/LMAR=0/XLINE=10/FONT#0=METL/FONT#1=METLI/FONT#2=METS/FONT#3=MUS[ C6,LCS]/FONT#4=MUZ[ C6,LCS]/FONT#5=BASL35
␈↓ α∧␈↓␈↓ ε↔71␈↓ 
T


␈↓"β␈↓ α∧␈↓␈↓ ¬GCHAPTER VI


␈↓"β␈↓ α∧␈↓␈↓ α5ALTERNATING PROGRESSIONS AND INDIRECT RELATIONSHIPS


␈↓"β␈↓ α∧␈↓␈↓ αd The␈α⊗simplest␈α↔form␈α⊗of␈α⊗alternating␈α↔progression␈α⊗is␈α↔that␈α⊗in
␈↓ α∧␈↓which␈α
a␈α
particular␈α∞chord␈α
is␈α
approached␈α∞from␈α
two␈α
points␈α∞of␈α
view
␈↓ α∧␈↓with␈α∞regard␈α∞to␈α∞its␈α∞harmonic␈α∞function.␈α∞ In␈α∞most␈α∞cases␈α∞there␈α∞is␈α
not
␈↓ α∧␈↓the␈αslightest␈αdoubt␈αas␈αto␈αthe␈αprimary␈αfunction␈α(usually␈αdominant)
␈↓ α∧␈↓of the final chord.
␈↓"β␈↓ α∧␈↓␈↓ β}␈↓¬⊂⊗⊃L[0,%-2.75]:N68X.PLT[C6,LCS]⊂⊗⊃␈↓
␈↓"β␈↓ α∧␈↓Example 68
␈↓"β
␈↓"β
␈↓"β
␈↓"β
␈↓"β
␈↓"β
␈↓"β
␈↓"β␈↓ α∧␈↓Figure 68
␈↓"β
␈↓"β
␈↓"β
␈↓"β
␈↓"β

␈↓"β␈↓ α∧␈↓␈↓ αdHere␈αthe␈α
delayed␈αresolution␈αof␈α
the␈αD7th␈αchord␈α
to␈α␈↓↓its␈↓␈αtonic,␈α
␈↓&G␈↓)αβ,
␈↓ α∧␈↓may␈α
be␈α
shown␈α
as␈α
above.␈α
 The␈α
primarily␈α
dominant␈α
function␈α
of␈αthe
␈↓ α∧␈↓G␈α∪chord␈α∪is␈α∪ensured␈α∪by␈α∪the␈α∪immediately␈α∪preceding␈α∪subdominant
␈↓ α∧␈↓(II␈↓∧H␈↓)␈αfunction.␈α Thus␈αthe␈αG␈αmajor␈αchord␈αis␈αtonicized␈αby␈αthe␈αsecond
␈↓ α∧␈↓chord␈αand␈α"dominantized"␈αby␈αthe␈αthird␈αchord,␈αthe␈αlast␈α
relationship
␈↓ α∧␈↓in␈α∀the␈α∪series␈α∀being␈α∀the␈α∪most␈α∀influential.␈α∪ Here,␈α∀once␈α∀more,␈α∪the
␈↓ α∧␈↓voice-leading␈α
or␈α
contrapuntal␈α
element␈α
becomes␈α
relevant␈αand,␈α
from
␈↓ α∧␈↓a␈αbroad␈α
point␈αof␈αview,␈α
the␈αbass␈αnotes␈α
F␈↓βS␈↓,␈αA␈↓βF␈↓,␈αand␈α
G␈αform␈αa␈α
kind␈αof
␈↓ α∧␈↓cambiata␈αfigure␈αwhich␈αminimizes␈αthe␈αeffect␈αof␈αthe␈αD7th␈αchord␈αas␈α
a
␈↓ α∧␈↓␈↓ ε↔72␈↓ 
T


␈↓"β␈↓ α∧␈↓dominant.*␈α⊂In␈α⊂detail,␈α⊂however,␈α⊂the␈α⊂above␈α⊂example␈α⊂␈↓↓does␈↓␈α⊂offer␈α∂us
␈↓ α∧␈↓the musical effect indicated by the analysis.

␈↓"β␈↓ α∧␈↓␈↓ αdSimilar␈α
progressions␈α
occur␈α∞in␈α
the␈α
␈↓↓Mazurka␈α∞No.38␈↓,␈α
Op.59,#3,
␈↓ α∧␈↓of Chopin (measures 16-24):
␈↓"β
␈↓"β␈↓ α∧␈↓Example 69a
␈↓"β␈↓ α∧␈↓␈↓ βU␈↓¬⊂⊗⊃L[%-.02,%-2.95]:N69XA.PLT[C6,LCS]⊂⊗⊃␈↓













␈↓"β␈↓ α∧␈↓␈↓ αdAs␈α∞the␈α
progressions␈α∞under␈α∞study␈α
become␈α∞more␈α∞complex,␈α
the
␈↓ α∧␈↓following␈α⊃method␈α∩for␈α⊃clarifying␈α⊃the␈α∩relationships␈α⊃may␈α∩be␈α⊃used.
␈↓ α∧␈↓The␈α→horizontal␈α_bars␈α→connecting␈α→various␈α_parts␈α→of␈α→the␈α_Chordal
␈↓ α∧␈↓Reduction␈α
serve␈α
the␈α
purpose␈α∞of␈α
showing␈α
which␈α
of␈α∞the␈α
harmonies
␈↓ α∧␈↓may␈α∞be␈α∞directly␈α∞related␈α∞to␈α∞one␈α∞another.␈α∞ ␈↓↓On␈α∞any␈α∞given␈α∞level,␈α∞the
␈↓ α∧␈↓↓horizontal␈α≥bar␈α≥connects␈α≥chords␈α≤which␈α≥all␈α≥serve␈α≥the␈α≤same
␈↓ α∧␈↓↓temporary␈α⊃tonic␈↓.␈α⊃ It␈α⊂should␈α⊃be␈α⊃noted␈α⊂that␈α⊃sometimes␈α⊃a␈α⊃chord␈α⊂of
␈↓ α∧␈↓substitute␈α∪function␈α∪will␈α∪be␈α∀found␈α∪on␈α∪a␈α∪given␈α∪tonic's␈α∀bar␈α∪even
␈↓ α∧␈↓though␈α∀the␈α∀chord␈α∀is␈α∀at␈α∃the␈α∀same␈α∀time␈α∀more␈α∀clearly␈α∃related␈α∀to
␈↓ α∧␈↓another␈α⊂tonic.␈α⊂ These␈α⊂Chordal␈α⊃Reductions␈α⊂are␈α⊂not␈α⊂to␈α⊃be␈α⊂confused

␈↓"β␈↓ α∧␈↓__________
␈↓"β␈↓ α∧␈↓*␈α∂Many␈α∂books␈α∂on␈α∂harmony␈α∞would␈α∂call␈α∂this␈α∂D7␈α∂chord␈α∂simply␈α∞II␈↓βS3␈↓.
␈↓"␈↓ α∧␈↓This␈α∩seems␈α∪like␈α∩an␈α∩oversimplification.␈α∪ A␈α∩dividing␈α∩line␈α∪must␈α∩be
␈↓"␈↓ α∧␈↓drawn␈α
somewhere␈α
in␈α∞these␈α
matters;␈α
in␈α∞this␈α
book␈α
the␈α∞sharped␈α
4th
␈↓"␈↓ α∧␈↓and␈α5th␈αdegrees␈αof␈αthe␈α
scale␈αwill␈αonly␈αbe␈αadmitted␈α
as␈α"functional"
␈↓"␈↓ α∧␈↓when␈α_they␈α_are␈α_part␈α_of␈α_augmented␈α_sixth␈α_or␈α_augmented␈α↔fifth
␈↓"␈↓ α∧␈↓chords.
␈↓ α∧␈↓␈↓ ε↔73␈↓ 
T


␈↓"β␈↓ α∧␈↓with␈α
the␈α
diagrams␈α
outlining␈αTonic␈α
Guide␈α
Tones.␈α
 Tonic␈αGuide␈α
Tones
␈↓ α∧␈↓will␈α∂be␈α∂used␈α∂solely␈α∂as␈α∂a␈α∂means␈α∂of␈α∂clarifying␈α⊂relationships␈α∂among
␈↓ α∧␈↓the ␈↓↓tonics␈↓ involved in any progression.  (See page 57.)
␈↓"β
␈↓"β␈↓ α∧␈↓Figure 69
␈↓"β
␈↓"β␈↓ α∧␈↓Chordal Reduction
␈↓"β␈↓ α∧␈↓␈↓ βu␈↓¬⊂⊗⊃L[%-.15,%-3.5]:N69F.PLT[C6,LCS]⊂⊗⊃␈↓

















␈↓"β␈↓ α∧␈↓␈↓ αdHere␈α⊂the␈α∂control␈α⊂tonic␈α⊂of␈α∂III␈α⊂(␈↓&A␈↓)αβ)␈α∂has␈α⊂been␈α⊂established.␈α∂ The
␈↓ α∧␈↓section␈α∃in␈α∃␈↓&A␈↓)αβ␈α∃is␈α∃far␈α∃too␈α∀brief␈α∃to␈α∃warrant␈α∃the␈α∃use␈α∃of␈α∃the␈α∀term
␈↓ α∧␈↓"modulation".␈α
 In␈α
measure␈α17␈α
the␈α
G␈α
and␈αthe␈α
clearly␈α
implied␈αC␈↓βS␈↓␈α
form
␈↓ α∧␈↓a␈αtritone␈αwhich␈αis␈αmost␈α
readily␈αheard␈αas␈αdominant␈αto␈α␈↓&D␈↓)αβ.␈α
 However,
␈↓ α∧␈↓measure␈α∀18␈α∀first␈α∀offers␈α∀us␈α∀a␈α∀7th␈α∀chord␈α∀on␈α∀B␈α∀--␈α∀this␈α∀heard␈α∪as
␈↓ α∧␈↓dominant␈αto␈α␈↓&E␈↓)αβ.␈α Then␈α
follows␈αa␈αd␈αminor␈α
chord,␈αthe␈αlogical␈αresult␈α
of
␈↓ α∧␈↓measure␈α17.␈α In␈αmeasure␈α19␈αis␈αheard␈αan␈αE7th␈αchord␈α(over␈αa␈αtonic␈αA
␈↓ α∧␈↓pedal)␈α⊂which␈α⊂is␈α⊂a␈α⊂substitute␈α⊂for␈α⊂the␈α⊂simple␈α⊂tonic␈α⊂expected␈α∂after
␈↓ α∧␈↓the␈α↔B7th␈α↔chord.␈α↔ At␈α↔measure␈α↔21␈α↔things␈α↔become␈α↔a␈α↔little␈α↔more
␈↓ α∧␈↓complex.␈α≡ The␈α∨last␈α≡chord␈α≡contains␈α∨an␈α≡A␈↓βS␈↓,␈α≡which␈α∨could␈α≡be
␈↓ α∧␈↓interpreted␈α≠merely␈α≠as␈α≠a␈α≠chromatic␈α≠passing␈α≠note,␈α≤but␈α≠which
␈↓ α∧␈↓certainly␈α∃does␈α∃tend␈α∃to␈α∃tonicize␈α∃the␈α∃following␈α∃B␈α∃(as␈α⊗the␈α∃sixth
␈↓ α∧␈↓␈↓ ε↔74␈↓ 
T


␈↓"β␈↓ α∧␈↓degree,␈α
normally␈α
a␈α
minor␈α
tonic,␈αof␈α
␈↓&D␈↓)αβ),␈α
which␈α
then␈α
functions␈α
as␈αit
␈↓ α∧␈↓did␈αearlier.␈α At␈αthe␈αend␈αof␈αmeasure␈α22,␈αthe␈αtonic␈αexpected␈αafter␈α
the
␈↓ α∧␈↓A7th chord of four beats back is replaced by the II␈↓∧I␈↓ of ␈↓&A␈↓)αβ.

␈↓"β␈↓ α∧␈↓␈↓ αdSince␈αthe␈αsuccessive␈αfunctions␈αin␈αsuch␈αmusic␈αsometimes␈αbear
␈↓ α∧␈↓only␈α_a␈α_secondary␈α_relation␈α_to␈α_each␈α_other,␈α_very␈α_skillful␈α↔voice
␈↓ α∧␈↓leading,␈α∂as␈α∞in␈α∂the␈α∞Chopin␈α∂example,␈α∞is␈α∂necessary␈α∞in␈α∂order␈α∂that␈α∞the
␈↓ α∧␈↓progression␈α⊂remains␈α⊂clear.␈α⊃ From␈α⊂one␈α⊂point␈α⊃of␈α⊂view,␈α⊂there␈α⊃is␈α⊂no
␈↓ α∧␈↓doubt␈α⊃at␈α⊃all␈α⊂that␈α⊃this␈α⊃passage␈α⊃can␈α⊂be␈α⊃interpreted␈α⊃as␈α⊃a␈α⊂chromatic
␈↓ α∧␈↓"working out" of the A chord.
␈↓"β
␈↓"β␈↓ α∧␈↓Example 69b.  (Reduction of Example 69a.  The doubling of the
␈↓"β␈↓ α∧␈↓                highest part at the octave below is omitted.)
␈↓"β␈↓ α∧␈↓␈↓ βw␈↓¬⊂⊗⊃L[%0,%-1.9]:N69XB.PLT[C6,LCS]⊂⊗⊃␈↓










␈↓"β␈↓ α∧␈↓␈↓ αdHowever,␈αthe␈α
particular␈αform␈α
the␈αchromaticism␈α
takes␈αin␈α
this
␈↓ α∧␈↓Mazurka␈α∀also␈α∀gives␈α∀the␈α∀unmistakable␈α∀impression␈α∀of␈α∀a␈α∃series␈α∀of
␈↓ α∧␈↓varied harmonic functions.


␈↓"β␈↓ α∧␈↓␈↓ αdFor␈αmore␈αexamples␈αof␈αchords␈αwhich␈αhave␈αboth␈αcontrapuntal
␈↓ α∧␈↓and␈α≠harmonic␈α≠significance␈α~we␈α≠will␈α≠turn␈α~to␈α≠the␈α≠opening␈α~of
␈↓ α∧␈↓Schubert's ␈↓↓Quintet in C␈↓, Op.163.
␈↓ α∧␈↓␈↓ ε↔75␈↓ 
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␈↓"β␈↓ α∧␈↓Example and Figure 70.  Schubert, String Quintet in C, Op.163
␈↓"β␈↓ α∧␈↓                (Reduction of measures 1-26.)
␈↓"β␈↓ α∧␈↓␈↓ βb␈↓¬⊂⊗⊃L[%-.07,%-3.66]:N70X.PLT[C6,LCS]⊂⊗⊃␈↓

















␈↓"β␈↓ α∧␈↓␈↓ αdComplete␈αdiminished␈α7th␈αchords␈α(at␈αbars␈α4␈αand␈α13)␈αare␈αoften
␈↓ α∧␈↓used␈α
non-functionally,␈αas␈α
multiple␈αneighboring␈α
notes.␈α Taking␈α
this
␈↓ α∧␈↓point␈α∩of␈α∩view,␈α∩Figure␈α∩70a␈α∩treats␈α∩most␈α∩of␈α∩the␈α∩altered␈α∩chords␈α∩as
␈↓ α∧␈↓purely␈αcontrapuntal.␈α Thus␈αthe␈αharmonic␈αmovement␈αremains␈αquite
␈↓ α∧␈↓simple␈α∩and␈α∩without␈α∪any␈α∩new␈α∩tonicization␈α∪until␈α∩the␈α∩end␈α∪of␈α∩the
␈↓ α∧␈↓excerpt.␈α∪ This␈α∪is␈α∪very␈α∪likely␈α∪the␈α∪way␈α∪the␈α∪music␈α∪is␈α∀heard␈α∪(and
␈↓ α∧␈↓intended to be heard).

␈↓"β␈↓ α∧␈↓␈↓ αdAs␈α∩we␈α∪come␈α∩to␈α∪know␈α∩the␈α∩piece␈α∪rather␈α∩well,␈α∪especially␈α∩as
␈↓ α∧␈↓regards␈α
the␈αvioloncellos'␈α
repetition␈αof␈α
the␈α
opening␈αtheme␈α
at␈αbar␈α
33
␈↓ α∧␈↓(see␈α
Example␈α
71),␈αwe␈α
may␈α
feel␈α
that␈αthe␈α
various␈α
altered␈α
chords␈αin
␈↓ α∧␈↓the␈α≥first␈α≥part␈α≥also␈α≡carry␈α≥a␈α≥potential␈α≥of␈α≡having␈α≥functional
␈↓ α∧␈↓implications.␈α~ Any␈α~given␈α≠listener␈α~may␈α~not␈α~always␈α≠hear␈α~this
␈↓ α∧␈↓example␈αin␈αthe␈αsame␈αway,␈αeven␈αif␈αhe␈αhas␈αmemorized␈αit.␈α While␈αthe
␈↓ α∧␈↓main␈α∂purpose␈α∂of␈α∂our␈α∂analyses␈α⊂is␈α∂to␈α∂show␈α∂how␈α∂the␈α∂harmony␈α⊂of␈α∂a
␈↓ α∧␈↓piece␈α∪is␈α∪most␈α∪simply␈α∪heard,␈α∪we␈α∪should␈α∪also␈α∪try␈α∪to␈α∪provide␈α∩for
␈↓ α∧␈↓other, less simple possibilities that may be inherent in the music.
␈↓ α∧␈↓␈↓ ε↔76␈↓ 
T


␈↓"β␈↓ α∧␈↓␈↓ αdFigure␈α∩70b␈α∩shows␈α∪the␈α∩implications␈α∩of␈α∩the␈α∪various␈α∩altered
␈↓ α∧␈↓chords.␈α⊂ The␈α⊂diminished␈α⊃chord␈α⊂at␈α⊂bar␈α⊃13␈α⊂is␈α⊂shown␈α⊃as␈α⊂␈↓&d␈↓)αβ:␈α⊂Vs␈α⊃of␈α⊂V
␈↓ α∧␈↓(A␈↓βF␈↓=G␈↓βS␈↓)␈αsimply␈αbecause␈αof␈αits␈αbeing␈αin␈αa␈αposition␈αanalogous␈αto␈αthat
␈↓ α∧␈↓of␈α
the␈αfirst␈α
diminished␈α
chord,␈αbar␈α
4.␈α Bar␈α
13␈α
has,␈αof␈α
course,␈α
at␈αthe
␈↓ α∧␈↓same␈α⊗time␈α↔the␈α⊗role␈α⊗of␈α↔Vs␈α⊗of␈α⊗␈↓&C␈↓)αβ.␈α↔ This␈α⊗is␈α⊗demonstrated␈α↔by␈α⊗the
␈↓ α∧␈↓indications␈α∞below␈α
the␈α∞second␈α∞analysis.␈α
 Thereby␈α∞the␈α∞symmetry␈α
of
␈↓ α∧␈↓the␈α_first␈α↔and␈α_second␈α_phrases␈α↔is␈α_clearly␈α↔shown.␈α_ At␈α_(*)␈α↔three
␈↓ α∧␈↓functions␈αare␈αgiven␈αfor␈αthe␈αd␈αminor␈αharmony.␈α They␈αrepresent,␈α1)
␈↓ α∧␈↓its␈α⊂relation␈α⊂to␈α∂the␈α⊂previous␈α⊂function,␈α∂2)␈α⊂its␈α⊂present␈α⊂function,␈α∂as
␈↓ α∧␈↓defined␈α
by␈α
a␈α
new␈α
statement␈α
of␈α
the␈α
main␈α
motive,␈α
and␈α
3)␈αits␈α
relation
␈↓ α∧␈↓to␈α∞the␈α
following␈α∞function.␈α
Such␈α∞triple␈α
indications␈α∞should␈α∞be␈α
used
␈↓ α∧␈↓sparingly,␈α∃since␈α∀they␈α∃could␈α∀easily␈α∃obscure␈α∀the␈α∃most␈α∀important
␈↓ α∧␈↓elements of a progression.

␈↓"β␈↓ α∧␈↓␈↓ αdPerhaps␈α
Schubert␈αwished␈α
to␈αprove␈α
that␈αthese␈α
altered␈αchords
␈↓ α∧␈↓could␈α∩have␈α⊃harmonic␈α∩functions,␈α⊃since␈α∩his␈α⊃␈↓&varied␈↓)αβ␈α∩restatement␈α⊃of
␈↓ α∧␈↓the opening gives the following progression.
␈↓"β
␈↓"β␈↓ α∧␈↓Example 71.  Schubert, Quintet in C, Op.163 
␈↓"β␈↓ α∧␈↓             (Reduction of bars 33-46)
␈↓"β
␈↓"β
␈↓"β
␈↓"β
␈↓"β
␈↓"β
␈↓"β␈↓ α∧␈↓Figure 71
␈↓"β␈↓ α∧␈↓␈↓ βr␈↓¬⊂⊗⊃L[%00,%-1.00]:N71X.PLT[C6,LCS]⊂⊗⊃␈↓






␈↓"β␈↓ α∧␈↓␈↓ αdNow,␈α⊂the␈α⊂first␈α⊂diminished␈α⊂chord␈α⊂is␈α⊂certainly␈α⊂working␈α⊂as␈α∂a
␈↓ α∧␈↓tonicizing␈α∞agent␈α∞to␈α∞␈↓&G␈↓)αβ.␈α∞ The␈α∂three␈α∞chords␈α∞found␈α∞in␈α∞measures␈α∂40␈α∞to
␈↓ α∧␈↓44␈αgive␈α
the␈αeffect␈α
of␈αa␈αdeceptive␈α
progression␈αin␈α
␈↓&a␈↓)αβ,␈αthe␈α
final␈αchord
␈↓ α∧␈↓of␈α⊃the␈α⊂group␈α⊃being␈α⊂also␈α⊃subdominant␈α⊂in␈α⊃terms␈α⊂of␈α⊃what␈α⊂follows.
␈↓ α∧␈↓␈↓ ε↔77␈↓ 
T


␈↓"β␈↓ α∧␈↓Note␈αthat␈αno␈αpivotal␈αtonic␈α
is␈αused␈αwhen␈αthe␈αcontrol␈α
tonic␈αreturns
␈↓ α∧␈↓to␈α␈↓&I␈↓)αβ.␈α It␈αis␈αfelt␈αthat␈αthe␈αtime␈αspent␈αunder␈αthe␈αcontrol␈αtonic␈αof␈α␈↓&ii␈↓)αβ␈α(␈↓&d␈↓)αβ)
␈↓ α∧␈↓is␈αof␈αsuch␈αrelatively␈αbrief␈αduration␈αthat␈αC␈αcould␈αscarcely␈αbe␈αheard
␈↓ α∧␈↓as␈α⊃a␈α⊃tonicized␈α⊃VII.␈α⊃ However,␈α⊃some␈α⊃other␈α⊃piece␈α⊃with␈α∩a␈α⊃different
␈↓ α∧␈↓␈↓↓presentation␈↓␈α∩of␈α∩a␈α∩similar␈α∩progression␈α∩might␈α∩be␈α∪analyzed␈α∩rather
␈↓ α∧␈↓differently.

␈↓"β␈↓ α∧␈↓␈↓ αdIn␈α≤the␈α≠␈↓↓March␈α≤to␈α≠the␈α≤Scaffold␈↓␈α≠from␈α≤Berlioz'␈α≠␈↓↓Fantastic
␈↓ α∧␈↓↓Symphony␈↓␈α
occurs␈α
a␈αpassage␈α
that␈α
has␈αpuzzled␈α
many␈α
musicians.␈α Its
␈↓ α∧␈↓dramatic␈α∪effect␈α∩is␈α∪highly␈α∩dynamic␈α∪and␈α∩specific,␈α∪but␈α∪its␈α∩musical
␈↓ α∧␈↓justification␈α↔has␈α_been␈α↔difficult.␈α↔ The␈α_problem␈α↔arises␈α_from␈α↔the
␈↓ α∧␈↓alternation␈α⊃of␈α⊃the␈α⊂tonic␈α⊃␈↓&g␈↓)αβ␈α⊃minor␈α⊃harmony␈α⊂and␈α⊃the␈α⊃D␈↓βF␈↓␈α⊃chord.␈α⊂ It
␈↓ α∧␈↓might␈α∩seem␈α∪that␈α∩the␈α∩closest␈α∪link␈α∩between␈α∪these␈α∩tritone-related
␈↓ α∧␈↓minor␈α∞and␈α
major␈α∞chords␈α∞would␈α
be␈α∞found␈α∞at␈α
the␈α∞fourth␈α∞above␈α
the
␈↓ α∧␈↓tonic, or ␈↓&c␈↓)αβ minor.  Thus the relationship could be shown:
␈↓"β
␈↓"β␈↓ α∧␈↓Figure 72
␈↓"β␈↓ α∧␈↓␈↓ ∧␈↓¬⊂⊗⊃L[%0,%-.9]:N72F.PLT[C6,LCS]⊂⊗⊃␈↓





␈↓"β␈↓ α∧␈↓␈↓ αdHowever,␈α∞the␈α∞composer␈α∞does␈α∂not␈α∞seem␈α∞to␈α∞take␈α∞this␈α∂view␈α∞of
␈↓ α∧␈↓the␈α∩relationship␈α∪(nor␈α∩does␈α∩he␈α∪treat␈α∩D␈↓βF␈↓␈α∩in␈α∪this␈α∩manner␈α∪when␈α∩it
␈↓ α∧␈↓appears␈α≠a␈α≠few␈α≤moments␈α≠earlier).␈α≠ The␈α≠alternation␈α≤of␈α≠chords
␈↓ α∧␈↓continues␈α∃until␈α∀D␈↓βF␈↓␈α∃is␈α∀almost␈α∃heard␈α∀as␈α∃a␈α∀new␈α∃and␈α∀functionally
␈↓ α∧␈↓unrelated␈α⊗tonic.␈α∃ But,␈α⊗as␈α∃the␈α⊗drive␈α∃of␈α⊗the␈α∃passage␈α⊗subsides,␈α∃it
␈↓ α∧␈↓progresses␈α∞to␈α∞E␈↓βF␈↓7␈α∞and␈α∞thence␈α∂to␈α∞a␈α∞tutti␈α∞chord,␈α∞at␈α∞which␈α∂time␈α∞the
␈↓ α∧␈↓previous␈α∩happenings␈α⊃may␈α∩be␈α⊃reassessed.␈α∩ The␈α∩analysis␈α⊃following
␈↓ α∧␈↓the␈α∂example␈α⊂represents␈α∂the␈α⊂␈↓↓result␈↓␈α∂of␈α⊂this␈α∂reassessment.␈α⊂ There␈α∂is
␈↓ α∧␈↓inadequate basis for choice until the end of the passage.
␈↓ α∧␈↓␈↓ ε↔78␈↓ 
T


␈↓"β␈↓ α∧␈↓Example and Figure 73.  Berlioz, Fantastic Symphony 
␈↓"β␈↓ α∧␈↓                                (Reduced from the fourth movement)
␈↓"β␈↓ α∧␈↓␈↓ βu␈↓¬⊂⊗⊃L[%0,%-3.75]:N73X.PLT[C6,LCS]⊂⊗⊃␈↓

















␈↓"β␈↓ α∧␈↓␈↓ αdBelow␈α∞the␈α∞main␈α
body␈α∞of␈α∞the␈α
analysis␈α∞is␈α∞shown␈α∞the␈α
separate
␈↓ α∧␈↓movement␈α
of␈α
each␈αof␈α
the␈α
two␈αalternating␈α
progressions.␈α
 The␈αone␈α
in
␈↓ α∧␈↓␈↓&g␈↓)αβ␈α∞is␈α∞quite␈α∞simple;␈α∞in␈α∞fact,␈α∞the␈α
whole␈α∞g␈α∞chord␈α∞acts␈α∞as␈α∞a␈α∞pedal␈α
until
␈↓ α∧␈↓the␈α
augmented␈α
sixth␈α
chord␈α
leads␈α
to␈α
the␈α
dominant.␈α
 The␈α
progression
␈↓ α∧␈↓begun␈αby␈αthe␈α
D␈↓βF␈↓␈αchord␈αis␈α
listed␈αunder␈αan␈α
␈↓&A␈↓βF␈↓␈↓)αβ␈αtonic␈αbecause,␈αin␈α
view
␈↓ α∧␈↓of␈α∂the␈α∂ultimate␈α⊂hearing␈α∂of␈α∂the␈α∂E␈↓βF␈↓7␈α⊂(enharmonic),␈α∂␈↓&A␈↓βF␈↓␈↓)αβ␈α∂is␈α⊂the␈α∂most
␈↓ α∧␈↓direct␈α∞connecting␈α∂link␈α∞to␈α∞␈↓&g␈↓)αβ,␈α∂even␈α∞though␈α∂the␈α∞I␈α∞of␈α∂␈↓&A␈↓βF␈↓␈↓)αβ␈α∞is␈α∂not␈α∞used.
␈↓ α∧␈↓The␈α~functions␈α~listed␈α≠in␈α~parentheses␈α~might␈α~be␈α≠interpreted␈α~as
␈↓ α∧␈↓chromatic␈αelaboration␈αof␈αthe␈αD␈↓βF␈↓␈αchord␈α(see␈αExample␈α70).␈α Thus␈αthe
␈↓ α∧␈↓overall␈αprogress␈αfrom␈αthe␈αD␈↓βF␈↓␈αchord␈αis␈αlikewise␈αsimple␈α--␈α␈↓&A␈↓βF␈↓␈↓)αβ:␈αIV...V,
␈↓ α∧␈↓wherein␈αthe␈α
V␈αserves␈αdoubly␈α
as␈αthe␈αG6␈α
of␈α␈↓&g␈↓)αβ.␈α Notice␈α
that␈αin␈αall␈α
this
␈↓ α∧␈↓the␈αpossibility␈αof␈αtreating␈αthe␈αD␈↓βF␈↓␈αchord␈αas␈αa␈α␈↓βF␈↓V␈αor␈α␈↓βS␈↓IV␈αrelationship
␈↓ α∧␈↓in␈α␈↓&g␈↓)αβ␈αis␈αavoided.␈α A␈αtrue␈αdirect␈αrelation␈αof␈αthe␈αtritone␈αbetween␈αtwo
␈↓ α∧␈↓tonics␈α∞tends␈α∞to␈α∞destroy␈α∞both␈α∞of␈α∞them.␈α∞ Such␈α∞a␈α∞relationship␈α
would
␈↓ α∧␈↓merely␈α∃constitute␈α∀a␈α∃juxtaposition␈α∀of␈α∃keys␈α∀whose␈α∃tonic␈α∀chords
␈↓ α∧␈↓were␈αincompatible␈α
except␈αas␈α
they␈αboth␈αserved␈α
as␈αsubsidiaries␈α
to␈αa
␈↓ α∧␈↓third tonic (see page 46).
␈↓ α∧␈↓␈↓ ε↔79␈↓ 
T


␈↓"β␈↓ α∧␈↓␈↓ αdFollowing␈α∪is␈α∪the␈α∪well-known␈α∪introduction␈α∪to␈α∀the␈α∪second
␈↓ α∧␈↓movement␈αof␈αDvorak's␈α
␈↓↓New␈αWorld␈αSymphony␈↓.␈α The␈α
notation␈αhere
␈↓ α∧␈↓differs enharmonically from the original.
␈↓"β
␈↓"β␈↓ α∧␈↓Example and Figure 74
␈↓"β␈↓ α∧␈↓␈↓ βb␈↓¬⊂⊗⊃L[%-.05,%-4.52]:N74X.PLT[C6,LCS]⊂⊗⊃␈↓





















␈↓"β␈↓ α∧␈↓␈↓ αdEven␈α∞though␈α∞the␈α∞movement␈α∞proper␈α∞is␈α∞in␈α∞␈↓&D␈↓)αβ␈↓βF␈↓,␈α∞the␈α∞key␈α∂at␈α∞the
␈↓ α∧␈↓beginning,␈α∂as␈α⊂listed␈α∂on␈α⊂the␈α∂highest␈α⊂level,␈α∂is␈α⊂␈↓&E␈↓)αβ.␈α∂ This␈α⊂represents␈α∂a
␈↓ α∧␈↓continuation␈αof␈αthe␈α
␈↓&e␈↓)αβ␈αof␈αthe␈α
first␈αmovement.␈α The␈α
tritone␈αrelation
␈↓ α∧␈↓between␈αtwo␈αmajor␈αchords␈α(E␈αand␈αB␈↓βF␈↓)␈αis␈αusually␈αheard␈αas␈αV-␈↓βF␈↓II␈αor
␈↓ α∧␈↓vice␈α∀versa,␈α∃the␈α∀former␈α∀being␈α∃used␈α∀in␈α∀this␈α∃case␈α∀because␈α∃of␈α∀the
␈↓ α∧␈↓positions␈α∨of␈α∨the␈α∨two␈α≡chords,␈α∨V␈↓βH␈↓-␈↓βF␈↓II␈↓β6␈↓,␈α∨and␈α∨because␈α∨of␈α≡the
␈↓ α∧␈↓subsequent␈α∩harmonic␈α∪developments.␈α∩ By␈α∩the␈α∪time␈α∩we␈α∪reach␈α∩the
␈↓ α∧␈↓third␈α⊃measure␈α∩we␈α⊃are␈α∩sure␈α⊃that␈α⊃the␈α∩E␈α⊃chord␈α∩was␈α⊃working␈α∩as␈α⊃a
␈↓ α∧␈↓dominant to ␈↓&A␈↓)αβ.
␈↓"β␈↓ α∧␈↓␈↓ ε↔80␈↓ 
T


␈↓"β␈↓ α∧␈↓Example 75a
␈↓"β␈↓ α∧␈↓␈↓ βj␈↓¬⊂⊗⊃L[%0,%-1.22]:N75XA.PLT[C6,LCS]⊂⊗⊃␈↓






␈↓"β␈↓ α∧␈↓␈↓ αdHowever,␈α
the␈α
D␈↓βF␈↓␈α
chord␈α
which␈α
broke␈α
the␈α
continuity␈α∞is␈α
most
␈↓ α∧␈↓simply␈αheard␈αas␈αdominant␈αto␈α␈↓&A␈↓)αβ's␈αsixth␈αdegree,␈α␈↓&f␈↓)αβ␈↓βS␈↓.␈α It␈αmust␈αbe␈αnoted
␈↓ α∧␈↓that␈α≠the␈α≤absence␈α≠of␈α≤emphasis␈α≠in␈α≠the␈α≤first␈α≠two␈α≤bars␈α≠makes
␈↓ α∧␈↓immediate␈αrecognition␈αof␈αthe␈αfunctions␈αof␈αall␈αbut␈αthe␈αfirst␈αtonic␈α␈↓&E␈↓)αβ
␈↓ α∧␈↓very␈α∂difficult.␈α∞ Until␈α∂more␈α∂is␈α∞heard␈α∂any␈α∞chord␈α∂may␈α∂be␈α∞dominant,
␈↓ α∧␈↓subdominant,␈α⊂or␈α⊂tonic,␈α⊂etc.␈α⊂ When␈α∂the␈α⊂phrase␈α⊂is␈α⊂complete␈α⊂--␈α∂and
␈↓ α∧␈↓thus␈α∂has␈α∂developed␈α∂points␈α⊂of␈α∂emphasis␈α∂--␈α∂these␈α⊂distantly␈α∂related
␈↓ α∧␈↓chords␈α
are␈α
retrospectively␈αassigned␈α
functions␈α
in␈αterms␈α
of␈α
the␈αend
␈↓ α∧␈↓results.␈α∃ The␈α⊗f␈↓βS␈↓␈α∃chord␈α⊗serves␈α∃as␈α∃VI␈α⊗to␈α∃␈↓&A␈↓)αβ␈α⊗(Example␈α∃75a);␈α⊗␈↓&f␈↓)αβ␈↓βS␈↓␈α∃is
␈↓ α∧␈↓tonicized␈α∂by␈α∂the␈α∂progression␈α∂from␈α∞the␈α∂fourth␈α∂to␈α∂the␈α∂sixth␈α∞chord
␈↓ α∧␈↓(Example␈α75c);␈α
and␈αthe␈α
f␈↓βS␈↓␈αchord␈α
is␈αIV␈↓βFF3␈↓␈α
(g␈↓βF␈↓)␈αto␈α
␈↓&D␈↓)αβ␈↓βF␈↓␈α(Example␈α
75b).
␈↓ α∧␈↓␈↓&A␈↓)αβ␈α⊂has␈α⊂been␈α⊂tonicized␈α⊂by␈α⊂the␈α⊂first␈α⊂three␈α⊂chords,␈α⊂but␈α⊂the␈α⊂A␈α⊂chord
␈↓ α∧␈↓also serves as ␈↓βFF␈↓VI (B␈↓βFF␈↓) to ␈↓&D␈↓)αβ␈↓βF␈↓ (Example 75b).
␈↓"β
␈↓"β␈↓ α∧␈↓Example 75b
␈↓"β␈↓ α∧␈↓            
␈↓"β
␈↓"β
␈↓"β
␈↓"β
␈↓"β
␈↓"β
␈↓"β
␈↓"β␈↓ α∧␈↓Example 75c
␈↓"β␈↓ α∧␈↓␈↓ βl␈↓¬⊂⊗⊃L[%0,%-1.25]:N75XB.PLT[C6,LCS]⊂⊗⊃␈↓
␈↓ α∧␈↓␈↓ ε↔81␈↓ 
T


␈↓"β␈↓ α∧␈↓␈↓ αdThe␈α∞later␈α∞appearances␈α∞of␈α∞this␈α∞material␈α∞in␈α∞the␈α∂movement␈α∞are
␈↓ α∧␈↓somewhat simpler because they both begin and end in ␈↓&D␈↓)αβ␈↓βF␈↓.
␈↓"β
␈↓"β␈↓ α∧␈↓Example and Figure 76
␈↓"β␈↓ α∧␈↓␈↓ βu␈↓¬⊂⊗⊃L[%0,%-2.86]:N76X.PLT[C6,LCS]⊂⊗⊃␈↓













␈↓"β␈↓ α∧␈↓␈↓ αdIn␈αthe␈αtwentieth␈αof␈αBeethoven's␈α␈↓↓Diabelli␈αVariations␈↓,␈αOp.120,
␈↓ α∧␈↓the␈α
listener␈α
is␈α
frequently␈α
kept␈α
in␈α
doubt␈α
as␈α
to␈α
whether␈α
or␈α
not␈α
the
␈↓ α∧␈↓chromaticism␈α∪is␈α∪functional.␈α∪ The␈α∩slow,␈α∪regular␈α∪rhythm␈α∪and␈α∩the
␈↓ α∧␈↓constant␈α⊗use␈α∃of␈α⊗free␈α⊗imitation␈α∃makes␈α⊗it␈α∃difficult␈α⊗to␈α⊗specify␈α∃a
␈↓ α∧␈↓functional␈α∂or␈α∂non-functional␈α∂role␈α⊂for␈α∂every␈α∂note.␈α∂ Notes␈α⊂such␈α∂as
␈↓ α∧␈↓the␈α⊃C␈↓βS␈↓␈α⊂of␈α⊃bar␈α⊂4,␈α⊃which␈α⊂had␈α⊃virtually␈α⊂no␈α⊃functional␈α⊂significance
␈↓ α∧␈↓earlier␈α∩in␈α∩the␈α∩work␈α∩(see␈α∩Variation␈α∩I,␈α∩bars␈α∩4␈α∩and␈α∩6),␈α∩now␈α⊃share
␈↓ α∧␈↓equal␈α∞status,␈α∞timewise,␈α∞with␈α∂some␈α∞of␈α∞the␈α∞most␈α∂clearly␈α∞functional
␈↓ α∧␈↓notes.␈α Another␈αfactor␈α
which␈αcreates␈αdoubt␈α
is␈αthe␈αoccasional␈αuse␈α
of
␈↓ α∧␈↓notes␈α
in␈α
the␈α
upper␈α
voices␈α
which␈α
may␈α
have␈α
double␈α∞significance␈α
as
␈↓ α∧␈↓both␈α⊂dissonant␈α⊂pedal␈α⊂points␈α⊂and␈α⊂true␈α⊂chord␈α⊂tones␈α⊂(see␈α⊂bars␈α⊂5,␈α∂7,
␈↓ α∧␈↓etc.).␈α∪ The␈α∪voice␈α∪leading␈α∪is␈α∪extremely␈α∪carefully␈α∪worked␈α∪out␈α∪--
␈↓ α∧␈↓every␈α
chromatic␈α
change␈α
has␈α
its␈α
logical␈α
linear␈α
result.␈α
 However,␈α
the
␈↓ α∧␈↓harmonic␈α∩implications␈α∩of␈α∩the␈α∪combinations␈α∩of␈α∩the␈α∩lines␈α∪may␈α∩be
␈↓ α∧␈↓experienced␈α∀on␈α∀their␈α∀own␈α∃plane.␈α∀ Of␈α∀course,␈α∀it␈α∀must␈α∃never␈α∀be
␈↓ α∧␈↓forgotten␈α⊃that␈α⊃particular␈α∩harmonic␈α⊃functions␈α⊃never␈α⊃have␈α∩a␈α⊃real
␈↓ α∧␈↓existence␈α∂apart␈α∂from␈α∂the␈α⊂total␈α∂music␈α∂which␈α∂produces␈α⊂them.␈α∂ The
␈↓ α∧␈↓alternating␈α⊃functions␈α∩in␈α⊃this␈α∩variation␈α⊃certainly␈α∩grow␈α⊃out␈α∩of␈α⊃a
␈↓ α∧␈↓mode of thought that considers all musical factors simultaneously.
␈↓ α∧␈↓␈↓ ε↔82␈↓ 
T


␈↓"β␈↓ α∧␈↓Example 77.  Beethoven, Diabelli Variations, Op.120
␈↓"β␈↓ α∧␈↓␈↓ βh␈↓¬⊂⊗⊃L[%0.0,%-8.30]:N77X.PLT[C6,LCS]⊂⊗⊃␈↓
␈↓ α∧␈↓␈↓ ε↔83␈↓ 
T


␈↓"β␈↓ α∧␈↓␈↓ αdFrom␈α∩the␈α∩broadest␈α⊃point␈α∩of␈α∩view,␈α⊃all␈α∩the␈α∩altered␈α∩notes␈α⊃in
␈↓ α∧␈↓bars␈α∞4-8␈α∞and␈α∞17-20␈α∞may␈α∞be␈α∞taken␈α∞as␈α∞non-functional␈α∞elaborations
␈↓ α∧␈↓of␈α⊃the␈α⊃dominant.␈α⊂ (The␈α⊃same␈α⊃is␈α⊂true␈α⊃for␈α⊃bars␈α⊂21-24,␈α⊃but␈α⊃with␈α⊂a
␈↓ α∧␈↓different␈αtonic.)␈αIn␈αbars␈α2␈αand␈α
3␈αthe␈αbass␈αis␈αmelodic,␈αso␈α
there␈αneed
␈↓ α∧␈↓be no question of a ␈↓βA␈↓ chord.
␈↓"β
␈↓"β␈↓ α∧␈↓Figure 77a
␈↓"β␈↓ α∧␈↓␈↓ βa␈↓¬⊂⊗⊃L[%0.0,%-1.00]:N77FA.PLT[C6,LCS]⊂⊗⊃␈↓





␈↓"β␈↓ α∧␈↓␈↓ αdAs␈α∞the␈α∞variation␈α∞continues,␈α∞we␈α∞are␈α∞faced␈α∞with␈α
progressions
␈↓ α∧␈↓which␈α
do␈α
not␈α
respond␈α
so␈α
well␈α
to␈α
this␈α
approach.␈α
 The␈α
chords␈αof␈α
each
␈↓ α∧␈↓dotted␈αhalf-note␈αseem␈αto␈αacquire␈αmuch␈αmore␈αseparate␈αsignificance.
␈↓ α∧␈↓With␈α_this␈α_in␈α_mind,␈α→we␈α_might␈α_make␈α_an␈α_alternative␈α→(but␈α_not
␈↓ α∧␈↓necessarily␈α
"better")␈α
analysis␈αof␈α
the␈α
above␈α
discussed␈αmeasures.␈α
 Let
␈↓ α∧␈↓us␈αconsider␈αthat␈αA␈↓βF␈↓=G␈↓βS␈↓␈αin␈α
bar␈α4␈αand␈αthat␈αthe␈α
G␈↓βN␈↓␈αof␈αbars␈α4,␈α5,␈α
and␈α7
␈↓ α∧␈↓(and␈α∞17,␈α∞18,␈α∞and␈α∞19)␈α∂is␈α∞an␈α∞intermittent␈α∞pedal␈α∞point␈α∞within␈α∂the␈α∞d
␈↓ α∧␈↓minor␈α
chord.␈α
 Now␈α
the␈α
elaborations␈α
are␈α
shown␈α
as␈αfunctional␈α
under
␈↓ α∧␈↓ii (␈↓&d␈↓)αβ), concluding in each case with a C half-cadence.
␈↓"β
␈↓"β␈↓ α∧␈↓Figure 77b
␈↓"β␈↓ α∧␈↓␈↓ βc␈↓¬⊂⊗⊃L[%0.0,%-1.60]:N77FB.PLT[C6,LCS]⊂⊗⊃␈↓








␈↓"β␈↓ α∧␈↓␈↓ αdFor␈α⊃the␈α⊃sake␈α⊃of␈α⊃simplicity,␈α⊃the␈α⊃first␈α⊃diagram␈α∩(Figure␈α⊃77a)
␈↓ α∧␈↓will be used in the complete analysis.
␈↓ α∧␈↓␈↓ ε↔84␈↓ 
T


␈↓"β␈↓ α∧␈↓␈↓ αdThe␈α∞motive␈α
heard␈α∞in␈α∞bars␈α
17-20␈α∞is␈α
continued␈α∞in␈α∞bars␈α
21-24
␈↓ α∧␈↓as␈α∞an␈α∂elaboration␈α∞of␈α∂a␈α∞diminished␈α∂7th␈α∞chord.␈α∂ There␈α∞is␈α∂little␈α∞basis
␈↓ α∧␈↓for␈α∂settling␈α∂on␈α∂any␈α∂one␈α∂tonic,␈α∞although␈α∂␈↓&d␈↓)αβ␈α∂or␈α∂␈↓&f␈↓)αβ␈α∂would␈α∂seem␈α∂to␈α∞be
␈↓ α∧␈↓indicated␈αby␈αthe␈αnotation.␈α For␈αthe␈αfinal␈αanalysis,␈α␈↓&f␈↓)αβ␈αwill␈αbe␈αchosen
␈↓ α∧␈↓because␈α⊂the␈α⊂tonics␈α⊂involved␈α⊂in␈α⊂the␈α⊂last␈α⊂part␈α⊂of␈α⊂the␈α⊂variation␈α∂all
␈↓ α∧␈↓stand in simple relation to that tonic.

␈↓"β␈↓ α∧␈↓␈↓ αdAll␈α∞the␈α∞subtleties␈α∞of␈α
the␈α∞alternating␈α∞progressions␈α∞at␈α∞bars␈α
9-
␈↓ α∧␈↓13␈α∂and␈α⊂25-28␈α∂would␈α∂be␈α⊂difficult␈α∂to␈α∂express.␈α⊂ In␈α∂the␈α⊂first␈α∂phrase
␈↓ α∧␈↓the␈αapproach␈αto␈α␈↓&d␈↓)αβ␈αas␈αa␈αtemporary␈αtonic␈αseems␈αclear;␈αand␈αthat␈αthis␈α␈↓&d␈↓)αβ
␈↓ α∧␈↓should␈αbecome␈αmajor␈αand␈αthe␈αdominant␈αto␈α␈↓&G␈↓)αβ␈αis␈αquite␈αconventional.
␈↓ α∧␈↓The␈α∞unexpected␈α∂appearance␈α∞of␈α∞the␈α∂C␈α∞chord␈α∞at␈α∂bars␈α∞11␈α∞and␈α∂12␈α∞has
␈↓ α∧␈↓the␈α⊃effect␈α⊃of␈α⊃prematurely␈α∩wrenching␈α⊃away␈α⊃the␈α⊃tonic␈α⊃role␈α∩of␈α⊃d.
␈↓ α∧␈↓Because␈α of␈α!the␈α alien␈α surroundings,␈α!this␈α C␈α chord␈α!is␈α most
␈↓ α∧␈↓immediately␈α
heard␈α
as␈α
a␈α
sudden␈α∞return␈α
to␈α
the␈α
I␈α
which␈α∞might␈α
have
␈↓ α∧␈↓been␈αexpected␈αafter␈αthe␈αclear␈αV␈αof␈αbar␈α8.␈α Then␈αthe␈αC␈αchord␈αworks
␈↓ α∧␈↓as␈α
a␈α
quite␈α
normal␈α
pivot␈α
to␈α
a␈αfull␈α
cadence␈α
on␈α
V␈α
(␈↓&G␈↓)αβ),␈α
which␈α
may␈αbe
␈↓ α∧␈↓listed briefly as a new control tonic at bar 15.
␈↓"β
␈↓"β␈↓ α∧␈↓Figure 77c
␈↓"β␈↓ α∧␈↓␈↓ βV␈↓¬⊂⊗⊃L[%0.03,%-3.25]:N77FC.PLT[C6,LCS]⊂⊗⊃␈↓
␈↓ α∧␈↓␈↓ ε↔85␈↓ 
T


␈↓"β␈↓ α∧␈↓␈↓ αdThe␈α→second␈α→phrase␈α→including␈α→alternating␈α~progressions␈α→is
␈↓ α∧␈↓more␈α∂difficult.␈α∂ At␈α∂measure␈α⊂25␈α∂the␈α∂b␈↓βFA␈↓␈α∂eventually␈α⊂assumes␈α∂three
␈↓ α∧␈↓important␈α⊗functions.␈α∃ One␈α⊗of␈α⊗these,␈α∃II␈α⊗of␈α∃A␈↓βF␈↓,␈α⊗does␈α⊗not␈α∃become
␈↓ α∧␈↓apparent␈α⊃until␈α⊂bar␈α⊃27,␈α⊂however.␈α⊃ The␈α⊂E␈↓βF7␈↓␈α⊃chord␈α⊂of␈α⊃measures␈α⊂27
␈↓ α∧␈↓and␈α28␈α
might␈αhave␈α
been␈αlisted␈α
only␈αas␈α
the␈αG6␈α
function␈αof␈α
␈↓&g␈↓)αβ,␈αsince
␈↓ α∧␈↓there␈α#are␈α$no␈α#other␈α#chords␈α$following␈α#which␈α$bear␈α#direct
␈↓ α∧␈↓relationship␈α⊃to␈α⊃it.␈α⊃ The␈α⊃earlier␈α⊃b␈↓βFA␈↓␈α⊃chord␈α⊃does␈α⊃form,␈α⊃however,␈α⊂a
␈↓ α∧␈↓conventional␈α∞preparation␈α∂for␈α∞the␈α∂function␈α∞of␈α∂E␈↓βF␈↓␈α∞as␈α∂the␈α∞dominant
␈↓ α∧␈↓of␈α
␈↓&A␈↓βF␈↓␈↓)αβ.␈α
 Thus,␈α
these␈α
two␈α
functions␈αof␈α
the␈α
E␈↓βF7␈↓␈α
chord␈α
can␈α
be␈αshown␈α
in
␈↓ α∧␈↓alternation with the G6 of ␈↓&b␈↓βF␈↓␈↓)αβ.
␈↓"β
␈↓"β␈↓ α∧␈↓Figure 77d
␈↓"β
␈↓"β␈↓ α∧␈↓␈↓ β←␈↓¬⊂⊗⊃L[%0.03,%-3.5]:N77FD.PLT[C6,LCS]⊂⊗⊃␈↓
















␈↓"β␈↓ α∧␈↓␈↓ αdIt␈α⊗may␈α⊗be␈α⊗noticed␈α⊗that␈α⊗after␈α⊗the␈α⊗first␈α⊗few␈α⊗bars␈α⊗in␈α∃this
␈↓ α∧␈↓Beethoven␈α⊃variation,␈α⊂very␈α⊃few␈α⊂␈↓↓simple␈↓␈α⊃tonic␈α⊂functions␈α⊃(i.e.,␈α⊂not
␈↓ α∧␈↓substitutes␈α⊂for␈α∂tonics)␈α⊂are␈α∂heard.␈α⊂ Only␈α∂the␈α⊂tonics␈α∂at␈α⊂bars␈α∂15-16
␈↓ α∧␈↓and␈α
at␈α
the␈α
end␈α
are␈α
decisive.␈α
 In␈α
the␈α
last␈α
12␈α
bars,␈α
even␈α
most␈α
of␈α
the
␈↓ α∧␈↓dominant␈αfunctions␈αare␈αpresented␈αby␈αsubstitutes.␈α It␈αwill␈αbe␈αfound
␈↓ α∧␈↓that␈α⊗most␈α⊗of␈α↔the␈α⊗harmonic␈α⊗vagueness␈α↔of␈α⊗later␈α⊗tonal␈α↔music␈α⊗is
␈↓ α∧␈↓␈↓ ε↔86␈↓ 
T


␈↓"β␈↓ α∧␈↓attributable␈α≤to␈α≤a␈α≤low␈α≤percentage␈α≤of␈α≤simple␈α≤tonic␈α≥(or␈α≤even
␈↓ α∧␈↓dominant)␈α∀functions␈α∃within␈α∀rapidly␈α∀changing␈α∃temporary␈α∀tonic
␈↓ α∧␈↓areas.

␈↓"β␈↓ α∧␈↓␈↓ αdDespite␈α≤the␈α≤complications,␈α≠our␈α≤analysis␈α≤will␈α≤show␈α≠the
␈↓ α∧␈↓simplicity␈α⊃of␈α⊃the␈α⊃largest␈α⊃harmonic␈α⊃design␈α⊃in␈α⊃this␈α⊃variation.␈α⊃ All
␈↓ α∧␈↓the␈αalternating␈αprogressions,␈αsubstitute␈αfunctions,␈αand␈αwhat␈αhave
␈↓ α∧␈↓you,␈α≠serve␈α≠only␈α≠as␈α~very␈α≠special␈α≠elaboration␈α≠of␈α≠the␈α~various
␈↓ α∧␈↓temporary␈α∂tonics,␈α⊂which␈α∂in␈α⊂turn␈α∂contribute␈α⊂to␈α∂the␈α⊂definition␈α∂of
␈↓ α∧␈↓the control tonics ␈↓&I␈↓)αβ ␈↓&V␈↓)αβ ␈↓&I␈↓)αβ ␈↓&iv␈↓)αβ ␈↓&I␈↓)αβ.
␈↓"β
␈↓"β␈↓ α∧␈↓Figure 77e.  The complete variation.
␈↓"β␈↓ α∧␈↓␈↓ βX␈↓¬⊂⊗⊃L[%0.03,%-5.85]:N77FE.PLT[C6,LCS]⊂⊗⊃␈↓
␈↓ α∧␈↓␈↓ ε↔87␈↓ 
T


␈↓"β␈↓ α∧␈↓␈↓ αdIn␈α∞this␈α∞chapter␈α
many␈α∞new␈α∞elements␈α
have␈α∞been␈α∞added␈α∞to␈α
the
␈↓ α∧␈↓analytical␈α≥diagram.␈α≡ One␈α≥must␈α≥always␈α≡be␈α≥on␈α≡guard␈α≥against
␈↓ α∧␈↓overloading␈α∩the␈α∩analysis␈α⊃with␈α∩non-essential␈α∩detail.␈α∩ When␈α⊃new,
␈↓ α∧␈↓and␈αpossibly␈αconfusing␈αindications␈αare␈αadded␈αto␈αthe␈αbasic␈αdiagram,
␈↓ α∧␈↓great␈α∪care␈α∪should␈α∪be␈α∩taken␈α∪that␈α∪the␈α∪music␈α∪under␈α∩consideration
␈↓ α∧␈↓really␈α_warrants␈α_their␈α_use.␈α_ Especially␈α_for␈α_the␈α_performer,␈α_the
␈↓ α∧␈↓potential␈α∪danger␈α∪of␈α∪too␈α∪much␈α∪attention␈α∪to␈α∪detail␈α∪in␈α∪analysis␈α∩is
␈↓ α∧␈↓probably greater than the danger of over-simplification.
␈↓"β␈↓ α∧␈↓␈↓ ∧4_______________
␈↓"β
␈↓"β␈↓ α∧␈↓Exercises for Chapter VI

␈↓"β␈↓ α∧␈↓␈↓ αdAnalyze␈α⊗the␈α∃following␈α⊗works.␈α⊗ Although␈α∃a␈α⊗great␈α⊗deal␈α∃of
␈↓ α∧␈↓chromaticism␈α_is␈α_involved␈α_in␈α→these␈α_excerpts,␈α_not␈α_all␈α→of␈α_them
␈↓ α∧␈↓contain alternating progressions.
␈↓"β
␈↓"β␈↓ α∧␈↓        1.  Chopin, Mazurka #1, in f␈↓βS␈↓, Op.6, #1, first 16 bars.
␈↓"β
␈↓"β␈↓ α∧␈↓        2.  Chopin, Mazurka  #6, in a,  Op.7,  #2, first 32 bars.
␈↓"β
␈↓"β␈↓ α∧␈↓        3.  Chopin, Mazurka #11, in e,  Op.17, #2, first 24 bars.
␈↓"β
␈↓"β␈↓ α∧␈↓        4.  Chopin, Mazurka #49, in f,  Op.68, #4, all.
␈↓"β
␈↓"β␈↓ α∧␈↓        5.  Chopin, Prelude in e,  Op.28, #4, all.
␈↓"β
␈↓"β␈↓ α∧␈↓        6.  Chopin, Prelude in f␈↓βS␈↓, Op.28, #8, all.
␈↓"β
␈↓"β␈↓ α∧␈↓        7.  Chopin, Prelude in f,  Op.28, #18, all.