/LMAR=0/XLINE=10/FONT#0=METL/FONT#1=METLI/FONT#2=METS/FONT#3=MUS[HHA,LCS]/FONT#4=FIX30/FONT#5=BASL35
␈↓ α≠␈↓␈↓ ε.56␈↓ 
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␈↓"β␈↓ α≠␈↓␈↓ ¬dCHAPTER V


␈↓"β␈↓ α≠␈↓␈↓ ∧pEXTENDED TONICIZATION

␈↓"β
␈↓"β␈↓ α≠␈↓Added Levels of Tonic Function

␈↓"β␈↓ α≠␈↓␈↓ α{ Almost␈αby␈αdefinition,␈αmusic␈αof␈αthe␈αtonal␈αera␈αdepends␈αon␈αthe
␈↓ α≠␈↓listener's␈α∪strong␈α∩memory␈α∪of␈α∪a␈α∩basic␈α∪tonic.␈α∪ The␈α∩basic␈α∪tonic␈α∪is␈α∩a
␈↓ α≠␈↓cohesive␈α
force␈α
which␈α
sets␈α
limits␈α
and␈α
acts␈α
as␈α
a␈α
reference␈α∞point␈α
for
␈↓ α≠␈↓all␈α↔types␈α↔of␈α↔harmonic␈α↔movement.␈α↔ Even␈α↔␈↓↓modulation␈↓␈α↔within␈α↔a
␈↓ α≠␈↓movement␈α⊃never␈α⊃really␈α⊃destroys␈α⊂this␈α⊃reference␈α⊃point;␈α⊃it␈α⊂merely
␈↓ α≠␈↓sets␈α⊂up␈α⊂a␈α⊂foremost␈α⊂subsidiary␈α⊂point.␈α⊂ When␈α⊂␈↓↓tonicization␈↓␈α⊂becomes
␈↓ α≠␈↓greatly␈α∃extended,␈α∃the␈α∃same␈α∀effect␈α∃is␈α∃produced␈α∃on␈α∃a␈α∀somewhat
␈↓ α≠␈↓smaller␈α∂scale.␈α⊂ The␈α∂difference␈α⊂between␈α∂extended␈α⊂tonicization␈α∂and
␈↓ α≠␈↓modulation␈α∩lies␈α∩in␈α∩the␈α∩role␈α∩the␈α∩particular␈α∩passage␈α∩is␈α∩playing␈α⊃in
␈↓ α≠␈↓relation␈α⊂to␈α⊂the␈α⊂whole.␈α⊂ There␈α⊂is␈α⊂much␈α⊂music␈α⊂wherein␈α⊂these␈α⊂two
␈↓ α≠␈↓concepts␈αtend␈αto␈αoverlap,␈αbut␈αin␈αthe␈αmain,␈αcomposers␈αof␈αthe␈αmusic
␈↓ α≠␈↓here␈αunder␈αconsideration␈αhave␈α
been␈αso␈αintent␈αupon␈α
formal␈αclarity
␈↓ α≠␈↓that␈α"the␈α"dependent␈α"character␈α"of␈α"tonicization,␈α#even␈α"when
␈↓ α≠␈↓extended, is maintained.

␈↓"β␈↓ α≠␈↓␈↓ α{ This␈α∞important␈α
facet␈α∞of␈α
tonal␈α∞music␈α
may␈α∞be␈α∞represented␈α
by
␈↓ α≠␈↓␈↓↓added␈α∂levels␈α∂of␈α∂tonicization␈↓␈α∂in␈α∞the␈α∂middle␈α∂area␈α∂of␈α∂the␈α∞analytical
␈↓ α≠␈↓diagram.␈α∃ These␈α∃added␈α∃levels␈α∀occur␈α∃when,␈α∃␈↓↓within␈↓␈α∃a␈α∀␈↓↓temporary␈↓
␈↓ α≠␈↓tonic␈α
area,␈α
again␈α∞a␈α
new␈α
tonic␈α
is␈α∞approached.␈α
 A␈α
simple␈α∞example␈α
of
␈↓ α≠␈↓this␈α→follows.␈α~ The␈α→basic␈α~key␈α→of␈α~␈↓&C␈↓)αβ␈α→is␈α~understood␈α→to␈α~be␈α→well
␈↓ α≠␈↓established both before and after the example.
␈↓"β
␈↓"β␈↓ α≠␈↓Example 59
␈↓"β␈↓ α≠␈↓␈↓ βd␈↓¬⊂⊗⊃L[%0.00,%-1.42]:N59X.PLT[HHA,LCS]⊂⊗⊃␈↓
␈↓ α≠␈↓␈↓ ε.57␈↓ 
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␈↓"β
␈↓"β␈↓ α≠␈↓Figure 59a
␈↓"β␈↓ α≠␈↓␈↓ βd␈↓¬⊂⊗⊃L[%0.06,%-1.20]:N59A.PLT[HHA,LCS]⊂⊗⊃␈↓






␈↓"β␈↓ α≠␈↓␈↓ α{ The␈α␈↓&D␈↓)αβ␈αarea␈αat␈α
(xx)␈αappears␈αin␈αdirect␈αrelationship␈α
only␈αwith
␈↓ α≠␈↓the␈α∪␈↓&G␈↓)αβ␈α∪(or␈α∪tonicized␈α∪V)␈α∪area.␈α∪ Even␈α∪though␈α∪every␈α∪numeral␈α∩that
␈↓ α≠␈↓appears␈α⊃in␈α⊃the␈α⊃middle␈α⊃area␈α⊃of␈α⊃an␈α⊃analysis␈α⊃is␈α⊃␈↓↓understood␈↓␈α⊃to␈α∩be␈α⊃a
␈↓ α≠␈↓tonic␈α⊃(i.e.,␈α∩working␈α⊃as␈α∩a␈α⊃"I"),␈α∩a␈α⊃new␈α∩I␈α⊃is␈α∩placed␈α⊃under␈α∩the␈α⊃first
␈↓ α≠␈↓presentation␈α∪of␈α∀V␈α∪as␈α∪a␈α∀tonic␈α∪in␈α∪order␈α∀that␈α∪the␈α∪interval␈α∀of␈α∪the
␈↓ α≠␈↓subsequent␈α⊃movement␈α⊂to␈α⊃␈↓&D␈↓)αβ␈α⊃(i.e.,␈α⊂the␈α⊃dominant␈α⊂relation␈α⊃to␈α⊃␈↓&G␈↓)αβ),␈α⊂is
␈↓ α≠␈↓readily␈α#apparent.␈α# Similarly,␈α$another␈α#I␈α#appears␈α$when␈α#the
␈↓ α≠␈↓progression␈α
returns␈α
to␈α
␈↓&G␈↓)αβ␈α
as␈α
the␈α
tonic.␈α
 In␈α
the␈α
previous␈α
example␈αit
␈↓ α≠␈↓will␈α⊃be␈α⊃noted␈α⊃that␈α⊃the␈α⊃tonicized␈α⊃␈↓&D␈↓)αβ␈α⊃was␈α⊃specifically␈α⊃major.␈α⊂ This
␈↓ α≠␈↓new␈α
I␈α
contains␈α∞F␈↓βS␈↓␈α
--␈α
not␈α
a␈α∞functional␈α
probability␈α
in␈α
terms␈α∞of␈α
the
␈↓ α≠␈↓original ␈↓&C␈↓)αβ, but completely compatible with the ␈↓&G␈↓)αβ scale.

␈↓"β␈↓ α≠␈↓␈↓ α{ This␈α
may␈α
be␈α
made␈αeven␈α
more␈α
clear␈α
if␈αwe␈α
set␈α
up␈α
what␈αwill␈α
be
␈↓ α≠␈↓called␈α␈↓↓tonic␈αguide␈αtones␈↓.␈α These␈αrepresent,␈αin␈αmusical␈αnotation,␈αthe
␈↓ α≠␈↓elements that appear in the middle area of the analysis.
␈↓"β
␈↓"β␈↓ α≠␈↓Figure 59b
␈↓"β
␈↓"β␈↓ α≠␈↓␈↓ βf␈↓¬⊂⊗⊃L[%0.00,%-1.60]:N59B.PLT[HHA,LCS]⊂⊗⊃␈↓
␈↓ α≠␈↓␈↓ ε.58␈↓ 
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␈↓"β␈↓ α≠␈↓␈↓ α{The␈αtonics␈αwhich␈αare␈αmost␈αclosely␈αrelated␈α(see␈αtable␈α
on␈αpage
␈↓ α≠␈↓46)␈α∪are␈α∩connected␈α∪by␈α∩horizontal␈α∪bars.␈α∩ The␈α∪black␈α∩notes␈α∪may␈α∩be
␈↓ α≠␈↓added␈α∞to␈α∞show␈α∂the␈α∞mode␈α∞of␈α∞each␈α∂tonic.␈α∞ When␈α∞dealing␈α∂with␈α∞very
␈↓ α≠␈↓complex␈α
progressions,␈α
it␈α
may␈α
often␈α
prove␈α
quite␈α
helpful␈α∞to␈α
sketch
␈↓ α≠␈↓out␈α∞the␈α∞tonic␈α∞guide␈α∞tones␈α
previous␈α∞to␈α∞making␈α∞any␈α∞final␈α
decisions
␈↓ α≠␈↓concerning the particular relationships of the temporary tonics.

␈↓"β␈↓ α≠␈↓␈↓ α{If␈α⊂some␈α∂of␈α⊂the␈α∂notes␈α⊂of␈α∂Example␈α⊂59␈α∂are␈α⊂altered␈α∂so␈α⊂that␈α∂we
␈↓ α≠␈↓arrive␈αat␈α␈↓&d␈↓)αβ␈αminor,␈αinstead␈αof␈αmajor,␈αits␈αrole␈αas␈αthe␈αtonicized␈αV␈αof␈α␈↓&G␈↓)αβ
␈↓ α≠␈↓is␈α⊃greatly␈α⊃weakened.␈α⊃ Voice␈α⊂leading␈α⊃is␈α⊃important␈α⊃in␈α⊂establishing
␈↓ α≠␈↓the␈α∩␈↓&d␈↓)αβ␈α∩area.␈α∩ The␈α⊃B␈α∩and␈α∩C␈↓βS␈↓,␈α∩6th␈α⊃and␈α∩7th␈α∩scale␈α∩degrees,␈α∩appear␈α⊃in
␈↓ α≠␈↓ascending lines, the B␈↓βF␈↓ and C␈↓βN␈↓ in descending lines.
␈↓"β
␈↓"β␈↓ α≠␈↓Example 60
␈↓"β␈↓ α≠␈↓␈↓ βd␈↓¬⊂⊗⊃L[%0.00,%-1.38]:N60X.PLT[HHA,LCS]⊂⊗⊃␈↓








␈↓"β␈↓ α≠␈↓␈↓ α{Now,␈α
since␈αthe␈α
I␈αchord␈α
of␈α
␈↓&d␈↓)αβ␈αdoes␈α
not␈αdisturb␈α
the␈α
material␈αof
␈↓ α≠␈↓the original scale, it is heard in direct relation to ␈↓&C␈↓)αβ.
␈↓"β
␈↓"β␈↓ α≠␈↓Figure 60
␈↓"β
␈↓"β␈↓ α≠␈↓␈↓ βg␈↓¬⊂⊗⊃L[%0.00,%-1.52]:N60F.PLT[HHA,LCS]⊂⊗⊃␈↓
␈↓ α≠␈↓␈↓ ε.59␈↓ 
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␈↓"β␈↓ α≠␈↓␈↓ α{Very␈α
often␈αthere␈α
will␈α
be␈αno␈α
clearcut␈αprocedure␈α
that␈α
may␈αbe
␈↓ α≠␈↓followed␈α∞when␈α
analyzing␈α∞situations␈α∞similar␈α
to␈α∞the␈α∞next␈α
example.
␈↓ α≠␈↓At␈α≠(*),␈α≠the␈α≠change␈α≠of␈α≠mode␈α≠on␈α≠the␈α≠G␈α≠root␈α≠makes␈α~varying
␈↓ α≠␈↓interpretations of the function of the ␈↓&d␈↓)αβ tonic possible.
␈↓"β
␈↓"β␈↓ α≠␈↓Example 61
␈↓"β␈↓ α≠␈↓␈↓ βg␈↓¬⊂⊗⊃L[%0.00,%-1.32]:N61X.PLT[HHA,LCS]⊂⊗⊃␈↓






␈↓"β
␈↓"β␈↓ α≠␈↓Figure 61a
␈↓"β
␈↓"β␈↓ α≠␈↓␈↓ βh␈↓¬⊂⊗⊃L[%0.02,%-1.24]:N61A.PLT[HHA,LCS]⊂⊗⊃␈↓





␈↓"β
␈↓"β
␈↓"β␈↓ α≠␈↓Figure 61b
␈↓"β
␈↓"β␈↓ α≠␈↓␈↓ βj␈↓¬⊂⊗⊃L[%0.02,%-1.38]:N61B.PLT[HHA,LCS]⊂⊗⊃␈↓






␈↓"β
␈↓"β␈↓ α≠␈↓        * When a tonic changes mode for more than the duration of
␈↓"β␈↓ α≠␈↓        an occasional chord, the change may appear superimposed on
␈↓"β␈↓ α≠␈↓        the continuous line running from the original occurrence
␈↓"β␈↓ α≠␈↓        of the tonic.
␈↓ α≠␈↓␈↓ ε.60␈↓ 
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␈↓"β␈↓ α≠␈↓Figure 61c
␈↓"β
␈↓"β␈↓ α≠␈↓␈↓ βj␈↓¬⊂⊗⊃L[%0.00,%-1.47]:N61C.PLT[HHA,LCS]⊂⊗⊃␈↓





␈↓"β
␈↓"β
␈↓"β
␈↓"β␈↓ α≠␈↓             * Here the ␈↓&g␈↓)αβ tonic is shown as subsidiary to ␈↓&d␈↓)αβ.  This
␈↓"β␈↓ α≠␈↓             interpretation might be preferred if the duration of
␈↓"β␈↓ α≠␈↓             the ␈↓&g␈↓)αβ tonic area were quite short in relation to the
␈↓"β␈↓ α≠␈↓             following ␈↓&d␈↓)αβ area (see Example 64).

␈↓"β␈↓ α≠␈↓␈↓ α{Notice␈α⊃that␈α⊃the␈α⊃above␈α⊃examples␈α⊃were,␈α⊃for␈α⊃the␈α∩purposes␈α⊃of
␈↓ α≠␈↓illustration,␈α⊗presented␈α∃without␈α⊗varied␈α∃rhythm.␈α⊗ As␈α⊗always,␈α∃in
␈↓ α≠␈↓more␈αcomplex␈αsituations,␈αthe␈αrelations␈αbetween␈αharmony,␈αmelody,
␈↓ α≠␈↓and␈α∀rhythm␈α∀will␈α∀combine␈α∀to␈α∀offer␈α∀a␈α∀basis␈α∀for␈α∀a␈α∀more␈α∀specific
␈↓ α≠␈↓analytical␈α⊃interpretation.␈α⊃ However,␈α∩it␈α⊃must␈α⊃be␈α∩emphasized␈α⊃that
␈↓ α≠␈↓the␈α
main␈α
profit␈αto␈α
the␈α
serious␈αmusician␈α
is␈α
found␈αin␈α
the␈α
process␈αof
␈↓ α≠␈↓wrestling␈α⊃with␈α⊃such␈α⊂problematical␈α⊃decisions.␈α⊃ The␈α⊃final␈α⊂decision
␈↓ α≠␈↓need␈αnot␈αbe␈α
considered␈αthe␈α␈↓↓only␈↓␈αright␈α
one,␈αbut␈αrather␈αas␈α
the␈αmost
␈↓ α≠␈↓clarifying of the actual effect of the music on the individual.

␈↓"β␈↓ α≠␈↓␈↓ α{ An␈α
extreme␈α
example␈α
of␈α∞added␈α
levels␈α
of␈α
tonicization␈α∞(and␈α
it
␈↓ α≠␈↓is often heard) is the progression through the "circle of fifths".
␈↓"β
␈↓"β␈↓ α≠␈↓Example 62
␈↓"β␈↓ α≠␈↓␈↓ βc␈↓¬⊂⊗⊃L[%0.03,%-1.32]:N62X.PLT[HHA,LCS]⊂⊗⊃␈↓
␈↓ α≠␈↓␈↓ ε.61␈↓ 
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␈↓"β␈↓ α≠␈↓Figure 62
␈↓"β␈↓ α≠␈↓␈↓ βc␈↓¬⊂⊗⊃L[%0.00,%-2.80]:N62F.PLT[HHA,LCS]⊂⊗⊃␈↓













␈↓"β␈↓ α≠␈↓ 
␈↓"β␈↓ α≠␈↓Example 63
␈↓"β␈↓ α≠␈↓␈↓ βd␈↓¬⊂⊗⊃L[%0.00,%-1.46]:N63X.PLT[HHA,LCS]⊂⊗⊃␈↓






␈↓"β␈↓ α≠␈↓ 
␈↓"β␈↓ α≠␈↓Figure 63
␈↓"β␈↓ α≠␈↓␈↓ βc␈↓¬⊂⊗⊃L[%0.00,%-2.60]:N63F.PLT[HHA,LCS]⊂⊗⊃␈↓
␈↓ α≠␈↓␈↓ ε.62␈↓ 
k


␈↓"β␈↓ α≠␈↓␈↓ α{These␈α⊃diagrams␈α⊃may␈α⊂appear␈α⊃somewhat␈α⊃unwieldy,␈α⊃but␈α⊂they
␈↓ α≠␈↓have␈α
the␈α
advantage␈α
of␈α∞giving␈α
clear␈α
pictures,␈α
in␈α∞intervallic␈α
terms,
␈↓ α≠␈↓of the relationships involved.

␈↓"β␈↓ α≠␈↓␈↓ α{Occasionally␈α∪a␈α∪very␈α∪rapid␈α∪movement␈α∪through␈α∪part␈α∪of␈α∩the
␈↓ α≠␈↓circle␈α⊃of␈α∩fifths,␈α⊃or␈α⊃the␈α∩successive␈α⊃use␈α⊃of␈α∩7th␈α⊃chords,␈α∩will␈α⊃cause
␈↓ α≠␈↓certain elements of a progression to stand in relief.
␈↓"β
␈↓"β␈↓ α≠␈↓Example 64
␈↓"β␈↓ α≠␈↓␈↓ βd␈↓¬⊂⊗⊃L[%0.00,%-1.45]:N64X.PLT[HHA,LCS]⊂⊗⊃␈↓






␈↓"β
␈↓"β␈↓ α≠␈↓Figure 64
␈↓"β␈↓ α≠␈↓␈↓ βg␈↓¬⊂⊗⊃L[%0.10,%-2.32]:N64F.PLT[HHA,LCS]⊂⊗⊃␈↓











␈↓"β␈↓ α≠␈↓␈↓ α{In␈αthe␈αabove␈αdiagram,␈αthe␈αabrupt␈αskip␈αdown␈αto␈αa␈α
third␈αlevel
␈↓ α≠␈↓of␈α⊂tonics␈α∂(which␈α⊂resolves␈α∂to␈α⊂a␈α∂I␈α⊂on␈α∂the␈α⊂second␈α⊂level)␈α∂accurately
␈↓ α≠␈↓parallels␈α
the␈α
effect␈α
of␈α
the␈α
example.␈α
 Notice␈α
the␈α
problems␈α
created␈α
by
␈↓ α≠␈↓the␈α
use␈α
of␈αa␈α
string␈α
of␈α
diminished␈αchords␈α
over␈α
a␈αbasically␈α
chromatic
␈↓ α≠␈↓line.␈α
 Such␈α
situations␈α
may␈α
be␈α
analyzed␈α
as␈α
substitutes␈α
for␈αthe␈α
"circle
␈↓ α≠␈↓of␈α∞fifths"␈α∞progression,␈α∞but␈α∞generally␈α∞it␈α∞is␈α∞best␈α∞to␈α∞consider␈α∞all␈α
but
␈↓ α≠␈↓the␈α∞first␈α∞and␈α
last␈α∞chords␈α∞of␈α
the␈α∞string␈α∞as␈α∞parallel-moving␈α
passing
␈↓ α≠␈↓␈↓ ε.63␈↓ 
k


␈↓"β␈↓ α≠␈↓chords␈α⊂(see␈α⊂Bach,␈α⊂␈↓↓Partita␈α⊂#1␈α⊂in␈α⊂B␈↓βF␈↓,␈α⊂Gigue;␈α⊂Mozart,␈α⊂␈↓↓Fantasy␈α⊂in␈α⊂C␈↓,
␈↓ α≠␈↓K.394).␈α However,␈αin␈α19th-century␈αmusic,␈αdetails␈αof␈αvoice␈αleading
␈↓ α≠␈↓(especially␈α→the␈α~melodic␈α→skips)␈α→often␈α~tend␈α→to␈α~give␈α→functional
␈↓ α≠␈↓importance␈α⊃to␈α⊃the␈α⊃inner␈α⊃chords␈α⊃of␈α⊃strings␈α⊃of␈α∩diminished␈α⊃chords
␈↓ α≠␈↓(see␈α≥Chopin,␈α≥␈↓↓Etude␈α≤in␈α≥E␈↓,␈α≥Op.10,#3,␈α≤measure␈α≥38,␈α≥etc.;␈α≤Liszt,
␈↓ α≠␈↓␈↓↓Transcendental Etude #6, "Mazeppa"␈↓, beginning).

␈↓"β␈↓ α≠␈↓␈↓ α{Most␈αoften␈αthe␈αreturn␈αto␈αthe␈αmain␈αtonic␈αwill␈αnot␈αbe␈αmade␈αby
␈↓ α≠␈↓the␈α
same␈α
route␈α
as␈α
was␈αthe␈α
departure.␈α
 When␈α
this␈α
happens,␈αa␈α
pivotal
␈↓ α≠␈↓tonic␈α
may␈α
appear␈α
in␈α
the␈α
middle␈αarea␈α
of␈α
the␈α
analysis␈α
(see␈α
below␈αat
␈↓ α≠␈↓the sign *).
␈↓"β
␈↓"β␈↓ α≠␈↓Example 65
␈↓"β␈↓ α≠␈↓␈↓ βc␈↓¬⊂⊗⊃L[%0.00,%-1.25]:N65X.PLT[HHA,LCS]⊂⊗⊃␈↓






␈↓"β
␈↓"β␈↓ α≠␈↓Figure 65
␈↓"β␈↓ α≠␈↓␈↓ βc␈↓¬⊂⊗⊃L[%0.00,%-2.60]:N65F.PLT[HHA,LCS]⊂⊗⊃␈↓
␈↓ α≠␈↓␈↓ ε.64␈↓ 
k


␈↓"β␈↓ α≠␈↓Example 66. Mozart, Sonata in D, K.576, 2nd movement.
␈↓"β␈↓ α≠␈↓␈↓ β←␈↓¬⊂⊗⊃L[%0.00,%-7.40]:N66X.PLT[HHA,LCS]⊂⊗⊃␈↓
␈↓ α≠␈↓␈↓ ε.65␈↓ 
k


␈↓"β␈↓ α≠␈↓␈↓ α{The␈α∞exact␈α∞location␈α∞of␈α∞the␈α∞pivotal␈α∞tonic␈α∞will␈α∞usually␈α
depend
␈↓ α≠␈↓on␈α∂the␈α∞association␈α∂of␈α∂the␈α∞particular␈α∂␈↓↓means␈↓␈α∞of␈α∂presenting␈α∂a␈α∞given
␈↓ α≠␈↓harmonic␈αfunction␈α
with␈αearlier␈α
presentation␈αof␈α
the␈αsame␈α
function.
␈↓ α≠␈↓In␈α∞other␈α∞words,␈α
the␈α∞return␈α∞to␈α∞the␈α
chord␈α∞of␈α∞departure,␈α∞even␈α
with
␈↓ α≠␈↓the␈α∞same␈α∞function␈α∞on␈α∂the␈α∞lowest␈α∞level,␈α∞can␈α∞be␈α∂inconclusive␈α∞until
␈↓ α≠␈↓we␈α
also␈α
return␈αto␈α
the␈α
same␈αmelodic␈α
and␈α
rhythmic␈α
presentation␈αof
␈↓ α≠␈↓that␈α∀function.␈α∀ In␈α∀Example␈α∀66␈α∀the␈α∀f␈↓βS␈↓␈α∀chord␈α∀at␈α∀(*)␈α∀has␈α∀a␈α∪tonic
␈↓ α≠␈↓function,␈α
but␈α␈↓&f␈↓βS␈↓␈↓)αβ␈α
as␈αa␈α
tonic␈αof␈α
the␈αmiddle␈α
area␈αis␈α
still␈α
subsidiary␈αto
␈↓ α≠␈↓another tonic (␈↓&D␈↓)αβ) until the return of the original material.
␈↓"β
␈↓"β␈↓ α≠␈↓Figure 66
␈↓"β␈↓ α≠␈↓␈↓ βh␈↓¬⊂⊗⊃L[%-.05,%-3.30]:N66F.PLT[HHA,LCS]⊂⊗⊃␈↓















␈↓"β␈↓ α≠␈↓␈↓ α{The␈α∀middle␈α∀area␈α∀of␈α∀the␈α∀first␈α∀analysis␈α∀is␈α∀preferred␈α∀at␈α∪(+),
␈↓ α≠␈↓because␈α⊃the␈α⊂tonic␈α⊃chord␈α⊃of␈α⊂f␈↓βS␈↓␈α⊃is␈α⊂completely␈α⊃consistent␈α⊃with␈α⊂the
␈↓ α≠␈↓scale␈α⊃of␈α⊃␈↓&D␈↓)αβ,␈α⊃and␈α⊃there␈α⊃are␈α⊃no␈α⊃other␈α⊃factors␈α⊃that␈α⊃might␈α⊃deter␈α⊃one
␈↓ α≠␈↓from␈αhearing␈αthe␈αpassage␈αas␈αa␈αstepwise␈αprogression␈αof␈αtonics␈α(I,␈αii,
␈↓ α≠␈↓iii).␈α⊂ If,␈α⊂for␈α⊂any␈α⊂reason,␈α⊂it␈α⊂seems␈α⊂undesirable␈α⊂to␈α⊂show␈α⊂a␈α⊂pivot␈α∂in
␈↓ α≠␈↓cases␈αwhere␈α
two␈αor␈αmore␈α
levels␈αof␈αtonics␈α
are␈αinvolved,␈α
the␈αwavy
␈↓ α≠␈↓vertical␈α⊃line␈α⊃(␈↓βW␈↓)␈α⊃might␈α⊃be␈α∩used␈α⊃to␈α⊃show␈α⊃the␈α⊃lack␈α∩of␈α⊃continuity
␈↓ α≠␈↓along␈α~any␈α~given␈α~level␈α→(see␈α~Figure␈α~71).␈α~ However,␈α~it␈α→rarely
␈↓ α≠␈↓happens that a logical connection between tonics cannot be made.
␈↓ α≠␈↓␈↓ ε.66␈↓ 
k


␈↓"β␈↓ α≠␈↓Control Tonics

␈↓"β␈↓ α≠␈↓␈↓ α{An␈α∪extension␈α∪of␈α∪the␈α∀previous␈α∪line␈α∪of␈α∪thought␈α∀will␈α∪serve
␈↓ α≠␈↓well␈αwhen␈αconsidering␈αthe␈αfollowing␈αanalysis␈αof␈αmusic␈α
typical␈αof
␈↓ α≠␈↓the work of Bach.
␈↓"β
␈↓"β␈↓ α≠␈↓Example 67.  Bach, Invention No.4 in d.
␈↓"β␈↓ α≠␈↓␈↓ βv␈↓∧⊂⊗⊃L[0,%-6.7]:N67XA.PLT[HHA,LCS]⊂⊗⊃␈↓
␈↓ α≠␈↓␈↓ ε.67␈↓ 
k


␈↓"β␈↓ α≠␈↓␈↓ βv␈↓∧⊂⊗⊃L[0,%-.75]:N67XB.PLT[HHA,LCS]⊂⊗⊃␈↓




␈↓"β␈↓ α≠␈↓Figure 67a.  Bach, Invention No.4 in d (bars 7-45).
␈↓"β
␈↓"β␈↓ α≠␈↓␈↓ βP␈↓∧⊂⊗⊃L[%-.05,%-3.2]:N67FA.PLT[HHA,LCS]⊂⊗⊃␈↓















␈↓"β␈↓ α≠␈↓␈↓ α{The␈α∪location␈α∩of␈α∪the␈α∩pivot␈α∪(at␈α∩+)␈α∪is␈α∩arbitrary,␈α∪because␈α∩the
␈↓ α≠␈↓following␈α
twelve␈α
bars␈α
are␈α
based␈α∞on␈α
the␈α
descending␈α
form␈α
of␈α∞the␈α
␈↓&d␈↓)αβ
␈↓ α≠␈↓scale␈α--␈α
which␈αis␈α
identical␈αwith␈αthe␈α
␈↓&F␈↓)αβ␈αscale.␈α
 If␈αit␈α
seems␈αnecessary
␈↓ α≠␈↓to␈α∂specify␈α∂the␈α∂dual␈α∂function␈α∂of␈α∂such␈α∂progressions,␈α⊂the␈α∂following
␈↓ α≠␈↓method␈αis␈αsuggested.␈α The␈α␈↓↓retrospective␈↓␈αfunctions␈αin␈α␈↓&F␈↓)αβ␈αare␈αcircled
␈↓ α≠␈↓to keep them distinct from the earlier perceived ␈↓&d␈↓)αβ functions.
␈↓"β
␈↓"β␈↓ α≠␈↓Figure 67b
␈↓"β␈↓ α≠␈↓␈↓ βZ␈↓∧⊂⊗⊃L[%-.2,%-1.5]:N67FB.PLT[HHA,LCS]⊂⊗⊃␈↓
␈↓ α≠␈↓␈↓ ε.68␈↓ 
k


␈↓"β␈↓ α≠␈↓␈↓ α{The␈α∀form␈α∀of␈α∀this␈α∀work␈α∀is␈α∀defined␈α∀mainly␈α∀by␈α∀a␈α∀group␈α∀of
␈↓ α≠␈↓cadential␈α∪formulas.␈α∪ The␈α∪strength␈α∩of␈α∪the␈α∪points␈α∪of␈α∪definition␈α∩is
␈↓ α≠␈↓greatly␈α⊂enhanced␈α⊂by␈α⊂the␈α⊂fact␈α∂that␈α⊂each␈α⊂cadence␈α⊂offers␈α⊂us␈α⊂a␈α∂new
␈↓ α≠␈↓tonal␈αcenter.␈α However,␈αdue␈αto␈αthe␈αexclusive␈αuse␈αof␈αa␈αsingle␈αset␈αof
␈↓ α≠␈↓motives␈α
and␈α
the␈α
brevity␈α
of␈α
the␈α
piece,␈α
modulation␈α
(as␈α
it␈α
is␈αknown
␈↓ α≠␈↓in␈α∀the␈α∃main␈α∀body␈α∃of␈α∀tonal␈α∃music)␈α∀does␈α∃not␈α∀occur.␈α∃ The␈α∀larger
␈↓ α≠␈↓harmonic␈α
movement␈α
of␈α
this␈α
piece␈α∞is␈α
certainly␈α
heard␈α
as␈α
a␈α∞series␈α
of
␈↓ α≠␈↓tonics,␈αwhose␈αrelations␈αto␈αthe␈αmain,␈αbeginning␈αtonic␈αare␈αat␈αleast␈αas
␈↓ α≠␈↓strong␈α∪as␈α∪their␈α∪relations␈α∪to␈α∪one␈α∪another.␈α∪ Thus,␈α∪even␈α∪though␈α∪␈↓&a␈↓)αβ
␈↓ α≠␈↓appears␈αfirst␈αas␈αiii␈αof␈α
␈↓&F␈↓)αβ,␈αit␈αis␈αfinally␈αestablished␈α
as␈αan␈αequal␈αof␈α␈↓&F␈↓)αβ␈α
(in
␈↓ α≠␈↓relation␈α∞to␈α∞␈↓&d␈↓)αβ)␈α∞by␈α∞the␈α∞occurrence␈α∞of␈α∞the␈α∞well-prepared␈α∞cadence␈α
at
␈↓ α≠␈↓bar␈α
38.␈α
 Please␈α
note,␈α
however,␈αthat␈α
␈↓&a␈↓)αβ's␈α
role␈α
as␈α
something␈αmore␈α
than
␈↓ α≠␈↓a␈α
transient␈α
tonic␈α
of␈α∞the␈α
␈↓&F␈↓)αβ␈α
scale␈α
is␈α∞not␈α
too␈α
definite␈α
until␈α∞the␈α
point
␈↓ α≠␈↓of␈α∪cadence.␈α∪ To␈α∪emphasize␈α∪these␈α∪varying␈α∪levels␈α∪of␈α∪relationships
␈↓ α≠␈↓among␈α
the␈α
tonics,␈α
we␈α
must␈α
start␈α
at␈α
the␈α
beginning␈α
of␈α
our␈α
diagram
␈↓ α≠␈↓with␈α
␈↓↓two␈↓␈α
levels␈α
in␈α
the␈α
middle␈α
ground,␈α
so␈α
that␈α
when␈α∞a␈α
temporary
␈↓ α≠␈↓tonic␈α
is␈α
somehow␈α∞given␈α
greater␈α
status␈α∞and␈α
becomes␈α
what␈α∞may␈α
be
␈↓ α≠␈↓called␈α∀a␈α∀␈↓↓control␈α∪tonic␈↓,␈α∀this␈α∀change␈α∪will␈α∀appear␈α∀in␈α∀a␈α∪consistent
␈↓ α≠␈↓form.␈α∪ In␈α∪the␈α∪above␈α∪analysis␈α∪note␈α∪that␈α∪on␈α∪the␈α∪highest␈α∀level␈α∪of
␈↓ α≠␈↓tonicization␈αthe␈αprogress␈αfrom␈αi␈αto␈αIII␈αto␈αv␈αcoincides␈αexactly␈αwith
␈↓ α≠␈↓the␈α
full␈αcadences.␈α
 However,␈α
␈↓&F␈↓)αβ␈αand␈α
␈↓&a␈↓)αβ␈α
are␈αfirst␈α
tonicized␈αwell␈α
before
␈↓ α≠␈↓the␈αcadences␈α(this␈αshows␈αon␈αthe␈αsecond␈αlevel␈αof␈αtonicization).␈α The
␈↓ α≠␈↓numerals of the control tonics will be underlined.

␈↓"β␈↓ α≠␈↓␈↓ α{The␈α
use␈α
of␈α
strong␈α
cadences␈αis␈α
not␈α
the␈α
only␈α
method␈αwhich␈α
can
␈↓ α≠␈↓give␈α∪a␈α∪temporary␈α∪tonic␈α∪the␈α∪status␈α∪of␈α∪a␈α∪control␈α∪tonic.␈α∩ Another
␈↓ α≠␈↓favorite␈α∂method␈α∂is␈α∂the␈α∂clear␈α∂presentation,␈α∂in␈α∂some␈α∂new␈α⊂tonic,␈α∂of
␈↓ α≠␈↓material␈α∞(either␈α∂old␈α∞or␈α∂new)␈α∞of␈α∂relatively␈α∞great␈α∂importance;␈α∞e.g.,
␈↓ α≠␈↓in␈α
the␈α
Bach␈α
Invention,␈αthe␈α
return␈α
to␈α
the␈αoriginal␈α
␈↓&d␈↓)αβ␈α
as␈α
the␈αcontrol
␈↓ α≠␈↓tonic␈α
is␈α
defined␈α
by␈α
the␈α
return␈α
of␈α
the␈α
opening␈α
statement␈α
(bar␈α44),
␈↓ α≠␈↓rather␈α⊃than␈α⊃by␈α⊃a␈α⊃full␈α⊃cadence.␈α⊃ The␈α⊃presentation␈α⊃should␈α⊃be␈α⊂long
␈↓ α≠␈↓enough␈α
so␈α
that␈α
the␈α
new␈α
tonic␈α
may␈α
be␈α
heard␈α
as␈α
independent␈α
beyond
␈↓ α≠␈↓the␈α∞extent␈α∂of␈α∞simple␈α∞tonicization.␈α∂ The␈α∞functions␈α∞under␈α∂a␈α∞control
␈↓ α≠␈↓tonic␈α~established␈α~in␈α~this␈α~manner␈α~need␈α~not␈α~include␈α≠a␈α~strong
␈↓ α≠␈↓cadence.␈α
 The␈α
music␈α
might␈αthen␈α
progress␈α
smoothly␈α
to␈α
yet␈αanother
␈↓ α≠␈↓control␈α⊗tonic.␈α⊗ If␈α⊗the␈α⊗important␈α⊗factors␈α⊗of␈α⊗the␈α⊗music␈α⊗seem␈α∃to
␈↓ α≠␈↓␈↓ ε.69␈↓ 
k


␈↓"β␈↓ α≠␈↓warrant␈αits␈αindependence,␈αa␈αnew␈αcontrol␈αtonic␈αmight␈αeven␈αappear
␈↓ α≠␈↓as␈α∂a␈α⊂lower␈α∂level␈α⊂of␈α∂tonicization,␈α⊂below␈α∂an␈α⊂old␈α∂control␈α⊂tonic␈α∂(see
␈↓ α≠␈↓next chapter, Schubert example).

␈↓"β␈↓ α≠␈↓␈↓ α{Much␈α↔music␈α↔can␈α↔best␈α↔be␈α↔analyzed␈α↔in␈α↔terms␈α↔of␈α↔series␈α⊗of
␈↓ α≠␈↓control␈αtonics,␈αthe␈α
term␈α"modulation"␈αbeing␈α
reserved␈αfor␈αa␈αshift␈α
of
␈↓ α≠␈↓the␈αbasic␈αtonic.␈α
 No␈αset␈αrule␈αcan␈α
be␈αgiven␈αas␈α
to␈αwhen␈αit␈αis␈α
advisable
␈↓ α≠␈↓to␈α∞use␈α∞an␈α∞extra,␈α∞higher␈α∞level␈α∞of␈α∞indications␈α∞in␈α∞the␈α∞middle␈α∞area␈α∞of
␈↓ α≠␈↓the␈α_analytical␈α↔diagram.␈α_ Any␈α↔variant␈α_of␈α↔the␈α_basic␈α_diagram␈α↔is
␈↓ α≠␈↓acceptable␈α∂just␈α∂so␈α∂long␈α∂as␈α∂it␈α∂contributes␈α∂to␈α∂the␈α∂understanding␈α∂of
␈↓ α≠␈↓the music under consideration.

␈↓"β␈↓ α≠␈↓␈↓ ∧K_______________


␈↓"β␈↓ α≠␈↓␈↓ α{It␈α_is␈α_very␈α_evident␈α→that␈α_as␈α_the␈α_complexity␈α→of␈α_harmony
␈↓ α≠␈↓increases␈α≡there␈α≡is␈α≡usually␈α≡a␈α≡corresponding␈α≡increase␈α∨in␈α≡the
␈↓ α≠␈↓ambiguity␈α
of␈α
individual␈α
harmonic␈α∞functions␈α
as␈α
they␈α
relate␈α∞to␈α
the
␈↓ α≠␈↓whole.␈α∂ This␈α∂is,␈α∂of␈α∂course,␈α∂the␈α∂reason␈α∂for␈α∂the␈α∂particular␈α∂effect␈α∞of
␈↓ α≠␈↓late␈α~"Romantic"␈α~and␈α≠"Impressionistic"␈α~harmony,␈α~and␈α≠also␈α~the
␈↓ α≠␈↓source␈α∃of␈α∃the␈α∃ultimate␈α∃breakdown␈α∃of␈α∃functional␈α∃tonality␈α⊗as␈α∃a
␈↓ α≠␈↓meaningful␈α~system.␈α~ When␈α→every␈α~harmonic␈α~function␈α→becomes
␈↓ α≠␈↓ambiguous,␈α∞then␈α∞something␈α∞other␈α∞than␈α∞a␈α∞tonal␈α∞center␈α∞(as␈α∞defined
␈↓ α≠␈↓by␈α∪harmonic␈α∀functions)␈α∪must␈α∀take␈α∪over␈α∀as␈α∪the␈α∀prime␈α∪cohesive
␈↓ α≠␈↓force␈α∀(see␈α∪last␈α∀chapter).␈α∪ It␈α∀is␈α∪significant␈α∀that␈α∪in␈α∀music␈α∀of␈α∪the
␈↓ α≠␈↓Classical␈α∩era␈α∩the␈α∪more␈α∩complex␈α∩harmonic␈α∩progressions␈α∪are␈α∩most
␈↓ α≠␈↓often␈αrelegated␈αto␈αdevelopmental␈αpassages␈α--␈αpassages␈αthat␈αdepend
␈↓ α≠␈↓greatly␈αon␈αmotivic␈αcontinuity.␈α In␈αsuch␈αinstances,␈αit␈αis␈αcommon␈αto
␈↓ α≠␈↓hear␈α→a␈α~series␈α→of␈α→tonics␈α~which␈α→seem␈α→to␈α~relate␈α→only␈α~to␈α→their
␈↓ α≠␈↓immediate␈α
surroundings.␈α
 (It␈α
is␈α
possible␈α
for␈α
even␈α
the␈αoriginal␈α
tonic
␈↓ α≠␈↓of␈α∪a␈α∪developmental␈α∪section␈α∪to␈α∪reappear␈α∪for␈α∪a␈α∪considerable␈α∪time
␈↓ α≠␈↓without␈α∪its␈α∩having␈α∪any␈α∩direct␈α∪functional␈α∩relationship␈α∪with␈α∩its
␈↓ α≠␈↓earlier␈α∂presentation.)␈α∂The␈α∞analysis␈α∂of␈α∂an␈α∂extended␈α∞developmental
␈↓ α≠␈↓passage␈αwill␈α
show␈αcontinually␈αadded␈α
levels␈αin␈αthe␈α
middle␈αground,
␈↓ α≠␈↓the␈αreturn␈αto␈αa␈αsingle␈αlevel␈αbeing␈αconditioned␈αby␈αthe␈αreappearance
␈↓ α≠␈↓of␈α⊂familiar,␈α⊃stable␈α⊂material␈α⊂in␈α⊃its␈α⊂proper␈α⊂key.␈α⊃ This␈α⊂traditionally
␈↓ α≠␈↓␈↓ ε.70␈↓ 
k


␈↓"β␈↓ α≠␈↓happens at the point of recapitulation in the sonata form.*
␈↓"β␈↓ α≠␈↓␈↓ ∧K_______________
␈↓"β
␈↓"β
␈↓"β␈↓ α≠␈↓Exercises for Chapter V
␈↓"β
␈↓"β
␈↓"β␈↓ α≠␈↓Analyze the following works:
␈↓"β
␈↓"β␈↓ α≠␈↓From the 371 Chorales of Bach:
␈↓"β
␈↓"β␈↓ α≠␈↓        1.  Chorale 21
␈↓"β␈↓ α≠␈↓        2.  Chorale 92
␈↓"β␈↓ α≠␈↓        3.  Chorale 200
␈↓"β␈↓ α≠␈↓        4.  Chorale 231
␈↓"β␈↓ α≠␈↓        5.  Chorale 279
␈↓"β
␈↓"β␈↓ α≠␈↓From the Two-Part Inventions of Bach:
␈↓"β
␈↓"β␈↓ α≠␈↓        6.  Invention 11, in g
␈↓"β␈↓ α≠␈↓        7.  Invention 12, in A
␈↓"β␈↓ α≠␈↓        8.  Invention 13, in a
␈↓"β
␈↓"β␈↓ α≠␈↓From the Well-Tempered Clavier, First Book, Bach:
␈↓"β
␈↓"β␈↓ α≠␈↓        9.  Fugue I, in C
␈↓"β␈↓ α≠␈↓       10.  Fugue X, in e
␈↓"β
␈↓"β␈↓ α≠␈↓From the Preludes, Op.28, of Chopin:
␈↓"β
␈↓"β␈↓ α≠␈↓       11.  Prelude  5, in D
␈↓"β␈↓ α≠␈↓       12.  Prelude 22, in g



␈↓"β␈↓ α≠␈↓__________
␈↓"β␈↓ α≠␈↓ Among␈α
the␈α
numerous␈α
exceptions␈αto␈α
the␈α
above␈α
statements␈α
are␈αthe
␈↓"␈↓ α≠␈↓first␈α"movement␈α#recapitulations␈α"of␈α#Mozart's␈α"␈↓↓Sonatas␈α#in␈α"D␈↓,
␈↓"␈↓ α≠␈↓K.284c(311)␈α∨and␈α∨␈↓↓in␈α∨C␈↓,␈α∨K.545.␈α≡ In␈α∨the␈α∨first␈α∨of␈α∨these,␈α≡the
␈↓"␈↓ α≠␈↓recapitulation␈α⊃begins␈α⊃with␈α⊃the␈α⊃material␈α⊃of␈α⊃the␈α⊃second␈α⊃key␈α⊃area,
␈↓"␈↓ α≠␈↓but␈α∪now␈α∪heard␈α∪in␈α∪␈↓&D␈↓)αβ␈α∪instead␈α∩of␈α∪␈↓&A␈↓)αβ.␈α∪ The␈α∪recapitulation␈α∪of␈α∪the␈α∩␈↓&C␈↓)αβ
␈↓"␈↓ α≠␈↓sonata␈α%offers␈α$the␈α%original␈α%opening␈α$material,␈α%but␈α%in␈α$the
␈↓"␈↓ α≠␈↓subdominant, ␈↓&F␈↓)αβ.