/LMAR=0/XLINE=10/FONT#0=METL/FONT#1=METLI/FONT#2=METS/FONT#3=MUS[HHA,LCS]
␈↓ α≠␈↓␈↓ ε.40␈↓ 
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␈↓"β␈↓ α≠␈↓␈↓ ¬↑CHAPTER IV


␈↓"β␈↓ α≠␈↓␈↓ ∧iFUNCTIONS OF THE MINOR

␈↓"β
␈↓"β␈↓ α≠␈↓Major-minor Interchangeability

␈↓"β␈↓ α≠␈↓␈↓ α{ As␈αstated␈αearlier,␈α
minor␈αscales␈αwill␈α
be␈αtreated␈αas␈α
existing␈αas
␈↓ α≠␈↓the␈α∂result␈α∂of␈α∂a␈α∂fairly␈α∂consistent␈α∂set␈α∂of␈α∂alterations␈α∂of␈α∂the␈α∂parallel
␈↓ α≠␈↓major␈α∞scales␈α∞(see␈α
page␈α∞8␈α∞and␈α
following).␈α∞ While␈α∞minor␈α∞scales␈α
may
␈↓ α≠␈↓not␈α∂have␈α∂originated␈α∂in␈α∂this␈α∂way,␈α∂it␈α∂is␈α∂probable␈α∂that␈α∂their␈α∂use␈α∂in
␈↓ α≠␈↓tonal␈αmusic␈α
may␈αbest␈αbe␈α
approached␈αfrom␈αthis␈α
point␈αof␈αview.␈α
 Two
␈↓ α≠␈↓alterations␈α_suffice␈α_to␈α_give␈α_the␈α_complete␈α_impression␈α_of␈α_minor
␈↓ α≠␈↓harmony␈α--␈αthe␈αflatted␈αthird␈αand␈αthe␈αflatted␈αsixth.␈α In␈αsome␈αcases,
␈↓ α≠␈↓even␈α
the␈α
sixth␈αneed␈α
not␈α
be␈α
altered.␈α However,␈α
the␈α
sixth␈α
degree␈αis
␈↓ α≠␈↓lingered␈α⊃upon,␈α⊃the␈α⊃minor␈α⊃effect␈α⊂will␈α⊃be␈α⊃weakened␈α⊃unless␈α⊃it␈α⊂has
␈↓ α≠␈↓been␈α
flatted.␈α Conversely,␈α
the␈α
␈↓βF␈↓6␈αmay␈α
be␈α
found␈αin␈α
proximity␈αto␈α
the
␈↓ α≠␈↓␈↓βN␈↓3 without completely destroying the major quality.

␈↓"β␈↓ α≠␈↓␈↓ α{When␈α∞the␈α∞third␈α∞or␈α∞sixth␈α∞of␈α∞a␈α∞scale␈α∞is␈α∞flatted␈α∞and␈α∂appears␈α∞as
␈↓ α≠␈↓the␈αthird␈αof␈α
a␈αchord,␈αthere␈α
is␈αmost␈αoften␈α
no␈αchange␈αin␈αthe␈α
function
␈↓ α≠␈↓of␈α∪the␈α∪chord.␈α∪ The␈α∪flatted␈α∩seventh␈α∪of␈α∪the␈α∪scale␈α∪␈↓↓can␈↓␈α∪change␈α∩the
␈↓ α≠␈↓function␈αof␈α
the␈αV␈α
chord,␈αespecially␈αif␈α
it␈αis␈α
used␈αin␈α
some␈αascending
␈↓ α≠␈↓manner.␈α∞ It␈α∞is␈α∞rare␈α∞that␈α∞a␈α∞real␈α∞V␈↓βF3␈↓␈α∞chord␈α∞is␈α∞heard␈α∞in␈α∞a␈α∞position␈α
of
␈↓ α≠␈↓structural␈α⊂importance.␈α⊂ When␈α⊂it␈α⊂exists,␈α⊂the␈α⊂V␈↓βF3␈↓␈α⊂usually␈α⊃loses␈α⊂its
␈↓ α≠␈↓"dominant"␈α
function,␈α
unless␈α
the␈α
composer␈α
has␈α
made␈α
a␈α
special␈α
effort
␈↓ α≠␈↓to␈α∩impress␈α∩upon␈α∪the␈α∩listener␈α∩that␈α∩the␈α∪"leading␈α∩tone"␈α∩is␈α∩to␈α∪be␈α∩a
␈↓ α≠␈↓whole␈α≠step␈α~below␈α≠the␈α~tonic␈α≠note.␈α~ However,␈α≠it␈α~is␈α≠only␈α~by
␈↓ α≠␈↓examining␈αthe␈αwhole␈α
of␈αa␈αphrase␈αthat␈α
one␈αcan␈αascertain␈αwhether␈α
a
␈↓ α≠␈↓chord␈α⊂containing␈α⊂the␈α⊂flatted␈α⊂seventh␈α⊂of␈α⊂the␈α⊂scale␈α⊂is␈α∂functioning
␈↓ α≠␈↓exclusively␈αin␈α
the␈αoriginal␈α
minor␈αkey␈α
or␈αrather␈α
dually␈αin␈αthat␈α
key
␈↓ α≠␈↓and␈α∃the␈α∃relative␈α∃major,␈α∃or␈α∃some␈α∃other␈α∃closely␈α∃related␈α∃key.␈α∃ It
␈↓ α≠␈↓should␈α
be␈α∞mentioned␈α
that␈α∞the␈α
"closeness"␈α∞of␈α
any␈α∞two␈α
keys␈α∞to␈α
one
␈↓ α≠␈↓another␈α⊂depends␈α⊃largely␈α⊂on␈α⊃just␈α⊂how␈α⊂much␈α⊃their␈α⊂scales␈α⊃have␈α⊂in
␈↓ α≠␈↓common,␈α⊂or␈α⊂sometimes␈α∂␈↓↓potentially␈↓␈α⊂have␈α⊂in␈α∂common.␈α⊂ (By␈α⊂this␈α∂is
␈↓ α≠␈↓␈↓ ε.41␈↓ 
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␈↓"β␈↓ α≠␈↓meant,␈αthe␈αconventional␈αascending␈αand␈αdescending␈αforms␈αof␈αminor
␈↓ α≠␈↓scales␈α
must␈α
␈↓↓both␈↓␈α
be␈α
considered.)␈α
Thus␈α␈↓&C␈↓)αβ␈α
is␈α
a␈α
little␈α
"closer"␈α
to␈α␈↓&G␈↓)αβ␈α
than
␈↓ α≠␈↓it␈α∞is␈α∞to␈α∞␈↓&a␈↓)αβ,␈α∞because␈α∞only␈α∞one␈α∞note␈α∞(the␈α∞4th)␈α∞of␈α∞the␈α∞␈↓&C␈↓)αβ␈α∞scale␈α∞must␈α
be
␈↓ α≠␈↓altered␈α⊂to␈α∂produce␈α⊂the␈α∂␈↓&G␈↓)αβ␈α⊂scale,␈α∂but␈α⊂two␈α∂notes␈α⊂(the␈α∂4th␈α⊂and␈α∂5th)
␈↓ α≠␈↓must be altered to produce the ascending form of the ␈↓&a␈↓)αβ scale.
␈↓"β
␈↓"β␈↓ α≠␈↓Example 43





␈↓"β␈↓ α≠␈↓␈↓ α{ On␈αthe␈αother␈αhand,␈α␈↓&C␈↓)αβ␈αis␈αsomewhat␈α"closer"␈αto␈α␈↓&a␈↓)αβ␈αthan␈αa␈αis␈αto␈α␈↓&e␈↓)αβ
␈↓ α≠␈↓or␈α␈↓&E␈↓)αβ.␈α After␈αan␈α␈↓&a␈↓)αβ␈αtonic␈αis␈αestablished,␈α␈↓&C␈↓)αβ␈αmay␈αbe␈αtonicized␈αmerely␈αby
␈↓ α≠␈↓means␈α∞of␈α∂elements␈α∞already␈α∞found␈α∂in␈α∞the␈α∂conventional␈α∞descending
␈↓ α≠␈↓form␈α
of␈α
the␈α
␈↓&a␈↓)αβ␈α
scale;␈α
whereas␈α
the␈α
␈↓&e␈↓)αβ␈α
or␈α
␈↓&E␈↓)αβ␈α
scale␈α
requires␈α
at␈α
least␈αD␈↓βS␈↓␈α
for
␈↓ α≠␈↓its establishment.
␈↓"β
␈↓"β␈↓ α≠␈↓Example 44






␈↓"β␈↓ α≠␈↓␈↓ α{ In␈α_music␈α_where␈α_there␈α_is␈α_much␈α→major-minor␈α_alteration,
␈↓ α≠␈↓almost␈α⊃any␈α⊃keys␈α⊃may␈α⊃be␈α⊃directly␈α⊃related.␈α⊃ As␈α⊃to␈α⊃the␈α⊃problem␈α⊃of
␈↓ α≠␈↓"close"␈α≤or␈α≠"far",␈α≤the␈α≤absolute␈α≠number␈α≤of␈α≤chromatic␈α≠changes
␈↓ α≠␈↓required␈α∂to␈α∂establish␈α∂a␈α∂new␈α∂key␈α∂will␈α∂not␈α∂be␈α∂so␈α∂important␈α⊂as␈α∂the
␈↓ α≠␈↓question␈α⊂of␈α∂just␈α⊂what␈α∂role␈α⊂the␈α∂altered␈α⊂notes␈α∂play␈α⊂in␈α∂each␈α⊂of␈α∂the
␈↓ α≠␈↓scales␈α
involved.␈α
 The␈α
problem␈α
of␈α
the␈α
larger␈α
relationships␈αbetween
␈↓ α≠␈↓keys will be dealt with in subsequent chapters.
␈↓"β␈↓ α≠␈↓␈↓ ∧K_______________

␈↓"β␈↓ α≠␈↓␈↓ α{When␈α∀we␈α∀truly␈α∀have␈α∃a␈α∀group␈α∀of␈α∀functions␈α∀based␈α∃on␈α∀the
␈↓ α≠␈↓natural␈α
minor␈α
scale␈α
(i.e.,␈αthird,␈α
sixth,␈α
and␈α
seventh␈α
degrees␈αflatted
␈↓ α≠␈↓both␈α⊃ascending␈α⊃and␈α⊃descending),␈α⊂we␈α⊃may␈α⊃say␈α⊃that␈α⊃the␈α⊂harmony
␈↓ α≠␈↓␈↓ ε.42␈↓ 
k


␈↓"β␈↓ α≠␈↓formed␈αtherefrom␈α
is␈α␈↓↓modal␈↓.␈α
 Following␈αis␈α
an␈αexample␈α
of␈αmodal␈α
and
␈↓ α≠␈↓tonal treatments of the same melodic fragment.
␈↓"β␈↓ α≠␈↓ 
␈↓"β␈↓ α≠␈↓Examples 45a,b.  Bach, Chorale 28










␈↓"β␈↓ α≠␈↓␈↓ α{ The analysis of the first phrase is as follows:
␈↓"β
␈↓"β␈↓ α≠␈↓Figure 45a






␈↓"β␈↓ α≠␈↓␈↓ α{The␈α∩␈↓βN␈↓3␈α⊃in␈α∩the␈α⊃third␈α∩chord␈α∩must␈α⊃be␈α∩indicated,␈α⊃since␈α∩it␈α∩is␈α⊃a
␈↓ α≠␈↓deviation␈αfrom␈α
the␈αnorm.␈α
 The␈α␈↓βS␈↓3␈α
is␈αshown␈α
in␈αthe␈α
second␈αbar,␈α
since
␈↓ α≠␈↓the␈αV␈α
now␈αbecomes␈α
a␈αtrue␈α
tonal␈αdominant.␈α
 (The␈αsecond␈αchord␈α
may
␈↓ α≠␈↓be␈α_analyzed␈α_either␈α_as␈α_II␈α_or␈α_IV;␈α_in␈α_any␈α_case,␈α_the␈α→function␈α_is
␈↓ α≠␈↓subdominant.) The last phrase gives:*
␈↓"β␈↓ α≠␈↓ 
␈↓"β␈↓ α≠␈↓Figure 45b1





␈↓"β␈↓ α≠␈↓__________
␈↓"β␈↓ α≠␈↓*␈αNote␈αthat␈α
the␈αauxiliary␈αtone␈αE␈α
(instead␈αof␈αE␈↓βS␈↓)weakens␈α
the␈αtonic
␈↓"␈↓ α≠␈↓effect␈αof␈αthe␈αf␈↓βS␈↓␈αchord.␈α It␈αseems␈α
to␈αrefer␈αback␈αto␈αthe␈αmodal␈αV␈αof␈α
the
␈↓"␈↓ α≠␈↓first phrase.
␈↓ α≠␈↓␈↓ ε.43␈↓ 
k


␈↓"β␈↓ α≠␈↓␈↓ α{ We␈α
hear␈α
much␈αmore␈α
harmonic␈α
activity␈αin␈α
this␈α
phrase,␈αso␈α
our
␈↓ α≠␈↓diagram␈α∂becomes␈α⊂more␈α∂complicated.␈α⊂ It␈α∂might␈α⊂be␈α∂argued␈α⊂that␈α∂the
␈↓ α≠␈↓last␈α
eighth␈α
note␈α
of␈α
bar␈α
1␈α
does␈α
not␈α
form␈α
a␈α
new␈α
function.␈α
 There␈α
is␈α
in
␈↓ α≠␈↓the␈α
alto,␈α
however,␈α
a␈α
very␈α
distinctive␈α
leap␈α
of␈α
a␈α
4th␈α
across␈α∞the␈α
bar
␈↓ α≠␈↓line␈αwhich␈αtends␈αto␈α
make␈αus␈αhear␈αthe␈αB␈α
as␈αa␈αchord␈αnote.␈α A␈α
broader
␈↓ α≠␈↓interpretation␈αof␈αthis␈αpassage,␈αbased␈αon␈αthe␈αstepwise␈αmovement␈αof
␈↓ α≠␈↓the␈α⊂outer␈α∂voices␈α⊂at␈α∂this␈α⊂point,␈α⊂would␈α∂lead␈α⊂us␈α∂to␈α⊂the␈α⊂omission␈α∂of
␈↓ α≠␈↓both␈α∪the␈α∪last␈α∩eighth␈α∪of␈α∪bar␈α∪1␈α∩and␈α∪the␈α∪first␈α∩eighth␈α∪of␈α∪bar␈α∪2␈α∩as
␈↓ α≠␈↓structural chords.  Thus:
␈↓"β␈↓ α≠␈↓ 
␈↓"β␈↓ α≠␈↓Figure 45b2







␈↓"β␈↓ α≠␈↓␈↓ α{ Either␈αof␈αthese␈α
two␈αanalyses␈αof␈α
the␈αlast␈αphrase␈αis␈α
acceptable,
␈↓ α≠␈↓the␈α≤choice␈α≤depending␈α≤on␈α≤how␈α≤much␈α≤detail␈α≤is␈α≥desired.␈α≤ The
␈↓ α≠␈↓important␈α→thing␈α~is␈α→that␈α→the␈α~details␈α→be␈α~comprehended.␈α→ Many
␈↓ α≠␈↓examples␈α→of␈α_modality␈α→may␈α_be␈α→found␈α_in␈α→19th-century␈α_music,
␈↓ α≠␈↓especially␈α⊂in␈α⊂the␈α⊂works␈α⊂of␈α∂Chopin␈α⊂(see␈α⊂Mazurka␈α⊂#15,␈α⊂Op.24,␈α∂#2,
␈↓ α≠␈↓second␈α⊂section,␈α⊃Lydian␈α⊂mode;␈α⊂Mazurka␈α⊃#26,␈α⊂Op.41,␈α⊃#1,␈α⊂Phrygian
␈↓ α≠␈↓mode.)␈α∃These␈α∃self-conscious␈α∃exoticisms␈α∃might␈α∃be␈α∃called␈α∃"modal
␈↓ α≠␈↓tonality"␈α(as␈αopposed␈αto␈αmajor-minor␈αtonality)␈αand␈αare␈αmost␈αoften
␈↓ α≠␈↓presented␈αas␈αclear␈αdeviations␈αfrom␈αthe␈αnorm.␈α The␈αfunctions␈αof␈αthe
␈↓ α≠␈↓various␈αmodally-formed␈αchords␈αare␈αno␈αdifferent,␈αbut␈αthese␈αchords
␈↓ α≠␈↓can␈α∩serve␈α∩as␈α⊃direct␈α∩pivots␈α∩to␈α∩tonal␈α⊃areas␈α∩which␈α∩might␈α∩be␈α⊃more
␈↓ α≠␈↓distant from an ordinary major-minor tonality.

␈↓"β␈↓ α≠␈↓␈↓ ∧K_______________
␈↓ α≠␈↓␈↓ ε.44␈↓ 
k


␈↓"β␈↓ α≠␈↓␈↓ α{It␈α∂will␈α∂be␈α∂seen␈α∂that␈α∂any␈α∂degree␈α∂of␈α∂either␈α∂a␈α∂major␈α⊂or␈α∂minor
␈↓ α≠␈↓scale␈α∞may␈α∂be␈α∞tonicized.␈α∂ Usually␈α∞the␈α∂new␈α∞tonics␈α∂will␈α∞be␈α∂major␈α∞or
␈↓ α≠␈↓minor,␈αdepending␈αon␈αthe␈αnormal␈α
forms␈αof␈αthe␈αvarious␈αtriads␈αin␈α
the
␈↓ α≠␈↓original␈α
tonic.␈α∞ When␈α
the␈α∞original␈α
key␈α
is␈α∞major,␈α
II,␈α∞III␈α
and␈α∞VI␈α
will
␈↓ α≠␈↓most␈α⊃often␈α⊃be␈α∩tonicized␈α⊃as␈α⊃minor␈α⊃keys,␈α∩while␈α⊃IV␈α⊃and␈α⊃V␈α∩will␈α⊃be
␈↓ α≠␈↓major.␈α VII␈α
will␈αrarely␈α
be␈αtonicized,␈αsince␈α
it␈αpresents␈α
a␈αdiminished
␈↓ α≠␈↓chord␈αin␈αthe␈αhome␈α
key.␈α (The␈αchord␈αbuilt␈α
on␈αthe␈αleading␈αtone␈α
of␈αC
␈↓ α≠␈↓major␈α∞is␈α∞B,␈α
D,␈α∞F␈↓βN␈↓.)␈α∞On␈α
the␈α∞other␈α∞hand,␈α
VII␈α∞frequently␈α∞appears␈α∞as␈α
a
␈↓ α≠␈↓tonic␈α∂goal␈α∞when␈α∂the␈α∞first␈α∂key␈α∞is␈α∂minor.␈α∞ (The␈α∂chord␈α∞built␈α∂on␈α∞the
␈↓ α≠␈↓seventh␈α
tone␈α∞of␈α
the␈α
c␈α∞minor␈α
scale␈α
is␈α∞B␈↓βF␈↓,␈α
D,␈α
F.)␈α∞With␈α
a␈α∞minor␈α
scale
␈↓ α≠␈↓we␈αhave␈αIII,␈αVI,␈αand␈αVII␈αforming␈αmajor␈αtonics,␈αand␈αIV␈αand␈αV␈αminor
␈↓ α≠␈↓tonics.␈α Since␈αthe␈αchord␈αon␈αthe␈αsecond␈αdegree␈αof␈αthe␈αminor␈αscale␈αis
␈↓ α≠␈↓normally␈αdiminished,␈αII␈α
now␈αbecomes␈αrare␈α
as␈αa␈αtonic,␈α
whereas␈αthe
␈↓ α≠␈↓major␈α↔tonic␈α↔on␈α↔␈↓βF␈↓II,␈α↔the␈α↔Phrygian␈α↔second,␈α↔is␈α↔often␈α_used.␈α↔ (See
␈↓ α≠␈↓Beethoven,␈α∞␈↓↓Sonata␈α∂#23␈α∞in␈α∂f␈↓,␈α∞Op.57,␈α∞opening␈α∂bars;␈α∞␈↓↓Sonata␈α∂#29␈α∞in
␈↓ α≠␈↓↓B␈↓βF␈↓,␈α∞Op.106,␈α∞third␈α∞movement.)␈α∞In␈α∞actual␈α∞practice,␈α∞especially␈α∞in␈α
the
␈↓ α≠␈↓music␈α∪of␈α∀the␈α∪19th␈α∀century,␈α∪the␈α∪major␈α∀and␈α∪minor␈α∀elements␈α∪are
␈↓ α≠␈↓freely interchangeable.

␈↓"β␈↓ α≠␈↓␈↓ α{ ␈↓↓From␈α∃this␈α∃point␈α∃on,␈α∀the␈α∃distinction␈α∃between␈α∃major␈α∀and
␈↓ α≠␈↓↓minor␈α∀tonics␈α∃in␈α∀the␈α∀upper␈α∃two␈α∀levels␈α∀of␈α∃an␈α∀analysis␈α∃will␈α∀be
␈↓ α≠␈↓↓indicated␈α⊂by␈α⊂the␈α⊂use␈α⊂of␈α⊂upper␈α⊂and␈α⊂lower␈α⊂case␈α⊃Roman␈α⊂numerals
␈↓ α≠␈↓↓respectively␈↓.␈α
 The␈α
functions␈α
␈↓↓within␈↓␈α
the␈α
tonics␈α
(the␈α
lowest␈α
level␈α
of
␈↓ α≠␈↓an␈α∂analysis)␈α∂will␈α∂continue␈α∂to␈α∂be␈α∂shown␈α∂by␈α∂upper␈α⊂case␈α∂numerals.
␈↓ α≠␈↓Non-functional␈αalterations,␈αsuch␈αas␈αthe␈α"tierce␈αde␈αPicardie"␈α(I␈↓βS3␈↓␈αin
␈↓ α≠␈↓the minor), may be shown in the usual fashion.

␈↓"β␈↓ α≠␈↓␈↓ α{ However,␈α⊃when␈α⊂a␈α⊃temporary␈α⊂tonic␈α⊃appears␈α⊂as␈α⊃major␈α⊂after
␈↓ α≠␈↓the␈α∩preceding␈α∩music␈α∩leads␈α∩one␈α∩to␈α∩expect␈α∩a␈α∩minor␈α∪tonic,␈α∩certain
␈↓ α≠␈↓problems␈αare␈αsometimes␈αraised.␈α Often␈αsuch␈αchords␈αare␈αexperienced
␈↓ α≠␈↓as␈α
dominant␈α
functions␈α∞to␈α
chords␈α
more␈α∞closely␈α
related␈α
to␈α∞the␈α
scale
␈↓ α≠␈↓of the original key, as in bar 8 following (see also Chapter V).
␈↓ α≠␈↓␈↓ ε.45␈↓ 
k


␈↓"β␈↓ α≠␈↓Example 46.  Schubert, Meeres Stille, Op.3, #2














␈↓"β
␈↓"β␈↓ α≠␈↓Figure 46










␈↓"β␈↓ α≠␈↓␈↓ α{ On␈α∞the␈α∞next␈α∞page␈α∞is␈α∞a␈α∞complete␈α∞table␈α∞of␈α∞indications␈α∞for␈α∞the
␈↓ α≠␈↓possible␈α∂temporary␈α∞tonics␈α∂that␈α∞might␈α∂be␈α∞found␈α∂in␈α∂␈↓↓direct␈↓␈α∞relation
␈↓ α≠␈↓to␈αa␈αbasic␈αtonic␈αof␈α␈↓&C␈↓)αβ␈αmajor.␈α Add␈αthe␈αappropriate␈α
accidentals␈αwhen
␈↓ α≠␈↓dealing with other basic tonics.
␈↓ α≠␈↓␈↓ ε.46␈↓ 
k


␈↓"β␈↓ α≠␈↓Figure 47













␈↓"β␈↓ α≠␈↓␈↓ α{ Group␈α
1␈α∞lists␈α
the␈α
tonic␈α∞chords␈α
available␈α
from␈α∞the␈α
resources
␈↓ α≠␈↓of␈α∞the␈α∞unaltered␈α∞␈↓&C␈↓)αβ␈α∞scale.␈α∞ The␈α∞second␈α∞group␈α∞includes␈α∂tonic␈α∞chords
␈↓ α≠␈↓that␈αare␈αavailable␈αas␈αthe␈αresult␈αof␈αflatting␈αany␈αof␈αthe␈αoriginal␈α
scale
␈↓ α≠␈↓degrees␈αexcept␈αthe␈α1st,␈α4th␈αand␈α5th;␈αhence,␈α␈↓&c␈↓)αβ␈αminor.␈α (The␈α␈↓βF␈↓vii,␈α␈↓&b␈↓)αβ␈↓βF␈↓,
␈↓ α≠␈↓as␈α⊃a␈α⊂tonic␈α⊃is␈α⊂rare,␈α⊃but␈α⊂see␈α⊃the␈α⊂opening␈α⊃of␈α⊂Mozart's␈α⊃␈↓↓Quartet␈α⊃in␈α⊂C␈↓,
␈↓ α≠␈↓K.465.)␈α∂Group␈α∞3␈α∂is␈α∂set␈α∞apart␈α∂because␈α∂it␈α∞includes␈α∂the␈α∂less␈α∞common
␈↓ α≠␈↓temporary␈αtonics,␈αall␈αof␈αwhich␈αinvolve␈αeither␈αflatting␈αor␈αsharping
␈↓ α≠␈↓of␈αthe␈α1st,␈α4th␈αor␈α5th␈αof␈αthe␈αoriginal␈αscale␈αin␈αorder␈αto␈αproduce␈αthe
␈↓ α≠␈↓new␈α∞tonic␈α∞chord.␈α
 These␈α∞chords,␈α∞even␈α
when␈α∞surely␈α∞approached␈α
as
␈↓ α≠␈↓tonics,␈α⊃often␈α⊃prove␈α⊃to␈α⊃be␈α⊃working␈α⊃as␈α⊃dominant␈α∩or␈α⊃subdominant
␈↓ α≠␈↓from the largest point of view.*
␈↓"β
␈↓"β␈↓ α≠␈↓Example 48








␈↓"β␈↓ α≠␈↓__________
␈↓"β␈↓ α≠␈↓*␈α
This␈αtype␈α
of␈αprogression␈α
will␈α
be␈αtreated␈α
somewhat␈αdifferently␈α
in
␈↓"␈↓ α≠␈↓the section on added levels of tonicization in Chapter V.
␈↓ α≠␈↓␈↓ ε.47␈↓ 
k


␈↓"β␈↓ α≠␈↓Figure 48







␈↓"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≠␈↓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:
␈↓ α≠␈↓␈↓ ε.48␈↓ 
k


␈↓"β␈↓ α≠␈↓Example 49






␈↓"β␈↓ α≠␈↓␈↓ α{ Strictly␈αspeaking,␈αthey␈αshould␈αbe␈αindicated␈αthus␈αfor␈αa␈αmajor
␈↓ α≠␈↓key such as ␈↓&C␈↓)αβ:






␈↓"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
␈↓ 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 50






␈↓"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50,␈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≠␈↓␈↓ ε.49␈↓ 
k


␈↓"β␈↓ 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 zzz).

␈↓"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
␈↓"β␈↓ α≠␈↓Example 51





␈↓"β␈↓ α≠␈↓ 
␈↓"β␈↓ α≠␈↓Figure 51






␈↓"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∪zzz.)␈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
␈↓"β␈↓ α≠␈↓Example 52
␈↓ α≠␈↓␈↓ ε.50␈↓ 
k


␈↓"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≠␈↓␈↓ 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 53.  Schubert, Sonata in A








␈↓"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 53
␈↓ α≠␈↓␈↓ ε.51␈↓ 
k


␈↓"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
␈↓ 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 54.  Chopin, Prelude, Op.28, #23
␈↓ α≠␈↓␈↓ ε.52␈↓ 
k


␈↓"β␈↓ α≠␈↓␈↓ α{And then there is the standard "Blues" progression:
␈↓"β
␈↓"β␈↓ α≠␈↓Figure 55








␈↓"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
␈↓ 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_______________






␈↓"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.53␈↓ 
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.