“Rameau`s `Nouvelle méthode`.” Journal of the American

Transcription

Rameau's "Nouvelle Méthode"
Author(s): Deborah Hayes
Source: Journal of the American Musicological Society, Vol. 27, No. 1 (Spring, 1974), pp. 61-74
Published by: University of California Press on behalf of the American Musicological Society
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Rameau's"Nouvelle M thode"
BY DEBORAH HAYES
OF THE THEORETICAL SYSTEM of
Jean-Philippe Rameau (I1683are
1764)
ordinarily concerned with the origin and significance of
the basse fondamentale and related concepts and with Rameau's scientific
or Cartesian bias, which served to attract the attention of the philosophes
and Encyclopedists. Such discussions often pay insufficient attention to
the fact that one of the principal sources of Rameau's system, and probably the main reason for its endurance, was his activity as a composer,
performer, and teacher. His stated purpose was always to simplify and
thus improve harmonic practice in conformance with the natural, scientific
procedures and principles that he had discovered. Traditional methods
of continuo realization required an abundance of chords, chord progressions, and rules-rules of doubling, voice leading, and dissonance
treatment. But the principle of the fundamental bass-the succession of
chord roots-was supposed to make possible a simpler, more natural,
and therefore better method of learning keyboard accompaniment and
composition. The fundamental bass principle told the performer or composer the key or tonal center of the piece of music, the various keys
through which it passed, the functions of the chords, the harmonic
rhythm, the lengths of the phrases, and the location of the cadences.
In i732 Rameau published a short treatise entitled Dissertation sur les
DISCUSSIONS
diffdrentesme'thodesd'accompagnementpour le clavecin ou pour l'orgue;
avec le plan d'une nouvelle me'thode,ftablie sure une me'chaniquedes
doigts, que fournit la successionfondamentalede l'harmonie: et d l'aide
de laquelle on peut devenir sfavant compositeur,& habile accompagna-
teur, meme sans sfavoir lire la musique1 ("Dissertation on the different
methods of accompaniment for the harpsichord or organ, with the plan
for a new method, based on a fingering technique furnished by the fundamental succession of the harmony, and with the aid of which one can
become a knowledgeable composer and skillful accompanist, even
without knowing how to read music"). By this time his theories were
generally known, mainly from the Traite de l'harmonie (1722) and the
Nouveau Systkme (1726). He was now fifty years old and was living
in Paris. Although not yet known as a dramatic composer (the opera
1 Facsimile edition by Erwin R. Jacobi, Rameau: Complete Theoretical Writings
(n.p.: American Institute of Musicology, 1969), Vol. V.
62
JOURNAL
OF THE AMERICAN
MUSICOLOGICAL
SOCIETY
Hippolyte et Aricie datesfrom 1733), he had publishedseveralcollections
and composition
of Piecesde clavecinandwas teachingaccompaniment
A
andMontea
method.
debate
between
Rameau
to
new,
according
quick
methods
clairoverthe relativemeritsof the new methodandtraditional
had occupiedthe pagesof the Mercurede France(in the style of the
Paris)from 1729 to 1731.2Whether
manypaperwarsof 18th-century
as a resultof thispublicityor of an increasingdemandfor musicinstruction, especiallysimplifiedmusicinstruction,the Dissertationapparently
enjoyedsomepopularity,for it was the only one of Rameau'streatises
to go into a secondeditionin the I8th century-in 1772,a few years
afterhisdeath.3
Rameau'snew methoddependedon a new notationdesignatinga
keyboardfingeringtechnique(mechaniquedes doigts), for the four
fingersof the righthand,that producedthe standardchordsand chord
The accompanist,
by meansof a few patternsof movement.4
progressions
musicalnotationandplay
ratherthanreada continuopartin traditional
andproduce
wasto reada fingeringchartof the realization
a realization,
When Rameaustatesthatthis fingeringtechnique
his partmechanically.
he meansthat
de l'harmonie,
is furnishedby the successionfondamentale
or root positionchordand its inversionsare all
becausea fundamental
the samefundamental
harmony,the accompanistcan simply play the
most convenientchord positions,accordingto the fingeringpatterns,
andstill maintainthe fundamental-forRameauthe essential-harmonic
progression.
thatit is not necessary
Rameauclaims,in the title of the Dissertation,
or
in
order
read
to
music
to be ableto
accompany to compose.He was
tend to promotesalesof the
would
this
claim
undoubtedlyawarethat
notationinhibitsbothmechanical
book.Buthe alsoexplainsthattraditional
continuomethods,he
traditional
In
skill andintellectualunderstanding.
observes,the student,and even the experiencedplayer,has two main
problems:the imprecisenotationof the continuoand the profusionof
He mustlook at the continuoandtry to
rulesconcerningits realization.5
whatchordsthe bassnotesrequire.In his effortto remember
remember
voiceleading-hisfingers
alltherules-chordtones,accidentals,
doublings,
2
For a list of the articles, see Jacobi, op. cit., III, xii. For a discussion and partial
translation of the articles, see Sister Maria Michaela Keane, The Theoretical Writings of J.-P. Rameau (Washington, D.C., I96i), pp. 86-I12.
8 Jacobi, op. cit., V, xvi-xxi.
4In the second and third books of Pieces de clavecin, Rameau gives information
on the mdchanique des doigts that covers the correct position of the hands on the
keyboard, the flexibility of the fingers and wrist, and the correct distance of the
arm from the keys. But after the Dissertation the phrase has a special meaning; see
for instance the brief summary of the method in the Code de musique pratique
(Paris, 1760), Chap. 5.
5 Dissertation,pp. 2-16. Rameau includes a chart of the signs and figures currently
used and various directions for their interpretation.
RAMEAU'S "NOUVELLE METHODE"
63
get tense, losing their natural flexibility and inclination to movement.'
His headbobs up and down from music to keyboardas he triesto find the
notes. He plays wrong notes, incorrect chords. He fails to locate the re-
quiredaccidentalsin time to convey the full expressiveforce of a change
of key. And after all his attempts, his ear, having heard more wrong
successionsthan right ones, is totally befuddled. But by using the new
mechanicalnotation, even the beginner can play the chord progressions
readily, without hesitation,from the very outset of his training,and thus
developsthe naturalflexibilityand supplenessof his fingers.His ear hears
only the correct fundamentalharmonicprogressions.And his brainsimultaneouslylearnsthe progressionsand develops an understandingof them.
This understandingconsistssimply of a constantawarenessof the fundamentalbass.
The first section of the treatise,the "Dissertationsur les diffirentes
methodes d'accompagnement"(pp. i-i6), and the main section, the
"Pland'une nouvelle m'thode" (pp. 17-48), are followed by five shorter
sections:a "Recapitulation"
of the plan (pp. 48-53); a "Parallele"or comof
the
new
method
with traditionalmethods (pp. 53-59); "De
parison
du
l'exclusion pouce," explainingthe use of only the four fingers (pp.
59-60); "Des octaves,"on the irrelevanceof contrapuntalrules--here the
rule prohibitingconsecutive octaves--to the new method (pp. 6o-62);
and a "Conclusion"(pp. 62-63). A chart facing the last page of the treatise, reproducedhere in Figure i, shows the realizationof the continuo
part of No. 3 of Corelli'sViolin SonatasOp. 57in Rameau'snew notation.
A transcriptionof Rameau'schart for the Corelli accompaniment
appearsin Example i, second staff of each score. (Corelli'ssonata is on
the first and third staves, and the fundamentalbass that Rameau'srealization indicates is on the bottom staff, for comparison.) In Rameau's
notation (Fig. i), the numbers on the lower line (i, 2, 3, 4) indicate
beats, and the dots between the numbersindicate divisions of the beat.
The letters, numbers,and dots on the upper line indicate the chords.
It is immediatelyapparentthat Rameau'srealizationrepresentsa rather
thick harmonictexture, probably thicker than Italianstyle of ca. 1700oo.
In many cases he has added sevenths,even ninths,to harmoniesthat, according to Corelli'scontinuo, could be simply triads.The white notes in
Example I are these "extra"dissonantnotes. Rameau adds these notes
6 Dissertation,p.
io: "Lorsquel'oreilleattendtout de l'xicution pour se former
on tient cette 'x'cution en arrit, les doigts n'y marchentpendant
1'Harmonie,
long-tempsqu'atitons, &n'y font pas un pas sansl'ordredu jugement."Cf. Francois
Couperin,L'Artde toucherle clavecin(1717; Wiesbaden,1933),p.-3: "On devrait
ne commencera montrerla tablatureaux enfantsqu'apresqu'ils ont une certaine
quantit-de piices dansles mains.II est presqu'impossiblequ'enregardantleur livre,
les doigtsne se dbrangentet ne se contorsionnent."
7 12 sonatea violinoe violoneo cimbalo(Rome,
1700).
64
JOURNAL OF THE AMERICAN MUSICOLOGICALSOCIETY
64
S ONATAIR.DE
CORELLI.
C
C
4xC x C x C 'YI
2.3 4 1 2 3 4.
3 41
12
GEXG 2 4aG x G x G
G
xoG2
:
Ge
32
G
,
4'xGC
0:
Ax
24C4
4.2
yx.cAarA
:
:0
2 3941
11
J.3
34
:
23
f5
:
4
a, hBIE4xE C
1 2 3.4.11 2.3 4.11 2.3 4. 14.2.3 41
, :c,
1
.3
, : 94ca2I e4xc eG
:c 1acC4xc
. 2 o.0.4 4 . 3.3 4
s.2.3.4
Ij.cr
. 3.94
1.2
3 ec
.1..i2.3
e
4
.
4.
4.91.2.3
.34c41
Figure i. Rameau's realization of Corelli's continuo
"NOUVELLE
RAMEAU'S
METHODE
65
Examplei
Transcriptionof Rameau's realization with Corelli's Sonata and the fundamentalbass
Adagio
Corelli's melody
Rameau'srealization
Corelli'scontinuo
4
6
5
3
Fundamentalbass
67 77
7
7
IO
5
7
7
66
b
7
6
-7
67
7
7
7
7
7
7
7
7
7
7
76
15
7
6
7
7
7
3
7
7
7
7
7
76
7
7 6r7 7
7
7
7
RAMEAU'S
"NOUVELLE
67
METHODE"
20
2IF
5
7
7
6
5
7
7
6
77
7
4
2
7
7
and statesthat accompanimentshould produce full, complete chords8because he wants the performerto hear the function of each harmony-tonic, dominant,or subdominant-in the very makeupof the chord. Triads occur only on tonics; thus the sound of a triad signals arrivalat a
new key.9 Phrasesare built of successions of dissonant harmonies,or
The subdominantchord, which is a triad with added
seventh-chords."0
sixth, likewisebecomesa seventh-chordthroughRameau'sconcept of the
double emploi of this added sixth (the second degree of the scale) as a
fundamental."
Most of Rameau'stheoreticalideas may be found representedin his
realizationof Corelli'scontinuo. In the Dissertation,however, he deals
mainly with the mechanics of the keyboard method and not with its
theoreticalbasis.He refers to his two previoustreatisesfor severalpoints
of theory and also promisesa "d6monstration"
or mathematicalproof of
the basis of this method in a forthcoming "ouvragede theorie."' This
work, the Gine'ration harmonique (1737), must be consulted if the
method is to be understood.
du Clavecinconsiste executer sur
8Dissertation,p. 17: "L'Accompagnement
cet instrumentune harmoniecomplette& reguliere."He is criticalof the practiceof
chord, for
omittingnotes from variousforms (inversions)of the dominant-seventh
instance(p. ii).
9Ibid.,p. 2I: "L'Accordconsonant,connu sous le nom de Parfait,convienta la
seule Tonique."
10Ibid.:"Lasuccessiondes AccordsDissonansentr'euxse fait
geniralementdans
un memeTon; la dissonancey lie, pour ainsi dire, le sens harmonique;un Accord
y fait souhaiterl'autre;le sens,par ce moyen,n'estpas fini; & c'est cette succession
qui fournittoujoursles phrasesles plus longuesen harmonie."Rameaualso reviews
his reasonsfor consideringthe seventh-chordto be the only fundamentaldissonant
chord,referringthe readerto the Traitede l'harmoniefor furtherexplanation(pp.
12-14).
11 Ibid., p. 33. Rameaurefers the readerto the Nouveau Systeme for further
information.
12
Ibid.,pp.42, 47.
68
Firstin importancein Rameau'ssystem-the pillarsof the harmonic
structure-arethe consonantchordsor tonic triads.Triadsare representedin FigureI by largeletters("CA C"in m. i). Thus,Rameauexplains,the performerknowsnot only the mainkey of the piece (C, in
Fig. i), but alsothe variouskeys throughwhichthe piecewill move (A,
G, E, D). He can play the chordtonesin any order;for "C"he may
harplay C-E-G,E-G-C,or G-C-Ewithoutchangingthe fundamental
in
indeed
to
as
In
from
one
consonant
chord
another,
mony. moving
all progressions,
the playeris taughtto holdthe commontonesandmove
notesby step.(Becausethe first"C"chordcouldbe played
the remaining
in anyform,andbecausethe fingersalwaysmoveto the nearestnotes,the
in Ex. 1,secondstaff,representsonly one of manypossible
transcription
renditionsof Rameau's
chart.)
All otherchordsare dissonantchords,or variouskindsof seventhin Rameau'snotationby smallletters(x,
chords.Theseare represented
x
itself
indicatesthe dominant-seventh
dots.
An
and
harmony
aj,etc.)
by
sensible
or
chord")belongingto the next tonic
(accord
"leading-tone
bassof this chord is the "tonic dominant"or
triad.The fundamental
fifth degree.The x chordis usuallyfollowedby its tonic triad,forming
a "perfectcadence"(V7-I); the letters"x C" (m. 2) and"x G" (m. 6),
for example,indicateperfectcadenceson C andG.
on the seconddegree.The two alterThe "2"meansa seventh-chord
notesof this chord,the secondand fourth (subdominatefundamental
bassof Examplei. The
nant) degrees,arebracketedin the fundamental
G"
in m. 9), formingan
triad
tonic
followed
its
be
chordmay
("2
by
it
More
often
cadence"
(IV-I).
goes to x, which in turn
"imperfect
not a chordbut a suspenindicates
The
"4"
goesto the tonic (IV-V-I).
tonic
and
the
sion,producing second,fifth,
degrees,andit usuallyoccurs
nor
a dissonantchord(seventha
triad
neither
between"2"andx; being
devisedthe conceptof the
note.
Rameau
chord),it has no fundamental
double emploi so that the fundamental bass could always move by fifths
(and fourths) within one key.'3 For example, in the progression "C 2 4
x C" (mm. 1-2), the fundamental bass moves from C (tonic) to F (subdominant) and then from D (alternate subdominant fundamental) to G
(dominant).
The abbreviation aj (ajoute) indicates an added-sixth chord on the
tonic (C-E-G-A in C major). This chord, however, being dissonant, does
not function as a tonic. In measure 3 it functions as a subdominant harmony in the key of the dominant ("C aj x G"). When its fifth is raised,
it functions as the tonic dominant of the supertonic key (G (G?A, in
m. 14).
13
In the Generation, Chaps. 2-6, 9 (on the double emploi), 1o, and II, Rameau
is concerned with showing that all diatonic progressions are "products"of a fundamental bass moving by fifths.
RAMEAU'S
"NOUVELLE
METHODE"
69
The "4" means the tonic, third, fourth, and sixth degrees. This is
simply another dissonant chord, like aj, but even more distant from the
tonic; that is, a greater number of chords is required to arrive at a tonic
triad.14 The "4" in measure io (the b cancels the F# of "x G" in mm.
9-1o) begins a phrase that does not end until "A" in measure I2.
Movement from one dissonant chord to the next in a phrase is indicated in Rameau's notation by from one to four dots, representing the
four fingers of the right hand. Each dot means that one finger moves
down by step. (When the hand has moved too far down the keyboard
the player simply moves it up to the top again and resumes the downward patterns.) The first or "one dot" finger, Rameau explains, is the
uppermost finger if the chord is by thirds, or, what amounts to the same
thing, the lower of two adjacent fingers (in musical terms, the seventh
of the chord). For example, whether the chord D-F-A-C progresses to
D-F-A-B, or F-A-C-D progresses to F-A-B-D, the fundamental harmonic
succession is the same. If two dots appear (this is the most usual pattern)
the finger below the first finger (the fifth of the chord) also moves; for
example, D-F-A-C goes to D-F-G-B. Three dots would add a third finger,
the one below the second finger (the third of the chord), and four dots
would indicate the entire hand. An x may replace one of the dots (in
m. 3, for instance), meaning that the note is sharped, and, coincidentally,
confirming the fact that this is the accord sensible of a new tonic (G, in
m. 4). Using the new notation, Rameau explains, the performer does not
need to know key signatures; accidentals are indicated for specific fingers
as they occur.
In Figure I it appears that the two-finger progression is Rameau's
favorite; certainly it is the most useful in playing Corelli. The long phrase
in measures io-i 2 is made up of a series of two-dot or two-finger progressions, indicating a series of seventh-chords in a fundamental succession
by descending fifths, ending with an accord sensible and its tonic chord,
as shown in Example i. Rameau has added many sevenths to Corelli's
continuo, undoubtedly in order to avoid the consonant sound of a triad
that would signal a new (temporary) key and the end of the phrase.
On the third beat of measure 13, Rameau adds a seventh and a ninth;
for the F in the continuo he chooses the aj chord in C major. The continuo in such a case is considered by Rameau to be a note par supposition
a third below the fundamental, used simply to add melodic interest to
the continuo. The same harmony occurs in measure 18, first beat, where
Corelli has indicated a ninth-chord. Because fundamental harmonies contain no more than the four pitches of the seventh-chord, only four fingers
are required to play them.
14 Rameau describes one more chord in the Dissertation. a chord similarly distant
from the tonic, although he does not use it in his Corelli realization: the "7," meaning the tonic triad plus the seventh degree.
JOURNAL
70
OF THE AMERICAN
MUSICOLOGICAL
SOCIETY
In the final phrase,in measurezo, Rameauadds dissonantnotes and
also adds chord changes (first, second, and third beats). Here his purpose
in correctingCorelli'sharmonyseems to be to create a seriesof seventhchords in a fundamentalsuccessionby descendingfifths. Corelli'serror
is that he has simply indicated triads on A (beat i), E (beat 2) and F
(beat 3), whereasin Rameau'ssystem triadsare only proper at cadences.
Further,the fundamentalbassof Corelli'scontinuowould move by a second from E to F, an intervalwhich in Rameau'ssystem should not occur
in a diatonic progression,but only in certain special cases, or "licenses,"
concerningthe enharmonicgenus.15
Rameau's"nouvelle methode" thus consists of learning the fundamental harmonicsuccessionsby playing accompanimentswritten in the
new notation. (At the end of the Dissertationhe pleads for a reengraving of existing continuo parts in this notation.) At first, only the chord
progressionor right hand part is involved. It is not necessaryfor the beginner to play the continuo itself, Rameau explains,as another instrument in the ensemblewill be playing it and as it is only a melodic line
(la Basse... que dicte le goat du chant) and thus an extra, nonessential
(hors d'oeuvre) part as far as the fundamentalharmonic succession is
concerned."1Nor is it necessary for the beginning accompanistto be
able to read music and to understandkey signaturesand accidentals,as
the new notationshows him how to move about the keyboard and even
indicates each sharp or flat. Finally, the accompanistdoes not need to
learnthe rulesfor the preparationand resolutionof dissonancesand other
rules of counterpoint,becauseby holding common tones and moving by
step, the player is automaticallypreservingthe "connection"(Liaison)
between successivefundamentalharmonies,the connection that Rameau
believes is the source or principle of all counterpointrules.17This new,
simplifiedmethod allows the beginnerto become a "skillfulaccompanist"
in only a few months, in comparisonwith the ten or twelve years that
traditionalmethodsrequire.18
15Rameau discusses enharmonic progressions in the Generation, pp. 149-55, and
reviews the licenses by which the fundamental bass moves by second on pp. I82-88.
A similar instance of Rameau's "corrections" of Corelli's figures may be found in
the Nouveau Systdme, Chap. 23. His corrections of Lully's continuo, in the same
treatise, have been illustrated by E. Cynthia Verba, "The Development of Rameau's
Thoughts on Modulation and Chromatics,"this JOURNAL, XXVI (1973), 69-91. In
later treatises,she finds, Rameau seems to advocate changing many simple dominants
into tonic dominants, implying a greater number of (temporary) tonics, for greater
expression; for example, by chromatic alteration, vi7 becomes V7/ii, and ii7 becomes
VT/V.
16
Dissertation,pp. 17-19.
35: "Les sons qui se conservent ainsi d'un Accord a un autre, en font
necessairementsentir la liaison; par ce moyen, leur succession nous devient agr6able."
In the Gendration, Chap. io, Rameau explains his concept of "connection" in detail, extending it, through a concept of "forced connection," to cover stepwise
motion as well as common tones.
is Dissertation, pp. 15, 34, 6o, 63.
17 Ibid., p.
METHODE"
RAMEAU'S
"NOUVELLE
7P
It remainsto examinehow the beginneris to become a "knowledgeable
composer."The method describedin the Dissertationtakes the beginner
to the point where he can begin to composeat the keyboard-to preludize
and to improvise (priluder; toucher les Fantaisies)."9At some point the
beginner learns to read music, adds the left hand part to his accompani-
ments, and then learnsto compose music notated in the usual way. He
continuesto use the fundamentalbass, not only imaginingit and hearing
it in all progressions,but also writing it down as a guide (it is of course
never performed).
While Rameaudiscussesthe use of the fundamentalbass in accom-
paniment and composition in both the Traitd de I'harmonie and the
Nouveau Systeme, the clearestexplanationof his compositionmethod is
found in the Gindration harmonique.It is significantthat this work, in
which he intended to provide mathematicalor geometrical proof that
all music depends on the fundamentalbass principle, initiated his perpetualbattle wih the Encyclopedistsover his standingas a philosopheand
scientist of harmony.20For this treatiseis as practicalas it is speculative.
Here Rameaurefersthe readerto the Dissertation,statingthat his explanation of the use of the fundamentalbass in musical composition in the
Gindrationis a parallelto the keyboardmethod.21
In the Gendration(Chap. 18)22Rameaugives two alternatemethods
of composition.In the first the would-be composer begins by writing a
fundamentalbass. He uses it to ascertain that the keys, phrases, and
cadences are proper. The fundamental bass in Example i, for Rameau's
own harmonicprogressions,can serve as an illustrationof a correct fundamental bass. Tonics have no number, dominantsare given a "7" (the
"tonic dominant"is the main dominantin a key), and subdominantsa "6"
(the second degree, the alternatefundamental,is a dominant).The cor-
rect "routes" Rameau describes here correspond to the fingering patterns
in the Dissertation.The fundamentalbass usually moves by fifth, the
19Ibid.,pp. 8,
I5.
20 For an account
of
the issuesinvolved,see JamesDoolittle,"A Would-Be'PhiRameau,"Publicationsof the ModernLanguageAssociation
losophe':Jean-Philippe
of America,LXXIV (r959),233-48.
21 Geniration,pp. 215-16:"Voiez ma Dissertationsur les diff6rentesM6thodes
d'Accompagnement,
vous y retrouvereztout ce qui vient d'8treannonc6;. . . par
la comparaisonque vous pourrezfaire des regles qui y sont contenuesavec celles
de la Bassefondamentale,
vous reconnoitrezque les unes sont tir6es des autres,&
que leur differencene consisteque dans la diffirencedes deux objets auxquelson
les appliquepour lors: lR,ces rigles sont relativesa la Mechaniquedes Doigts dans
l'&xcutiond'une Musiquedj)a composee,ici elles le sont au fondementde tout
cette Musique;& rien n en prouvemieuxla certitude,puisqu'ellessont donneespour
y suivreson imagination,aussi-bienque celle des autres,qui s'y trouve necessairement soumise."Similarly,in the Dissertation,p. 29: "Ce que j'appliqueaux doigts,
aux Touches du Clavier,peut 6galements'appliqueraux Notes, independamment
de ces doigts & de ces Touches: ainsi je parlepar-toutau Compositeur,
aussi-bien
qu'i 1'Accompagnateur."
22 "De la Modulationen g6neral,avec un
abregi des reglespour la Composition,
&pourtrouverla Bassefondamentale
sousun Chantdonne."
72
for example,it movesby fifth
properintervalof the "diatonicgenus";23
in the perfectandimperfectcadencesandin a "chainof dominants"
(the
two-fingerprogressionof the Dissertation).A phrasebeginningwith
the tonicdominantis shortbecauseit goes directlyto the tonic ("Cx C"
in mm.2-3). A longerphrasebeginson a moredistantdominant("aj"in
m. 16, or "i) " in m. io) becausethen the fundamental
bass,movingby
fifths from dominantto dominant,takeslonger to reacha tonic (one
bassmovesby third
chordafteraj, nine after"4"). The fundamental
in the "chromatic
It movesamong
that
where
the
is,
genus,"
key changes.24
A
In
third-related
in
measure
i
measures
("C
C").
3-4, "Caj x G,"
keys
it movesby thirdfrom"C"to "aj",to changekey;thenceit movesby fifth
to "x"wherethe changeof key is confirmedby the chromaticalteration
of F to F#,andfinallyby fifthto the new tonic.Likewisein a longphrase
andmovingfromdominantto domi(onebeginningat a distantdominant
the
a tonicdominantby chromatic
of
dominants
be
made
nant),any
may
alteration,makingthe next chorda (new) tonic triad;for example,in
measuresio--i2, the phrasebeginsin C with a c" ", andthe ninthof the
that follow is madea tonic dominant(x) throughchromatic
dominants
so thatthe phraseendson a new tonic,A. Finally,the fundaalteration,
bass
mental movesby secondin the "enharmonic
genus,"butrarely.25
corhis
fundamental
bassis harmonically
Havingassuredhimselfthat
kind
it
of
rect, the composerproceedsto give some
rhythm,preferably,
Rameauadvises,a dancerhythm,wherethe cadenceand phrasestructuresareclearandregular.Then he writesa continuoandothermelodic
partssimplyby stringingtogetherthe variouschordtonesmadeavailable
bassnote. He can also add, depending
by each successivefundamental
tones(Notes de goazt)for
on his talentsandhis taste,somenonharmonic
melodicornamentation
(pourle gozitdu Chant);in this regard,Rameau
mentions"suppositions"
(continuo)and suspensions(upperparts) and
tonesthatoccurin the melodicparts,similar
describesothernonharmonic
in the continuoof Examplei (D andB in m. i, E
to the sixteenth-notes
in m. 2, andso on).
In the secondmethod,which Rameauoffersin casesomemightfeel
that the first "stiflestheir naturalgenius,"the musicianbeginswith a
bass,andthenwritesthe othermelodic
melody,thenfindsits fundamental
the
the
Like
accompanist, composerdoes not need to know any
parts.
bassis correcthe is assuredthathe
if his fundamental
rules;
counterpoint
whichis the sourceof these
hasobservedthe principleof "connection"
Rameauobserves,he must rely on
rules.But unlikethe accompanist,
talentandtaste,whichmaygo beyondtherulesor principles.26
23See fn. I3.
Gindration, Chap. 14.
25 See fn.
15.
26
Gindration, p. i7o: "A l'6gard du g6ut, du genie, cela ne se donne pas, mais
on peut du moins en procurer des idies assez distinctes A la faveur de la Basse
24
RAMEAU'S
"NOUVELLE
METHODE"
73
Rameau believed that the fundamental bass provided a simpler and
quicker method than traditional continuo methods because it allowed
him to omit or circumvent the details of melody, counterpoint, rhythm,
ornamentation, and the like. However, it was apparently oversimplified.
Subsequent theorists have used the fundamental bass, but in combination
with the details that Rameau omitted.
He also believed that the fundamental bass was a natural principle,
scientifically and mathematically demonstrable. The triad, he observed,
which was the starting point of his theoretical system and of a piece of
music, is made up of intervals with the simplest ratios, and further, it
is contained in the first few harmonic sounds or overtones of a single
fundamental. The most natural interval (discounting the octave as lacking
harmonic significance) is the fifth; therefore the movement of the fundamental bass by fifth, as from dominant to dominant or from tonic
dominant to tonic, Rameau reasoned, was the most natural harmonic succession. The tonic note and its triad, being the first sound in the fundamental bass, became a first principle of Rameau's system of harmony.
Here he met with criticism from scientists and philosophes. As Diderot
(among many) observed, if the triad were truly a natural principle of
music, then the music of every time and place would sound the same.27
It appears that the fundamental bass principle resulted from a fortunate
coincidence of musical style and acoustical knowledge. In the context of
musical practice, Rameau's contention that it was a natural principle is
quite plausible. He saw the fundamental bass method as an improvement
not only on continuo methods in general but specifically on the contemporary French method called the "regle de l'octave."28 This rule was a
shorter method, whereby each note of the octave scale in the continuo
was given a certain chord. As Rameau observed, it depended on the
performer's knowing the key; it also used only tonic, dominant, and
subdominant chords.2 The "octave rule" may be taken as evidence that
musicians were beginning to redefine their harmonic language in terms of
these three kinds of chords, a process that Rameau only carried further.
In the light of this stylistic change, Rameau's statements that the fundafondamentale." Also, from the Dissertation, p. 9: "D'autres [Maitres] enseignent
totalement la Composition, ou conseillent de l'apprendre avant I'Accompagnement;
comme si cet Accompagnement n'etoit pas la Composition meme, aux talens
pros,
qu'il faut joindre a l'un pour faire usage de l'autre."
27
IDnis Diderot, Principes generaux d'acoustique (i748). Similarly, Jean Le Rond
d'Alembert, although undertaking to clarify Rameau'sharmonic system (Elemens de
musique, theorique et pratique, suivant les principes de M. Rameau [1752]), argues
that while the triad may exist in nature, it cannot be "demonstrated"to be the
naturalsource of an entire harmonic system.
28
pp. 7-8,
29Dissertation,
From the Trait6, Bk.53-59.
III, Chap. Ii. Note that at this earlier stage in his thinking, Rameau used an alternate fundamental on the tonic (third note) rather than
on the subdominant,in order that the fundamentalbass move only by fifths (Ex. 2).
74
Example 2
6
6
6
5
Fundamentalbass
7
77
"•0
-EI•-j
7
.
6
-5
6
7
0
7
7
61
4# 6
6
7
7
mentalbasswas naturalmay be interpretedto meanthat it was "familiar"
or "useful."As a practicaltool, perhapsthe fundamentalbass was indeed
the "ear's unique compass," the "musician'sinvisible guide," and, as
Rameauso often stated,a "naturalfeeling."•0
Notwithstandingthe argumentsof the philosophes,Rameauapparently
projected the fundamentalbass beyond contemporarypractice. He evidently felt that Corelli had been on the verge of discoveringthis principle, and thus his harmonicprogressionsneeded only a little correction.
Further, once establishedor "proved," the fundamentalbass principle
would always continue to guide musicians.31Rameauevidently believed
that in playing correct fundamentalprogressionsthe performerbecame
one with the physico-mathematicalorder of the universe.Surely it does
Rameauno disserviceto observethat he also believed that the performer
should be able to play his part, hear what he was playing, and, above all,
learnto understandit.
Universityof Colorado
so Ginrration, Preface: "Je suis enfin parvenu, si je ne me trompe, a pouvoir
dimontrer ce principe de l'Harmonie, qui ne m'avoit encore &te suggere que par
la voie de
cette Basse fondamentale, l'unique Boussole de l'Oreille, ce
l'explrience,
guide invisible du Musicien, qui l'a toujours conduit dans toutes ses productions, sans
qu'il s'en soit encore apperu, mais dont il n'a pas plut6t oui parler, qu'il l'a regardk
comme son propre bien; je connoissois d6j~ cette Basse fondamentale, a-t'il dit;
cependant s'il se fit bien examine, il auroit dit simplement, je la sentois: c'est effectivement un de ces sentimens naturels auxquels on peut fort bien ne pas penser,
mais qui se diveloppent en nous au moment qu'on nous les rappelle."
31
Dissertation, p. 42: "En attendant que je puisse justifier toutes
' ces veritis, par
une dimonstration &vidente,les Ouvrages de Musique composes & composer, m'en
seront garants; je dis a composer, parce que la nature est une, & qu'elle guidera
toujours le Musicien comme elle l'a guidi jusqu'ici, quant au fond de l'harmonie."
Rameau'swritings after the Generation continue to explain the fundamental bass as
a physico-mathematical principle (notably the Demonstration du principe sonore
[17501) and as an innate feeling (notably the Observations sur notre instinct pour
la musique et pour son principe [x754]).

“Rameau`s `Nouvelle méthode`.” Journal of the American

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