octave is not

merely "pragmatic"

egerdemain

(Christensen

1993,

170)

,

but the

crucial

step

toward a theorlzation

of

thoroughbass.

It

is not

solely

a

concrete statement of

compositional

norms but

aboye

all an instrument

of

harmonic

nalysis.12

he Rule of the Octave codifies what is

generally

under-

stood

by

the terms

"major-minor onality,"

"cadential

harmony,"

or "modern

tonality."

With the Rule of the Octave

thoroughbass

becomes a

Harmonielehre

in

the modern sense. The Rule of the Octave frees

thoroughbass

from

tradi-

tional

thinking

in

terms of model-bound

(contrapuntal)

contexts,

isolates

the

individual

Klang,

and leads to a hitherto unknown verticalization

of

harmonic

discourse

the Rule of the Octave is a

theory

of harmonic

functionality.

12

Scholars did not follow

up

on Walter Heimann's remarks

on

"Rule-of-the-Octave texture"

(Oktavregelsati)

in his

splendid

study

of Bach's chorale

style

(Heimann

1973,

62f.).

Only

with

Wolfgang

Budday's

Harmomelehre Wiener Klassik.

Théorie-

Satztechnik-Werkanalyse (Harmony

in

Viennese

Classicism;

2002)

was the Rule of the Octave

brought

back

into the discourse of practical music theory. FranckThomas

Arnold's monumental

study

on

thoroughbass

from 1931

must also be mentioned

in

this context.

Arnold comes close

to

many

of the

insights

that were

presented

in

the

works of

Heimann

and

Budday.

But

his

general

historical

approach

is

underpinned by

that

tenacious

neo-Ramellianism

that was

so

typical

for his time.






12

JOURNAL

of

MUSK.

THEORY

No one more

clearly

recognized

the verticalization of

harmonic dis-

course

and more

radically

formulated it than Rameau.

If

one does a

close

reading of his Traitéde l'Harmonie 1722), then there can be no doubt that

Rameau's

theory

of the basse

ondamentale

rose

from

the

attempt

to

theoreti-

cally

pinpoint

the Rule

of

the Octave

(see

Heinichen

1728,

764).

In

the first

two books

of the

Traité,

he

develops

theoretically

what

in

the

central,

third

book he achieves

by

practical

application

in

the

example

of

the Rule of the

Octave.

That

is,

the basse

ondamentale xplains

the modus vivendi of the Rule

of the

Octave,

its

ruling principe.

The

basse

ondamentale

onstitutes the inner

"essence" of

harmony,

the

Rule of the Octave its outward

appearance.13

t is

no

doubt

correct

that,

after the

Traité,

Rameau's

music

theory

distanced itself

ever further

from its

origins

in the Rule

of the Octave.

From

the

publication

of the Nouveausystème1726) onward, Rameau's theory becomes noticeably

more abstract

and

formalistic.

The

internal

aspects

of the

theory

turn ever

more

clearly

toward

the

external.

The basse

ondamentale

ecomes the

para-

mount

principle

which

usurps

even

musical

practice.

Paradoxically,

he Rule

of

the Octave

itself

becomes,

at least

dating

from the

public argument

between

Rameau

and

Michel-Pignolet

Montéclair

in the Mercure

eFrance

Rameau

and

Montéclair

1729/30;

Christensen

1993,

56)

,

first a

counterproposal

to the basse

fondamentale,

nd

finally

the

epitome

of a

spiritless,

atheoretical

practice

pitted

against

the

lone

scientific

theory

in the form

of the

basse

ondamentale.™

One

must

always

bear

in mind

the

Janus-faced

character

of Ramellian

theory

in order

to understand

its

complex reception history.

This divides

along

two

main

paths,

which

one could

reify

and

characterize

as the

"practical"

nd

the

"speculative."

The

practical

takes

its

point

of

departure

from the

third

and

fourth

books

of

the

Traité,

n which the

Rule

of the Octave

plays

a central

role.

The

speculative

derives

from the

first two

books,

which deal

exclusively

with the

basse

ondamentale.

The

German,

and above

all the

north

German,

reception

of

Rameau

can be

predominantly

assigned

to the

speculative

path,

the

French and

Italian

reception,

save

for isolated

exceptions,

to

the

practical.

The

Viennese

tradition

of

thoroughbass

teaching

is,

as

already

mentioned,

in

the

broadest

sense

associated

with the Italian

tradition.

In the French

and Ital-

ian

school

of

teaching

composition

(and

the Viennese

school can be

regarded

as belonging to it), the basseondamentaleirmlyintegrated itself into the deep-

seated

educational

tradition

of the

Rule

of the Octave.

There the

Rule could

hold

its central

position

across

the

whole

of the

eighteenth

century

without

13 The

Rule of

the Octave

occupied

Rameau's

attention

his

whole

life. He

was

always

finding

new

interpretations

of

it

(Christensen

1993).

14 This

becomes

clear,

for

instance,

in

the

statement

by

Friedrich

Wilhelm

Marpurg

that "since

the

time of

his

[Rameau]

Traité

de

l'Harmonie,

the Testore

musico

of some-

one

likeTevo

cuts as

poor

a

figure

as,

for

example,

the

logic

of ChristianWeisen since the advent of [Christian)Wolff's

philosophy

of reason"

("seit

der

zeit seines

[Rameausl

Traité

de

l'Harmonie macht

der Testore musico

einesTevo

und

andrer eine

so schlechte

Figur,

als

etwa eine

Logik

von

Christian

Weisen,

seit die

WolfscheVernunftlehre

existiert";

Marpurg

1760,

57).

That the basse

fondamentale succeeded

to become

the

epitome

of

"modern" scientific

method

may

have been

the essential

reason behind

the

extraordinary

success

story

of Ramellian

theory.






Ludwig

Holtmeier

Heinichen, Rameau,

and

Italian

Thoroughbass

13

any

real

dispute.

On the other

hand,

already

n

the works

of

Friedrich

Wilhelm

Marpurg

and

Johann Philipp Kirnberger,

who more than

any

others

spread

Ramellian theory into German-speakinglands, the Rule of the Octave plays

only

a

marginal

role.

And

from the

early writings

of the

German Harmonie-

lehre radition

(Gottfried

Weber,

Adolf Bernhard

Marx)

it

finally

disappeared

almost

completely.

In the first half of the nineteenth

century

the Rule of the

Octave also

begins

to lose its

significance

in

France and

Italy.

Toward the end

of

the

century

it was

displaced

across

nearly

all of

Europe

by

the

modern scale-

degree

(i.e.,

Roman

numeral)

theory

of the German H

armonielehreradition

a

global

export

success.

It was

completely forgotten

that the Rule of

the Octave

had once

actually

founded the

"modern"

conception

of

tonality.

A digression on Rameau reception

The

reception

of Rameau's

eachings

wasalso

hampered

by

the

fact

that,

apart

roma

relatively

arly

ranslation

f the thirdand fourth

books nto

English

Rameau 737),

no further

ranslations

ere

published

during

the

eighteenth

and nineteenthcentu-

ries.

Rameau's

heory

came

to

Germany

rincipally

hrough

FriedrichWilhelmMar-

purg's

ranslation

f the

"theory-laden"ummary

f

Jean

Le RondD'Alembert

1757).

Yetthere

were tracesof

Italianmusic

theory

even

in

the

Prussian orth. Maximilian

von

Droste-Hûlshoff,

friendof

Haydn,brought

he

Italian radition o the district f

Munster

Droste-Hûlshoff

821;

Fellerer

1939;

Kantsteiner

974/75);

BernhardKlein

brought

he

partimento

raditionof the Paris

Conservatory

o the

Sing-Akademie

n

Ramellian erlin Eitner1882).Klein's upil, he archivistnd music heoristSiegfried

Dehn,

was a

great

connoisseur

of Italianmusic

theory.

Toward he mid-nineteenth

century,

Dehn

published

wo

notable

extbooks

n the Italian

pirit

Dehn

1840,

1859).

Characteristically,

lein

brought

down on himself

he

opposition

of the

all-powerful

Carl

Friedrich

Zelter

Eitner

1882),

and

Dehn's

harmony

ook became he

target

of a

famous

polemical

ttack

rom

Adolf

BernhardMarx

1841).

The fact that

the Rule

of the Octave was

consistently

understood as

"practice"

nd

not as

"theory"

s

based

on the nature

of

the Rule of the Octave

itself.

In contrast to

the closed

system

of Ramellian

theory,

the Rule of

the

Octave

developed

through

a

long history

and melded

together

different,

occa-

sionally divergent music-theoreticalcontents and traditions.The Rule of the

Octave

has

neither a

sole "inventor"

nor an

unambiguously

defined

form. But

one can

come

up

with three

factors that define

the nature of the Rule of the

Octave,

and which

I would like

to describe

schematically

as the

sequential,

the

cadential,

and the

systematic.

The intrinsic

multiplicity

of

the Rule

of the

Octave

even

explains

its diverse

manifestations some

emphasize

the

sequen-

tial

factor,

others

the cadential

or the

systematic.

The Rule

of the

Octave is

usually

described as

standing

in

the tradition

of

models

used

in

improvised

contrapunto

lla mente

from Guilielmus

Monachus

(1965)

to

Fray

Tomâs

de Sancta Maria

(1565)

to

Spiridionis

(1670/71/75;

Lamott

1980;

Christensen

1992;Jans 2007; Gjerdingen 2007, 467f.). Thus,






14

JOURNAL

of

MUSIC THEORY

666 66

66 6

66

Example

2. An

improvised

scale harmonization

as

precursor

to the

Rule of the Octave

the Rule of the Octavecarries orward he traditional

ategories

of intervals

and their

"dynamic" ualities.

The triad

representsperfect

consonance,

he

persistent

"cadential"

onority

of

repose,

the initialand

goal

chord

of a har-

monic

progression.

By

contrast,

he chord

of the sixth

represents

mperfect

consonance,

he

sonority

of

motion,

whichdemandsa

stepwise

ontinuation.

Therefore,the primitivemodel of the Rule of the Octavewouldinvolvea

stepwise

uccessionof chords

of the

sixth,

linking

a

perfect

consonance

on

the first

degree

to a

perfect

consonance

on the fifth

degree,

and

ultimately

o

a

perfect

consonanceon the

eighth

degree

(see

Example

2).

But the

specific

Gestaltof the Rule of the

Octavecannot

be attributed

solely

to the tradition

of

improvised

cale harmonizations.

On the

contrary,

there is an auraof

mystical

evelation

hat surrounds he

description

of the

Ruleof the Octave

n

quite

a few

early

eventeenth-century

ources.15 ne

can

still sense it

in

that

intrinsicallyGerman-language,

usic-theoretical

oncept

of the "natural cale"

(naturlicher

mbitus)

r "natural

armony"

naturliche

Harmonie)Heinichen

1728,

750

and

register

.v.

"Ambitus")"It

eems to

me

asif this harmonic calehas been

implanted

nto our ears romthebeginning

of the world"

"Mir

eucht,

es

sey

dièse harmonische

Leiterunserm

Gehôr

von

Anbeginn

der Welt

eingepflanzt"]; iepel

1996,

580),

and the

many

claims

of

priority

makeclear that the Rule's

appearance

was elt as

a remarkable

vent

and an

important

emarcation

within he histories f

composition

nd

theory.

Thatwould

hardly

equireexplanation

were t

nothing

more thana

pure

con-

tinuationof the traditional

nterval-progression

odels.

The forerunners

f

the Rule

of

the

Octave

presupposed separation

between

a

logic

of

progres-

sion tied to a model

in

the sense

of

improvisedGymel

Jans

1987)

and of

a

cadential,

punctuating

egment.

Modeland cadence

are the

central

catego-

riesof compositionalnstructionn the seventeenth entury.Tocompose,one

might

say

somewhat

implistically,

meant an

alternating

xchange

between

cadential

and

sequential

models.The second

half of the seventeenth

entury

can be describedas a

process

during

which these

sequential

and

cadential

modelscome ever closer to each other.The

Rule of the Octave

inally

melds

both factors

ogether.

15 Here one must mention

François Campion

(1716,

1730),

who claimed

for himself the

authorship

of the Rule

of the

Octave

-

an old musician

bequeathed

it to

him,

as

it

were,

on his deathbed

(Mason

1981).

This

story spread

quickly

and

remained

in

circulation for a

long

time

in northern

Europe,

particularly hrough David Kellner'sfrequently reprinted Treu-

licher Unterricht

im

General-Bass

(Kellner

1732).






Ludwig

Holtmeier

~

Heinichen, Rameau,

and Italian

Thoroughbass

15

In

the

early eighteenth

century, contemporary

writers

clearly recognized

that

the

changed

role of the "false"

diminished)

fifth and the

"major" aug-

mented) fourth was the central sign of the new harmonic language. It is also

one

of the central

theorems

of Italian music

theory

and

of

Ramellian

teaching

that

the

relationship

between the

"leading

tones" 7 and

4

forms the core of

a

theory

of

harmony.

As a matter

of

fact,

the feature

that most

clearly

differ-

entiates

the

Rule-of-the-Octave

harmony

in

the

eighteenth

and

nineteenth

centuries

from the

harmony

of the seventeenth

century

is the

compelling

assignment

of the

(dominant-function)

six-four-two

chord to the

descending

fourth

degree.16

It is

precisely

that new

role for the "false"

ifth and

"major"

fourth

that

differentiates

the

Rule of the

Octave,

in

qualitative respects,

from

all

the older

harmonization

models of the

scale.17

A

digression

on the

"false" fifth

A

remark

made

by Angelo

Berardi

in

the

context of

discussing

a resolution

of the dis-

sonant

second

into a

"false"

ifth

supports

the thesis

that the "consonant"

and free use

of

the diminished

fifth

in the modern

harmony

at the close

of the seventeenth

century

was borrowed

from

popular

music:

"Some

moderns have

resolved the

suspended

sec-

ond to

the false

fifth;

one

allows this

method of

resolution,

it

being

hard and

harsh,

only

in

popular

song

for

the

expression

of certain

words.

Thus,

one should use it

with

caution"

("Alcuni

moderni

hanno

legato

la seconda

con la

quinta

falsa:

questo

modo

di

legare,

per

essere duro

e

aspro,

si concede

solamente

nelle cantilene

volgari per

esprimere qualche parola. Si deve perciô usare con prudenza";Berardi 1687, 137).

Mattheson

grasped

the

changed

role of

the diminished

fifth

precisely

when,

in Der

volikommene

apellmeister,

e maintained

one would

have

"good

reasons"

(billige

Ursache)

for

"appending

it to

the

consonances,"

since

"itdoes far more

harmonious

service than

the

perfect

fifth"

(Mattheson

1739,

235).

At the

beginning

of the nineteenth

century,

Jerome

Joseph

de

Momigny

still

maintained

that one

had to

treat the tri one and

the

false

fifth

"as

if

they

were

consonant,

... for

thirds,

sixths,

false

fifths,

and tritones

are the

true

harmonic

intervals

that

can be used

in

two-partcomposition"

("comme

s'ils

étaient

des

consonnans,

... les

tierces,

les sixtes

et les fausses

quintes

ou tritons

sont les

vrais

ntervalles

harmoniques,

employable

dans la

composition

à deux

partie";

Momigny

1803/1806,

1:284).

Similarly,

Fétis

regarded

both

the diminished

fifth and

the

augmented

fourth

as

consonant

intervals

(Simms

1975,

122).

Nicolô

Zingarelli

16 And

likewise,

the

(dominant)

six-five chord

on the

ascend-

ing

seventh

degree.

In

terms

of historical

development,

the

fact that

(along

with the

four-two

chord on

the

descending

fourth

degree)

it concerns

a harmonic

passing-chord

phe-

nomenon

remains

evident

for a

long

time

in

the

Italian

par-

timento

tradition.

According

to Giovanni

Paisiello

(Dellaborra

2007),

the dominant

four-two

chord occurs

"when

one

descends

from

the fifth

of the

key

to the

third of

the

key"

("quando

discende dalla

Quinta

delTono allaTerza

delTono";

Paisiello

1782, 5;

Holtmeier,

Menke,

and

Diergarten

2008).

In the course

of this

development,

however,

this

passing-

chord phenomenon becomes emancipated from its origin,

and one

could thus with

equal justification

designate

the

fifth

degree

as a

"preparation"

for the

descending

fourth

degree.

17

Johann

Georg

Albrechtsberger

stresses that

there is a

"bass scale

of the old

composers"

and a "bass scale

of

the newer

composers" (Albrechtsberger

1790,

12/13).

For

the

chord on the

descending

fourth

degree,

the four-two

chord

suits the "newer"

scale

-

the modern Rule

of the

Octave,

while the

simple

six-three

chord,

which

only

serves

the distinction between

perfect

and

imperfect

triads,

suits

the older

scale.






16

JOURNAL

of

MUSIC

THEORY

opened

up

his

lessons

in

composition

with what he considered

to

be

the core rela-

tion

of

harmony.

He wrote the tritone

and the diminished

fifth

and

their

resolutions

on a piece of paper with the words:'You shall begin from the scale in two voices; and

remember,

in

harmony

the

fourth

descends,

and the seventh ascends"

(Sanguinetti

2005,

451f.).

It is not

difficult to discern

the derivation

of the

harmonic

formula for

the

descending

4-3-2-1

scale-degree progression

in

the Rule of the Octave:

its

source is the cadenza

doppia

see

Example

3)

,

which

plays

such a

prominent

role

in

the music of

the seventeenth and

eighteenth

centuries

(Gjerdingen

2007,

169).

Early-eighteenth-century

talian

thoroughbass

manuals

recognized

three

types

of

cadences,

which

were

designated

in

the

eighteenth-century parti-

mento tradition

by

the terms

semplicesimple), compostacompound)

,

and

dop-

pia

(double).18

Thus,

semplice enerally

signifies

a

simple

dominant-tonic rela-

tionship,

composta

he

classical 4-3

suspension

cadence,

and

doppia

he

"grand"

cadence with

the

consonant fourth. These cadences have not

merely

an artic-

ulating, punctuating

function,

but in

the seventeenth

century

they

become

comprehensive

compositional

models

that

pervade

entire

compositions.

It

is

crucial

to

note

that

these cadences

are

contrapuntal

models. At its

core,

each

cadence consists of

three

voices,

which

relate to each other

in

triple

counter-

point:

although

the

unfigured

bass

clausula

of the

cadenza

doppia(Example

3a)

can

only

be set over a

soprano

clausula,

not over the tenor

clausula,

some

other standardizedfigurations (c-f ) even permit the laterarrangement.19

Underlying

the

Rule of the

Octave

is

less a collection of

interval-progres-

sion

models and

more a

Durchkadenzierungthorough

cadentializing)

of the

scale

by

means of

these

contrapuntal

cadence models

-

above all the cadenza

doppia.

Starting

points

for

the

emergence

of the Rule of

the Octave

might

be

phrases

"in

the

style

of

Corelli,"

as in

Example

4.

In

Example

4a,

the slurs

mark the

doppia

ersions

of tenor

clausulae,

the

brackets mark

the

doppia

ersions of

soprano

clausulae

(see

also

Example

4b),

and the

wavy

ine

designates

the

figuration

of a

doppia

bass

clausula. One can

easily

clarify

the

derivation

of

the Rule of

the

Octave from

the modern Italian

18 See

Gjerdingen

2007,

141

f. A

historical

investigation

of

this

concept

is a

topic

of

current

scholarship

and

would

exceed the

limits of

this

essay.

The term

doppia

and the

quasi-standardized

use of

the

conceptual

triad

of

semplice,

composta,

and

doppia

is a

relatively

late feature of

Italian

music

theory.

Also,

the

terms are

hardly

used

in

a

consis-

tent

way.

Even in

the

late

eighteenth

century,

depending

on

the

author,

the

terms

may

overlap

in

content,

espe-

cially

with

semplice

and

composta.

In

earlier

sources

the

doppia

cadence

is

designated

by

a

multiplicity

of

terms

like

cadenza

major, gro&e

Cadenz,

grande

cadence,

great

cadence

(Godfrey

Keller),

gantze

Cadenz

or

cadentia

maior

perfectis (Muffat),and so forth. Even later- despite a clearly

perceptible process

of

standardization the

terminology

is

by

no

means

consistent.

Similarly

ambiguous

are the

deriva-

tion

and

meaning

of the

term

doppia

(double).

On the one

hand,

it

can refer

to the

(metrical)

breadth of the

cadence,

and on

the other

hand,

to the

combination of

semplice

and

composta

into one

"doubled"

cadence.

19

The fifth

scale

degree thereby

becomes a

superjectio

of

the

fourth

degree.

The bass

clausula

thus

actually

becomes

a

variant

in

double

counterpoint

of

the alto

clausula. This

quasi

identity

between

figurations

of bass and alto

clausulae

is an

essential

element of

innumerable

contrapuntal

designs

in

the

music

of the

seventeenth and

eighteenth

centuries.






Ludwig

Holtmeier

~

Heinichen,

Rameau,

and Italian

Thoroughbass

17

(a) (b) (c)

(d)

(e)

(f)

I*

==r

rHJ

r

fJ liK Jh' flr^rll1

i r =t=

|J-J,Jlj Fr^rlf1

i r *=

|j;J,

r

J|-jII

==r i r 1

r

|-

--f

ri r =t=

rrrr

f

- ri r *=

^r

rr

-f

\-}; " N

Trrr

I>J

rJrrM Tr

r

'iJ I

r

r

r

rI

J

Tr

r

I>J

Example

3. The cadenza

doppia

as a model of

triple counterpoint

(a)

l

|

k , i ,

j|| lrrnTrrr_

rfT]^^

666 754 3

46716

676

5 2

(b)

.OjJjjJ^ijjl

ill

I.

b : "

1 ^

? \ f

I r r

^ ^

Example

4.

The Rule of the

Octave

in

the

style

of Corelli

"tonality"f the Corelli-stylerio-sonataormat f one makesa "reduction"f

Example

4a.20

o

that

end,

one firstremovesall the

suspension

igures,.

hat

includes he 7-6

suspensions

n mm.

4

and

5,

the 4-3

suspension

n the third

measure,

nd even the 7-5

progression

n

thatsame

bar,

which

s

actually nly

an "elision" f

a 7-6-5-4-3

progression.

n

this

form the

progression

also

appears

n the

then-currentmodel-based

hrases

hown n

Example

5. If one

20

In

the

early

eighteenth

century,

this kind of

dissonance

reduction is a

common

procedure

in

thoroughbass peda-

gogy.

In

particular,

see Michel de Saint Lambert 1707 and

Godfrey

Keller 1707.






18

JOURNAL

of

MUSIC

THEORY

^

^^F= ^r

^ i p

W [r

n r

I f

765

43

765 43 765 43

Example

5. The

7-6-5-4-3 model

^ f

F r T M r H ^

f e

f l

r _ x

r T 7 ^ J

666

66

616

466

5

5

2

Example

6. The

classical Rule of

the

Octave:

reduction

of

Example

4a

now

retaining

his

organizing

principle

also

begins

the

descending

scale

witha

perfect

consonance,

here

emerges

he classical ormof the Ruleof the

Octave

Example

6).

It

becomes clear

during

this

process

of

derivationwhat s

really

revolu-

tionary

about the

Rule of the Octave:

he

derhythmization

f the

cadence,

the

decoupling

of

dissonance from

ligatura,

rom

syncopatio.

n

short,

the

breakup

of

the traditional

adential

nterrelationships.

nly

the dissolution

of

the "bonds"

ties)

in

the

clausulae

rees the

Klang.21

his

emancipation

f

individual

onorities

nevitably

ccompanies far-rangingoosening

of

super-

ordinate

rhythmic

nd

linear

relationships.

Thus,

in

the context

of

the

dop-

piatenorclausula, he thirdscaledegreein the bassactuallybecomesonlya

"passing

hord"on a

weak

beat,

carrierof a consonant

preparation

or the

following

dissonant enor

clausula

Example

7a).

The

principle

of the

step-

wise

progression

solates

he sonorities

and

permits

a

largelyderhythmicized

"binary

elationship"

f chords to

replace

the three-and four-notecontexts

21

Nowhere can

one more

clearly

discern the

factor

of

abstraction,

the

"material character"

of the Rule of

the

Octave,

than

in

this

process.

Here too lies

the crucial differ-

ence

between the

sequential

and cadential

models,

which

as concrete

compositional

building

blocks

can

be,

as it

were,

directly

adopted

and

employed

in

compositional

prac-

tice. The

Rule of the

Octave,

by

contrast,

always requires

positioning

within the

rhythmic

design.






Ludwig

Holtmeier

~

Heinichen, Rameau,

and Italian

Thoroughbass

19

(a)

(b)

é i

|h

id

j

6 6

6 6

( b - f

^ i

|f

® ® ® ®

® ®

"

® ®

Example

7

of the clausulae

Example

7b).

Thus,

the third

degree

takeson a

sonority

n

its ownright.

It is

particularly

ere

in

the Ruleof the

Octave hatone

finds"old"nter-

val

progressions

nd the "new"

Corelli-style

adential

harmony

n

a

relation-

ship

of

dialectical ension.As a chord of

motion,

the

imperfect

consonance

on the third

scale

degree

leadsacross he

imperfect

econd

degree

to

resting

point

on the

perfect

first

degree

(Example

7a)

Yetas a more

"emancipated"

component

of

the cadenza

oppia,

he chord of the sixth s a

goal

and

point

of

resolution or the

dissonant ix-four-twohord on the fourth

degree,

which

precedes

t

(Example

b)

It is thus

ust

as mucha chordof

repose.

The cadenza

doppia

arries he factorof

harmonic ensionand relaxation nto the

old

pro-

gression

model. This is

exactly

where Rameaus

theorybegins

the model

of

tension and relaxationbecomes the central eatureof his basseondamentale.

Consonance

and dissonanceassume he

place

held

by perfect

and

imperfect

consonance n the music

heory

of

the seventeenth

entury.

Dissonance

akes

over he

functionof

imperfect

onsonance.

Harmonicmovement s

no

longer

the

progression,by

means

of a

multiplicity

f

imperfect

consonances,

rom

an

opening perfect

consonance

through

a series of intermediatecaesura-

like

perfect

consonances o a

closing perfect

consonance

(the

so-called

pip-

principle; ans

1987).

Now harmonic

movement s a routine

consequence

of

dissonanceand

consonance,

of tension and relaxation

(Christensen

1993,

120f.).22

or

Rameau,

he

juxtaposition

of

doppia

lausulae

n

the

Rule of the

Octavebecomes a routineconsequenceof two-stage adencesarfaites. he

close

dependence

developedby

Rameaus basse

ondamentale

n the cadential

harmony

f the Rule of

the Octavebecomesclear f one sets belowthe

doppia

cadencesof

Example

4a a bass

voice without

iguration Example

a

gives

wo

alternative

ersions)

and then

compares

his

supporting

"fundamental

oice"

22 Or

the connection of two consonances

by

a

chain

of dis-

sonances. Thomas Christensen

points

out that for Rameau

"every

non-tonic

scale

degree

carries a seventh chord"

(1993,

129).






20

JOURNAL

of

MUSIC THEORY

(a)

rfbjp^J

w ^ = ^

J J ft J J , J Jm_J J J ... ,

w ^ = ^

,

s p F ^

y

« =

,>>'.V_[J

j |j

J

I

o

|o

|..

;

(b)

gÉÊÉgÉ

Biffe-ContftJS" tf 6 A 7

&-f-è^ A I

^T^^^|'^V-l^^U^r-4«^-T-

Domini-*

e

pNo«Ti__.

«

^-^.t

T™' I"

None

toniqti

HlWf,

f-He.«*jwMo«t-*

»»»»"

-

t»NotM.->

ianbU' «^

i

.

\,

,

^~-t^»

r#»

majeur

\)t.

BASSE-FONDAMENTALE,

^

1

7

777747.

Example

8. Rameau's

interpretation

of the Rule of the

Octave






Ludwig

Holtmeier

~

Heinichen, Rameau,

and Italian

Thoroughbass

21

6 6

5 6

6 5

6»

6

?o .. o » ;>°

»

°

°

|

[7]

I

2 3 7 I

2

[7]

|

|

Example

9.

"Implicit"

harmonic structure of Rameau's

ascending

Rule of the Octave

with the basse

ondamentale

Example

8b)

that Rameau

provided

for

the

Rule

of

the Octave

(Rameau

1722,

382).

Even Rameau's basseondamentale ses only the tones of the doppiabass

clausulae:

C, G,

and D.23

One

clearly recognizes,

however,

the differences.

Rameau

applies,

as it

were,

the same

model to the succession

of

the

descend-

ing

scale as to the

ascending

scale.

Thus,

in

the

descending

scale,

the fifth

degree

is

treated

like a

first

degree

(as

a notte

onique)

and the

leading

tone

(

notte

ensible)

s treated

like

a

third

degree

( mediante)

These

degrees

are thus

interpreted

as if

ascending:

for

Rameau,

the schematic

progression

in

Exam-

ple

9

implicitly

underlies the

ascending

scale

(Rameau

1722,

208).

The diatonic

arrangement

of the mode

prohibits

the

leading

tone to the

fifth

degree

from

actually

sounding

(Rameau

conceives the fifth

degree

comme

une notte

onique)

Rameau

1722,

213).

Yet

regarded

functionally,

the

progres-

sion of the

leading

tone to the tonic

{notte

ensible o notte

onique)

s identical

to

that of the fourth

degree

to the dominant

(quatrième

o

dominante) Rameau

1722,

208).

At the end of

Rameau's

ascending

scale

(Example

8b)

a

scarcely

motivated,

apparent

leap

from

the

leading

tone to the fifth

degree

owes its

existence to

Rameau's

logic

of

progressions.

It clarifies the dual

function of

the seventh

scale

degree,

which must at

the same time

support

an

inversion

of a

perfect

triad

(parfait)

and a seventh chord

(Vaccord

e la

septième).

On the

one

hand,

it is a mediante f

a "tonicized"dominant

accordingly

ushered

in

by

its own dominant

(D3

in

the basse

ondamentale

f

Example

8b) (Rameau

1722,

211).

On the other

hand,

it

really

is the notte

ensible,

bliged

to lead

into

the

tonic and to support a (dominant) six-five chord (l'accordde lafausse quinte).

One can

clearly

detect these

changes

of

function from the basse

ondamentale.

The basse

ondamentale

nder the

leading

tone

(G3)

does not bear

the

signa-

ture of a seventh

chord,

because the

sounding

dissonance of the six-fivechord

on this

seventh scale

degree

is

just

an

apparent

one.

In

its true essence

this

dissonance is a

parfait

n

first-inversionform.

Only

with the next chord

does

the fundamental seventh chord

become "material" nd resolve itself

properly.

23

The much discussed

problem

area of the double

emploi

(see

Example

8b,

m.

3)

lies outside the

scope

of this

essay.






22

JOURNAL

of

MUSIC THEORY

That the seventh

of the basse

ondamentale

under the sixth scale

degree

(C

above

D),

which

performs

the function

of

a dominant

to

the medianteoî the

tonicized dominant, is not resolving correctly but ascends to the D, justifies

Rameau

in the

prohibition

of

doubling

the

leading

tone

(B),

which a

proper

resolution

of

that

dissonant

seventh would

violate

(Rameau

1722, 213;

see also

Rousseau

1768).

So

just

as

that six-five

chord over the seventh scale

degree

is

actually

a

perfect

triad,

then

conversely

the

six chord over the sixth scale

degree

is

actually,

n a functional

sense,

a

dissonant seventh chord.

Already

we can

clearly

make out that

tendency

toward

ormalistic abstrac-

tion

and

esprit

u

système

hat

in

the late

writings

of Rameau often

takes on such

abstruse

manifestations.24

n the

Traité,

however,

Rameau

s

complex

opera-

tions

still

have

a

recognizable

basis

in

experience

and

in the musical features

themselves.The thesis that the fundamental principle of modern (Rule of the

Octave)

harmony

was the

dogmatization

of the

cadence,

understood

as the

transition

from

a dissonant

sonority

to

a consonant

one

(and

vice

versa)

actu-

ally grasps

an

essential

aspect

of the

new chordal

basis of

composition

in

the

style

of Corelli's

trio

sonatas.

But

one can

also

clearly

distinguish

in

Rameau

s

basse

ondamentale

he

difficulties

and

problems

of

a one-dimensional

system-

ization

of

the

Rule

of the

Octave.

In concert

with

his

theory

of

inversion,

Rameau

s consonance-dissonance

dichotomy

eliminates

the

concept

of

imper-

fect

consonance.

It

may

still

be

present

as a

phenomenon

in

compositional

technique,

but

as a

music-theoretical

category

it

disappears

completely.25

The

consequences

are

far

reaching.

As

imperfect

consonances

merge

with

perfect

consonances

in the

concept

of

chord,

the

concept

of harmonic

movement

is

tied

exclusively

to dissonance.

Beyond

dissonance,

Rameau

s

system

reaches

an

impasse.

Thus

it

is

literally

impossible

for

two

accords

arfaits

(each

with

a

different

basse

ondamentale)

o

follow

one

another.

At their

core,

the

labored

constructions

of the

cadence

rregulière

sixte

ajoutée),

he later

sous-dominante,

and

the

infamous

double

mploi

nly

serve

the

purpose

of

maintaining

the

rigid

logic

of

progression,

which

enforces

the exclusion

of

imperfect

consonances

and

the

dogmatization

of dissonance.

Rameau

s

music

theory

does

not

engage

the

dialectical

tension

between

the

old interval

progressions

and

the

"new"

cadential

harmony

of

the

Corelli

style,

which

was

worked

out as

a central

fac-

tor in the Ruleof the Octave.Witha revolutionarygesture he simplywiped the

centuries-old

and

autonomous

theory

of

intervallic

qualities

off the

table.

Toward

an

"Italian"

concept

of

chord

No

music-theoretical

theorem

of the

eighteenth

century

did

more

to

imple-

ment

a

break

with

tradition

than

Rameau's

theory

of renversement

"inversion"

24

In

the

Traité,

Rameau

himself

points

repeatedly

to the

fact that

the

basse

fondamentale

is "of

little use

in

practical

music"

(inutile

à la

pratique;

Rameau

1722,

381).

25

Christensen

refers

to the difference

between

a

concept

of

inversion

based

on

"inversional

derivation,"

which

was

already

common

before

Rameau,

and

one based

on

this

new "inversional equivalence" (1993, 70f.).






Ludwig

Holtmeier

~

Heinichen, Rameau,

and

Italian

Thoroughbass

23

sealed

the fate of the

old intervallic

qualities.

No other

concept

of Ramel-

lian

theory

would have

a

comparably

wide diffusion. Even

traditions of music-

theory teaching that took themselves to be anti-Rameau and rejected in par-

ticular

his

theory

of

chord

progression26

nevertheless

adopted

as self-evident

the

concept

of inversion.

By

the end

of

the

eighteenth century

it

had

already

gained

acceptance

across

all of

Europe,

and

by

the middle of the nineteenth

century

it

finally

achieved

a

position

where it had almost no

competition.

Even

today,

it still

holds

sway

so

naturally,

so

unchallenged

that it is worth-

while

drawing

attention

to what a radical break it once

represented

from

a centuries-old

tradition.

According

to

Rameau,

a chord of the sixth is no

longer

an

independent

sonority

in its own

right,

but becomes a "derivative"

chord,

an

"inversion"

of a "fundamental"

triad. The old

pivotal

distinction

between fifth and sixth, between a sonority of rest and one of motion, was

not

only completely

leveled,

but

perfect

and

imperfect

consonances

became,

in Rameau's

thoughts

on

inversion,

nearly

"identical."His new

principle

of

the

stacking

of

thirds

takes the

place

of the old

intervallic

qualities.

From it

Rameau

derives

both

of

his

"root

chords": the

triad

{parfait)

and the seventh

chord

(dominante-tonique).

e even

bases the essential

opposition

between

consonant

and

dissonant

chords

between

consonance and dissonance

-

on

his

principle

of the

stacking

of thirds.

The

partisans

and

interpreters

of Rameau

have

always

nvoked the idea

that

his

theory

was the

first to

actually

develop

a

precise

concept

of harmonic

dynamism (Christensen 1993, 132).

That would be

correct

if

one

has in mind

his

attempt

to trace

harmonic

process

back to

the "basic units"

of tension

and

release,

to

the dominant-to-tonic

progression,

and

his efforts

to

develop

a

holistic

concept

of

harmonic

space.

Yet one could

as

easily argue

the

oppo-

site

that

in its schematized

ideas of

inversion and

the

stacking

of

thirds,

Rameau's

theory

leads

to

a

complete

antidynamic

enervation of harmonic

process.

For

ust

as

the difference

between

perfect

and

imperfect

consonance

vanishes,

so does

any

factor

of

linearity

in the

concept

of

chord.27

One

can

unproblematically

ascribe the

sonorities

of the Rule of the

Octave

to a

series of

cadences

arfaites

on the notes

of the basse

ondamentale

as

long

as

it behaves

like

forms of

cadenzedi

grado,

thus as

long

as there is a

soprano or tenor clausula in the bass.The fifth degree of the ascending Rule

of the

Octave

as

the

penultimate

tone

in

a

bass clausula

properly requires

a

leap

and

so becomes

a

problematic

case

for Ramellian

theory,

a

problem

whose

elaborate

solution

has been

discussed

in detail above.

26

In

the

eighteenth

century,

Rameau's

theory

of chord

progressions

-

the actual

heart

of his

theory

-

only plays

a

subordinate

role,

and even

German

scale-degree

theory

of

the

early

nineteenth

century only marginally

takes

up

this

aspect

of it.

Only

with the

"neo-Ramellian

turn" of funda-

mental

bass

in Vienna

(Sechter)

and of

functions

theory

in

Leipzig (Hauptman) does Rameau's theory of progression

finally

become

relevant

for musical

practice.

27 In

the

early

twentieth

century,

it was Heinrich Schenker

who time

and

again

pointed

out Rameau's

"overemphasis

on

the

vertical"

(1930,

11).

As

much

as he was

unconsciously

bound to

an

understanding

of

tonality

that was Ramellian

at

its

core,

it is his

undisputed

historical achievement to have

highlighted

the

significance

of the

compositional

framework

and its figuration for "classical" tonality.






24

JOURNAL

of

MUSIC

THEORY

(a)

(b)

(c)

(d)

p

\t

1 1 1

l i

i i

I f L M I

7 6

6

5

Example

10

The cadential effect of the fifth degree is actuallysuperior in the Rule of

the

Octave,

even if in

a

sense

different

from

the one

Rameau

thought

of.

The

triad

(Example

10a),

but

especially

the

seventh

chord

(Example

10b),

on

the

fifth

degree

almost

compels

a

cadential

resolution,

thus

a

drop

of a

fifth or

third

following

it.

The

example

makes it

clear

that

in

the Rule of

the

Octave,

degrees

6

and 7

following

the

dominant

(Example

lOd)

should

be

understood

as

merely

a

stepwise

filling

out of

the

ascending

cadential

leap

of

a

fourth,

and

are

treated

as

"passing

chords"

(Schulz

[Kirnberger]

1773,

36).

If

one consid-

ers m.

2

in

Example

4a,

one will

see

that the

rising

scalar

passage

from

D3 to

G3 in

the bass

actually

presents

the

figuration

of a

doppia

bass

clausula.

One

can

glean

from

this

and other

examples

that

Rameau s

interpretation

of the

Rule

of

the

Octave is

doomed to

failure

because

it does

not

respect

the func-

tional

differences

and

the

functional

variability

of

the

individual

degrees

and

their

sonorities. For

Rameau,

cadenze

doppie,

cadenze

emplici,

passing

chords,

chords

resulting

from

figurations

in

short,

everything

must conform

to the

unitary

mechanism of

the

consonance-dissonance

succession of

the

cadence

parfaite.

To

be

sure,

the

Rule of

the

Octave

also

isolates

individual sonori-

ties from

their

originally

linear

contexts.

Nonetheless,

one

can still

document

within

it a

contrapuntal

provenance

from

three-voice

compositional

and

cadential

models. In

Rameau's

theory

of

chords,

however,

chordal

sonorities

become

radically

equalized.

Chordal

relationships

that extend

beyond

the

simple two-stageprogression from consonance to dissonance fall completely

outside

the

system.

The

functional

variability

of

chordal

scale

degrees

(Stuferi)

an be

clearly

demonstrated

by

the

chord

of

the sixth on

the

third

degree,

one of

the out-

wardly

most

stable

harmonic

constellations

within

the Rule of

the

Octave

(Example

11).

On

the

one

hand,

the

chord of the

sixth on

the third

degree

can

essentially

serve,

in

Rameau's

sense,

the

function of

a tonic

chord

in

inver-

sion

(Example

lia).

But

given

its

placement

on

a

mi-degree,

it can also

be

part

of a

cadenza

emplice

nd

exercise

the

function of

a "local"

dominant to the

fourth

degree,

which in

turn

will

be

treated

like a

Mitteltonika

Riepel

1996,






Ludwig

Holtmeier

~

Heinichen, Rameau,

and Italian

Thoroughbass

25

(a) (b) (c)

p

|H^

' ^ i ' f

m

6 6 6 6

6

4

3

5

Example

11.

The

multifunctionality

of the

sixth

chord on the

third

scale

degree

585) (Example ib). Moreover,t is alsofrequently artof a dominantprepa-

ration,

one that

prepares

he dissonant ix-five hord on the fourth

degree

(Example

ie).

Such fine differentiationsind no resonance

n

the

mechanism

of the

basse

ondamentale.

ence,

the

vanishing

of the distinctionbetween

perfect

and

imperfect

consonance

ultimately

eads to an

impoverishment

n the con-

cept

of

harmonic

unctionality.

Given he

disappearance

f all linear

factors,

harmonic

dynamism

ppears

n

the

form of a

monotonous,

basically

undy-

namic"

ogic

of

progressions.

Johann David Heinichen and the

systematization

of the

Rule of the Octave

To

speak

of a

concept

of chord in the

Italian

horoughbass

radition

raises

its own

problems.

On the one

hand,

the notion is

hardly

more

than a

rough

summary

f

certain raditions f

instruction,

which each

ought

to be

histori-

cally

and

geographically

ifferentiated. he reader

may

have

noted withsome

confusion that the

partimento

radition,

he Italian

horoughbass

radition,

and the Rule of the Octaveare not

clearly

et

apart

rom one another

n this

text.

In

fact,

it is

scarcely

possible

o drawclear boundariesbetween

hem.

If

one refers o

partimenti

s the didactical

horoughbass

xercises

hemselves,

it isnotdifficult o showa continuous raditional ontextthroughoutEurope,

extending

ar nto the twentieth

entury,

n which he difference

between

tal-

ian, French,

or

even German

heoretical

pproaches,

etween he

Ruleof the

Octave,

basse

ondamentale,

r

scale-degree

Roman-numeral)

heory

(Stufen-

theorie)

re of

secondary

ignificance.

f one takes

partimenti

as

a didactic

tradition,however,

n

whichthe

accompaniment

f

unfigured

basses

s of fun-

damental

mportance,

hen

"partimento"

lso containsa theoretical

pproach

that is

inseparably

ied to

the

principles

of the Rule

of the Octave

and the

compositional

models.

If I

referhere also to an Italian

horoughbass

radition,

it is

becausethis theoretical

approach

s not bound to the didacticism

f the






26

JOURNAL

of

MUSIC

THEORY

partimenti,

even

if

it

developed

from them.

Many

schools of

thoroughbass

are

certainly

in

the

partimento

tradition,

even if

they

do not

make use of actual

partimenti (e.g., Kellner 1732). What they have in common is the central

concept

of the Rule

of the Octave.

On the other

hand,

as

already pointed

out,

there was no

explicitly

articu-

lated

theory

and

comprehension

of chord

that,

in the

sense

that one

might

contrast "Italian

music

theory

versus

French music

theory,"

one could set

in

opposition

to

the Ramellian basse

ondamentale.

he

singular

and indeed

puz-

zling

success

of Ramellian

theory

can

substantially

be

attributed

to the fact

that Rameau

never

fledged

a real theoretical

opponent,

someone who could

have

confronted

his basse

ondamentale

ith a

competing concept.

Thus,

in

the

course

of the

eighteenth

century

the

Rule of the Octave took

on

ever

more

clearly the role of conservative,"old Catholic,"and pretheoretical teachings

that shut

themselves

off from

contemporary

Enlightenment

innovations,

even

before

their subversive

progressive

potential,

the basis for Rameau's

own basse

fondamentale,

ould

have

penetrated

at all into

the

general

consciousness.

It would

be

incorrect,

however,

to

state

absolutely

that

no

theoretical

counterproposals

to

Rameau

came

forward.

The

attempts

made

seem to have

found

neither

the

language

nor the

form of

presentation

that would have

been

recognized

as

"theoretical"

n

the

discourse

of the

early Enlightenment,

nor did

they

develop

in a sociocultural

environment

that

would have facili-

tated

a

broad

European

impact

transcending

their

narrower

regional

and

lin-

guistic borders.28

If one

wished

to

nominate

one such

counterproposal

to

Rameau's

the-

ory,

then

first and

foremost

the

monumental

second

edition

(1728)

of

Johann

David

Heinichen's

Der

General-Bass

n der

Composition

(Thoroughbass

n

Composi-

tion)

comes

to

mind. The

second

part

of this

work,

"On

the

Complete

Sci-

ence

of

Thoroughbass"

("Von

der vollkommenen

Wissenschaft

des

General-

Basses"),

explicitly

represents

the

unique

attempt

of its

time to

systematize

and

theoretically

substantiate

the

music

theory

of the Italian

partimento

tradi-

tion

(Horn

2000).

No other

eighteenth-century

author

made the

Rule of the

Octave

the

basis

of

his

theory

to such

a

degree

(Horn

2001,

2002).

A

digression

on

Heinichen

The

modern

functionality

of the

Rule

of the

Octave,

which

Heinichen

develops

in his

thoroughbass

treatise

of

1728,

stands

at

the

top

of a

hierarchy.

The

"natural" armonies

of

unfigured

basses

"permit

themselves

to be discovered

in three

ways**

Heinichen

1728,726-27):

28 Heinichen's

work

was therefore

unable to find

an interna-

tional

audience

because

German,

in contrast to French and

Italian,

was not a

"European"

cultural

language.

His influ-

ence on

composition teaching

in

German

was,

however,

considerable.

See,

for

instance,

Carl

Philipp

Emanuel Bach's

very similar concept of chord (C. R E. Bach, 1753/62).






Ludwig

Holtmeier

~

Heinichen, Rameau,

and

Italian

Thoroughbass

27

I. From the vocal or instrumental voice written over

the bass.

II. From some

easy general

rules,

or

from characteristic

intervals of the

modes.

II.

From

some

special

rules,

or

from

the

ambitus of the

modes themselves.

On

the one

hand,

this acts

like a

systematic

hierarchy.

In

order "to

guess

at"

(erraten;

Heinichen

1728,

731)

the

missing

voices from the intervallic

relationships

between the

upper

and lower

voices,

only

a

knowledge

and

mechanical

application

of chord

theory

is

required.

To move to the second hierarchical

level

where one

applies "general

rules,"

however,

already

calls for a

clearly higher understanding

and level

of

knowledge.

Here

"general

rules"

mean the old

Klangschrittregeln

rules

for chord

progressions)

derived

from the

tabulanaturalis.

Hardly any

treatise of the seventeenth and

early eighteenth

centuries

lacks these rules

for standardized chord

combinations,

for

example,

1. The 5th [scale degree] in the majorand minor modes naturally has a major

3rd

above

itself,

and in the

system

of modes it

may

or

may

not be notated.

2.

The

4th

[scale

degree]

in the minor modes

naturally

has

a minor 3rd above

itself,

and

in the

system

of

modes it

may

or

may

not be notated. 3. The semitone

[lead-

ing

tone]

beneath

the

major

and minor

mode,

by

which one

modulates,

natu-

rally

has a "6"over itself.

. . .

(Heinichen

1728,

739)

"He who

acquaints

himself with these

general

rules,"

continues

Heinichen,

"will fre-

quently

acquire

great

facility

in the

practice

of an

unfigured thoroughbass"

(738).

Attaining

the

highest

hierarchical

level, however,

requires

"the solid

understanding

of

the musical

ambitus"

(731)

-

by

this

is meant

nothing

else than the Rule of the Octave.

It is "the

main source from

which

flow the aforesaid

general

rules"

(738).

The

Klang-

schrittregelnive rules for chord progressions, but they are based on a mere intervallic

relationship.

Only

the Rule

of the Octave

gives

a

precise place

to those free intervallic

relations

in the harmonic

space

of the scale.

It is obvious

that this

hierarchical

order of

precedence

is

also a didactic order

("the

easiest

comes

first";

Heinichen

1728,

727).

That Heinichen 's course of

study

begins

quite

traditionally

with

chord

theory

and then

leaves

Klangschrittregeln

o follow

means

that it

represents,

at

the same

time,

a historical

order of

precedence. Klangschrit-

tegeln, specially

as

explicated

in

the German

tradition

(compare,

e.g.,

the treatises of

Matthâus

Gugl

1719 and

Johann Baptist

Samber

1704,

1707)

is,

as it

were,

a histori-

cal

prehistory

(Christensen

1992,

113),

now

surpassed

and nullified

by

the new func-

tionality

of the

Rule of the Octave.

One can

perceive

the same

relationship

between

Heinichen's later treatise and his own earlier one (1711; see Gjerdingen 2007, 15-16).

Although

in

1728

Heinichen asserts

that he had

already

explicated

the Rule of the

Octave

"in the

year

1710

during

the

preparation

of

my

old edition of this treatise"

(763),

that

is not

really

the case.

Had his

1711

Klangschrittequence

extended across

all

eight

tones

of the

scale,

it would take

on

just

as little of

the

obligatory

form of

the

Rule

of the Octave

as

with the treatises

of

Samber,

Gugl,

and

Spiridionis

a

qualitative

difference

exists

between

the

Klangschrittregeln

nd the Rule

of the Octave

(Gjerdingen

2007,

15-16).

Rameau's

schematized

thoughts

on inversion and the

stacking

of thirds

break

with

a further core

aspect

of the traditions of

music

theory

and the his-

tory of composition: one of the oldest elements in European compositional






28

JOURNAL

of

MUSIC THEORY

Schemata

Modorum,

4

Example 12. Heinichen's Schema (Rule of the Octave)

teaching

is

the distinction

between

step

and

leap.

The notion that

stepwise

progression

is,

as

it

were,

the

prototype

of

all harmonic and melodic motion

hearkens back to a

centuries-old tradition.

Thus,

in a sense the

leap

is the

exception

to

the norm of

regular stepwise

motion.

In

Rameau s music

theory,

based on the

prototypical

falling

fifth of the cadence

arfaite,

he

leap

not

only

takes the

place

hierarchically

of the

step progression,

but

the

step progres-

sion,

as an

independent

music-theoretical

category,

became

completely

mean-

ingless:

in Rameau s

theory every step

is based on a

leap.

Heinichen's music

theory,

as we will

see,

retains the old distinction between

gradus

and saltus

(step

and

leap).

If

the Rule

of the Octave is to

become the basis

of a

music-theoretical

sys-

tem,

then

two central

questions

must be answered:

(1)

what

happens

when

the

bass moves

by leap,

and

(2)

how

does

one

explain

and

categorize

sonorities

that

do

not

reside

in

the model

of the classic Rule

of

the Octave? The Rule of

the

Octave must

become both

a

comprehensive theory

of chord

progression

and a

theory

of the

chord

morphology.

Example

12

shows Heinichen's version of

the Rule

of the

Octave.

Though

Heinichen also

understands the Rule of the

Octave

as a

practical

aid to

impro-

visation, it is primarilythe representation of a harmonic systemin itself: it rep-

resents a

comprehensive

"schema."

The

systematic

character

of

Heinichen's

Rule

of

the Octave is

immediately

apparent,

for

it

differs

conspicuously

from

its

Italian and French

precursors.

Aside from

the

obligatory passing

six-four-

two chord on

the fourth scale

degree,

Heinichen does not

present

any

(disso-

nant)

four-note chords-

only

the

"pure"perfect

(vollkommene)

nd

imperfect

(unvottkommene)

hords. The

absence of the six-five chord on the ascend-

ing

fourth scale

degree

(l'accord

de la

grande

sixte)

is

especially conspicuous.

"Through

a

complete

omission of certain

figures"

("durch

gânzliche Hinweg-

lassung einiger

Ziffern";

Heinichen

1728,

765),

Heinichen here establishes

something like a "PrimaryRule of the Octave"made up of the most simple






Ludwig

Holtmeier

~

Heinichen, Rameau,

and

Italian

Thoroughbass

29

«

4

4

Example

13.

Gasparini's

Rule of

the Octave after Heinichen

chordal elements:

as

in

a

modular

system,

all

more

complex

and dissonant

variants

an be derived

rom

this

prototype,

s I show

ateron.

The form

of

representation

s also

noteworthy:

Heinichen

s Rule

of the

Octavedoes

not move

through

the

entire

octave,

as is the

case

with Rameau

and

n

many

ources

romthe Italian

partimento

radition;

nstead,

his schema

ends on the sixth

scale

degree

and then

changes

direction.

The

similarity

o

Francesco

Gasparini's

ersion

of the

Ruleof the Octave

s

deceptive,

however,

for

Gasparini

irecdy

ollowshis Rule

of the Octave

n

major

with

a harmo-

nization

of the

descending

scale

degrees

8-7-6-5,

in

order

to

make it

clear

thaton the

descending

ixth

degree

the

chord

withthe

major

ixth

should

be

placed(Example13) 29

For

Heinichen,

this

is

unacceptable:

he stresses

hat

he "omitted

he

major

ixth

over the sixth

scale

degree

because

t

adds

a new

It

hat

does

not

belong

to the mode"

"die

6.

maj.

uber

die 6ta

modi

maj.

deswegengar

wegge-

lassen,

weilsie ein

neues

I

angiebet,

welches

gar

nicht

zu dem

Modo

gehôret";

1728,

765).

He considers

what

Gasparini

oes

"already

alf a

cadence

and a

digression

nto

D

major"

"schon

eine

halbe Cadenz

und

Ausschweifung

n

das

D.dur";

65).

For

Heinichen,

however,

he

unity

of the

mode

is an

ines-

capableprerequisite

f the

"schema,"

f the

"naturliche

Ambitus."

hus,

he

lets

his Rule of the

Octaveascend to

the sixth scale

degree

in

order to

make

it particularlylear thatits functiondoes not fundamentallyhangewhether

its motion s

ascending

or

descending.

The

fact that

he retains

he traditional

representation

f the

modes,

and

first lets his

notte

onique

escend

to

the

leading

tone,

also stems

from this strict

understanding

f

mode:

being

the

29

Gasparini

admittedly

notes that "the

sixth can be

major

or minor"

whether

ascending

or

descending

{la

Sesta

porrà

essere,

o

maggiore,

o

minore)

(Gasparini

1722,

61),

but he

leaves

no doubt that

major

sixths on

the

descending

sixth

degree

"are

necessary

for their cadential

effect"

("neces-

sarie

per

esser

specie

di

Cadenze")

but do

not constitute

a modulation to a different note {non fanno mutare

il

tono;

57).






30

JOURNAL

of

MUSIC THEORY

"inseparable

characteristic of all modes"

("das

unzertrennliche Kennzeichen

aller

Modorum")

he has

"placed

the

leading

tone next to the

tonic at the

very

outset" ("dasSemitonium modi . . . gleich Anfangs neben sein 8vam lociret";

764).

For our

topic,

however,

something

else is far

more decisive: Heinichen

repeatedly emphasizes

that his "schema" s "much more universal

and

applica-

ble"

("viel

mehr universaler

und

applicabler";

1728,

765)

than

Gasparini's

and

Rameau's

versions of the Rule

of the Octave.

According

to

him,

they

introduce

"many pecial signatures

that

only

pertain

for as

long

as the notes march

along

nicely

in the order

in which

they

were written down"

("viel

péciale Signaturen,

die

nicht

langer

gelten,

als die

Noten fein

in

der

Ordnung

marschieren,

wie sie

hingeschrieben

worden";

765)

,

that

is,

for as

long

as the bass moves

in

stepwise

motion. For the main purpose of Heinichen's reduction to the basic (perfect

and

imperfect)

chords

is to turn

the Rule of the Octave

into an

explanatory

model

that also

encompasses

"leaping"

bass

progressions.

One

sees

that Heinichen

sets the

figures

5 and

6 one after the other over

the

second

degree

(and

the

sixth

degree)

of the

F-major

cale. The intention

is

by

no

means a

model-bound

progression

like,

for

instance,

a

sequence

of

5-6

motions,

as

is sometimes

maintained

("that

you

are

not allowed to

play

the

sig-

natures

one after

another,

as is

usually

done

in

thoroughbass"

["daB

man also

nicht

beyde

Ziffern nacheinander

(wie

sonst

im General-Bass

gebrâuchlich)

anschlagen

darff"];

1728,

750]).

Instead

Heinichen

explains

the

deeper

sense

of this double figuring as follows:

But

concerning

he

major

mode one should

particularly

bserve

hat because

its second

degree supports

a

perfect

ifth,

one

is thusfree to

use eithera

5 or a

6 over

the said

second

degree.

The 6

sounds

more natural

f

[the

bass]

should

rise

stepwise

o

the third

degree

or

go

backward

down

o the first

degree]

If,

however,

ne

is at the

second

degree

midst

a

leap,

then the

5 seems more

natural.

743)30

Here

one can

still

clearly

recognize

the

persistence

of the old

differentiation

between

perfect

and

imperfect

consonance.

Particular

types

of

motion are

assigned

to

particular

sonorities:

the

leap

is

assigned

to the

perfect

conso-

nance of the five-three chord; the step, to the imperfect consonance of the

six-three

chord.

The chord

of the

sixth

is

placed

"more

naturally,"

namely,

in

a

stepwise

progression,

on

the second

degree.

But

if a

sonority

made

from

stacked-up

thirds

(a

triad

or even

a seventh

chord)

takes the

place

of the

30

Wegen

des modi

maj.

aber ist besonders

zu

mercken,

daft

weil seine

2da

modi

allerdings

eine 5te

perfect,

in

ambitu

hat,

so stehet

auch

frey,

ob man

uber

besagter

2da

modi die

5te oder die

6te

gebrauchen

will.

Naturlicher

lautet

die 6.

wenn man

gradatim

in die

3e

auff oder ruckwerts

gehet.

. . .

Kômt

aber die 2da modi mitten

im

Sprung

zu ste-

hen, so fallet die 5te naturlicher aus. . . .






Ludwig

Holtmeier

~

Heinichen, Rameau,

and

Italian

Thoroughbass

31

six-three chord on the

second

degree,

then a

leap

ensues.

(In

case the

leap

does

not

happen,

as

with the "tonic-like"

Riepel]

triad on

the fourth

degree,

the five-three sonority has the effect of a caesura.) Even if Heinichen does

not

fully

work out

all the

consequences

of these central ideas of his

theory,

it

nevertheless becomes

clear that one

functionally

differentiates between a

degree's step

unction

and

leap

unction.

Of course a three- or

four-note stack-

of-thirds

sonority

can

occur on

any

scale

degree

on

which a chord of the sixth

occurs

in the classic Rule

of the Octave.

Such a

sonority

would

only require

a

change

in

the

modusmovendi

from

step

to

leap.31

A

digression

on

training

manuals

In structureand organization, partimento textbooks follow popular training manuals

like Oratio

Scaletta's

requently

reissued

solfège

textbook

Scaladi musicamoltonecessaria

perprincipianti

1595).

In these solmization

manuals,

the first

things taught

were the

ascending

and

descending

scales

(portar

a voce

ascendendo,

t

descendendo;

caletta

1595,

9).

Then followed

likewise

ascending

and

descending

-

diatonic

patterns

with

leaps

of

a

third,

fourth, fifth,

sixth,

and octave.

In the seventeenth

century,

Klangschritt

ables

of the

so-called

tabulanaturalis

Christensen

2008, 113;

Dahlhaus

1990,

108;

Heimann

1973,

55f.)

were

arranged

according

to the same

paradigm.

The

compositional

models

in the

partimento

tradition

were

imparted

according

to the identical

paradigm:

harmo-

nization

models

of the

scale

ascending (principally

chains

of

5-6,

7-6,

and 9-8

suspen-

sions and

progressions

of

alternating

sixths

and

thirds)

the

scale

descending

(chains

of 7-6

suspensions

and

progressions

of

alternating

seconds

and

sixths),

leaping

thirds

ascending

and

descending,

and so

forth.

Neapolitan

composition

manuals,

above all

the exercises

in

style

found

in Francesco

Durante

s

partimenti

bassi diminuiti

(2003),

follow

this

organization,

and

many

German

training

manuals

are

similarly

structured.

Examples

would

be Friederich

Erhardt Niedt's

Handleitung

ur Variation

Musicalische

Handleitung,

ol.

2,

1721),

as

well

as

Bach's

Vorschriften

1930),

and also

Handel's

(1978)

thoroughbass

exercises.

Fedele

Fenaroli

systematically

cultivates the

teaching

of com-

positional

models

in his

Partimenti

1978;

Holtmeier

2007,

s.v.

"Satzmodelle").

Renversement

versus

Verwechslung

This

puts

in

sharp

relief

one of

the central

distinctions

between

the func-

tionality

of the

Rule

of

the

Octave

and that

of Rameau

s basse

ondamentale

the former

is

totally

aligned

with

movement.

Rule-of-the-Octave

unctionality

not

only distinguishes

between

a

degree's

meaning

in the context of

a

step

or a

leap,

but

also

differentiates

the

meaning

of

a

degree

according

to the

direction

of

the

motion,

whether

ascending

or

descending.

Thus,

the

fourth

degree

in ascent

takes

the

six-three

or six-five

chord,

but

in

descent the

"domi-

nant"

six-four-two

hord;

the seventh

degree

in ascent

takes the six-five

chord

31

Riepel

(1996,

580f.)

and

Kellner

(1732)

follow Heinichen's

conception relatively faithfully and even expand it.






32

JOURNAL

of

MUSIC THEORY

but in

descent the

plain

six-three

chord,

and so forth.

For its

reception

his-

tory,

one thus

encounters a

problem

with Rule-of-the-Octave

unctionality.

Its

"animate"dynamics elude being fixed by a "physicalist"ystematizationthat

permits

the derivation of more

complex

structures from

simple

basic

axioms.

For Rameau s

supporters,

one

of

the central

arguments

in favor of the basse

fondamentale

s

that

it

can

explain

the

basic

principles

of harmonic

tonality

in

the shortest time

and,

as

it

were,

free of

presumptions.

As has often been

stressed,

the

principle

of inversion

adapted

by

Rameau

was not

new

(Christensen

1993, 67f.;

Barbieri

1991).

The

interchangeability

of the voices

was

one of

the

elementary assumptions

of

three-voice

models for

sixteenth- and

seventeenth-century

cadences,

sequences,

and

the

"contrapun-

tal"orientation

of

teaching

composition.

Heinichen

was well

acquainted

with

Rameau s Traité e 'Harmonie. boveall the concept of renversementinversion)

left

lasting

traces

in

his own

theory.

But an

approach

can

be observed

here

that is

typical

for the

history

of

the

French,

Italian,

and also Viennese

thor-

oughbass

tradition:

though

Ramellian basse

ondamentale

inds an

entry

into

the

teachings,

it still

cannot

displace

(or

only very slowly)

the old

theorems.

For

Heinichen,

a six-three chord can be

regarded

as

being

the inverted

form

of

a five-three chord. But the

long commentary

in footnotes that he dedicates

to notions of inversion

(1728, 146-51)

stands

surprisingly

detached

from the

received

thinking

in

terms of intervallic

qualities

which unfolds

in the main

text.

Heinichen, however,

completely

distances

himself from the

procedure

of

systematicthird-stacking,

and thus from the basic

principle

of

basse

onda-

mentale.His

term

Verwechslung

recombination)

designates

a concrete

proce-

dure of

compositional

technique

-

the

regrouping

of

a

sonority (usually

with

an

eventual return to its

starting position;

Heinichen

1728,

624-25).

32

Thus,

each

chord can

become "recombined": f

a six-four-twochord is followed

by

a

seventh

chord,

built with

the same notes

(Kellner

describes this

concept

of

inversion as

based

on

a relation of

"pitch

classes";

1732,

32),

then

this

later

chord

represents

the

"first

nversion"

(

Verwechslung)

f the

first,

and

so forth.

To

speak

in

Ramellian

terms,

every type

of

chord can be

considered

as

a

"root

chord."

Rameau's idea of

inversion, however,

is

theoretically

an a

priori

every

sonority

has to be

reduced to

its stack-of-thirds

prototype.

Beyond

third-stacking:

Toward an

Italian

morphology

of

chords

For

Heinichen,

the

functional

meaning

of a chord is

not determined

by

the

principle

of

third-stacking.Just

as

he

brings

leaping

bass

motions under the

interpretive

authority

of the

Rule of

the Octave

by

falling

back

on traditional

categories,

so

too he

explains

the

complex

chord

morphology

of the

advanced,

32 In

this

regard,

Daube

follows Heinichen

(see

Diergarten

2008).






Ludwig

Holtmeier

~

Heinichen,

Rameau,

and Italian

Thoroughbass

33

"theatrical"

armony

of his era his own focus with the traditional terms of

Italian

music

theory.

To

begin

with,

his

concept

of chord has an

entirely

dif-

ferent basis from that of Rameau. For Rameau the chord is its own entity,an

inherently

closed unit. Even here

the

ideal of the four-voice texture

(

Vierstim-

migkeit)

tands

in the

background. Though

certain functions and tendencies

for linear

motion are attributed to

individual elements

(notte

ondamentale,

otte

sensible,

dissonance

majeure

nd

mineure,

tc.),

these constituents

always

pre-

sent themselves

in

combination

and remain

functionally

invariant even in the

process

of

inversion,

as

will be shown.

They

are

subject

to a

rigid,

hierarchi-

cal

organizing

principle.

For

Rameau,

chords are

primarily

vertical blocks of

stacked-up

thirds

in which the linear tendencies

have been frozen.

Heinichen

's

way

of

thinking

was

shaped

by

his

early

"contrapuntal"

schooling in Germany,but above all by the Italian tradition of apprenticeship

that he

got

to know so

well

during

his

long

stay

in

Italy

(Buelow 1994).

Yet

even

though

his

theory

of

thoroughbass

stands well

apart

from

contemporary

sources

on account

of

its

high

degree

of theoretical

awareness,

neither

with

him nor

with

any

other

contemporary

author does

one find a

comprehensive,

systematically

rticulated

theory

of chord.

In what

follows,

I

have tried to

work

out

the

"implicit"

ystematics

of Heinichen's

theory

of chord.

For Heinichen

and

traditional

Italian music

theory,

the

polyphonic

chord

at

heart was

always

something put together

-

a

composite.

The

contrapuntal

pairing

of

two main

voices

formed the framework

of a

composite sonority,

which

could

be

supplemented by

Neben-Stimmen

secondaryvoices;

Heinichen

1728,

171)

to create

a texture

of

three,

four, five,

or

more voices. Understood

in this

way,

a distinct

hierarchy

controls

multivoice

sonorities,

giving priority

to the

chordal

components,

which

effectively

determines

the

comprehension

and

functionality

of the

chord,

and which

has

consequences

for the

forma-

tion

of voice

leading,

consequences

that extend the

far

beyond

the

chord-

progression,

part-writing

rules of the

modern

Harmonielehre

radition.

A

digression

on

counterpoint

This other

concept

of chord

also

presupposes

another

concept

of

counterpoint.

It is

significant thatJohann Joseph Fux's Gradusadparnassum(1725), the founding docu-

ment of

the

modern,

autonomous

teaching

of

counterpoint,

originated

and was

pub-

lished

in

close

chronological

proximity

to

Rameau s

Traitéde l'Harmonie.

n

terms

of

reception

history,

Fux's

treatise

plays

a role

quite comparable

to

that of the Traité. t

monopolized

the

term

counterpoint

uch as Rameau

s treatise did

for

that

of

harmony.

It

is above

all the

idea of

"strict

counterpoint"

(strenge

Satz)

or even more

so what

the Fux

reception

made

of

it,

that

obstructs

the view of

what,

at the

beginning

of the

eighteenth

century, "counterpoint"

really

was. In the

nineteenth-century

Harmonie-

lehre

radition,

"strict

counterpoint"

changed

from

a

stylistic category

(stilo

antico,

the

"Kônigsdisziplin"

f

counterpoint)

to the

epitome

of

counterpoint

itself.

As

a result

of

this

development

the

intrinsically comprehensive

doctrine

of

counterpoint

became






34

JOURNAL

of

MUSIC THEORY

bound to

a

markedly

narrowand invariable

concept

of dissonance and

resolution.

The

dissonant intervals are

static sizes.

Not

only

are the

"false" ifth and

"major

ourth,"

as

diminished and augmented intervals, alwaysdissonant, but also the technical voice-

leading

behavior of the dissonances

second, fourth,

seventh,

and ninth

is fixed

once and for all. With the

fourth, seventh,

and

ninth,

the

upper

note

is

dissonant.

With the

second,

the

lower

note.

Thus,

dissonance

completely

solidifies into intervallic

quality

and

abandons what it was

in

the consciousness

of the

early eighteenth

century

when it

actually represented

something

more: a

rhythmic

constellation.

Significantly,

Berardi treats the dissonances

under

the

heading

"Introduction

to

syncopation

or dis-

sonances"

("Introduzione

aile

legature

owero

dissonanze"; 1687,

134).

Essential for

the

contrapuntal concept

of dissonance

in the late seventeenth

or

early eighteenth

century

is the distinction between

subsyncopatio

nd

supersyncopatio.

he fourth

of strict

composition

is a

quarta upersyncopata

4ta

sopra

yncopata)

which resolves

to a third.

By

contrast a quartasubsyncopata4ta sotto yncopata;Heinichen 1728, 171), in which the

lower note must be

"bound,"

resolves in the ideal case

to the sixth

(as

in

\

to

§).

In addi-

tion,

an

intrinsically

consonant interval

can,

by

virtue

of a

tie,

become a dissonance

or

be treated like a dissonance.

("Often

the

quintaperfecta

s used as a dissonance

and a

quintasyncopata"

Heinichen

1728,

179],

as in

f.)

In

place

of

rigid

intervallic

categories,

the

early eighteenth century

recognized

an abundance

of intervallic functions

(quarta

consonans,

quarta

dissonans

[quarta

sopra

syncopata], Hulffsquarte

[quarta

sotto

syncopata],

quarte irregolare

quarta

italica],

quarta

transiens,

quarta

suavis,

quinta perfecta,

quinta syn-

copata,

exta

perfecta,

exta

syncopata,

tc.;

see

Muffat

1699,

8-bis).

It is this

open

concept

of interval

that allows

harmony

and

counterpoint

to be conceived

as a

unity.

Examples 14 and 15 clarifythe differences between Rameau's and Hei-

nichen's

concept

of

chord,

using

the case of the dominant seventh chord and

its inversions.

For

Rameau,

not

only

the

(dominant)

six-five chord

(V

ccord

de la

fausse

quinte;

Example

14b),

but also the four-three chord

(/

'accord e la

petite

sixte-,

Example

14c)

and

the four-two chord

(Vaccord

u

triton;

Example

14c)

are

nothing

but derivative forms

of the stack-of-thirdsdominant seventh

chord

(dominante-tonique;xample

14a).

The functional roles of the chordal

components

are

clearly

distributed:G is the root

(basse

ondamentale),

he third

B

is

the

leading

tone

(notte

sensible)

and must move

up

a

step

as a dissonance

majeure,

he

chordal fifth D

takes on

the role of filler

voice,

and

F is

disso-

nant

seventh,

which

must

resolve down

a

step

as dissonance

mineure

Example

14e).

The

structurally

controlling

interval is the seventh. It

is,

so to

speak,

the

mother

of all

(chordal)

dissonances. For

Rameau's

thinking

about

inversion,

it is

essential

that the

functional roles of

chord tones

remain

fixed once and

for

all,

and

persist

in

every

inversion.

Thus,

B

is

always

a

leading

tone,

F

a dis-

sonant

seventh,

D

always

a

filler

tone,33

and

G

always

a

root,

regardless

of

the

particular

constellation in

which

the

tones occur.

33

Significantly,

the fact that

the chordal fifth

in

effect ful-

filled a

dual

function- both that

of the filler tone

and that

of the

tenor

clausula

-

hardly

plays

a

role

in

Rameau's

idea

of inversion.






Ludwig

Holtmeier

~

Heinichen,

Rameau,

and Italian

Thoroughbass

35

(a)

(b)

(c) (d)

(e)

£ IB I[°g

I,ub

!...§ II~^" I*'"" II

Example

14

(a)

(b)

(c) (d)

J B

I " "

I » "

"

Û (6) r(o)i (oi _ -

\

ramework

,

^ ^ (6V

Ô\

(O)

_

65)

=

I

voices

<ro

(9L

l/ffL4-z »~'\ gS

H

=

-9-J^-

-Gt-*=3é=

'Toi

few

E

\/

rVici

l^*^

" Uvel

Secondary

/ X X

voiccs

ft _. .X-^ X^y^

»

l$(o?

ft _.

rof

V FO)

o]

1

»>

Example

15

In

contrast o

this

novel,

invariant hord

morphology,

ne can

posit

a

concept

of chord that

clearly

derives ts

origin

from

the

contrapuntal

hink-

ing

of

the sixteenth

and seventeenth

centuries,

and

in whose tradition

Hei-

nichen

also stands.

n

Example

15,

one

again

sees

Rameau's

asic

chord and

its forms

of

inversion,

but

now examined

n

light

of

Heinichen's

concept

of

chord

(Example

15).

Eachchord

s based

on a two-voice

ramework

Example

15,

staff

I).

It is assembled rom

those chord

tones

most

clearly

and

unmis-

takably

ble

to

represent

each

sonority

n a two-voice

etting.

This two-voice

frameworks far more than a systematic ategoryof organization.Rather,t

designates

an "ideal

placement,"

real

aesthetic

and didactic

standard

or

the

relationship

etweenbassand

melody.

The fact that

as a

theory

of

correct

voice

eading

t

was

assigned

o

training

n

counterpointprovides

vidence

or

the

extensive,

till ntact

unity

of

contrapuntal

nd

harmonic

hinking.

Under

the term

of

disposizione

r

besteLage

Fôrster

818,

1)

it wasa

central,

practical

topic

of

eighteenth-century

omposition

eaching.

This

compositional

ramework

an most

clearly

be

derived

by way

of a

reductive

process,

one that at the

same time

uncovers

he internal

hierarchi-

cal structure f the chords.

For

nstance,

he chordal

ifth

occupies

he lowest

levelin the hierarchy f Rameau's asicdominantchord{dominante-tonique).






36

JOURNAL

of

MUSIC THEORY

It

is a classic

filler voice that

enjoys

a relative freedom

in

voice

leading.

It can

appear

both as a classic

"pedal"

or

"common tone"

(Liegestimme)

nd as a tone

free to leap; it can (in the sense of a tenor clausula) be treated like a voice in

parallel

upper

thirds

with the chordal

third

(the

leading

tone)

or even like

a voice

in

parallel

lower thirds

with the chordal seventh.

The chordal third

(leading

tone)

is one

hierarchical

level below the

framework

tones,

which are

formed

here

by

the

mandatory

bass note and

the "characteristic" issonance

of the

seventh.

The chordal

third thus

supplements

the two-voice framework

to achieve

the ideal

three-voice

setting.

In

Example

15a, I,

square

brackets

ndicate framework

ones of the dom-

inant

seventh

chords

that form

a diminished

fifth

between the tones

B

and

F.

This alternative

framework

refers

to the

alleged

"root" one G

being

at times

able to appear as a secondaryvoice, as a lower third to the leading tone. That

is

especially

the case

when

the dominant

seventh

chord

does not

progress

with

a

genuine

root

progression

(i.e.,

by leap)

to a

(cadential)

chord

of

resolution,

but

almost

appears

in transitu

tself,

that

is,

appears

to be a

passing

chord

(see

Example

lOd).

In the

six-five

chord

(Example

15b)

the

framework

is formed

by

the

framing

interval

of

the diminished

fifth.

The sixth

(G),

as bearer of

the dis-

sonance,

is an

important

but

nevertheless

hierarchically

subordinate

voice.

Functionally,

it can

appear

upper

sixth

to the bass

note

(B).

Here,

the

third

(D)

takes

over the

role of the

supplementary,

filler

voice.

In the four-three

chord

(Example 15c),

the

framework

set is

formed

by

the

major

sixth

between

the

bass

note

and the

leading

tone.

The third

(F)

as a

voice

in

parallel

thirds

with the

bass,

supplements

the

two-voice

framework

to

form

a three-voice

setting.

The

fourth

(G)

is,

however,

pure

filler a dissonant

common

tone

that

received

special

attention

from

contemporary

theorists

due

to its

special

dissonance

treatment.

It was

called

quanta

rregolaris,

uanta

irregolare

Heinichen

1728,

151),

or

quarta

talica

(Muffat

1699,

8).

The

special

position

of

this fourth

highlights

the

fact

that

for

many eighteenth-century

theorists

thus

also

for

Heinichen

-

the

four-three

chord did

not

appear

as

an

independent

chordal

category,

but

was

treated

as a

special

form

of the six-

three

chord.

Quarta

rregolaris,

ften

not

marked

even

in a

figured

bass

("The

irregular

fourth is not alwaysexpressly indicated above the notes" ["Eswird

aber

. . .

diese

irregulaire

4 ...

nicht

iederzeit

ûber

denen

Noten ausdrûck-

lich

angedeutet"];

Heinichen

1728,

151),

was a

quasi-"improvisational"

ddi-

tion

to the

basic

three

voices

of a

six-three

chord.

The French term

petite

ixte

testifies

to

this

origin.34

34

Riepel

perceived

the

quarta irregolaris

as a fashionable

aberration.

He labeled

such

intervals

pejoratively

as "Turkish

fourths"

since

they

reminded

him

of Turkish

"fifes"

blowing

"a

loud series

of fourths one

after the

other,"

which he had

heard

"in

the

year

1737

near

Banja

Luka"

(1757,

39).






Ludwig

Holtmeier

~

Heinichen, Rameau,

and Italian

Thoroughbass

6 6 6

15

4

14 I

3 3

Example

16.

Two

of

the

examples

Heinichen

gives

for the 3a

syncopata

Naturally,

hat is not the

only

form

in

which the

four-three hord can

occur. t can alsoappearas a terzayncopatas shown n someexamplesbyHei-

nichen

(see

Example

16)

(Heinichen

1728,

163).

The four-three hord

with

terza

yncopata

ost

closely

resemblesa Ramellian hord

of inversion.Yet

n

the

improvisatory

nd

compositionalpractice

of the

eighteenth

century,

his

chord,

when

compared

o the four-three

hord with

quarta

rregolaris,

s

just

the

exception.

Heinichen stresses hat the

"syncopated"

our-three hord

is

properly

understoodas a variant

f

the four-two

hord

("related

o the

synco-

pated

second"

["der

2da

syncopata

. .

anverwandt"];

einichen

1728,

163).

And in factthe chord s also mostoften utilized n thisform

(see

Arnold

1931,

632,

his

example

9).

Finally,

he six-four-twohord

(Example

15d)

rests

on the framework

f

theaugmented ourth(F-B).Heinichendescribes hisfourth,whichresolves

to the

sixth,

as

a

"helper-fourth"Hulffs-4te)

as ancilla dae

handmaiden

o the

second) (Heinichen

1728,

171).

Here,

one

can

clearly ecognize

how

the hier-

archical

concept

of chord also

implies

a hierarchical

oncept

of

dissonance.

The

notion

of the

ancilla2dae

s

based

on

the central

distinctionbetween

dis-

sonantiadominans nd dissonantia oncomitans

Heinichen

1728,

186),

between

a

"controlling"

nd an

"accompanying"

issonance.For

Heinichen,

he disso-

nant fourth s an

"accompanying"

issonance,

n

upper

third o the

"control-

ling"

dissonant

econd.In

the musical

practice

f

the

eighteenth

century,

ow-

ever,

he circumstanceseem to be

just

the reverse: he seventhscale

degree

is the "ideal" ppervoice for the fourthscaledegreein thebass,andonlythe

augmented

ourth can

unambiguously epresent

he six-four-two

hord

in

a

two-voice

etting.

Yet

for

Heinichen this fourth

(B)

is,

according

o its

inner

nature,

an

upper

hird o the second

(G).

Conversely

he G becomes

he lower

third o the

leading

tone

(B).

The sixth

(D)

appears

as its

upper

third

or as a

"free"

econdary

oice. In the

special

case of this chord one can

hardly

peak

of

a hierarchical

riority

etween he two

secondary

oices.

In

order to make this

hierarchical

oncept

of

chord

still

clearer,

Exam-

ple

1

7 constructs

few chords not

from

the

perspective

f Ramellian nver-

sion,

but ratheron the basis

of

the

relationship

etweena two-voice

omposi-






38

JOURNAL

of

MUSIC THEORY

(I) (ID

(HI)

(a) (fo éfl3LXT ̂ | J I J <\ | j l[g U |.w] J^ [ j 1 bjg [ j 1 -f]g [rfTzz

®

-Ô-W^J

-«J.I «J »J- r ... *J r ji «L TfJi

"«"""

M^

r

il N il

i^|

.J,

\f\4m^

Example

17

tionalframework nd

secondary

oices.The

"leading-tone"

ramework

oices

determine

the function

of chords on the

ascending

and

descending

second

degree

in

major

and

minor,

on the

descending

ixth

degree

in

minor,

and

on

the

descending

ourth

degree

in

major

and minor

(Example

17,

col.

I).

They

mark he invariantsf the functional

concept

of chord.The

obligatory

hird

joins

in as

the first

secondary

oice added to the

sixth on the second

degreeand to the

augmented

ixth on the sixth

degree (Example

17,

col.

II,

stavesa

andb)

and eithera sixth

(Example

17,

col.

II,stafFd)

r a second

(Example

7,

col.

II,

staff

e)

can be addedwith

equal

effect as a thirdvoice to

the tritone

on

the fourth

degree.

For

the

fourth,

"filler"

oice,

even

more tones are

possible.

Not

only

the

fourth but also the diminished

or

perfect

fifth can

supplement

the sixth

on

the second

degree (Example

17,

col.

Ill,

8taff

).

A

fourth

or fifth

can be added to the

augmented

ixth on the sixth

degree (Example

17,

col.

Ill,

staff

b).

And if a sixth is added as thirdvoice to the tritone

on the fourth

degree,

the

second,

the minor

third,

or the

major

hird can

enter as a

filler

voice

(Example

17,

col.

Ill,

staff

e).

Differentchords

(with

"step

unction")

canthusrepresent he scaledegree. Thoughthe choiceof the fillertone can

crucially

hape

the auraand color of a

chord,

the function

of that

cbord

its

dynamic

endency

is

exclusively ssignedby

the framework

oices.

The function of chord tones

In Rameau's

heory,

chord

tones

retainthe

same

functional

qualities

n

vari-

ous inversion hat had accrued to them

in

the

"root-position"

hord.

The

function-defining

issonanceremains he same

in all inversions.

n

the

Ital-

ian

thoroughbass

raditionas

systematized y

Heinichen,

however,

hordal






Ludwig

Holtmeier

~

Heinichen,

Rameau,

and

Italian

Thoroughbass

39

elements are

subject

to a

great degree

of functional

variability.

The

inter-

connected circles

n

Example

15

try

to

clarify

his

point.)

Not

only

do these

elementsbelong to differenthierarchical hordlevels,thushavinga differ-

ent structural

ignificance

n

different

chords,

but

they

also alter

theirvoice-

leading properties

n

the context of differentchords.

Only

the

leading

tone

maintainsts

function,

evenfor

Heinichen,

n all formsof Ramelliannversion.

The

seventh,however,

ppears

n

three

functionally

istinct

orms

(Example

18):

(1)

as

prototype

f the

(suspended

r

passing)

dissonance,

t

appears

nly

in the

basic,

root-position

hord itself

(Example

18,

1)

and

in

the

six-four-two

chord

(Example

18,

II); (2)

in

the six-five

hord,

it

forms

a

"semiconsonant"

diminished ifthwith

the

bass,

which

does not

requirepreparation

Example

18,

III);

and

(3)

in

the four-three

hord it

appears

as

a

parallelupper-third

voice to thebass,consequently s an imperfect onsonancenotsubject o the

need to resolveand thus free to move

stepwiseup (Example

18,

FVa),

own

(Example

18,

IVb),

or even to

leap (Example

18,

IVc).

With

Rameau,

he chordal

ifth

takes

over

the function

of a fillervoice.

It

approaches

his functionwith Heinichen

too,

but

in

the

four-three hord

it

lies

in

the bassvoice and there its function

changes.

It becomes the

penul-

timate one of a tenor

clausulaand

is

therefore

ubject

o

a need to

progress

stepwise Example

18,

IV).

The second scale

stage

(the

chord

fifth)

is func-

tionally

ambiguous.

t can be

understoodas a

component

of a tenor clausula

or

as

a

pure "patch

one"

(Riepel),

as so to

speak

a variant f an alto

clausula.

(la)

(b) (lia) (b) (III)

(IVa)

i f j

\ h ' j | i l j d i | d

j i H

l i U d

> n

I

r l i

H r

I r r ' r

I ' '

1 ^ ^

(b)

(c) (Va) (b)

(Via)

(b)

lA-J I'll-] L'l II P lj

J

IJ J IJ J Ile g le Ë II

Example

18






40

JOURNAL

of

MUSIC THEORY

Also

with

the

six-three, six-five-three,

and six-four-twochords

they mostly pro-

gress stepwise,

in

the sense of a

tenor

clausula.

This

voice

leading

is

not,

how-

ever, mandatory.The fifth of the root chord can likewise leap to the fifth of

the

chord of

resolution,

even

if it should result

in

consecutive fifths

(Example

18,

Va)

or

if

a fifth

in

the

outer voices is reached

by

direct motion

(motus

rec-

tusr,

xample

18,

Vb).

If

the

chordal fifth of the six-four-twochord lies in the

upper

voice,

then

a

leap

is

actually

the

rule: it is

necessary

to avoid the

empty

cadential

perfect

consonance of the octave

in

the

outer voices of the chord of

resolution

(Example

18,

Via)

and to

go

instead to the

imperfect

tenth

in

the

outer

voices

(Example

18,

VIb).

The

difference,

however,

with Rameau s static

functionality

shows

itself most

clearly

when

one

regards

the functional vari-

ability

of

the

very

voice

that,

in Rameau's

theory, represents

the foundation of

the chord. For Heinichen as well, the "root"appears in three distinct forms.

In

the

six-five

and six-four-two

chords it

is the lower third or

upper

sixth of

the

leading

tone,

and

thus

simply

a

secondary

voice.

In the four-three

chord,

as

quarta

rregolaris,

t

actually

takes the

lowest

place

in

the

chordal

hierarchy.

Only

in the

basic,

root-position

chord

is it what Rameau saw

in it the centre

harmonique

f the

Klang.

If one allows

a "contrast-enhanced"

ormulation

of

Heinichen

's

theory

of

chord,

then there

are two basic

chords

from which all other chord

forms

are derived

the five-three

sonority

and the

six-three chord. One sees the

old

opposition

of

perfect

and

imperfect

consonance

that

already

determined

Hei-

nichen's concept of the Rule of the Octave, seamlessly brought

forward

into

modern

chord

theory.

In

harmonic

discourse,

the

third,

on which the whole

Ramellian

system

is

based,

had

long

become an

unmarked filler interval

that

indiscriminately

characterized

the

pattern

of all

chords,

whether consonant

or dissonant.

And so there

are

essentially

two intervals

that determine

the

nature

of chords:

a fifth or

sixth

distinguishes

the

basic functional orientation

of a

sonority.

The crucial difference

between Rameau's

basic

chord and its inverted

forms

can be

viewed

from the

perspective

that while the basic chord

is deter-

mined

by

"static"

ifth,

the

inversions are characterized

by

the

"mobile" nterval

of the

sixth. This

difference

is

categorical

in

nature

and cannot be waived

by

a

simple process

of derivation,in the sense of Rameau's idea of inversion. For

Rameau,

dissonance

connects

the basic

chord with its inversional forms

and

makes obsolete

the

differentiation

between

perfect

and

imperfect

consonance.

In this

understanding

of

chord,

however,

the dissonant

character of a

sonority

replicates

the distinction

between fifth

and

sixth,

since it is these intervals that

determine

the

fundamental

dynamic

nature of sonorities.

Rameau's inver-

sion

forms

are

first and

foremost sixth

chords and

require stepwise

motion

(a

"variety

f sixth

chords";

Christensen

1993,

172).

The fifth of the basic

chord,

by

contrast,

requires

a

leap.

Dissonance

is added to the sixth or the

fifth,

as it

were,

externally.

To the sixth

one can add a fifth

(Example

19,

la),

or a fourth






Ludwig

Holtmeier

~

Heinichen, Rameau,

and Italian

Thoroughbass

41

(Ilia)

(b) (c)

(Via) (b)

(c)

n ï

r ^ t

* *

(I) (a)\

(b) (c) (II) (a)

/

Step

6

A-

6

¥cendiPS Ç

,

..

l^aP

/

ascending

-

4

descending

4

descending

..

/

a

6 5

3 2 5

7

(IVa)

(b)

v'

(Va)

/

(b)

Example

19

and third

(Example

19,

Ib),

or a fourth

and second

(Example

19,

Ic).

To the

fifth one can add a seventhas its

upper

third

(Example

19,Ha).

In so

doing,

the

original

endencies or motionare

onlystrengthened y

the

requirement

or dissonance esolution. t is as if dissonance

epresents

n

autonomous

ontrapuntal

lementwithin he chord.The dissonant

"auxiliary

note"does not

change

the

fundamental unctional haracter

f

the

chord,

but

rather

ntensifies ts

tendency

or motionand

spécifies

tsdirectionof

motion.35

The added fifth lends a

risingtendency

o the six-three hord

(Example

19,

la)

because

moving

downward

tepwise

asily

eadsto

parallel

ifths

(Example

19,

Ilia),

an addedfourth

(whether

"Turkishourth" r as

an

accompanying

note to the terza

yncopata)ermits

motion

in

either direction

(Example

19,

IV),and an added second forces the sixth downward Example19,V). The

chords

are

not

strictly

bound to these forms of motion. The six-five

hord

can

resolvedown a

step

into a six-four

uspension Example

19,

IIIc),;and

n

certainharmonic

ormulas he dominant ix-four-twohordcan

move

up step-

wise

(Example

19,

Vb).

Notwithstanding

he

inganno

deceptive

cadence),

a

35

"Vonder

Sextenkette,

die zur Oktave strebt unterscheidet

sich Rameaus

Septakkordfolge

deren

Ziel ein

Dreiklang,

ein

Accord

parfait'

bildet,

zwar

graduell,

aber

nicht

prinzipiell"

(Dahlhaus

1990,

27).






42

JOURNAL

of

MUSIC THEORY

stepwise

scending

eventhchord

s

often a

passing

hord

(septima

n

transitu)

(Example

19,

Via)

or an

unresolved

-6

suspension

a

"retarded"ixth chord

so to saythatfinds its resolution n the followingconsonanceor dissonance

(Example

19, VIb,

c).

But

according

o their basictendencies he six-five s a

rising

chord,

the six-four-two

s a

falling

chord,

and the four-three hord can

either

rise or fall.

* *

*

The idea

of

chord

and

sonority Klang)

dealt with here is

fundamentally

if-

ferent

romthatof

Rameau.His

rigidsystem,

made

up

of a fewbasic

elements

and

based

on a

logic

of chord

derivation,

s

set

against

a

sophisticated

rame-

work

of variation

nd

relational

omplexity.It is

perhaps

his

very

richness hat

spelled

doomfor this

understanding

of chord:

as

is well

known

historically,

t was

to succumb

o Rameaus

theory.

It could

raisescant

opposition

o

the manifest

ogic

of

Rameau's

rinciple

of

inversion.

We

can assume

hat

Rameau's

heory

wasable

to

gain

such

popu-

larity

only

because

his

concept

of chord

filled a

widelyperceived

vacuum.

t

seems

self-evident

hat

the modern

harmonic

anguage

of the seventeenth

and

eighteenth

centuries

craved

a new

explanatory

model that transcended

the

old

counterpoint

nstruction

f the

sixteenth

and seventeenth enturies.

Rameau

offered

a

clear and

at the same

time

simple response

o a

question

that

had never

been

put

quite

so

explicitly

before,

but that had

clearly

been

hanging n the air:what s Klang}

Heinichen

also

offers

a

resoundingresponse

in

favor

of the Italian

tradition,

s it were.

But much

of whathas

been

"implicitly"

econstructed

n

this

essay

remains

unspoken

by

Heinichen,

as

in

the

entire Italian

horough-

bass tradition:

he

neither

develops

the

concept

of

framework

oices

in

any

consistent

manner

nor

systematizes

he

functionality

of

steps

and

leaps

conclusively.

No modern

approach

an

remedy

his

alleged

lack

of

systematic

hink-

ing,

and this

text,

too,

bearswitness

o

the

difficulty

of

coming

closer to

a

concept

of chord

and

tonality

dealt

withhere

in a

very

imited

way)

hat ies

beyondthe Ramellian onceptof inversionand third-stacking.he internal

contradictions

f

an account

that

describes

a

four-voice

hord,

on the

one

hand,

as

being

a

five-three

r sixth

chord

supplemented

by

a

"contrapuntal"

auxiliary

note,

and

on the

other

hand,

as

a

composite

sonority

made

up

of

a two-voice

ramework

nd

secondary

oices,

are

obvious:

ollowing

he

first

interpretation,

he dominant

six-four-two

hord

on the

descending

fourth

degree

s

a

variant

f

a sixth

chord,

withthe

sixth

being

the

function-defining

interval.

Following

he

second

interpretation,

he tritone

appears

as the cen-

tralbasis

and

the

sixthas a

secondary

oice,

a

hierarchically

ubordinate ote

that

could

easily

be omitted

rom a

three-voice exture.






Ludwig

Holtmeier

~

Heinichen,

Rameau,

and Italian

Thoroughbass

43

Upon

closer

nspection,

however,

we must

concede that t is not so

much

a

contradiction

s ratherone

and the same

phenomenon

viewedfrom dif-

ferentperspectives.f the idea of chordprogressionss basedon the dichot-

omy

of

perfect

(vollkommeri)

nd

mperfect

unvollkommeri)

hords,

dissonance

becomes a subordinate

parameter.

But if the

movementof

the dissonances

itself s the focus

of

consideration,

he

distinctionbetween

perfect

and

imper-

fect consonance

becomes

of

secondary

mportance.

It s

precisely

he

uxtaposition

f thesedifferent

perspectives

hatreflects

the historical

ituation round he

turnof the

century:

he modern unctional-

ity

of the Rule

of the Octaveand the traditional

ontrapuntal

extureof the

trio

sonata

compete

with each

other,

though

the one

grows

out of the other

in an

organic

ashion,

as

I

have

attempted

o demonstrate.

Onemightconsider tadeficit hat he tradition f Italian horoughbass

does not

offer a

comprehensive

nd

straightforward

ystematics,

ut

perhaps

this s

precisely

where

ts true

strength

ies: hat t does not seek to deduce har-

mony

and

melody,

ine and

sonority Klang),

hord

and

counterpoint

rom a

single

coherent

principle,

as

Rameau

does,

but

permanently

works

hrough

the tension

between hose

poles

in

a dialectical

way.

Heinichen

constantly

wavers

etween he new

chord

functionality

f the

Ruleof the

Octave

and the

"classical"

heory

of

counterpoint

nd

dissonance

treatment.

This is

not

merely

a

sign

of his theoretical

ndecision,

however,

but also

reveals

his

deep-seated

aversion

o a certain

concept

of natureand

science

that

he sees

prevailing

n Rameaus

theory:

he confronts

his form of

systematic

hinking

withhis "rules f art"

Arth-Regeln)

hat

"German,

rench

and

Italian

authors

. . have

provided

or the use

of

unfigured

horoughbass

a

long

time

ago,

which he

latter

[i.e.,

the Italian

authors]

ince then

brought

to the

highest

perfection"

"welche

deutsche,

franzôsische

und italienische

Autores

...

vom

General-Bass

hne

Signaturen

heils von

langer

Zeit her

zu

geben

angefangen,

heils

etzterezeithero

zurVollkommenheit

ebracht";

Heinichen

1728,

19).

Heinichen

draws he

principles

f his

theory olely

rom

musical

practice

and tradition:

or

him,

"nature"

manifests

tself

n

the "con-

ventional

schemata

of

composition"

"den

gebrâulichen

passibuscomposi-

tionis";

9),

but

it cannot

be deduced

from the

physical

nature

of

the

corps

sonore.t is thisproximityo compositionalpracticeand musicalexperience

in

particular

hat

makes

he Italian

(and

accordingly

he

Italian-influenced)

thoroughbass

radition

o

interesting

or

us

today.

It

goes

without

aying

hat he

complex

concept

of harmonic unctional-

ity

on which

his

Italian

radition

f the

late seventeenth

nd

earlyeighteenth

centuries

s based

would

always

avemerited

our historical nterest.

Another

question,

however

and

perhaps

actually

he crucial

one is what

we are to

makeof

this renaissance

f

Italian

music

theory.

t

opens up

the

possibility

f

interpreting

nd

analyzing

he

compositional

echniques

of

the seventeenth

and

eighteenth

centuries

n

a different

way.

Elucidating

he

possible

nature

of






44

JOURNAL

of

MUSIC THEORY

this

different

way

would exceed the

scope

of

this

essay;

a

study

of such a

kind

is

in

progress,

however,

and will

appear

at a later date.

Works Cited

Aerts,

Hans.

2006.

"Thoroughbass

in

Practice,

Theory,

and

Improvisation."

Zeitschrift

er

Gesell-

schaftfur

Musiktheorie .

http://xjuww.gmth.

e/zeitschrift/artikel/01

5/01

15.html.

.

2007.

"'Modeir und

Topos'

in der

deutschsprachigen

Musiktheorie

seit Riemann."

Zeitschrift

er

Gesellschaftur

Musiktheorie

/1-2.

http://www.gmth.de/zeitschrift/artikel/0123/

0123.html.

Albrechtsberger,Johann Georg.

1790.

AnweisungzurKomposition

mit

ausfuhrlichen xempeln,

um

Selbstunterrichterlautert.

Leipzig:

Breitkopf

and Hârtel.

Arnold,

Denis.

1978.

"The

Corellian

Cult in

England."

Studi

Corelliani2:

37-51.

Arnold, Franck Thomas. 1931. TheArtofAccompanimentroma Thorough-Basss Practicedn the

XVIIthand XVIIIthCenturies.Oxford: Oxford

University

Press. Facs.

New York:

Dover,

1965.

Bach,

Carl

Philipp

Emanuel.

1753/62.

Versuch berdie wahre

Art das Clavier

zu

spielen.

Berlin:

Christian Friedrich

Henning/Berlin: Ludewig

Winter.

Bach,

Johann

Sebastian.

1930.

Vorschriften

nd

Grundsàtze

um

vierstimmigen pielen

des General-

Bass. In

fohann

Sebastian

Bach,

ed.

Philipp Spitta,

2

vols.,

4th ed.

Leipzig:

Breitkopf

and

Hârtel.

Reprint.

Darmstadt,

1962,

913-50.

Barbieri,

Patrizio. 1991.

"Calegari,

Vallotti,

Riccati e le teorie

armoniche

di Rameau:

Priorita,

concordanze,

contrasti." Rivista Italiana

di

musicobgia

26: 241-302.

Bazin,

François.

1875. Coursd'harmonie

héorique

t

pratique.

Paris: Escudier.

Berardi,

Angelo.

1687. DocumentiArmonici.

Bologna:

Monti.

.

1689. Miscellaneamusicali.

Bologna:

Monti.

Budday,

Wolfgang.

2002.

HarmonielehreWienerKlassik. Théorie Satztechnik

Werkanalyse.

tutt-

gart:

Berthold and Schwerdtner.

Buelow,

Georg J.

1994.

"The Italian Influence in Heinichen's

'Der

General-Bass

n der

Composi-

tion.'"

Baslerfahrbuchur

historische

Musikpraxis

8:

47-65.

Cafiero,

Rosa.

1993. "La didattica del

partimento

a

Napoli

fra

Settecento

e Ottocento: Note

sulla fortuna delle

Regole

di Carlo Cotumacci." In Gli

affetti

convenienti ll'idee:

Studisulla

musicavocale

taliana,

ed. Rosa Cafiero and

Maria Caraci

Vela,

549-80.

Naples:

Edizioni

Scientiflche

Italiane.

.

1999.

"Metodi,

progetti

e riforme

dell'insegnamento

della 'scienza armonica' nel

Real

Collegio

di

musica di

Napoli

nei

primi

decenni dell'Ottocento." Studi musicali

28:

425-81.

.

2001.

"Teorie

armoniche di

scuola

napoletana

ai

primi

dell'Ottocento:

Cenni sulla

fortuna di Francesco Durante fra

Napoli

e

Parigi."

In Giacomo rancescoMilano e il ruolo

dell'aristocrazia el

patrocinio

delle attività musicali

nel secolo

XVIII,

ed.

Gaetano

Pitorresi,

171-98.

Reggio

Calabria:

Laruffa.

.

2005. "Conservatories and

the

Neapolitan

School:

A

European

Model at the End of the

18th

Century?"

In

Musical

Education n

Europe

1770-1914):

Compositional,

nstitutional,

and

Political

Challenges,

d. Michael

Fend and

Michel

Noiray,

vol.

1,

15-29.

Berlin:

BWV

Berlin

Wissenschafts-Verlag.

Campion,

François.

1716.

Traité

d'Accompagnement

t de

Composition

elon la

règle

des Octavesde

Musique.

Paris.

Facs. Geneva:

Minkoff,

1976.

.

1730.

Addition au

Traité

d'Accompagnementar

la

règle

d'octave.Paris. Facs. Geneva:

Minkoff,

1976.






Ludwig

Holtmeier

~

Heinichen, Rameau,

and Italian

Thoroughbass

45

Catel,

Charles-Simon.

1802.

Traitéd'harmonie

onforme

l'éditiondu

conservatoire. aris: Leduc.

Cherubini,

Luigi.

1847. Marchesd'harmonie. aris:

Heugel.

Choron, Alexandre-Etienne. 1808. Principesde compositiondes écolesd'Italie. .. 3 vols. Paris:

Leduc.

Choron,

Alexandre-Etienne and

Vincenzo Fiocchi. 1804.

Principesd'accompagnement

es Ecoles

d'Italie.

. .

Paris:

Imbault.

Christensen,

Thomas.

1992.

"The

Règle

de l'Octave n

Thorough-Bass Theory

and Practice." Acta

Musicologica

4: 91-1

17.

. 1993. Rameau and

Musical

Thought

n the

Enlightenment.

Cambridge: Cambridge

Uni-

versity

Press.

.

2008.

"Fundamenta

Partiturae:

Thorough

Bass and Foundations

of

Eighteenth-

Century Composition

Pedagogy."

In The

Century f

Bach

and Mozart:

Perspectives

n Histo-

riography,

Composition,

Theory,

nd

Performance,

d. Sean

Gallagher

and Thomas Forrest

Kelly,

17-40.

Cambridge,

MA:

Harvard

University

Press.

Dahlhaus, Carl.

1990.

Studieson

the

Originof

Harmonic

Tonality,

rans. Robert

Gjerdingen.

Prince-

ton,

NJ:

Princeton

University

Press.

Originally

published

as

Untersuchungen

berdie

Enste-

hung

der

harmonischen

onalitàt.

Kassel:

Bârenreiter,

1968.

D'Alembert,

Jean

Le Rond.

1757.

Systematische

inleitung

in

die musicalische

etzkunst,

nach den

Lehrsàtzen

es Herrn

Rameau;

aus

demFranzôsischen

bersetzt

nd mit

Anmerkungen

ersehen

von

FriedrichWilhelm

Marpurg.

Leipzig:

Breitkopf.

Daube,

Johann

Friedrich.

1756.

General-Bap

n

drey

Accorden.

Leipzig:

Andrâ.

Dehn,

Siegfried

W.

1840.

Theoretisch-fraktische

armonielehre

mit

angefùgten

Generalbassbeispielen.

Berlin:

Wilhelm

Thome.

. 1859.

Lehre om

Contrapunkt

emCanon

und

derFuge,

nebst

Analysen

von

Duetten,

Terzetten

etc. von

Orlando

di

Lasso,

Marcello,

Palestrina

u. A. und

Angabe

mehrer

Muster-Canons nd

Fugen.

Berlin:

Ferdinand

Schneider.

Dellaborra,

Mariateresa.

2007,

"'Musico

Pratico al

cimbalo.'

Paisiello e le

regole per

bene

accompagnare

il

partimento

(1782)."

StudiMusicali 36: 443-67.

Diergarten,

Felix.

2008.

"'Anleitung

zur

Erfindung.'

Der Musiktheoretiker

Johann

Friedrich

Daube."

Musiktheorie

:

293-312.

Dittrich,

Marie-Agnes.

2007.

"Teufelsmuhle'

und

'Omnibus.'"

Zeitschrift

der

Gesellschaftur

Musiktheorie

.

http://www.gmth.de/zeitschrift/artikel/0I20/0l20.html

Dodds,

Michael

R.

2006.

"Columbus's

Egg:

Andreas

Werckmeister's

Teaching

on

Contrapuntal

Improvisation

in

Harmonologia

musica

(1702)."

Journal

of

Seventeenth-Century

usic

12.

http://sscm-jscm.press.uiuc.edu/vl2/nol/dodds.html.

Droste-Hulshoff,

Maximilian

von.

1821.

Einige Erklàrungen

uber

den

General-Bap

nd die

Tonsetz-

kunst

uberhaupt

in

derKurze

Zusammengefafit.

S,

Schloss

Hulshoff.

Durante,

Francesco. 2003.

Bassi

efughe.

Un

manuale inedito

per

riscoprire

a vera

prassi

esecutiva

delta

Scuola

Napoletana

del

Settecento.

d. G.

A. Pastore. Padova:

Armelin

Musica.

Dûrrnberger,Johann August. 1841 Elementar-LehrbucherHarmonie-und Generalbafi-Lehre.inz:

Verlag

der

k.k.

Normal-Hauptschule.

Eitner,

Robert. 1882.

"Bernhard

Klein."

In

Allgemeine

Deutsche

Biographie,

78-87.

Leipzig:

Duncker

and Humblot.

Fellerer,

Carl Gustav.

1939.

Der

Partimentospieler.

bungen

n

Generalbass-Spiel

nd

in

gebundener

Improvisation.

eipzig:

Breitkopf

and

Hârtel.

Fenaroli,

Fedele.

1978.

Partimenti

sia Basso

numerato

i Fedele enaroli

Per uso

degli

Alunni del

R.°

Academia

delle

Belle

Arte

diFirenze,

2nd

ed.

Florence

and

Milan: Giovanni

Canti.

Reprint

éd.,

Sala

Bolognese:

Forni.

Fladt,

Hartmut.

2005.

"Modell

und

Topos

im musiktheoretischen

Diskurs." Musiktheorie

:

341-69.






46

JOURNAL

of

MUSIC

THEORY

.

2007.

"Satztechnische

Topoi."

Zeitschrift

er

Gesellschaft

ur

Musiktheorie: 189-96.

Florimo,

Francesco.

1882/83.

La scuola musicaledi

Napoli

e

i suoi Conservatorii.

vols.

Naples:

Morano.

Fôrster,

Emanuel

Aloys.

1818. Emanuel

Alois Fôrster

Practische

Beyspiele

ls

Fortsetzung

u seiner

Anleitung

des

Generalbasses,

n 3

parts.

Vienna: Artaria.

Froebe,

Folker.

2007.

"Satzmodelle des

'Contrapunto

alla

mente' und ihre

Bedeutung

fur

den Stilwandel um 1600."

Zeitschrift

er

Gesellschaftur

Musiktheorie.

http://wxvw.gmth.de/

zeitschrift/

rtikel/01

1

7/01

1

7.html.

Fux,

Johann

Joseph.

1725.

Gradusad

parnassum.

Vienna: Ghelen.

Gasparini,

Francesco.

1722.

L'armonico

ratico

alcimbalo

(1708).

Bologna:

Antonio

Silvani.

Gingras,

Bruno.

2008.

"Partimento

Fugue

in

Eighteenth-Century Germany:

A

Bridge

between

Thoroughbass

Lessons

and

Fugal Composition." Eighteenth

Century

Music b:

51-74.

Gjerdingen,

Robert

O.

2007.

Music in the Galant

Style.

New

York:Oxford

University

Press.

Grampp,

Florian.

2004/2005.

"Partimenti: Musik fur Generalbass

solo." Concerto

93:

23-29

(Part 1: "Johann Matthesons 'GroBe Generalbass-Schule'"); 194: 23-27 (Part 2:

"Rômische

Quellen

zur

Partimento-Praxis");

196-98:

26-28

and

27fT.

(Part

3: "Zurnea-

politanischen

Partimento-Tradition");

199:

32-36

(Part

4:

"Solistischer

GeneralbaB

in

Nord-

und

Mitteldeutschland").

Grandjean, Wolfgang.

2006.

Mozartals TheoretikererHarmonielehre. ildesheim:

Olms.

Gugl,

Matthâus. 1719. Fundamenta

partiturae

n

compendio

ata.

Das ist: Kurzerund

grundlicher

Unterricht,

en

General-Bass,

der

Partitur,

nach denen

Reglen

echtund wohl

schlagen

u

lernen.

Salzburg: Mayr.

Hândel,

Georg

Friedrich. 1978.

Aujzeichnungen

ur

Kompositionslehre.

d. Alfred

Mann.

Leipzig:

VEB.

Heimann,

Walter. 1973. Der

Generalbafi-Satz

nd seine Rolle in Backs Choralsatz.

Munich:

Katzbichler.

Heinichen,

Johann

David.

1711. Neu

erfundene

und Grundliche

Anweisung

zu

vollkommener

Erlernung

des General-Basses.

amburg: Benjamin

Schillers.

Reprint.

Kassel:

Bârenreiter,

2000.

.

1728.

Der

General-Bassn

der

Composition.

resden:

Selbstverlag.

Holtmeier,

Ludwig.

2002.

"Reconstructing

Mozart." Music

Analysis

21: 307-25.

.

2007.

"Modulation,"

"Chromatik,""GeneralbaB,"

"Oktavregel,"

"Satzmodelle,"

"Teufel-

smûhle,"

"Tonart/Tonalitât,"

"Fôrster,"

"Albrechtsberger,"

and

"Vogler."

In Beethoven-

Lexikon,

d.

Heinz von

Loesch and Claus

Raab. Laaber:

Laaber.

.

2008. "Emanuel

Aloys

Fôrster und das

Wiener Partimento: Zum

Prinzip

der besten

Lage."

In uIm

Schattendes

Kunstwerks :

Komponisten

ls Theoretikern Wienvom 1

7.Jahrhun-

dert

bis

Anfang

des

1

9.

Jahrhunderts,

d.

Dieter Torkewitz. Vienna: Universitât fur Musik

und

Darstellende

Kunst.

Holtmeier,

Ludwig

and

Felix

Diergarten.

2007.

"Partimento."Musik n Geschichte

nd

Gegenwart

2, Supplement: 653-59.

Holtmeier,

Ludwig, Johannes

Menke,

and Felix

Diergarten.

2008.

Praxis

und Théorie es Parti-

mentospiels.

Wilhelmshafen:

Noetzel.

Horn,

Wolfgang.

2000. Preface to

Johann

David

Heinichen,

Neu

erfundene

und Grundliche

Anweisung

zu

vollkommener

Erlernung

des

General-Basses

(171 1),

5*-27*.

Hamburg: Benja-

min

Schiller.

Reprint.

Kassel:

Bârenreiter.

.

2001.

"GeneralbaBlehre als

pragmatische

Harmonielehre. Teil I:

Bemerkungen

zum

harmonischen Denken

Johann

David

Heinichens." In

fahrbuch

2001

der

Stàndigen

Kon-

ferenz

Mitteldeutsche

arockmusik,

-40.

Beeskow:

Ortus

Musikverlag.

.

2002. "GeneralbaBlehre als

pragmatische

Harmonielehre. Teil

II: Die

Besprechung

der

Cantata

'Delia mia

bella Clori'

von

Carlo

Francesco Cesarini in

Johann

David Heini-

chens

Anweisung

zum

Generalbaft

(1711)."

In

Jahrbuch

2002

der

Stàndigen Konferenz

Mit-

teldeutsche arockmusik,13-36. Beeskow: Ortus Musikverlag.






Ludwig

Holtmeier

~

Heinichen,

Rameau,

and Italian

Thoroughbass

47

Irmen,

Hans

Josef.

1974.

Engelbert

Humperdinck

als

Kompositionsschuler

heinbergers.

vols.

Cologne:

Arno

Volk-Verlag.

Jans, Markus. 1987. "Allégegen Eine: Satzmodelle in Note-gegen-Note-Sâtzen des 16. und 17.

Jahrhunderts."

Basler

ahrbuch

ur

historische

Musikpraxis

1:

101-20.

. 1993. "Modale

'Harmonik.'

Beobachtungen

und

Fragen

zur

Logik

der

Klangverbind-

ungen

im 16. und fruhen

17.

Jahrhunderts."

Basler

ahrbuch ur

historische

Musikpraxis

17:67-88.

.

2007.

"Towards

a

History

of

the

Origin

and

Development

of the Rule of

the Octave."

In Towards

Tonality:

Aspectsof Baroque

Music

Theory,

119-43.

Leuven: Leuven

University

Press.

Kaiser,

Ulrich.

2000.

Gehôrbildung:

atzlehre

Improvisation Hôranalyse.

2

vols.

Kassel:

Bâren-

reiter.

.

2007a.

Die Notenbucher

er Mozartsals

Grundlage

der

Analyse

von W. A. Mozarts

Komposi-

tionen 1761-1767.

Kassel:

Bârenreiter.

.

2007b.

"Was

st ein

musikalisches

Modell?"

ZeitschriftderGesellschaftfùrMusiktheorie4/S.

http://-urww.gmth.de/zeitschrift/artikel/0134/01B4.html

Kantsteiner,

Armin.

1974/75.

"Der

'Musiktheoretiker'

Max von Droste

Hulshoff und seine

Schûlerin

Annette.

Ein

Beitrag

zur

Grundlage

des

kompositorischen

Schaffens

der

Dichterin."

In

Kleine

Beitràge

ur

Droste-Forschung

,

ed.

Winfried

Woesler,

107-23.

Dul-

men: Laumann.

Keller,

Godfrey.

1707.

A

Compleat

Method

or

Attaining

to

Play

a

Thorough

Bass

upon

Either

Organ

or

Harpsichord

r

Theorbo ute.

London: Cullen.

Kellner,

David.

1732.

Treulicher

nterricht

m

General-Bass.

amburg:

KiBner.

Kûhn,

Clemens.

1994.

"Akkord."

n Musik in Geschichte

nd

Gegenwart

,

vol.

1,

356-66.

Kassel:

Bârenreiter.

Lamott,

Bruce

A. 1980.

"Keyboard

Improvisation

According

to

'Nova instructio

pro

pulsandis

organis

(

1670-ca.

1675)

'

by Spiridion

à

Monte Carmelo."

Ph.D.

diss.,

Stanford

University.

Ledbetter,

David. 1990. Continuo

Playing

According

o Handel.Oxford: Oxford

University

Press.

Louis,

Rudolf

and

Ludwig

Thuille.

1907.

Harmonielehre.

tuttgart:

Klett.

Marpurg,

Friedrich

Wilhelm.

1760.

Kritische

Briefe

uberdie

Tonkunst,

ol. 1. Berlin:

Birnstiel.

Marx,

Adolf

Bernhard.

1830.

"Johann

Bernhard

Logiers

'

System

er

Musikwissenschaf

en.'"

Allge-

meine

musikalische

eitungS2:

413-14.

. 1841 Die

alte Musiklehre

m Streit

mit unserer

Zeit.

Leipzig:

Breitkopf

and Hârtel.

Mason,

Kevin.

1981.

"François

Campion's

Secret

of

Accompaniment

for the

Theorbo,

Guitar,

and Lute."

Journal

of

the Lute

Society f

America

11: 69-87.

Mattei,

Padre

Stanislao.

1850.

Bassi numerati

per

accompagnare.

Ridotti

ad Intavolatura.

A Due

Violini

e viola.

Mailand:

F. Lucca.

Reprint.

Bologna:

Forni,

1969.

Mattheson,

Johann.

1739.

Der vollkommene

apellmeister.

amburg:

Christian

Herold.

Reprint.

Kassel:

Bârenreiter,

1999.

Menke, Johannes. 2008. "Historisch-systematischeLJberlegungen zur Sequenz seit 1600." In

MusikAheorien

er

egenwart

,

ed.

Clemens

Gadenstâtter

and

Christian Utz

(forthcoming)

.

Momigny,

Jérôme-Joseph

de.

1803/1806.

Cours

complet

'harmonie

t de

composition.

aris:

Chez

l'Auteur.

Monachus,

Guilielmus.

1965.

Depreceptis

rtis

musicae

t

practicae

ompendiosus

ibellus

1480]

. Ed.

Albert

Seay.

Rome:

American

Institute

of

Musicology.

Muffat,

Georg.

1699.

Regulae

concentuum

Partiturae.

Ed. Bettina

Hoffmann

and Stefano

Loren-

zetti.

Rome:

Bardi,

1998.

Niedt,

Friederich

Erhardt.

1721.

Handleitung

zur Variation.

Vol. 2

of Musicalische

Handleitung.

Hamburg: Benjamin

Schiller.

Reprint.

Hildesheim:

Olms,

2003.

Nottebohm,

Gustav.

1873.

Beethoven

Studien.

Leipzig:

Rieter-Biedermann.






48

JOURNAL

of

MUSIC

THEORY

Paisiello,

Giovanni.

1782.

Regole

con ben

accompagnare

l

Partimento,

o sia il Basso

Fondamentale

sopra

l Cembalo. t.

Petersburg.

New annotated edition

in Praxis und Théorie es

Partimen-

tospiels, ol. 1. Wilhelmshaven: Noetzel, 2008.

Piel,

Peter. 1887. Harmonie-Lehrenter

besonderer

erucksichtigung

er

Anforderungen

ur

das kirch-

liche

Orgelspiel

unàchst

ur

Lehrer-Seminare.usseldorf: Schwann.

Rameau,

Jean-Philippe.

1722.

Traité

de

l'Harmonie.

Paris: Bal ard.

. 1

726.

Nouveau

système

e

musique héorique.

aris: Bal ard.

.

1737. A Treatise

f

Music. London:

J.

French.

Rameau,

Jean-Philippe

and

Michel-Pignolet

Montéclair.

1729/30.

Conférence,

Mercure e France

June

1729,

1281-89,

2369-77;

February

1730, 253-63;

June

1730, 880-92,

1337-44.

Reber,

Henri.

1862.

Traitéd'harmonie. aris: Colombier.

Rheinberger,Josef

Gabriel.

2001.

Bassùbungenfur

dieHarmonielehre.

d. Istvân P.

Korody.

Vaduz:

Verlag

des

Josef

Rheinberger

Archivs.

Riemann,

Hugo.

1889. Katechismus um

Generalbafi-Spiels.eipzig:

Hesse.

Riepel,Joseph. 1757. Grundliche rklàrungderTonordnung. rankfurt.

. 1996. Sechstes

Capitel

Vom

Contrapunkt.

n

JosephRiepel:

Sàmtliche

chriften

ur Musiktheo-

rie.

Ed. Thomas

Emmerig.

Vienna: Bôhlau.

Rousseau,

Jean-Jacques.

1768. S. v.

Règle

de l'octave. In Dictionnairede

musique,

ol.

2,

221-24.

Paris:

Veuve Duchesne.

Saint

Lambert,

Michel de. 1707. Nouveau traitéde V

ccompagnement

u

clavecin,

de

l'orgue,

et des

autres nstruments. aris: Bal ard.

Samber,

Johann

Baptist.

1704.

Manuductioad

organum.

. .

Salzburg:Johann Baptist

Mayr.

. 1707.

Continuatio

ad

Manuductionem d

organicam.

Salzburg:Johann Baptist

Mayr.

Sancta

Maria,

Fray

Tomâs

de.

1565. Lïbro lamadoarte de taner

a

fantasia.

Valladolid.

Sanguinetti,

Giorgio.

1999. "I

travagli

del 'celeste

impero':

La teoria délia

composizione

a

Napoli

nell'Ottocento fra tradizione

e

innovazione." In

Giorgio Sanguinetti,

Intersezioni.

Quattro

tudi di teoriae analisi

musicale,

137-83.

Cosenza:

Università

délia

Calabria.

. 2005. "Decline and Fall of the 'Celeste

Impero':

The

Theory

of

Composition

in

Naples

during

the Ottocento." Studi

musicaliM:

451-502.

Scaletta,

Oratio.

1595. Scala di

musicamoltonecessaria

er

principianti.

Como.

Reprint

ed.

Venice,

1626;

Bologna:

Forni,

1976.

Schenker,

Heinrich. 1930.

"Rameau oder Beethoven?

Erstarrung

oder

geistiges

Leben in der

Musik?" n

Das Meisterwerkn

der

Musik,

vol. 3. Munich: Drei Masken

Verlag.

Schulz,

Johann

Abraham

[J.

P.

Kirnberger].

1773. Die wahrenGrundsàtze um

Gebrauch

erHar-

monie.

Berlin/Kônigsberg:

Decker and

Hartung.

Schwab-Felisch,

Oliver.

2007. "Umriss eines

allgemeinen Begriffs

des musikalischen Satz-

modells."

Zeitschrift

der

Gesellschaftar

Musiktheorie

/3.

http://wmw.gmth.de/zeitschrift/

artikel/0135/0135.html.

Schwenkreis,

Markus.

2008.

"'Von dem

Fantasieren':

Methodik der

stilgebundenen

Improvisa-

tion nach Jacob Adlung." DutchJournalofMusic Theory 3:98-108.

Sechter,

Simon.

1830.

Practische

Generalbass-Schule.

eipzig:

Leuckart.

.

1852/54.

Die

Grundsàtze

der

musikalischen

Komposition,

vols.

Leipzig: Breitkopf

and

Hârtel.

Seidel,

Ernst. 1969. "Ein

chromatisches

Harmonisierungsmodell

in

Schuberts 'Winterreise.'"

Archiv

ur

Musikwissenschaft

6: 285-96.

Simms,

Brian

Randolph.

1975.

"Choron,

Fétis and the

Theory

of

Tonality."

Journal of

Music

Theory

9:

112-38.

Spiridionis

a

Monte

Carmelo.

1670/71/75.

Nova instructio

ropulsandis

organis,

spinettis,

Manu-

chordiis,

vols. No.

1,

Bamberg:J.J.

Immel,

1670;

no.

2,

Bamberg:J.

G.

Seyffert,

1671;

Reprint

ed.

Edoardo

Bellotti,

Colledara:

Andromeda,

2003.

Nos. 3 and

4,

Wûrzburg:

J.

Saliver,

1675.






Ludwig

Holtmeier

~

Heinichen, Rameau,

and

Italian

Thoroughbass

49

Sulzer,

Johann

Georg.

1771/74.

Allgemeine

Théorie erschônenKùnste.

Leipzig:

Wiedmann.

Vidal,

Paul and

Boulanger,

Nadia.

2006.

A

Collection

f

Given Basses

and Melodies.Ed. Narcis

Bonet. Barcelona: Dinsic.

Vincent,

Heinrich

Josef.

1830. Kein Generalbassmehr.Vienna:

Wallishauser.

Weber,

Gottfried.

1824.

Versuch einer

geordneten

Théorie

der

Tonsetzkunst zum

Selbstunterricht,

2nd

ed. Mainz: Schott.

.

1826.

"'Recension'

der

'Pratica

d'accompagnamento sopra

Bassi

numerati e

contrap-

punti

dal

Padre Maestro Stanislao Mattei.'"

Caecilia4/\4:

135-40.

Yellin,

Victor Fell. 1998.

TheOmnibus dea. Detroit

Monographs

in

Musicology,

Studies in Music

22.

Detroit:

Harmonie

Park.

Ludwig Holtmeier teaches music theory at the Hochschule fur Musik in Freiburg and historische

Satzlehre

at the

Schola Cantorum

in

Basel.

He is the editor of Musik

&

Àsthetik

and has

published

widely

on

the

history

of music

theory,

the Second Viennese

School,

and

Richard

Wagner.

U*v

heinichen, rameau and italian thoroughbass tradition

Documents