perm filename VP47.XGP[C4,LCS] blob
sn#456870 filedate 1979-07-08 generic text, type T, neo UTF8
/LMAR=0/XLINE=20/FONT#0=MBIG[HHA,LCS]/FONT#1=BMETI[HHA,LCS]/FONT#3=BMUS[HHA,LCS]/FONT#5=MBIG[HHA,LCS]
␈↓ β⊂␈↓␈↓ 647␈↓ ∀0
␈↓"β␈↓ β⊂␈↓Figure 48
␈↓"β␈↓ β⊂␈↓␈↓ ¬-␈↓¬⊂⊗⊃L[%0.00,%-2.30](17,22):FIG48.PLT[C4,LCS]⊂⊗⊃␈↓
␈↓"β
␈↓"β␈↓ β⊂␈↓␈↓ ∧PIt␈α∨will␈α∨be␈α∨noted␈α∨that␈α∨there␈α∨is␈α∨␈↓↓no␈↓␈α∨temporary␈α∨tonic␈α∨listed␈α≡in
␈↓ β⊂␈↓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
␈↓ β⊂␈↓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
␈↓ β⊂␈↓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
␈↓ β⊂␈↓such␈α≤a␈α≤direct␈α≤relationship␈α≠of␈α≤tonics.␈α≤ (See␈α≤Chapter␈α≤VI,␈α≠Alternating
␈↓ β⊂␈↓Progressions.)
␈↓"β␈↓ β⊂␈↓␈↓ πq_______________
␈↓"β
␈↓"β
␈↓"β␈↓ β⊂␈↓Pivot Chords in the Minor
␈↓"β␈↓ β⊂␈↓␈↓ ∧PBecause␈α0of␈α/the␈α0ambiguities␈α/inherent␈α0in␈α/the␈α0minor␈α/scale
␈↓ β⊂␈↓certain␈α_problems␈α↔can␈α_occur␈α_in␈α↔regard␈α_to␈α↔pivot␈α_chords.␈α_ In␈α↔Example
␈↓ β⊂␈↓49a␈α→the␈α~ascending␈α→form␈α~of␈α→the␈α~minor␈α→scale␈α~produces␈α→a␈α~chord␈α→(IV␈↓βN␈↓)
␈↓ β⊂␈↓which␈α→can,␈α→in␈α→a␈α~slightly␈α→different␈α→context␈α→(Example␈α→49b),␈α~lead␈α→to
␈↓ β⊂␈↓a brief new tonicization of VII.
␈↓"β
␈↓"β␈↓ β⊂␈↓Example 49
␈↓"β␈↓ β⊂␈↓␈↓ ¬5␈↓¬⊂⊗⊃L[%0.06,%-4.30](17,22):N49X.PLT[C4,LCS]⊂⊗⊃␈↓
␈↓ β⊂␈↓␈↓ 648␈↓ ∀0
␈↓"β␈↓ β⊂␈↓␈↓ ∧PIn␈α_the␈α→minor,␈α_a␈α→direct␈α_progression␈α_from␈α→III␈α_(with␈α→the␈α_flatted
␈↓ β⊂␈↓fifth)␈α to␈α V␈α (with␈α!the␈α raised␈α third)␈α is␈α somewhat␈α!rare.␈α However
␈↓ β⊂␈↓the␈α!next␈α!example␈α"may␈α!be␈α!analyzed␈α!in␈α"this␈α!way␈α!because␈α"no␈α!real
␈↓ β⊂␈↓tonicization of III is involved.
␈↓"β␈↓ β⊂␈↓
␈↓"β␈↓ β⊂␈↓Example and Figure 50
␈↓"β␈↓ β⊂␈↓␈↓ ¬5␈↓¬⊂⊗⊃L[%0.06,%-4.84](17,22):N50X.PLT[C4,LCS]⊂⊗⊃␈↓
␈↓"β
␈↓"β␈↓ β⊂␈↓␈↓ ∧PThe␈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
␈↓ β⊂␈↓the␈α≤conventions␈α≤regarding␈α≤the␈α≥usage␈α≤of␈α≤the␈α≤various␈α≤forms␈α≥of␈α≤the
␈↓ β⊂␈↓minor␈α⊗scale␈α⊗are␈α⊗followed.␈α⊗ In␈α⊗the␈α∃next␈α⊗example␈α⊗the␈α⊗pivot␈α⊗to␈α⊗III␈α⊗as␈α∃a
␈↓ β⊂␈↓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
␈↓ β⊂␈↓completely␈α≡compatible␈α≡with␈α≡both␈α≡␈↓&c␈↓)αβ␈α≡and␈α≡␈↓&E␈↓βF␈↓␈↓)αβ.␈α≡ However␈α≡the␈α≡return
␈↓ β⊂␈↓from␈α-III␈α-to␈α-i␈α.as␈α-the␈α-middle-ground␈α-tonic␈α-involves␈α.an␈α-abrupt
␈↓ β⊂␈↓chromatic shift. Thus no pivot is shown.
␈↓"β␈↓ β⊂␈↓
␈↓"β␈↓ β⊂␈↓Example and Figure 51
␈↓"β␈↓ β⊂␈↓␈↓ ¬5␈↓¬⊂⊗⊃L[%0.06,%-4.64](17,22):N51X.PLT[C4,LCS]⊂⊗⊃␈↓
␈↓"β ␈↓ β⊂␈↓␈↓ 649␈↓ ∀0
␈↓"β
␈↓"β␈↓ β⊂␈↓Augmented Sixth Chords
␈↓"β␈↓ β⊂␈↓␈↓ ∧PIt␈α#is␈α#now␈α#clear␈α#that␈α"chromatic␈α#alteration␈α#in␈α#a␈α#chord␈α"very
␈↓ β⊂␈↓often␈α∃changes␈α⊗its␈α∃function.␈α⊗ This␈α∃will␈α⊗most␈α∃often␈α⊗be␈α∃true␈α⊗when␈α∃the
␈↓ β⊂␈↓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
␈↓ β⊂␈↓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
␈↓ β⊂␈↓before,␈α.every␈α.judgment␈α.must␈α.be␈α.based␈α.on␈α.the␈α.whole␈α.of␈α.any
␈↓ β⊂␈↓particular context under consideration.
␈↓"β␈↓ β⊂␈↓␈↓ ∧PThe␈α∃alterations␈α∃that␈α∃go␈α∃into␈α∃making␈α∃chords␈α∃of␈α∃the␈α∀augmented
␈↓ β⊂␈↓sixth␈α↔(A6)␈α↔give␈α_us␈α↔a␈α↔special␈α↔case.␈α_ Such␈α↔chords␈α↔evolved␈α_as␈α↔separate
␈↓ β⊂␈↓entities␈α⊗from␈α⊗the␈α⊗practice␈α∃of␈α⊗"freezing"␈α⊗the␈α⊗chromatic␈α⊗passing␈α∃tone
␈↓ β⊂␈↓between␈α⊗the␈α⊗4th␈α⊗and␈α⊗5th␈α↔of␈α⊗the␈α⊗scale.␈α⊗ When␈α⊗these␈α⊗chords␈α↔are␈α⊗used
␈↓ β⊂␈↓in␈α≥their␈α≡conventional␈α≥manner␈α≥and␈α≡within␈α≥a␈α≥single␈α≡tonality,␈α≥they
␈↓ β⊂␈↓give␈α↔us␈α↔an␈α↔exception␈α↔to␈α↔the␈α↔rule␈α↔that␈α↔the␈α↔4th␈α↔of␈α↔a␈α↔scale,␈α↔as␈α_a␈α↔chord
␈↓ β⊂␈↓tone,␈α∨may␈α∨not␈α be␈α∨altered␈α∨without␈α∨causing␈α a␈α∨shift␈α∨of␈α tonics.␈α∨ The
␈↓ β⊂␈↓traditional␈α%names␈α%for␈α%the␈α%three␈α%most␈α%common␈α%augmented␈α%sixth
␈↓ β⊂␈↓chords are as follows:
␈↓"β
␈↓"β␈↓ β⊂␈↓Example 52
␈↓"β␈↓ β⊂␈↓␈↓ ¬5␈↓¬⊂⊗⊃L[%0.06,%-2.00](17,22):N52X.PLT[C4,LCS]⊂⊗⊃␈↓
␈↓"β
␈↓"β␈↓ β⊂␈↓␈↓ ∧P Strictly␈α⊗speaking,␈α↔they␈α⊗should␈α↔be␈α⊗indicated␈α↔thus␈α⊗for␈α↔a␈α⊗major
␈↓ β⊂␈↓key such as ␈↓&C␈↓)αβ:
␈↓"β␈↓ β⊂␈↓␈↓ ¬8␈↓¬⊂⊗⊃L[%0.06,%-1.20](17,22):N52Z.PLT[C4,LCS]⊂⊗⊃␈↓
␈↓"β␈↓ β⊂␈↓␈↓ ∧PIt␈α7will␈α8generally␈α7suffice␈α8to␈α7refer␈α7to␈α8them␈α7all␈α8in␈α7the
␈↓ β⊂␈↓abbreviated␈α>manner,␈α>A6.␈α> When␈α=they␈α>actually␈α>are␈α>used␈α=as
␈↓ β⊂␈↓augmented␈α2sixth␈α2chords,␈α1they␈α2almost␈α2always␈α2have␈α1primarily
␈↓ β⊂␈↓␈↓ 650␈↓ ∀0
␈↓"β␈↓ β⊂␈↓contrapuntal␈α∃significance,␈α∃the␈α∃outer␈α∃voices␈α∃expanding␈α∃by␈α∃half␈α∃step
␈↓ β⊂␈↓movement.
␈↓"β␈↓ β⊂␈↓
␈↓"β␈↓ β⊂␈↓Example 53
␈↓"β␈↓ β⊂␈↓␈↓ ¬5␈↓¬⊂⊗⊃L[%0.06,%-1.30](17,22):N53X.PLT[C4,LCS]⊂⊗⊃␈↓
␈↓"β
␈↓"β␈↓ β⊂␈↓␈↓ ∧PHowever,␈α3since␈α3they␈α3are␈α3so␈α3often␈α3used␈α3as␈α3a␈α3means␈α3of
␈↓ β⊂␈↓tonicizing␈α≤new␈α≥areas␈α≤(see␈α≥Example␈α≤33),␈α≤it␈α≥is␈α≤usually␈α≥advisable␈α≤to
␈↓ β⊂␈↓make␈α$their␈α$presence␈α$clear␈α#in␈α$an␈α$analysis.␈α$ The␈α$augmented␈α#sixth
␈↓ β⊂␈↓interval␈α'creates␈α'a␈α'situation␈α'wherein␈α'the␈α'dominant␈α'tends␈α'to␈α&be
␈↓ β⊂␈↓tonicized␈α_(Example␈α_53,␈α_F␈↓βS␈↓␈α_leads␈α_to␈α_G)␈α_and␈α_at␈α_the␈α_same␈α_time␈α_a␈α_tonic
␈↓ β⊂␈↓role␈α→for␈α→the␈α→dominant␈α→is␈α→weakened␈α→by␈α→the␈α→effect␈α→of␈α~presenting␈α→its
␈↓ β⊂␈↓2nd␈α∃as␈α∃flatted␈α∃(A␈↓βF␈↓␈α∀to␈α∃G).␈α∃ The␈α∃actual␈α∀result␈α∃is␈α∃that␈α∃added␈α∃strength␈α∀is
␈↓ β⊂␈↓given␈α#to␈α$the␈α#␈↓↓dominant␈α$role␈↓␈α#of␈α$the␈α#final␈α$"resolution"␈α#of␈α$the␈α#A6
␈↓ β⊂␈↓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
␈↓ β⊂␈↓original␈α,tonic.␈α, Thus,␈α,augmented␈α,sixth␈α,chords␈α,will␈α,be␈α,said␈α,to
␈↓ β⊂␈↓function␈α∃as␈α∃part␈α∃of␈α∃a␈α∃tonic␈α∃a␈α∃major␈α∃3rd␈α∃␈↓↓above␈↓␈α∃the␈α∃␈↓↓lower␈↓␈α∃member␈α∀of
␈↓ β⊂␈↓the augmented sixth interval (see Example 53).
␈↓"β␈↓ β⊂␈↓␈↓ ∧PBecause␈α6the␈α6G6␈α6chord␈α6presents␈α6the␈α6identical␈α6acoustical
␈↓ β⊂␈↓situation␈α+as␈α+an␈α*ordinary␈α+dominant␈α+7th␈α*chord␈α+(i.e.,␈α+major␈α*3rd,
␈↓ β⊂␈↓minor␈α→3rd,␈α_minor␈α→3rd),␈α_its␈α→enharmonic␈α_form␈α→will␈α_often␈α→be␈α→used␈α_as
␈↓ β⊂␈↓a means to move rapidly to a relatively distant tonic.
␈↓"β␈↓ β⊂␈↓
␈↓"β␈↓ β⊂␈↓Example 54
␈↓"β␈↓ β⊂␈↓␈↓ ¬5␈↓¬⊂⊗⊃L[%0.06,%-3.44](17,22):N54X.PLT[C4,LCS]⊂⊗⊃␈↓
␈↓ β⊂␈↓␈↓ 651␈↓ ∀0
␈↓"β␈↓ β⊂␈↓␈↓ ∧P Even␈α⊗without␈α⊗recourse␈α↔to␈α⊗enharmonic␈α⊗change,␈α⊗the␈α↔F6␈α⊗chord
␈↓ β⊂␈↓may␈α∃work␈α⊗as␈α∃the␈α⊗V␈↓βG␈↓␈α∃structure␈α⊗of␈α∃the␈α⊗original␈α∃key's␈α⊗dominant␈α∃(see
␈↓ β⊂␈↓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$of
␈↓ β⊂␈↓Schubert's ␈↓↓Quintet in C␈↓, Op.163.
␈↓"β␈↓ β⊂␈↓
␈↓"β␈↓ β⊂␈↓Example 55
␈↓"β␈↓ β⊂␈↓␈↓ ¬5␈↓¬⊂⊗⊃L[%0.06,%-2.04](17,22):N55X.PLT[C4,LCS]⊂⊗⊃␈↓
␈↓"β␈↓ β⊂␈↓␈↓ ∧P In␈α8this␈α8particular␈α8case␈α8it␈α8might␈α8be␈α8inferred␈α8(perhaps
␈↓ β⊂␈↓fancifully)␈α"that␈α!this␈α"chord␈α"is␈α!used␈α"to␈α!point␈α"in␈α"the␈α!subdominant
␈↓ β⊂␈↓direction, a tradition of long standing for endings. Thus:
␈↓"β␈↓ β⊂␈↓␈↓
∩might imply
␈↓"β␈↓ β⊂␈↓␈↓ ¬7␈↓¬⊂⊗⊃L[%0.18,%-1.56](17,22):N55F.PLT[C4,LCS]⊂⊗⊃␈↓
␈↓"β
␈↓"β␈↓ β⊂␈↓␈↓ ∧P For␈α%a␈α%stronger␈α%example,␈α%this␈α%time␈α%employing␈α%the␈α%G6,␈α$we
␈↓ β⊂␈↓turn␈α∨to␈α≡Schubert's␈α∨posthumous␈α∨␈↓↓Sonata␈α≡in␈α∨A␈↓.␈α≡ Here,␈α∨there␈α∨is␈α≡little
␈↓ β⊂␈↓possibility␈α≤of␈α≠confusion␈α≤with␈α≤an␈α≠altered␈α≤V,␈α≤since␈α≠there␈α≤is␈α≤no␈α≠root
␈↓ β⊂␈↓of V present.
␈↓"β
␈↓"β␈↓ β⊂␈↓Example 56
␈↓"β␈↓ β⊂␈↓␈↓ ¬5␈↓¬⊂⊗⊃L[%0.06,%-3.00](17,22):N56X.PLT[C4,LCS]⊂⊗⊃␈↓
␈↓ β⊂␈↓␈↓ 652␈↓ ∀0
␈↓"β
␈↓"β␈↓ β⊂␈↓␈↓ ∧P Of␈α∃the␈α⊗two␈α∃following␈α∃possible␈α⊗analyses,␈α∃the␈α∃second␈α⊗is␈α∃better.
␈↓ β⊂␈↓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,
␈↓ β⊂␈↓though␈α~not␈α~present,␈α~might␈α~be␈α~implied.␈α~ (Even␈α~so,␈α~this␈α~would␈α~give
␈↓ β⊂␈↓the␈α,sound␈α,of␈α,the␈α,subdominant's␈α+F6.)␈α,In␈α,the␈α,second,␈α,we␈α+more
␈↓ β⊂␈↓reasonably␈α_assume␈α_that␈α_the␈α_F␈α→persists␈α_in␈α_the␈α_memory␈α_and␈α→that␈α_the
␈↓ β⊂␈↓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
␈↓ β⊂␈↓inversion of ␈↓&A␈↓)αβ: VII␈↓βG␈↓.
␈↓"β
␈↓"β␈↓ β⊂␈↓Figure 56
␈↓"β␈↓ β⊂␈↓␈↓ ¬7␈↓¬⊂⊗⊃L[%0.06,%-2.40](17,22):N56F.PLT[C4,LCS]⊂⊗⊃␈↓
␈↓"β␈↓ β⊂␈↓␈↓ ∧P It␈α1should␈α0be␈α1pointed␈α1out␈α0again␈α1that␈α0no␈α1chord␈α1may␈α0be
␈↓ β⊂␈↓evaluated␈α#until␈α#all␈α#its␈α#parts␈α#have␈α#been␈α#heard.␈α# However,␈α#no␈α#set
␈↓ β⊂␈↓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
␈↓ β⊂␈↓determining␈α∨factor.␈α≡ In␈α∨the␈α∨Schubert␈α≡␈↓↓Sonata␈↓,␈α∨the␈α≡B␈↓βF␈↓␈α∨chord␈α∨fills␈α≡a
␈↓ β⊂␈↓measure␈α≠and␈α≤a␈α≠quarter␈α≤before␈α≠the␈α≤appearance␈α≠of␈α≤the␈α≠G␈↓βS␈↓.␈α≤ Thus␈α≠the
␈↓ β⊂␈↓relatively␈α!simple␈α!progression␈α!of␈α!I␈α!to␈α!␈↓βF␈↓II␈α!has␈α!time␈α!to␈α!be␈α accepted
␈↓ β⊂␈↓before␈α∨the␈α∨function␈α≡is␈α∨altered␈α∨by␈α∨the␈α≡addition␈α∨of␈α∨a␈α∨fourth␈α≡pitch.
␈↓ β⊂␈↓Such␈α⊗particulars␈α⊗are␈α↔certainly␈α⊗open␈α⊗to␈α⊗varying␈α↔interpretations.␈α⊗ In
␈↓ β⊂␈↓both␈α*of␈α*these␈α*Schubert␈α*pieces,␈α*such␈α*ambiguous␈α*procedures␈α*are
␈↓ β⊂␈↓possible␈α~because␈α~of␈α~the␈α~extremely␈α~firm␈α~establishment␈α~of␈α~the␈α~main
␈↓ β⊂␈↓tonic in the preceding passages.
␈↓"β␈↓ β⊂␈↓␈↓ ∧P A␈α∃case␈α∀with␈α∃some␈α∃similarity␈α∀is␈α∃presented␈α∀in␈α∃the␈α∃␈↓↓Prelude␈α∀#23
␈↓ β⊂␈↓↓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
␈↓ β⊂␈↓chord.␈α⊗ This␈α⊗E␈↓βF␈↓␈α⊗is␈α⊗usually␈α↔heard␈α⊗merely␈α⊗as␈α⊗an␈α⊗intensification␈α↔of␈α⊗the
␈↓ β⊂␈↓already␈α*present␈α)7th␈α*partial␈α)of␈α*the␈α)bass␈α*note's␈α*overtone␈α)series.
␈↓ β⊂␈↓However,␈α9it␈α9is␈α9undeniable␈α9that␈α9some␈α9tendency␈α9toward␈α9the
␈↓ β⊂␈↓subdominant,␈α∃a␈α⊗tonal␈α∃area␈α∃which␈α⊗is␈α∃almost␈α∃completely␈α⊗neglected␈α∃in
␈↓ β⊂␈↓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⊂␈↓␈↓ 653␈↓ ∀0
␈↓"β␈↓ β⊂␈↓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
␈↓ β⊂␈↓welcome bit of fantasy.
␈↓"β
␈↓"β␈↓ β⊂␈↓Example 57. Chopin, Prelude, Op.28, #23
␈↓"β␈↓ β⊂␈↓␈↓ ¬5␈↓¬⊂⊗⊃L[%0.00,%-3.74](17,22):N57X.PLT[C4,LCS]⊂⊗⊃␈↓
␈↓"β␈↓ β⊂␈↓␈↓ ∧C And then there is the standard "Blues" progression:
␈↓"β
␈↓"β␈↓ β⊂␈↓Example 58
␈↓"β␈↓ β⊂␈↓␈↓ ¬#␈↓¬⊂⊗⊃L[%-0.16,%-3.60](17,22):N58X.PLT[C4,LCS]⊂⊗⊃␈↓
␈↓"β␈↓ β⊂␈↓␈↓ ∧P Many␈α↔variants␈α↔of␈α↔the␈α↔main␈α↔A6␈α↔chords␈α↔may␈α↔be␈α↔found␈α_in␈α↔later
␈↓ β⊂␈↓tonal␈α∀music.␈α∀ But␈α∀once␈α∀they␈α∃are␈α∀recognized␈α∀for␈α∀what␈α∀they␈α∃are,␈α∀they
␈↓ β⊂␈↓should␈α"cause␈α#no␈α"difficulties␈α#in␈α"an␈α#analysis.␈α" Similarly,␈α#there␈α"are
␈↓ β⊂␈↓many␈α⊗chromatic␈α∃variants␈α⊗of␈α∃the␈α⊗dominant,␈α∃subdominant␈α⊗(the␈α⊗A6␈α∃is
␈↓ β⊂␈↓one!),␈α&and␈α'other␈α&functions,␈α'except␈α&for␈α'the␈α&I␈α'function.*␈α&Various
␈↓ β⊂␈↓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⊂␈↓omitted,␈α&but␈α%if␈α&the␈α&root␈α%or␈α&5th␈α&are␈α%altered,␈α&the␈α&tonic␈α%function
␈↓ β⊂␈↓becomes dubious.
␈↓"β␈↓ β⊂␈↓__________
␈↓"β␈↓ β⊂␈↓*␈α~But␈α~remember␈α~that␈α~there␈α~is␈α→always␈α~the␈α~␈↓↓potential␈↓␈α~of␈α~a␈α~change␈α→of
␈↓"␈↓ β⊂␈↓function when any chromaticism is introduced.
␈↓ β⊂␈↓␈↓ 654␈↓ ∀0
␈↓"β␈↓ β⊂␈↓␈↓ ∧P Chromaticism␈α'has␈α(always␈α'caused␈α'composers␈α(trouble␈α'with
␈↓ β⊂␈↓notation.␈α→ The␈α→augmented␈α→sixth␈α→and␈α→diminished␈α→seventh␈α→chords␈α→in
␈↓ β⊂␈↓particular␈α≥have␈α≥raised␈α≤problems,␈α≥because␈α≥of␈α≤the␈α≥ambiguity␈α≥of␈α≤the
␈↓ β⊂␈↓situations␈α in␈α which␈α they␈α!are␈α often␈α found.␈α Composers␈α!cannot␈α be
␈↓ β⊂␈↓totally␈α1consistent␈α0in␈α1notating␈α0such␈α1chords␈α1when␈α0enharmonic
␈↓ β⊂␈↓equivalence␈α⊗is␈α⊗involved.␈α⊗ It␈α∃will␈α⊗always␈α⊗be␈α⊗necessary␈α⊗to␈α∃determine
␈↓ β⊂␈↓the␈α≤function␈α≤or␈α≤functions␈α≤of␈α≤chromatic␈α≤chords␈α≤by␈α≤studying␈α≤their
␈↓ β⊂␈↓surroundings rather than by taking their notation at face value.
␈↓"β␈↓ β⊂␈↓␈↓ πq_______________
␈↓ β⊂␈↓␈↓ 655␈↓ ∀0
␈↓"β
␈↓"β␈↓ β⊂␈↓Exercises for Chapter IV
␈↓"β
␈↓"β␈↓ β⊂␈↓␈↓ ∧PAnalyze␈α?the␈α?following␈α?works.␈α? Show␈α?the␈α?distinctions
␈↓ β⊂␈↓between␈α#major␈α"and␈α#minor␈α#tonics␈α"through␈α#the␈α"use␈α#of␈α#upper␈α"and
␈↓ β⊂␈↓lower case numerals on the two highest levels of the analyses.
␈↓"β
␈↓"β␈↓ β⊂␈↓
␈↓"β␈↓ β⊂␈↓From the 371 Chorales of Bach:*
␈↓"β
␈↓"β␈↓ β⊂␈↓ 1. Chorale 11, up to the 3/4.
␈↓"β␈↓ β⊂␈↓ 2. Chorale 37, all.
␈↓"β␈↓ β⊂␈↓ 3. Chorale 47
␈↓"β␈↓ β⊂␈↓ 4. Chorale 94
␈↓"β␈↓ β⊂␈↓ 5. Chorale 223
␈↓"β␈↓ β⊂␈↓
␈↓"β
␈↓"β␈↓ β⊂␈↓From the Sonatas of Mozart:
␈↓"β␈↓ β⊂␈↓
␈↓"β␈↓ β⊂␈↓ 6. Sonata in D, K.205b (284), last movement, Variation VII.
␈↓"β␈↓ β⊂␈↓
␈↓"β␈↓ β⊂␈↓ 7. Sonata in a, K.300d (310), first movement, 24 bars
␈↓"β␈↓ β⊂␈↓ starting at recapitulation. (In cases where there are
␈↓"β␈↓ β⊂␈↓ many suspensions and appoggiaturas it is usually best
␈↓"β␈↓ β⊂␈↓ to write out a chordal reduction of the passage before
␈↓"β␈↓ β⊂␈↓ working out the analysis.)
␈↓"β␈↓ β⊂␈↓
␈↓"β␈↓ β⊂␈↓ 8. Sonata in C, K.300h (330), second movement, first 20 bars.
␈↓"β␈↓ β⊂␈↓
␈↓"β
␈↓"β␈↓ β⊂␈↓From the Preludes, Op.28, of Chopin:
␈↓"β␈↓ β⊂␈↓
␈↓"β␈↓ β⊂␈↓ 9. Prelude 1, in C
␈↓"β␈↓ β⊂␈↓ 10. Prelude 6, in b
␈↓"β␈↓ β⊂␈↓ 11. Prelude 20, in c
␈↓"β
␈↓"β␈↓ β⊂␈↓_____________
␈↓"β␈↓ β⊂␈↓* Note that all bass lines in the Bach Chorales are probably
␈↓"β␈↓ β⊂␈↓intended to be doubled at the octave below. Hence, even if the
␈↓"β␈↓ β⊂␈↓notation of the bass part crosses above the tenor part, the bass
␈↓"β␈↓ β⊂␈↓part remains the true bass.