/LMAR=0/XLINE=10/FONT#0=METL/FONT#1=METLI/FONT#2=METS/FONT#3=MUS[HHA,LCS]/FONT#4=MUZ[HHA,LCS]/FONT#5=BASL35
␈↓ α≠␈↓␈↓ ε.47␈↓ 
k


␈↓"β␈↓ α≠␈↓Figure 48
␈↓"β␈↓ α≠␈↓␈↓ β{␈↓¬⊂⊗⊃L[%0.53,%-1.15]:48F.PLT[HHA,LCS]⊂⊗⊃␈↓




␈↓"β

␈↓"β␈↓ α≠␈↓␈↓ α{It␈α∂will␈α⊂be␈α∂noted␈α⊂that␈α∂there␈α⊂is␈α∂␈↓↓no␈↓␈α⊂temporary␈α∂tonic␈α⊂listed␈α∂in
␈↓ α≠␈↓Figure␈α∃47␈α∃that␈α∃has␈α∀as␈α∃its␈α∃␈↓↓root␈↓␈α∃a␈α∀sharping␈α∃of␈α∃any␈α∃part␈α∃of␈α∀the
␈↓ α≠␈↓original␈α∪tonic␈α∀major␈α∪scale␈α∀or␈α∪a␈α∪flatting␈α∀of␈α∪the␈α∀1st,␈α∪4th␈α∀or␈α∪5th
␈↓ α≠␈↓degrees.␈α⊂ It␈α⊂is␈α⊂very␈α∂difficult␈α⊂to␈α⊂make␈α⊂a␈α∂case␈α⊂for␈α⊂the␈α⊂existence␈α∂of
␈↓ α≠␈↓such␈α∞a␈α∞direct␈α∞relationship␈α∞of␈α∞tonics.␈α∞ (See␈α∞Chapter␈α∞VI,␈α
Alternating
␈↓ α≠␈↓Progressions.)
␈↓"β␈↓ α≠␈↓␈↓ ∧K_______________
␈↓"β
␈↓"β
␈↓"β␈↓ α≠␈↓Pivot Chords in the Minor

␈↓"β␈↓ α≠␈↓␈↓ α{Because␈α_of␈α_the␈α_ambiguities␈α↔inherent␈α_in␈α_the␈α_minor␈α↔scale
␈↓ α≠␈↓certain␈αproblems␈αcan␈αoccur␈αin␈αregard␈αto␈αpivot␈αchords.␈α In␈αExample
␈↓ α≠␈↓49a␈α
the␈α
ascending␈αform␈α
of␈α
the␈α
minor␈αscale␈α
produces␈α
a␈α
chord␈α(IV␈↓βN␈↓)
␈↓ α≠␈↓which␈α
can,␈αin␈α
a␈α
slightly␈αdifferent␈α
context␈α(Example␈α
49b),␈α
lead␈αto
␈↓ α≠␈↓a brief new tonicization of VII.
␈↓"β
␈↓"β␈↓ α≠␈↓Example 49 
␈↓"β␈↓ α≠␈↓␈↓ βd␈↓¬⊂⊗⊃L[%0.03,%-2.15]:N49X.PLT[HHA,LCS]⊂⊗⊃␈↓
␈↓ α≠␈↓␈↓ ε.48␈↓ 
k


␈↓"β␈↓ α≠␈↓␈↓ α{In␈αthe␈αminor,␈αa␈α
direct␈αprogression␈αfrom␈αIII␈α(with␈α
the␈αflatted
␈↓ α≠␈↓fifth)␈α⊂to␈α⊂V␈α⊂(with␈α⊂the␈α⊂raised␈α⊂third)␈α⊂is␈α⊂somewhat␈α⊃rare.␈α⊂ However
␈↓ α≠␈↓the␈α⊃next␈α⊂example␈α⊃may␈α⊃be␈α⊂analyzed␈α⊃in␈α⊃this␈α⊂way␈α⊃because␈α⊃no␈α⊂real
␈↓ α≠␈↓tonicization of III is involved.
␈↓"β␈↓ α≠␈↓ 
␈↓"β␈↓ α≠␈↓Example and Figure 50
␈↓"β␈↓ α≠␈↓␈↓ β←␈↓¬⊂⊗⊃L[%0.03,%-2.42]:N50X.PLT[HHA,LCS]⊂⊗⊃␈↓









␈↓"β

␈↓"β␈↓ α≠␈↓␈↓ α{The␈α∞III␈α∞chord␈α∞may␈α∞be␈α∞called␈α∞a␈α∞pivot␈α∞in␈α∞the␈α∞minor␈α∞so␈α∞long␈α∞as
␈↓ α≠␈↓the␈α∞conventions␈α∞regarding␈α∞the␈α∞usage␈α∞of␈α∞the␈α∞various␈α∞forms␈α∂of␈α∞the
␈↓ α≠␈↓minor␈αscale␈αare␈αfollowed.␈α In␈αthe␈αnext␈αexample␈αthe␈αpivot␈αto␈αIII␈αas␈α
a
␈↓ α≠␈↓tonic␈α⊂is␈α∂the␈α⊂III␈α∂chord␈α⊂itself␈α∂since␈α⊂the␈α∂chord␈α⊂appears␈α∂in␈α⊂a␈α∂context
␈↓ α≠␈↓completely␈α∂compatible␈α∂with␈α∂both␈α∂␈↓&c␈↓)αβ␈α∂and␈α∂␈↓&E␈↓βF␈↓␈↓)αβ.␈α∂ However␈α∂the␈α∂return
␈↓ α≠␈↓from␈α↔III␈α⊗to␈α↔i␈α↔as␈α⊗the␈α↔middle-ground␈α⊗tonic␈α↔involves␈α↔an␈α⊗abrupt
␈↓ α≠␈↓chromatic shift.  Thus no pivot is shown.
␈↓"β␈↓ α≠␈↓ 
␈↓"β␈↓ α≠␈↓Example and Figure 51
␈↓"β␈↓ α≠␈↓␈↓ βc␈↓¬⊂⊗⊃L[%0.03,%-2.32]:N51X.PLT[HHA,LCS]⊂⊗⊃␈↓
␈↓"β␈↓ α≠␈↓␈↓ ε.49␈↓ 
k


␈↓"β
␈↓"β␈↓ α≠␈↓Augmented Sixth Chords

␈↓"β␈↓ α≠␈↓␈↓ α{It␈α⊃is␈α∩now␈α⊃clear␈α∩that␈α⊃chromatic␈α⊃alteration␈α∩in␈α⊃a␈α∩chord␈α⊃very
␈↓ α≠␈↓often␈αchanges␈αits␈α
function.␈α This␈αwill␈αmost␈α
often␈αbe␈αtrue␈αwhen␈α
the
␈↓ α≠␈↓alteration␈αinvolves␈αthe␈α1st,␈α4th,␈α5th␈αor␈α7th␈αdegree␈αof␈αthe␈αscale,␈αor
␈↓ α≠␈↓when␈α∞it␈α
occurs␈α∞within␈α
a␈α∞phrase␈α
rather␈α∞than␈α
at␈α∞its␈α
end.␈α∞ As␈α
stated
␈↓ α≠␈↓before,␈α↔every␈α↔judgment␈α↔must␈α↔be␈α↔based␈α↔on␈α↔the␈α↔whole␈α↔of␈α↔any
␈↓ α≠␈↓particular context under consideration.

␈↓"β␈↓ α≠␈↓␈↓ α{The␈α
alterations␈αthat␈α
go␈αinto␈α
making␈αchords␈α
of␈αthe␈α
augmented
␈↓ α≠␈↓sixth␈α(A6)␈αgive␈αus␈αa␈αspecial␈αcase.␈α Such␈αchords␈αevolved␈αas␈αseparate
␈↓ α≠␈↓entities␈αfrom␈αthe␈αpractice␈αof␈α"freezing"␈αthe␈αchromatic␈αpassing␈α
tone
␈↓ α≠␈↓between␈αthe␈α4th␈αand␈α5th␈αof␈αthe␈αscale.␈α When␈αthese␈αchords␈αare␈αused
␈↓ α≠␈↓in␈α∂their␈α∂conventional␈α∞manner␈α∂and␈α∂within␈α∞a␈α∂single␈α∂tonality,␈α∞they
␈↓ α≠␈↓give␈αus␈αan␈αexception␈αto␈αthe␈αrule␈αthat␈αthe␈α4th␈αof␈αa␈αscale,␈αas␈αa␈αchord
␈↓ α≠␈↓tone,␈α⊂may␈α∂not␈α⊂be␈α⊂altered␈α∂without␈α⊂causing␈α⊂a␈α∂shift␈α⊂of␈α⊂tonics.␈α∂ The
␈↓ α≠␈↓traditional␈α∪names␈α∩for␈α∪the␈α∩three␈α∪most␈α∩common␈α∪augmented␈α∩sixth
␈↓ α≠␈↓chords are as follows:
␈↓"β
␈↓"β␈↓ α≠␈↓Example 52
␈↓"β␈↓ α≠␈↓␈↓ βc␈↓¬⊂⊗⊃L[%0.03,%-1.00]:N52X.PLT[HHA,LCS]⊂⊗⊃␈↓




␈↓"β

␈↓"β␈↓ α≠␈↓␈↓ α{ Strictly␈αspeaking,␈αthey␈αshould␈αbe␈αindicated␈αthus␈αfor␈αa␈αmajor
␈↓ α≠␈↓key such as ␈↓&C␈↓)αβ:
␈↓"β␈↓ α≠␈↓␈↓ βc␈↓¬⊂⊗⊃L[%0.03,%-0.60]:N52Z.PLT[HHA,LCS]⊂⊗⊃␈↓




␈↓"β␈↓ α≠␈↓␈↓ α{It␈α≤will␈α≤generally␈α≠suffice␈α≤to␈α≤refer␈α≠to␈α≤them␈α≤all␈α≤in␈α≠the
␈↓ α≠␈↓abbreviated␈α∨manner,␈α∨A6.␈α∨ When␈α∨they␈α∨actually␈α∨are␈α∨used␈α≡as
␈↓"β␈↓ α≠␈↓␈↓ ε.50␈↓ 
k


␈↓"β␈↓ α≠␈↓augmented␈α→sixth␈α→chords,␈α→they␈α→almost␈α→always␈α→have␈α_primarily
␈↓ α≠␈↓contrapuntal␈αsignificance,␈α
the␈αouter␈α
voices␈αexpanding␈α
by␈αhalf␈α
step
␈↓ α≠␈↓movement.
␈↓"β␈↓ α≠␈↓ 
␈↓"β␈↓ α≠␈↓Example 53
␈↓"β␈↓ α≠␈↓␈↓ β`␈↓¬⊂⊗⊃L[%0.03,%-0.65]:N53X.PLT[HHA,LCS]⊂⊗⊃␈↓

␈↓"β

␈↓"β␈↓ α≠␈↓␈↓ α{However,␈α~since␈α→they␈α~are␈α→so␈α~often␈α→used␈α~as␈α→a␈α~means␈α→of
␈↓ α≠␈↓tonicizing␈α∞new␈α∞areas␈α∞(see␈α∂Example␈α∞33),␈α∞it␈α∞is␈α∞usually␈α∂advisable␈α∞to
␈↓ α≠␈↓make␈α∩their␈α∩presence␈α∩clear␈α∩in␈α∩an␈α∩analysis.␈α∩ The␈α∩augmented␈α⊃sixth
␈↓ α≠␈↓interval␈α∪creates␈α∀a␈α∪situation␈α∀wherein␈α∪the␈α∀dominant␈α∪tends␈α∀to␈α∪be
␈↓ α≠␈↓tonicized␈α(Example␈α53,␈αF␈↓βS␈↓␈αleads␈αto␈αG)␈αand␈αat␈αthe␈αsame␈αtime␈αa␈αtonic
␈↓ α≠␈↓role␈α
for␈αthe␈α
dominant␈αis␈α
weakened␈αby␈α
the␈αeffect␈α
of␈α
presenting␈αits
␈↓ α≠␈↓2nd␈α
as␈α
flatted␈α
(Ab␈α
to␈α
G).␈α
 The␈α
actual␈α
result␈α
is␈α
that␈α
added␈α
strength␈α
is
␈↓ α≠␈↓given␈α∩to␈α∩the␈α⊃␈↓↓dominant␈α∩role␈↓␈α∩of␈α∩the␈α⊃final␈α∩"resolution"␈α∩of␈α∩the␈α⊃A6
␈↓ α≠␈↓chord,␈α
since␈α∞the␈α
flatted␈α
note␈α∞is␈α
most␈α∞easily␈α
taken␈α
as␈α∞the␈α
␈↓βF␈↓6␈α∞of␈α
the
␈↓ α≠␈↓original␈α⊗tonic.␈α⊗ Thus,␈α⊗augmented␈α⊗sixth␈α⊗chords␈α⊗will␈α⊗be␈α⊗said␈α⊗to
␈↓ α≠␈↓function␈α
as␈αpart␈α
of␈αa␈α
tonic␈αa␈α
major␈α3rd␈α
␈↓↓above␈↓␈αthe␈α
␈↓↓lower␈↓␈αmember␈α
of
␈↓ α≠␈↓the augmented sixth interval (see Example 53).

␈↓"β␈↓ α≠␈↓␈↓ α{Because␈α≠the␈α≠G6␈α≠chord␈α≠presents␈α≠the␈α≠identical␈α≠acoustical
␈↓ α≠␈↓situation␈α∃as␈α⊗an␈α∃ordinary␈α∃dominant␈α⊗7th␈α∃chord␈α∃(i.e.,␈α⊗major␈α∃3rd,
␈↓ α≠␈↓minor␈α3rd,␈αminor␈α
3rd),␈αits␈αenharmonic␈αform␈α
will␈αoften␈αbe␈α
used␈αas
␈↓ α≠␈↓a means to move rapidly to a relatively distant tonic.
␈↓"β␈↓ α≠␈↓ 
␈↓"β␈↓ α≠␈↓Example 54
␈↓"β␈↓ α≠␈↓␈↓ βd␈↓¬⊂⊗⊃L[%0.03,%-1.72]:N54X.PLT[HHA,LCS]⊂⊗⊃␈↓
␈↓ α≠␈↓␈↓ ε.51␈↓ 
k


␈↓"β␈↓ α≠␈↓␈↓ α{ Even␈αwithout␈αrecourse␈αto␈αenharmonic␈αchange,␈αthe␈αF6␈αchord
␈↓ α≠␈↓may␈αwork␈αas␈α
the␈αV␈↓βG␈↓␈αstructure␈αof␈α
the␈αoriginal␈αkey's␈αdominant␈α
(see
␈↓ α≠␈↓Example␈α∩52).␈α∩ One␈α∪notable␈α∩use␈α∩of␈α∩the␈α∪V␈↓βG␈↓␈α∩occurs␈α∩at␈α∩the␈α∪end␈α∩of
␈↓ α≠␈↓Schubert's ␈↓↓Quintet in C␈↓, Op.163.
␈↓"β␈↓ α≠␈↓ 
␈↓"β␈↓ α≠␈↓Example 55
␈↓"β␈↓ α≠␈↓␈↓ βc␈↓¬⊂⊗⊃L[%0.03,%-1.02]:N55X.PLT[HHA,LCS]⊂⊗⊃␈↓





␈↓"β␈↓ α≠␈↓␈↓ α{ In␈α≤this␈α≤particular␈α≤case␈α≤it␈α≤might␈α≤be␈α≤inferred␈α≤(perhaps
␈↓ α≠␈↓fancifully)␈α⊃that␈α⊃this␈α⊃chord␈α⊃is␈α⊂used␈α⊃to␈α⊃point␈α⊃in␈α⊃the␈α⊂subdominant
␈↓ α≠␈↓direction, a tradition of long standing for endings.  Thus:


␈↓"β␈↓ α≠␈↓␈↓ ¬\might imply
␈↓"β␈↓ α≠␈↓␈↓ βe␈↓¬⊂⊗⊃L[%0.09,%-0.78]:N55F.PLT[HHA,LCS]⊂⊗⊃␈↓


␈↓"β

␈↓"β␈↓ α≠␈↓␈↓ α{ For␈α∩a␈α∪stronger␈α∩example,␈α∪this␈α∩time␈α∪employing␈α∩the␈α∪G6,␈α∩we
␈↓ α≠␈↓turn␈α∂to␈α∂Schubert's␈α⊂posthumous␈α∂␈↓↓Sonata␈α∂in␈α⊂A␈↓.␈α∂ Here,␈α∂there␈α⊂is␈α∂little
␈↓ α≠␈↓possibility␈α∞of␈α∞confusion␈α∞with␈α∞an␈α
altered␈α∞V,␈α∞since␈α∞there␈α∞is␈α∞no␈α
root
␈↓ α≠␈↓of V present.
␈↓"β
␈↓"β␈↓ α≠␈↓Example 56
␈↓"β␈↓ α≠␈↓␈↓ βd␈↓¬⊂⊗⊃L[%0.03,%-1.50]:N56X.PLT[HHA,LCS]⊂⊗⊃␈↓
␈↓ α≠␈↓␈↓ ε.52␈↓ 
k


␈↓"β

␈↓"β␈↓ α≠␈↓␈↓ α{ Of␈αthe␈αtwo␈α
following␈αpossible␈αanalyses,␈α
the␈αsecond␈αis␈α
better.
␈↓ α≠␈↓In␈α⊂the␈α⊂first,␈α⊂we␈α⊂assume␈α⊂that␈α⊂since␈α⊂the␈α⊂F␈α⊂is␈α⊂omitted␈α⊂at␈α⊂(*),␈α⊃an␈α⊂E,
␈↓ α≠␈↓though␈α
not␈α
present,␈α
might␈α
be␈α
implied.␈α
 (Even␈α
so,␈α
this␈α
would␈α
give
␈↓ α≠␈↓the␈α⊗sound␈α⊗of␈α⊗the␈α⊗subdominant's␈α⊗F6.)␈α⊗In␈α⊗the␈α⊗second,␈α⊗we␈α∃more
␈↓ α≠␈↓reasonably␈αassume␈αthat␈αthe␈αF␈αpersists␈αin␈αthe␈αmemory␈αand␈α
that␈αthe
␈↓ α≠␈↓context␈α∂does␈α∂not␈α∂lead␈α∂us␈α∂to␈α∂interpret␈α∂the␈α∂chord␈α∂B␈↓βF␈↓-D-F-G␈↓βS␈↓␈α⊂as␈α∂an
␈↓ α≠␈↓inversion of ␈↓&A␈↓)αβ: VII␈↓βG␈↓.
␈↓"β
␈↓"β␈↓ α≠␈↓Figure 56
␈↓"β␈↓ α≠␈↓␈↓ βg␈↓¬⊂⊗⊃L[%0.03,%-1.20]:N56F.PLT[HHA,LCS]⊂⊗⊃␈↓






␈↓"β␈↓ α≠␈↓␈↓ α{ It␈α_should␈α_be␈α→pointed␈α_out␈α_again␈α→that␈α_no␈α_chord␈α→may␈α_be
␈↓ α≠␈↓evaluated␈α∩until␈α⊃all␈α∩its␈α⊃parts␈α∩have␈α⊃been␈α∩heard.␈α⊃ However,␈α∩no␈α⊃set
␈↓ α≠␈↓rules␈α∪can␈α∪be␈α∩given␈α∪for␈α∪this;␈α∩as␈α∪usual,␈α∪the␈α∩context␈α∪must␈α∪be␈α∩the
␈↓ α≠␈↓determining␈α∂factor.␈α∂ In␈α⊂the␈α∂Schubert␈α∂␈↓↓Sonata␈↓,␈α⊂the␈α∂B␈↓βF␈↓␈α∂chord␈α⊂fills␈α∂a
␈↓ α≠␈↓measure␈α∞and␈α∞a␈α
quarter␈α∞before␈α∞the␈α∞appearance␈α
of␈α∞the␈α∞G␈↓βS␈↓.␈α∞ Thus␈α
the
␈↓ α≠␈↓relatively␈α⊂simple␈α⊃progression␈α⊂of␈α⊃I␈α⊂to␈α⊃␈↓βF␈↓II␈α⊂has␈α⊃time␈α⊂to␈α⊃be␈α⊂accepted
␈↓ α≠␈↓before␈α∂the␈α⊂function␈α∂is␈α∂altered␈α⊂by␈α∂the␈α∂addition␈α⊂of␈α∂a␈α⊂fourth␈α∂pitch.
␈↓ α≠␈↓Such␈αparticulars␈αare␈αcertainly␈αopen␈αto␈αvarying␈αinterpretations.␈α In
␈↓ α≠␈↓both␈α∃of␈α∃these␈α∃Schubert␈α∃pieces,␈α∃such␈α∃ambiguous␈α∃procedures␈α∃are
␈↓ α≠␈↓possible␈α
because␈α
of␈α
the␈α
extremely␈α
firm␈α
establishment␈α
of␈α
the␈α
main
␈↓ α≠␈↓tonic in the preceding passages.

␈↓"β␈↓ α≠␈↓␈↓ α{ A␈α
case␈α
with␈αsome␈α
similarity␈α
is␈αpresented␈α
in␈α
the␈α␈↓↓Prelude␈α
#23
␈↓ α≠␈↓↓in␈α∪F␈↓␈α∪of␈α∪Chopin,␈α∩where␈α∪an␈α∪E␈↓βF␈↓␈α∪is␈α∩found␈α∪in␈α∪the␈α∪final␈α∩arpeggiated
␈↓ α≠␈↓chord.␈α This␈αE␈↓βF␈↓␈αis␈αusually␈αheard␈αmerely␈αas␈αan␈αintensification␈αof␈αthe
␈↓ α≠␈↓already␈α∃present␈α∃7th␈α∃partial␈α∀of␈α∃the␈α∃bass␈α∃note's␈α∃overtone␈α∀series.
␈↓ α≠␈↓However,␈α≥it␈α≤is␈α≥undeniable␈α≤that␈α≥some␈α≤tendency␈α≥toward␈α≤the
␈↓ α≠␈↓subdominant,␈αa␈αtonal␈α
area␈αwhich␈αis␈α
almost␈αcompletely␈αneglected␈α
in
␈↓ α≠␈↓the␈α⊗piece,␈α∃is␈α⊗heard.␈α∃ At␈α⊗the␈α⊗end␈α∃of␈α⊗a␈α∃piece␈α⊗devoted␈α⊗to␈α∃almost
␈↓"β␈↓ α≠␈↓␈↓ ε.53␈↓ 
k


␈↓"β␈↓ α≠␈↓nothing␈α∃more␈α∃than␈α∀figuration␈α∃on␈α∃I␈α∀and␈α∃V,␈α∃this␈α∀E␈↓βF␈↓␈α∃comes␈α∃as␈α∀a
␈↓ α≠␈↓welcome bit of fantasy.
␈↓"β
␈↓"β␈↓ α≠␈↓Example 57.  Chopin, Prelude, Op.28, #23
␈↓"β␈↓ α≠␈↓␈↓ βd␈↓¬⊂⊗⊃L[%0.00,%-1.87]:N57X.PLT[HHA,LCS]⊂⊗⊃␈↓










␈↓"β␈↓ α≠␈↓␈↓ αt        And then there is the standard "Blues" progression:
␈↓"β
␈↓"β␈↓ α≠␈↓Example 58
␈↓"β␈↓ α≠␈↓␈↓ β`␈↓¬⊂⊗⊃L[%-0.08,%-1.80]:N58X.PLT[HHA,LCS]⊂⊗⊃␈↓









␈↓"β␈↓ α≠␈↓␈↓ α{ Many␈αvariants␈αof␈αthe␈αmain␈αA6␈αchords␈αmay␈αbe␈αfound␈αin␈αlater
␈↓ α≠␈↓tonal␈α
music.␈α
 But␈α
once␈α
they␈α
are␈α
recognized␈α
for␈α
what␈α
they␈αare,␈α
they
␈↓ α≠␈↓should␈α⊃cause␈α⊃no␈α⊃difficulties␈α∩in␈α⊃an␈α⊃analysis.␈α⊃ Similarly,␈α∩there␈α⊃are
␈↓ α≠␈↓many␈αchromatic␈αvariants␈αof␈α
the␈αdominant,␈αsubdominant␈α(the␈αA6␈α
is
␈↓ α≠␈↓one!),␈α∪and␈α∪other␈α∪functions,␈α∀except␈α∪for␈α∪the␈α∪I␈α∀function.*␈α∪Various
␈↓ α≠␈↓notes␈α∞may␈α∞be␈α∞␈↓↓added␈↓␈α∞to␈α∂tonic␈α∞function,␈α∞and␈α∞the␈α∞root␈α∞may␈α∂even␈α∞be

␈↓"β␈↓ α≠␈↓__________
␈↓"β␈↓ α≠␈↓*␈α
But␈α
remember␈α
that␈α
there␈α
is␈α
always␈α
the␈α
␈↓↓potential␈↓␈α
of␈α
a␈α
change␈αof
␈↓"␈↓ α≠␈↓function when any chromaticism is introduced.
␈↓ α≠␈↓␈↓ ε.54␈↓ 
k


␈↓"β␈↓ α≠␈↓omitted,␈α∪but␈α∪if␈α∪the␈α∪root␈α∩or␈α∪5th␈α∪are␈α∪altered,␈α∪the␈α∪tonic␈α∩function
␈↓ α≠␈↓becomes dubious.

␈↓"β␈↓ α≠␈↓␈↓ α{ Chromaticism␈α∀has␈α∀always␈α∪caused␈α∀composers␈α∀trouble␈α∪with
␈↓ α≠␈↓notation.␈α
 The␈αaugmented␈α
sixth␈αand␈α
diminished␈αseventh␈α
chords␈αin
␈↓ α≠␈↓particular␈α∞have␈α∂raised␈α∞problems,␈α∞because␈α∂of␈α∞the␈α∞ambiguity␈α∂of␈α∞the
␈↓ α≠␈↓situations␈α⊂in␈α⊂which␈α⊂they␈α⊂are␈α⊂often␈α⊂found.␈α⊂ Composers␈α⊃cannot␈α⊂be
␈↓ α≠␈↓totally␈α_consistent␈α_in␈α→notating␈α_such␈α_chords␈α→when␈α_enharmonic
␈↓ α≠␈↓equivalence␈αis␈αinvolved.␈α It␈αwill␈αalways␈αbe␈αnecessary␈αto␈α
determine
␈↓ α≠␈↓the␈α∞function␈α∞or␈α∞functions␈α∞of␈α∞chromatic␈α∞chords␈α∞by␈α∞studying␈α∞their
␈↓ α≠␈↓surroundings rather than by taking their notation at face value.
␈↓"β␈↓ α≠␈↓␈↓ ∧K_______________
␈↓ α≠␈↓␈↓ ε.55␈↓ 
k


␈↓"β
␈↓"β␈↓ α≠␈↓Exercises for Chapter IV
␈↓"β

␈↓"β␈↓ α≠␈↓␈↓ α{Analyze␈α the␈α∨following␈α works.␈α∨ Show␈α the␈α∨distinctions
␈↓ α≠␈↓between␈α⊃major␈α⊃and␈α∩minor␈α⊃tonics␈α⊃through␈α∩the␈α⊃use␈α⊃of␈α∩upper␈α⊃and
␈↓ α≠␈↓lower case numerals on the two highest levels of the analyses.
␈↓"β
␈↓"β␈↓ α≠␈↓ 
␈↓"β␈↓ α≠␈↓From the 371 Chorales of Bach:*
␈↓"β
␈↓"β␈↓ α≠␈↓        1.  Chorale  11, up to the 3/4.
␈↓"β␈↓ α≠␈↓        2.  Chorale  37, all.
␈↓"β␈↓ α≠␈↓        3.  Chorale  47
␈↓"β␈↓ α≠␈↓        4.  Chorale  94
␈↓"β␈↓ α≠␈↓        5.  Chorale  223
␈↓"β␈↓ α≠␈↓ 
␈↓"β
␈↓"β␈↓ α≠␈↓From the Sonatas of Mozart:
␈↓"β␈↓ α≠␈↓ 
␈↓"β␈↓ α≠␈↓        6.  Sonata in D, K.205b (284), last movement, Variation VII.
␈↓"β␈↓ α≠␈↓ 
␈↓"β␈↓ α≠␈↓        7.  Sonata in a, K.300d (310), first movement, 24 bars
␈↓"β␈↓ α≠␈↓                starting at recapitulation.  (In cases where there are
␈↓"β␈↓ α≠␈↓                many suspensions and appoggiaturas it is usually best
␈↓"β␈↓ α≠␈↓                to write out a chordal reduction of the passage before
␈↓"β␈↓ α≠␈↓                working out the analysis.)
␈↓"β␈↓ α≠␈↓ 
␈↓"β␈↓ α≠␈↓        8.  Sonata in C, K.300h (330), second movement, first 20 bars.
␈↓"β␈↓ α≠␈↓ 
␈↓"β
␈↓"β␈↓ α≠␈↓From the Preludes, Op.28, of Chopin:
␈↓"β␈↓ α≠␈↓ 
␈↓"β␈↓ α≠␈↓        9.  Prelude  1, in C
␈↓"β␈↓ α≠␈↓       10.  Prelude  6, in b
␈↓"β␈↓ α≠␈↓       11.  Prelude 20, in c
␈↓"β
␈↓"β␈↓ α≠␈↓_____________
␈↓"β␈↓ α≠␈↓* Note that all bass lines in the Bach Chorales are probably
␈↓"β␈↓ α≠␈↓intended to be doubled at the octave below.  Hence, even if the
␈↓"β␈↓ α≠␈↓notation of the bass part crosses above the tenor part, the bass 
␈↓"β␈↓ α≠␈↓part remains the true bass.