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proportional relationship in .hich the second, faster dance A the Nachtanz, &roportz or !ripla A .ould offer a varied version of the first - variation principle informs even the originaldance$pairs of the 1#th century in"#-$!l -dd *==8>, $a Manfredina and $amento diTristano, each .ith its o.n Nachtanz called $a Rotta, a :uic6er, compressed and some.hatornamented version of the first dance thcentury !hat dance pieces .ere repeated, in part or as a .hole, is clear not only from thelength of the choreographic pattern compared to the notated music but also to e plicitdirections li6e 7Cuesta 4onata farassi due volte %7play this piece t.ice , in the balletto $aura suave+ and 74i torna D fare di nuovo detta 4ciolta in 4altarello D :uattro !empi %7&lay thesciolta to this piece as a saltarello four more times , in Furioso alla pagnuola (abritio)aroso, %o!ilt& di dame, 1EFF, ng trans , 1=8E, pp 1FA11+ "t seems plausible to suggestthat such repetitions .ere varied $aura suave is itself a 6ind of variation suite, consisting ofan opening pavan$li6e piece %including repetitions+, the piece played as a galliard, then intriple proportion as a saltarello and finally as a canary %e *+ -s !hoinot -rbeau .rote in1588 %'rch(sographie , 158=, ng trans , 1=E>+, 7you can amplify this music to suit your pleasure and fancy %p #3+ and 7some dancers divide up thedou!le that follo.s the t.o

simples, and instead of thedou!le comprising only four bars .ith four semi$breves, theyintroduce eight minims or si teen crotchets, resulting in a great number of steps, passages andembellishments, all of .hich fit into the time and cadence of the music %p EE+ !his connectsthe variations of steps performed by dancers A calledmutan)e by )aroso as early as 1581, in *l !allarino A .ith musical variations, as does -ntonio Valente's use of the termmutan)e forsets of variations on dance themes such as the romanesca and the gagliarda napolitana%Naples, 15>E+


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GdancerH must dance to that air that the instruments play (or even though they are playing oneGand the sameH ballo, each one .ill play .ith his o.n air G-ndH although they are playing thesame ballo, the sha.ms .ill play in one air, the organ in one air, the harp in another air, theGpipe and taborH in another air, but all .ill play one and the same ballo Bemember that thedancer must dance .ith that air and .ith that measure and .ith that rhythm that the said players are playing that is, dancing each one on its o.n -nd if the dancer al.ays dances.ith one air, even though he dances .ith measure and in time but does not follo. the air ofthe said players, his dancing .ill be imperfect and sho. little s6ill %'n the Practice or Art of +ancing , ng trans , 1==3, p *35+

The 16th century.

4ets of variations appeared for the first time in the 1Eth century and, as their themesoriginating in dance and song indicate, they captured t.o forms of improvisation, thevariations in repeated strains of dance music originating in its choreography and the variedsettings and diminutions given successive stanzas of a song .hose melody can be savoured asa cantus firmus or a springboard to figuration arly 1Eth$century dances on short ostinato basses, such as ugh -ston's ,ornp pe and the various forms of dump %e g M $ad .are s +ompe, ,AM , no 1F3+, reveal a flourishing variation practice in ngland !he importance ofdiminutions in improvising embellished lines in polyphony and to a cantus firmus is attested

by such treatises as 4ilvestro 0anassi, Fontegara %1535+, 9iego 2rtiz,Trattado de glosas%1553+ and 0irolamo dalla )asa, *l vero modo di diminuir %158#+ "ntabulations of vocal polyphony and related dance$pairs such as pavanAgalliard and passamezzoAsaltarello in the"talian lute and 6eyboard repertories also participated in this development -s early as 15F8,in I - 9alza's *nta!ulatura di lauto, t.o sorts of pavan herald the varied$reprise dance formsas .ell as the variation set per se; the pavana alla ferrarese .ith a series of open$ended phrases follo.ed by varied repeats % AA' ## '.. ' J+ and freer material, and the pavana alla

venetiana, .ith a some.hat longer phrase ending on the 7tonic follo.ed by a series ofvariations before a freer concluding passage % orsley, 1=5=, calls these 7multiple$strain and7single$strain variations respectively+ 74uites of dances .ith related incipits, such as 7&assae mezzo antico %or 7moderno + and 74alltarello , or 7&assamezoA&adoanaA4altarel %all baon the same song+ appear in 0iacomo 0orzanis s four boo6s of *nta!ulatura de liuto %15E1A >=+

!he earliest published sets of variations, ordiferencias, appeared in 4panish .or6s for

vihuela by @uis de Narvez % +elph0n de m1sica, 1538+ especially influential .ere %1+ thevariations on' gu2rdame las vacas %e 3+, the 4panish version of the romanesca %identified


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as such by (rancesco de 4alinas, +e musica li!ri septem, 15>>+, in .hich the first of threediferencias is much shorter than the theme .hile the third is follo.ed by a coda %*+.ondeclaros, on a t.o$bar theme and %3+diferencias on a plainchant %' gloriosa domina , - ,no 1**+ -fter the varied$reprise dances and ubi:uitousvacas of -lonso de udarra %Tresli!ros de m1sica, 15#E+, .ho used the termsmanera and diferencia interchangeably, and

nrK:uez de Valderrbano %ilva de irenas, 15#>, - , no 1*#+, came the importantdiminution treatise of 2rtiz %1553+, .hich offered a series ofrecercadas on 7plain songsGcanto llanoH .hich in "taly are commonly called tenors %b6 ii, f #>r + !heserecercadasresemble variations on the folia, romanesca and passame))o antico and moderno, .hile2rtiz's recercadas on polyphonic compositions %e g -rcadelt's madrigal' felici occhi miei+have the cumulative effect of variations since diminution techni:ues are differently applied toeach intabulation

-ntonio de )abezLn .as the first master of the 6eyboard variation, .ith some published in @uis Venegas's $i!ro de cifra nueva %155>+ and nine sets in his son ernando's'!ras de m1sica %15>8+, including three on' gu2rdame las vacas and several callingattention to direct "talian influence, such as +iferencias so!re la pavana italiana and so!re la gallarda milanesa )abezLn's four$voice polyphonic settings, .hile neither systematic nor progressive in figuration, often present diminutions first in the treble, then in the bass, then in

both hands )onstant$melody techni:ue is often present, sometimes .ith the theme melodylightly coloured 2ne .onders if such beautiful settings of plainchants as his Ave maris stella 3* , .hich maintains the cantus firmus in the middle voice and surrounds it .ith precisely the6inds of figurations found in thediferencias, .ere spurs to further variation in performance,especially in pieces based on a strophic original is soMourn in ngland .ith &hilip "" from155# to 155E has spurred theories of reciprocal influence in variation

!he flo.ering of 6eyboard music in the later 1Eth and early 1>th century in ngland

among composers later 6no.n as the 7 nglish virginalists .ent hand in hand .ith a voguefor variations on dances and popular tunes "n general these combine constant$melody,constant$harmony and melodic$outline types 4ometimes the varied repeats in the pavan A AA1 ## 1.. 1 A .ere follo.ed by yet another chain of varied repeats A A* A3 #* #3. *. 3 A beforethe metric variation of the galliard %perhaps .ith its o.n varied reprises+ 2ccasionally anunnamed 7alla venetiana model produced a one$strain pavan .ith a longer chain ofvariations, as in


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theme+ .ith si variations follo.ed by the 70aliardas &assamezzo .ith eight %(itz.illiamVirginal


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also includes the triumphant triplet variation 1*, .hich begins as a point of arrival and anotherrhythmic acceleration !he final variation disguises the theme melody in the alto andreharmonizes it .hile also crystallizing the up.ard and do.n.ard slopes of the theme into anarticulation that gro.s out of the :uasi$reprise variation 15 %e #+ !he tune6alsinghaminspired some of these composers' longest sets A 3F virtuoso variations from


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variation .ith the location of the chorale or song melody %e g 7)horalis in -lto , 7Variatio in!enore +, and :uic6, slurred figures to.ards the end of a variation are mar6ed 7imitatioviolistica /nli6e 4.eelinc6, he usually began .ith the 7theme as a simple chordal rendering before the 7variations

ith the rise of monody at the beginning of the 1>th century, the repetitive impulsefound outlet in t.o directions, both centred on retention of the bass; strophic arias .ithsuccessive modifications to the melody or different melodies in each strophe, and vocal pieces, largely solos and duets, over an ostinato bass !he prototype of the former is perhaps)accini's Ard il mio petto misero, the only strophic aria in his %uove musiche %1EF1+ to be.ritten out .ith some changes to the melody %fe.er to the bass+ %!here are, ho.ever,strophic songs .ith varied lute parts and slight vocal changes already in Narvez, 1538, e g

tantos halcones + - stri6ing later e ample is (rescobaldi's 7-ria di romanesca % Ariemusicali, 1E3F+, .hich also sho.s the incorporation of 1Eth$century dance frame.or6s intovocal music !he melody is different in each strophe e cept for the cadential note at the endof each three$bar phrase 2n the other hand, onteverdi'sciaccona for t.o voices and bass, 9efiro torna %1E3*+, e emplifies a non$coincidence bet.een bass and treble typical of hisstyle but differing from many vocal ostinato$bass pieces in this era % erula, 4chPtz+"nevitable cadencing in the t.o$bar bass line %a classic tonic$re:uiring pattern+ is mitigated by

shorter, longer and asymmetrical passages in the upper voices, .hile te turally the flat planeof the bass contrasts .ith the :uasi$imitative and often off$beat give$and$ta6e of the singers


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!he po.er of even the simple maMor$mode tetrachord may be seen in the opening and closingsections of the highly charged closing duet for Nero and &oppaea in onteverdi's $ incorona)ione di Poppea %1E#*+, set to + &assacaglias originated in the early 1>th century as a 6ind of

7.al6ing$around music for guitar that served as introductions, interpolated episodes andconclusions to songs and dances these passages .ere also 6no.n asriprese or ritornelli,repeated several or many times .ith improvised variations (rescobaldi's Partite sopra passacagli %1E*>+ may have been the earliest for 6eyboard )haconnes tended to be maMor and passacaglias minor, and each had characteristic though similar bass lines and chord progressions, but early differences .ere often ignored "ndeed, (rescobaldi's.ento partite sopra passacagli %econdo li!ro di toccate, 1E3> edition+ features sections headed

7passacagli as .ell as 7ciaccona ; both are in the minor, though .ith differing harmonicrhythms

"n addition to his vocal 7partite on dance$bass patterns, (rescobaldi .as thus the principal composer of variations and variation$inflected instrumental genres in the early 1>thcentury in "taly 2f the established or evolving genres in .hich he .as dra.n to e plore theconcept of variation A suite, capriccio, canzona and ricercar A only the first had a naturalconnection .ith variation, developing as a stylized representation of dances .ith roots in both

choreographic necessity and a form to .hich actual dancing occurred and to .hich repetition.ith improvised variations .ould have been common "ndeed, each of @orenzo -llegri's eight


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balli % *l primo li!ro delle musiche, 1E18+ supposedly reflects the contents of actual dances performed as part of anintermedio at the (lorentine court, and nearly all include pairs ofdances in .hich the second is built on the bass and melody of the first %e g 7Cuinto ballodetto le Ninfe di 4enna , .ith opening pair; untitled 7prima parte A 7)anario seconda partethe follo.ing 70avotta terza parte and 7)orrente :uarta Q ultima parte are unrelated+ !hree0erman publications .ith longer series of lin6ed dances later 6no.n as variation suitesappeared in the second decade of the 1>th century; &aul &euerl's %ewe Padouan: *ntrada: +;nt) unnd "alliarda %four$movement se:uence, 1E11+, "saac &osch's Musicalische Ehrenfreudt %three$movement se:uence, 1E18+ and the most celebrated of these, 4chein's #anchetto musicale %1E1>+ 4chein asserted that the dances are 7arranged so that theycorrespond to one another in both mode and invention , thus clearly referring to the rhetoricalnotion of the principal idea of each piece !he principal ideas are variations of each other,even if there is no literal bar$to$bar correspondence, .ith the most ornate version appearingfirst in the leisurely pavans %&adouana+, follo.ed by 0agliarda, )orente and finally the-llemande and its !ripla, a simplified metrical recasting of the allemande -s the dances progress from comple to simple, te turally and melodically, they also descend in style fromhigher to lo.er

!he canzona, ricercare and so$called capriccio %actually a type of ricercare+ .ere

contrapuntal single movements, often in multiple sections differentiated by metre anddominated by imitative te ture the term 7variation has been used to describe the rhythmictransformations of the imitative subMects and countersubMects of successive sections hilesuch a composition may be considered cyclic, it is not a variation form in the sense of acommon substratum underlying each section 2n the other hand, the impulse to connectcontrapuntal and variational forms suggests a relatively borderless connection bet.een them4everal composers of this era cultivated .hat modern scholars call the variation canzona and

variation ricercare; -ndrea 0abrieli, rcole &as:uini %1EFF+, -scanio ayone %1EF3+, 0!rabaci %1EF3+ and (rescobaldi beginning .ith his Primo li!ro di toccate %1E15+ @ade.ig%1=8>+ has persuasively placed the origin of the variation canzona in late 1Eth$century (errara.ith @uzzaschi, rcole &as:uini and 70iaches %de ert or


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%no 1* onumenti musicali italiani, viii, 1=8#, p >8+ treats the four phrases of the Buggiero bass % A#.+ + in a .ay that shares elements of the imitative ricercares and canzonas, on theone hand, and sets of variations on the other -pel %1=>*+ calls it a 7:uadruple fugue anddivides it into eight sections according to metre, principal cadences, and the presence of particular phrases of the bass!able 1 amends his chart to reveal the t.o variation structuresthat emerge first from the sections in .hich all four theme phrases are present %", """, V",labelled variations 1A3+ and second from alterations to the theme phrases themselves throughmetric and rhythmic changes %"", "V, V, labelled variations aAc+, as .ell as the 7finale $grouping of sections V"" and V""" %variation #d + .hich combines both types by speeding upthe figuration as .ell as presenting the #$phrase as a varied counter$figure %a chromatic #th, both ascending and descending+ !he sections identified as variations, ho.ever, treat the phrases of the Buggiero as separable entities, motivically and contrapuntally %e E+ they arenot structural variations li6e (rescobaldi's o.n Partite = sopra l aria di Ruggiero %Toccate e partite > primo li!ro , 1E15, e panded to 1* variations in the second edition+, on the same popular subMect already also set by ac:ue, ayone and !rabaci o.ever, his.apriccio sopra soggetto scritto sopra l aria di Ruggiero in the same volume adds the melody 7(raIacopino to the harmonic pattern % ., i+ 9ance$bass variations as .ell as variations onsuch melodies as 7!anto tempo hormai appeared in trio sonatas by 4alomone Bossi

%including 11 sets in his boo6s 3 and #, 1E13A**+, 0 <


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(rescobaldi's masterpiece in variations, the Partite sopra l aria della romanesca %1E15 - ,no 1=*+, offers both the bass and treble parts of the frame.or6 in the prima parte, though thetreble is much less important than the bass in the variations 4everal variations have adifferent structure from the first theripresa in particular is li6ely to be shortened - singlefigurative pattern dominates in a fe. variations, a 7middle section of slo.er variations %.ithnotes of double value+ right after the 7proportio tripla variation that effectively speeds up themotion !he surface of both treble and bass is often so irregular, free and ornate that theunderlying frame.or6 can scarcely be detected - magical final variation strips all that a.ay.ith simple off$beat chords and a ne.ly emergent thematic essence never other.ise seen inthis era

!he later 1>th century sa. fe. innovations in variation .riting "n "taly, composerscontinued to .rite dance$frame.or6 variations for 6eyboard % ichelangelo Bossi, FF+, imitated or coincidentally Moined .ithin a fe. years by Vitali, -lbicastro,Vivaldi and Beali+ -lessandro 4carlatti's toccata concluding .ith *= variations on the foliaconflates the trends by follo.ing )orelli on the 6eyboard 0 < Vitali carried the principles of

the variation suite into the sonata


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by harpsichord or organ, and to create 7descants to the ground , in .hich the viol ma6es a7different$concording part unto the 0round , resulting in a series of divisions, an improvisedvariation form % see 9ivision+ !he torch of the most prolific variation composers had passedto 0ermany and -ustria

(roberger, a 0erman musician .ho studied .ith (rescobaldi in Bome and travelled.idely before Moining the musical establishment of the imperial court in Vienna, .rote inseveral of the older genres, as can be seen in his $i!ro secondo %1E#=+; variation canzona %e gfb.v3F5, on an attractive songli6e subMect, rhythmically transformed in successivecontrapuntal sections in different metres+, fantasia on a soggetto treated contrapuntally %e gfb.v*F1, 7sopra ut re me fa sol la , in .hich the he achordal subMect is diminished, treated.ith countersubMects of decreasing rhythmic value, changed metrically and finally offeredchromatically+, and variation suite %e g fb.vEF1A5, all in -llemandA)ourantA4arabandformat e cept EF*, .hich adds a 0igue+ (roberger's most celebrated variation set ma6es upthe si th suite, 7auff 9ie aSerin , fb.vEFE, also 6no.n as 74ch.eiget mir vom (rauennehmen %the title of a poem by 0eorg 0reflinger published in 1E51 a variation set byBeinc6en .ith both titles made its .ay into the


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several series of pieces, among them a suite of dances %-llemandeA)ourenteA4arabandeA 0igue+ each .ith at least onedou!le, and an 7-ria -llemagna con alcuni variationi 4opral' tD della GaesHta VGosHtra , .ith *F variations to correspond to her maMesty's age !hedesignated characteristics include a 7lyra %hurdy$gurdy, variation 5+, 7


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until the final piece, .hich uses the 6ey signature of < but is in ( minor !he latter is in any

case anomalous in the set; it is in triple metre, its first reprise remains in the tonic, and it has atitle, 7-ria 4ebaldina , referring though .ith un6no.n import to the 4ebaldus6irche in

Nuremberg, .here &achelbel had .or6ed since 1E=5 !he collection as a .hole appears tohave had a serious purpose not often found in secular variations; .ith a preface attesting the7beliefs of many that music comes from the 79reymal$ eilig sung by angels as .ell as fromthe harmony of the 7heavenly bodies 6no.n by &ythagoras and &lato, it is dedicated to


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The early 18th century.

(i) Couperin and Ra eau.

(rench variations of the 1>th century had consisted primarily ofdou!les for lute%9enis 0aultier+ .ith figural patterns of the st le !ris(, dou!les and other variations forharpsichord %@ouis )ouperin, )hambonniUres, 9'-nglebert, variations on $es foliesd Espagne+, .hich used both st le !ris( and a more idiomatic 6eyboard 7division style , andno l variations for organ %@ebUgue, 0igault+ )haconnes and passecailles .ere usually enrondeau, .ith the theme serving as an unvaried refrain to punctuate thecouplets, rather thanas a source of continuous variations, although the latter appeared in rare instances %e g@ebUgue, )haconne in (+ )omposition in every one of these genres continued during the 18thcentury

(ranWois )ouperin's manyordres and pith$century sets, the first couplet is already a variation; the 7pure form of the theme must.ait until its presentation in the bass in semibreves in the seventh couplet

Bameau's 0avotte .ith si dou!les from the third collection of 6eyboard pieces% %ouvelles suites de pi*8+ is his longest variation set &art of its popularity derives


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from its harmonies .hich, li6e the )ouperin Folies, refer to several se:uences of chords fromearlier dance basses; in the first reprise, the opening iA"VAVAi from the chaconne anddescending tetrachord from the passacaglia, and in the second, the progression from """ to V isreminiscent of the folia, .hile the final melodic$minor inflected ascent recalls &urcell's)hacony irroring techni:ues animate the first fe. variations, .ith the melody appearingcomplete or in part in either upper or middle voice !he final variation returns to an ornateversion of the theme, rather than continuing an increasing rhythmic traMectory

(ii) !ach and "andel.

FF, include both varied and unvaried, long$note and matching$note presentations of the cantus firmus .ithin a single set, as do the greatest variations of this type,the canonic variations on4om ,immel hoch b.v>E= %1>#>+ !he length of each variation inthe latter is itself so variable that the structure suggests a lin6ed series of chorale preludes a

7set rhythm cannot develop !here e ist t.o different orderings for these variations; the printed version arranges the variations in order of increasing comple ity of canonic treatment.hile the autograph organizes the piece symmetrically around a central point

"n the Aria variata alla maniera italiana b.v=8=, probably .ritten before 1>1# ineimar %possibly for a special type of harpsichord; the most authentic source heads the piece

7alla man "tal , transcribed by another early source as 7alla manuale "taliana +, the setcombines elements of melodic$outline and constant$harmony techni:ues harmonic

progressions that occasionally resemble the dance$bass type, especially the move to """ afterthe double bar and the variation suite, in the different tempos %in some early sources+ and thechange from #R# metre to 1*R8 in variation >, a courante$type mar6ed -llegro !he finalevariation %1F+, after the toccata$li6e 8 and =, returns to the rhythm if not precisely the melodyof the theme, a :uasi$da$capo not too far from concluding variations in the (itz.illiamVirginal


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differently conceived; in the passacaglia, the 7middle section %variations 11 to 15+ ischaracterized by the subMect ascending in register, being itself decorated, and evendisappearing before the final section returns the subMect to its proper register in the chaconne,the middle section is articulated by a turn to maMor >#+, and (or6el called the Art of Fugue7variations on a great scale J to sho. .hat can possibly be done upon a fugue theme %D!er Johann e!astian #achs $e!en , 18F*+, subse:uent generations have reopened the :uestion of.hether successive individual movements generated by the same theme may be consideredvariations !he term 7variation ricercare may give comfort here .ithout actually providing anans.er


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variations by I ) , *F, *3, *E, *8 and *=+ offset by t.o variations in the minor %*1 and*5+, the second an -dagio ach part has its fugue, the (ughetta of variation 1F and thesecond part of the 72uverture , variation 1E, remar6ably staying .ithin the allotted number of bars !he final variation before the -ria da capo puts an end to the brilliant 6eyboard .ritingin favour of a contrapuntal :uodlibet .hose sources have been plumbed %one of them is thesame fol6tune as underlies + that the .or6originated as a detailed self$defence against 4cheibe's attac6 on


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The Classical period.

-t the middle of the 18th century, constant$harmony techni:ue .as firmly established, but ostinato variations A indeed, ostinatos of virtually every type A dropped by the .ayside!he sectional constant$bass variation had emerged, ho.ever, perhaps as a feature of figured bass practice hile the forces of innovation shifted to Vienna, variations in northern0ermany continued to develop in interesting .ays

(i) C.#.$. !ach.

) & ># article on variation in 4ulzer's encyclopedia and profoundlyinfluencing aydn


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of note among his earlier variations is the finale of the 4onata in 9 minor for 7due tastature%1>#>, h53, .:E=+, in .hich each of the nine variations A by far his longest variationmovement A is given a different registration

E+, .hich begins.ith a chromatically descending bass, ) ( (asch's registral contrasts in the -riette .ithvariations in - %8*+, and Neefe's variations on the &riests' arch from +ie

9au!erflCte %1>=3+, .hich features not only an e pansive cadenza$li6e coda .hich brings bac6 the ( maMor theme in ( , but also a variation in ( minor %as .ell as variation E in (

maMor+ .ith remar6able passages in common .ith aydn's ( minor Variations of the sameyear

(ii) "aydn.

!he variation principle and form .ere central to aydn's creative mind "ndeed, thevariation principle vied .ith the sonata principle in shaping his larger musical structures and became increasingly important to his style during his long and productive life >Fs


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he emerged as a profound innovator in variation form itself, by using it in .eighty slo.movements and by transforming its repetitive shape in hybrid mi tures .ith rondo and ternaryforms "t .as aydn's innovations A placing the variation set in every movement of the multi$movement cycle, broadening its array of theme types and transforming its larger shape A thatcreated a recognizable 7)lassical variation e .as lauded for these achievements bycontemporary .riters; ?och %4ersuch einer Anleitung )ur .omposition, iii, 1>=3, p 31#+claimed that he .as the first to .rite slo.$movement variations among his 7pre$eminentmasterpieces in this form Vogler %1>=3+ called him 7a true &hoebus J G.hoH sho.ed us insymphonies ho. .e should vary %p >F+ sets its opening period in t.o$partinvertible counterpoint .hich returns after a beautifully orchestrated middle section .ith the parts inverted 2nly t.o later strophic sets in these genres are in other than slo. movements%op 33 no 5, finale, and op >E no E, first movement+, .hereas the piano sonatas have no slo.movement variations at all -mong aydn's many sprightly or cantabile theme types are also

serene hymns %4ymphony no >5, second movement, an influence on ozart's &iano )oncerto6#5F+, ethereal chord progressions %op E# no *, second movement+ and character pieces %the


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Variations for piano in ( minor, h [V"";E, a set of alternating variations+ 2ne of aydn's.ittiest yet most reticent themes is that of the epigrammatic slo. movement of 4ymphonyno 5> %1>>#+, .hich alternates pizzicato cadential chords .ith bo.ed ornamental lines, but inunits of one, t.o or three bars .ith plentiful rests %e =+ !he rhetorical .it of beginning andending .ith the same gesture, especially .hen the final cadence reiterates a point alreadyreached, is refined in each variation

&erhaps as part of his professional interest in displaying the abilities of the first$ratesterhzy musicians, aydn often turned, during the 1>EFs, to the overt display of

concertante te tures hen this techni:ue came to the fore during variation movements, itmeant that the instruments in the ensemble, normally one to a variation, too6 turns revelling infiguration for e ample, in the finale of 4ymphony no 31 %7 ornsignal +, the variations on thestring theme feature by turns .ind, viola, flute, horn, violin, tutti and double bass !he figuredline also may migrate from instrument to instrument in a string :uartet %as in op *F no #+@ater in his career, concertante display might be localized to a single variation or to suchnovelties as a coda$cadenza for .ind %slo. movements of symphonies nos 8# and 8>, thelatter a monothematic sonata form .ith variation techni:ue+ -n error in ?urt von (ischer's M"" article on variation, replicated in the"roveH translation and left uncorrected in the M""G revision %by 4tefan 9rees+ refers to the concertante segments labelled 7variatio after

the minuet's second trio in the early string :uartet h """;= %op * no E+ .hich are really7alternativos rather than true variations Not only is this .or6 a divertimento .ith t.o horns%h "";*1\+ in a spurious arrangement, but, more critically, the 7variatio segments themselvesare not authentic %see the edition in Joseph ,a dn 6er5e , V"""R1+ -uthentic 7alternativo $style ones are in the 9ivertimento h "";*# %autograph inI -% pm+

2nly about a fifth of aydn's strophic variations %18+ have aminore, perhaps becausehis interest in alternating mode more often too6 the form of alternating variations on a maMor

and a minor theme -fter 1>>E, aydn never included more than four variations in amovement, so that aminore has the po.er to reorganize the .hole series by acting as if a7middle section perhaps for this reason theminore is most often the second variation Barelydecorative, aydn'sminores normally do not retain the harmonic structure of the theme,tending instead to.ards a simple first reprise closing in the relative maMor, then an intensifiedsecond reprise, as in variation * of the 74urprise 4ymphony %no =#, second movement, 1>=1+and the first movement of the 4onata in 9, h [V";#* %1>8#+ !he latter also opposes the

theme's improvisatory air, deriving from its fre:uent rests, to theminore's po.erfulcontrapuntal and suspension$laden development of its opening dotted rhythm in overture or


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preludial style "t is li6ely that suchminores provided the impetus for aydn's slo.movements in ternary % A#A+ form, in .hich the # section in the parallel minor varies ordevelops material from A he began .riting them the same year %1>8#+ in piano sonatas andtrios and developed them to a high degree in the -ndante of 4ymphony no 1F# %7@ondon +

and the first movement of the &iano !rio in h [V;*= 2nly rarely is there a fast concluding

section to a set of variations; op 33 no 5, h "V;*, and the fugue in op >E no E, and the codas oft.o symphony finales nos 31 and >* !he stereotyped concluding pattern of so many of

ozart's, a final -dagioA-llegro pair, the latter normally in a different metre, never appearsithin about 15 years %mid$1>5Fs toc1>>F+, aydn's variation types developed from

sets entirely in constant$bass variation to those that mi ed constant$harmony and melodic$

outline variation, until the last finally predominated !his process, .hich affected all of hisgenres, is most evident in the *1 baryton trios .ith first$movement variations -t about thesame time that melodic$outline variation came to the fore, aydn began to develop hybridtypes of variation based on recurrence and alternation, often in conMunction .ith thealternation of mode, in .hich recognition of the melodic theme is an important element of theform hile :uite a fe. composers varied one or more refrains in a rondo movement, aydn'srondos are often systematically rather than incidentally varied, to the point .here they can be

called 7rondo$variations or variations .ith episodes %e g A#A1.A *+ ?och's descriptionreinforces this point %4ersuch, iii, p 31#+ !he 13 movements of this type are most oftenfinales and slo. movements, but the three first movements reveal that variation rather thanrondo is the model !he latter include t.o piano trios h [V;*5 and 31 %although only the finalrefrain is a variation in the latter+, and the movement .hich furnishes the prototype for h[V;*5, namely the &iano 4onata h [V";3= !he .ell$6no.n 0 maMor &iano !rio h [V;*5 is particularly delightful, uniting a charming theme and variations .ith the rare feature of t.o

episodes in minor %parallel and relative, respectively, li6e the 4onata, h [V";3=+, the first of.hich sounds li6e a variation itself, the second li6e an episode

Virtually no$one but aydn .as dra.n to the idea of alternating variations on a maMorand minor theme % A#A1 #1 A* or A#A1 #1 A* #*+, and he made that form his o.n in *1movements and one independent set %Beicha modelled the description in hisTrait( de hautecomposition musicale, ii, 18*E, on aydn, although it does not tally .ith aydn's actual practice + !he very fe. precedents for this format, other than ) & #* ., i+, an -rietta con variationi in - included in @eopold


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ozart's %annerl %oten!uch %1>5=+ else.here attributed to agenseil, and the finale of I -]tepn's ) maMor 4onata op * no E %1>EF+ 2f aydn's younger contemporaries other than2ne element that might have appealed to aydn is the often close relationship bet.een thet.o themes; .hen they share melodic contour or rhythmic pattern, the second seems to be areaction to or interpretation of the first !hus, t.o themes of opposite character may findcommon ground by the end of the movement e .as also dra.n to Mu taposing tonic maMorand minor in successive movements and in the trios of minuets, in .or6s .ithout variationssuch as the 4tring Cuartet in ) op *F no * %1>>*+ and the &iano 4onata in < minor h [V";3*%1>>E+ 4ymphony no >F %1>>=+ e emplifies this trait .ith alternating variations in the slo.movement %the austere minor theme in invertible counterpoint is here unrelated to the t.o playfulmaggiores, and has the last .ord+ and a finale alternating chordal and fugal passagesfirst in the minor, then in the maMor oreover, the alternation of galant and learned style inthe slo. movement themes A the learned aspect underscored by the labelling of the A theme'smelody as 7canto fermo .hen it returns in the bass A is .rit large in the symphony as a.hole, .here the galant style of accessible sonata form and minuet in the first and third

movement alternates .ith the learned style of strict counterpoint and fugue in the second andfourth - uni:ue five$part alternating variation is the first movement of the &iano !rio h[V;1=, in .hich the fifth section is not a variation of A but rather a &resto sonata$forme pansion of the # theme aydn's richest si $part alternating variations, found in the slo.movement of the 79rumroll 4ymphony, no 1F3 %1>=5+, offer themes .ith contrasting scoring based on )roatian fol6tunes .ith similar opening bars "n the course of the movement eachta6es on some aspects of the scoring of the other !he only seven$part e ample of the form,

the celebrated Variations in ( minor for piano h [V"";E, is a revision of the original moretypical si $part form ending in the maMor aydn added a theme reprise and a lengthy,e traordinarily e pressive and chromatic coda to the already po.erful piece !he dar6$huedminor theme, .ith its ine orable dotted rhythms, registral shifts and dislocations and bruisingsyncopated Neapolitan chord to.ards the end, contrasts .ith the s.eet, even frivolous, maMortheme aydn's later reassertion of the po.er of the minor theme, attested by changes in theautograph, sho.s his desire to have the movement end not merely .ith melancholy but .ith

tragedy -lthough the piece fades to a .hisper, it contains some of his most dynamicallyvibrant piano music


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-fter 1>8F, aydn began to infuse variation into most of his slo. movements 2f thesymphonies from the &aris set on.ards, only the slo. movements of nos 83, =8 and == are.ithout significant variation is last strophic variation movement, the first movement of the4tring Cuartet op >E no E %1>=>+, e plores the constant$melody variation type found in threeother string :uartet movements of the 1>=Fs hile the beautiful 7?aiserhymn that aydnhad Must composed as the ne. -ustrian national anthem %70ott erhalte (ranz den ?aiser +seemed to call for this sort of treatment, the theme of op >E no E, on the other hand, isrepetitive, circular and rhythmically static %e 1Fa +, so there is a touch of amusement in thee aggerated .ay in .hich it is repeated; in overture style in variation *, .ith a moc6ing echoin variation 3 !he movement even ends .ith a .onderful -llegro fugato %.hosecountersubMect foreshado.s the countersubMect in the 7 roica finale+


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%1>8#+, each .ith five variations and coda, and that of the second movement of the &iano)oncerto 6#8* %1>85+, a rondo$variation !he themes of these last t.o are also rich ine pressive rhetorical figures and establish the idyllic pastoral .ind$serenade variation as animportant part of the concerto oeuvre

ozart's variation sets and movements .ere .idely 6no.n and admired during andafter his lifetime, as evidenced by contemporary accounts adducing the marvels of hisimprovising variations at the 6eyboard and by multiple editions of both independent sets andof piano arrangements of variation movements up to 181> 2ne of the sets most highly valued by ozart himself and his Viennese audiences has had a che:uered reputation in the *Fthcentury because its brilliantly rhetorical element has not been understood !his .or6, 6no.nas the Bondo in 9 maMor 638*, .as composed in arch 1>8* as a ne. finale to his earlier piano concerto 61>5 %1>>3+ "n sending a copy to his father %*3 arch 1>8*+, ozart notedthat it .as ma6ing a 7big noise in Vienna and .as al.ays greeted .ith torrents of applausehe as6ed that @eopold 7guard it li6e a 7ewel A and not give it to a soul to play J " composed it speciall for myself A and no one else but my dear sister must play it ozart continued to perform it for over a year, referring to it as a4aria)ion rondeau %4chmid, 1==*, adduces thetitle as evidence of a vocal origin of the theme+ "t is a theme and variations in .hich the firstreprise of the contredanse theme returns periodically li6e a ritornello or rondo refrain, as he

.as later to .rite in the piano variations 6E13 &ersuasively arranged, the sectional format ofthe movement has the ritornello recurring first after a single variation %the solo foil to the tuttiand thus the more personal signal of the genre+, then after t.o variations %each increasing thespeed of figuration+, then after three %each .ith an e pressive or characteristicreinterpretation;minore, scherzando .ith trill accompaniment, -dagio+ !he final ritornello isan -llegro in the triple metre flan6ing a real variation and a coda No other movement by

ozart asserts first genre, then technical strategy, then e pressive value; it is a rhetorical tour

de force4everal of ozart's improvised 6eyboard sets .ere later published, such as the ones

originating at a Viennese concert of *3 arch 1>83 %at the


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passages, t.o smaller and one fully fledged cadenza, bet.een the last four variations !heminore of variation # triggers the first of these .ith a change in phrase structure .hen the

melody returns to the opening in a ne. 6ey %- maMor+ rather than a return to the second

element %the theme isa!c! d , in .hich ! is a codetta toa, ! ', is on the dominant, andd is ashort conclusion+ here the short cadenza is -dagio and full of theminore's e pressive values!he scherzando trill variation E consists only ofa and ! and their varied repetition .ith thehands e changed %mirroring+ !.o altered bars and a short cadenza lead to a final variation in^tude style A triplets in right and left hand A in .hicha and ! are heard only once before thelengthy cadenza and coda based entirely on! !hus the last t.o and then the last threesegments of the theme are sheared off in the process of stripping the theme to its most

memorable elements!hat 63=8R#1Ee appeared in print so soon after its first performance suggests that

ozart may have changed it only little from the improvised form all the sources before 1>=8lac6 numbers for the variations and double bars bet.een them, suggesting the throughcomposition of an e tempore performance !he 0luc6 variations, on the other hand, came outmore than a year later and seem more highly crafted, especially in the .ays in .hich ozartdeparts from the strongly profiled unison descent from the tonic to the fifth degree of the scale

in the first four bars, .hether by substituting another melody completely %variation *+ or byfinding substitutes for the dominant chord on .hich it lands %as in variation #, .here everyversion of the phrase has a different chord and resolution+ - lengthy cadenza doubtless refersto its origin and perhaps increased the salability of such a .or6 by enabling the performer tomimic e temporization

ozart alluded to aydn's variations four times, and possibly used one as a model,during the 1>8Fs in Vienna !he variation movement from the ind 4erenade 63E1R3>Fa

employs a theme remar6ably li6e that in 4ymphony no >5 the minor variation of the sameserenade plays .ith the opening of the minor theme in aydn's 4ymphony no E3 %7@aBo elane + and the siciliana variation finale of ozart's 9 minor Cuartet 6#*1R#1>! dra.stogether the siciliana variation finale of aydn's 0 maMor Cuartet op 33 no 5 and ozart'so.n earlier 9 minor variations in a piano and violin sonata %63>>R3>#e, the si th variation of.hich is a siciliana+ (inally, one possible e planation for ozart's revision to the theme ofthe slo. movement of his &iano )oncerto 6#5F after he had already begun composing thevariations is that he realized that the material in the second reprise .as too close to his model,

aydn's 4ymphony no >5, .ith its triple$metre hymn theme 2ne classic locus for the


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inventio of a theme is in imitation of the theme of another, orimitatio, so this 6ind of homageis especially appropriate to variations

ozart's methods of organizing sets of strophic variations differ in nearly every particular from aydn's, but most obvious are cadenzas in 6eyboard sets and the .ay theychain variations together opposite$mode variations, especially the t.o movements in ) minor.ith t.o variations in t.o different 6eys %in the ind 4erenade 6388R38#a relative and parallel maMors, in the &iano )oncerto 6#=1 .ith submediant and parallel maMors the rondo$variation movement in the &iano )oncerto 6#8* also has relative and parallel maMor episodes+and the presence of an -dagio or an -dagioA-llegro pair 2f *= movements, *F haveopposite$mode variations %half in fourth position out of five or si +, seven have a penultimate-dagio variation, and 11 %including si of the sets .ith -dagios+ conclude .ith a faster andoften metrically altered variation ozart'sminore variations tend to be imitative, chromaticand highly e pressive, often .ith an air of mystery, as in the &iano )oncerto 6#53 or the9ivertimento for string trio 65E3

!he autograph of the 4tring Cuartet 6#E# supports the idea of a conscious plan for theordering of variations -fter completing five variations, ozart decided that the coda shouldincorporate the cello figuration of the fourth variation, and thus reversed the order of the lastt.o variations !he coda follo.ed the original fifth variation in the manuscript -t that point

the minore .as added and given the number #, and the original fourth variation .asrenumbered E !he real :uestion is .hy there .as nominore movement originally; .hat .asthe rationale of the original planZ "n fact, the most highly figured line in each variationdescends through the parts from first violin to cello until, .ith every register sounded, acontrapuntal epitome offers a summation, obviously intended to be the final variation %e 11+2ne other movement see6s to articulate its imminent close .ith a contrapuntal study, the slo.movement of the 9ivertimento 65E3, .hich has four variations and a coda ere the

contrapuntal variation is not imitative, as in 6#E#, but rather is a layered species e ercise in.hich the chorale$li6e cantus firmus, played by the viola, itself includes t.o different notevalues %minims and crotchets+ and represents the theme melody stripped do.n to a scale !hecello in semi:uavers creates a largely third$species relationship to the viola, .hile thedemisemi:uavers maintain a constant second$species relationship to the cello "n format, themovement resembles the ubi:uitous figure of refining %e?politio+ as described in the Ad ,erennium ; the theme e pressed simply, the theme e pressed in a ne. form %three$part

version in the varied repeats+, arguments from comparison, contrary and e ample %variations1A*, 3 and #, respectively+, and a conclusion that restates the theme


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2ther :uestions of ordering arise from the stri6ing finales to t.o piano concertos,6#53 %1>8#+ and 6#=1 %1>8E+ !he former has a labelled 7(inale after five variations ande tension, in .hich an entirely ne. &resto theme %of practically the same length as thevariation theme+ forms the first of five :uasi$paratactic segments, all of .hich containrepeated and sometimes varied material !hat these five segments might be intended to matchand sum up the theme and variations is suggested first by the resemblance of the finale themeand its piano reiteration to the tutti variation theme and solo first variation, and second by thereference of the moc6$seriousom!ra passages and ascending imitative se:uences .ithsuspensions to theminore !he finale of 6#=1 features alternation bet.een piano$dominatedand .ind$band$dominated opening periods and at the same time a 6ind of three$part form in.hich the 7middle section appears to develop aspects of the first, .ith a contrapuntal piano

variation alluding to the march$li6e variation 3 and themaggiore variations %# in - , E in )+,

developing the .ind$band sonority of variation * !he final section offers t.o variations.ithout repeats and a coda; the first is a melodic reprise uniting all instrumental groups andthe second has both a ne. time signature and a ne. au iliary$note motif from .hich the codadevelops

(i') !eetho'en.

"n .or6s by aydn and ozart, the decorum of a variation movement A its traditionaland hence normative technical and e pressive limits A depended upon position in the .or6,upon genre and upon the nature of the theme "n general, its implicit code included severaldifferent properties; ordering, in .hich simpler te tures appeared early in a set but imitative polyphony never did performance style, in .hich e tremes of orchestration and dynamics.ould be introduced for local contrasts, rarely as the topic of an entire variation and contrastand return, in .hich distantly related or contrasting material .ould be follo.ed by returns of

the theme melody (inally, the theme itself .ould observe certain properties, in its %usually+t.o$reprise phrase structure .ith clearly delineated phrases, its degree of repetition, andcontrast in melodic segments, rhythms and te tures -ll these properties devolve upon theconcept of familiarity and recognition, .ithout .hich, ?och said, 7Gthe variationsH give theimpression of a group of arbitrarily related pieces .hich have nothing in common .ith eachother, and for .hose e istence and ordering one can imagine no basis % Musi5alisches $e?i5on, 18F*+ !hus ==+, a grittycontrapuntal build$up starting in the cello .hich, by suddenly eradicating the harmony and


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registration of the theme, inserts a ne. level of difficulty into a previously more accessibleform

=FA=1+, .hich featured an imaginative arrayof both melodic outline and constant$harmony techni:ues and a .ide variety of pianofigurations and sonorities sometimes reminiscent of the thic6er and more contrast$orientatedmode of .riting for piano characteristic of such northern 0erman composers as ) ( (asch,I - & 4chulz and I 0 Pthel !he Viennese style in 6eyboard variations favoured thinnerte tures, as evidenced in the .or6s of such composers as ozart, Vanhal, ]tepn and?ozeluch (or his early Viennese sets, 3, 1>==+ concluding .ith an 7alla -ustriaca , E, 1>==+, in this ( maMor set are in 9 maMor, < maMor and ( maMor %-dagio+, follo.ed by an

-llegro fugue in the eighth variation .ith a chain of third$related 6eys after it reaches thedominant (or all his efforts, ho.ever, it .as reported % AM9 , 1>==, col EF>+ that 7he does notunderstand ho. to vary .ell in the same year aydn's ( minor Variations, Must published,received the comment 7varied as only a master can

!hat


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claims, mostly focussed on the demonstrably ne. elements in both sets; it has been suggested%?Pthen, 1=8#+ that the phrase 7.ir6lich gantz neue anier , ho.ever, .as intended as a parody of -ntoine Beicha's 7ne. 6ind of fugue in theLH Fugues dedicated to aydn in 18F3, %18F#A5+ adumbrates the traMectory of its beautifulhymn theme by combining the gradatio of register .ith that of rhythm in an arc$li6e shape,

.hile the finale of the maMor 4tring Cuartet op ># %18F=+, .ith a metrically ambiguous

theme, offers an alternation in dynamics .hich effectively groups the variations into piano forte dou!les in .hich the first of each pair is melody$orientated, the second more motivicand figural


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7resolving 9, future progressive developments are forecast; the follo.ing modulating episode

on - begins in maMor, develops the upbeat motif of the theme and generates the ne t round

of alternations, in .hich the # theme disappears and variations on A no. alternate .ith

fanfare episodes both on A and on the upbeat, each time beginning in and then modulating

through dar6er$hued 6eys !he tonal palette is e panded and the alternating principle ise tended to include the thematically derived episodic material, .hich is itself alternated togenerate the movement's clima "n the finale of the Ninth, chains of strophic variations onthe 7(reude theme are used to generate clima es as .ell, in the manner of the first section ofthe -llegretto of the 4eventh, a 6ind ofincrementum

"n chamber genres, F no * %18F8+, .here t.o consecutive variations of A interrupt

the alternations before an unusual ending in the minor "n the late 4tring Cuartet in - minorop 13* %18*5+, the ,eiliger +an5gesang apparently retreats from the progressive alternationof the symphonies in favour of the earlier five$part alternating model `et the movement isanything but aydnes:ue; the e traordinary modal polarities of the other.orldly A %chorale+sections set the stage for the deceptive yet emphatic tonal resolutions at the beginnings of the

virile # sections, .hile the tempo change is given a programmatic rationale %7Neue ?raftfPhlend + !he increasingly vigorous figurations of the already highly elaborated # sections become stile moderno foils to the gently accelerating contrapuntal figures of the stile anticovariation % A1+ and fugue % A*+ on the chorale


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episode .ith elements of a developmentalminore bet.een the ethereal fourth andretrospective fifth variations, the latter a conspectus of melodic reprise and t.o of the previous levels of rhythmic diminutions - comparable episode appears .ith even larger$

scale tonal resonances in op 1*>, because in that movement in - variation 3 is in maMor,

and the episode after variation # is in 9 R) minor, a connection reiterated in the coda !he

highly detailed part$.riting in variation 1, .ith its foretaste of ahler's -dagietto, isunprecedented in variations, as is the suspended$animation introduction, a slo.ly unfoldingdominant >th chord out of .hich the theme emerges very tentatively %e 1*+ "n op 131, thecentral variation movement has a role to play in the integrated design of the :uartet as a

.hole, beginning as the 7aria follo.ing the 11$bar third movement .ith its recitative$li6eclose &erhaps these suggestions of an earlier style prompted EFs %bars *3A# and 31A*+ and even, duringvariation 3 .ith its te ture of contrapuntal voice$pairs and false fugato, an ascending trio$sonata$li6e trill figure also found in the first movements of aydn's :uartets op *F no 1%copied out by


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opposite ends of the generational span, contributions from the elderly (Trster and 4chen6 andthe 11$year$old @iszt -s ?inderman's research has sho.n,


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itself into periphrastic figurations Virtuoso interludes and conclusions outside the variationchain assimilate the movement to the technically demanding cycle !he year 18*# sa. theornate "ntroduction and Variations onTroc5ne #lumen for flute and piano d8F*, the 4tringCuartet in 9 minor .ith slo. movement variations on +er Tod und das M;dchen, the 2ctet

.ith variations on a duet from +ie Freunde von alaman5a, and the - variations for piano

four hands, .ith its nod in variation 5 to the -llegretto of d

2f the composers ma6ing their name at the turn of the century .ho e celled atvariations, especially in the eyes of contemporary revie.ers, those .ho stand out are 4pohr%for violin, clarinet, harp and string chamber music+, ummel %mostly for piano but some inchamber music variations account for a :uarter of his published piano .or6s, some single

opus numbers containing up to three sets+, &rince @ouis (erdinand of &russia %for piano and piano chamber music+ and particularly eber, .ho .rote a number of variations on originalthemes and in ne. genres li6e the concertinos for clarinet and for horn, as .ell as on suchmuch$varied themes aschCne Min5a !hese last pieces have elaborate introductions, .hich.ere becoming more and more common, and lengthy lin6ed finales

!he 18*Fs and 3Fs sa. a vast increase in the number of sho.y variation sets for pianoon popular tunes tric6ed out .ith all manner of introductions, finales and virtuoso details in

such a .ay that they became nearly indistinguishable from the numerous fantasies on popularmelodies -lready under .ay in the 1>=Fs .ith 9aniel 4teibelt and -bb^ 0eline6, the trendaccelerated .ith the gro.ing concert scene in &aris, Vienna and , .ith contributions by @iszt, !halberg, )zerny, &i is, erz and)hopin "ndeed, the previous year sa. the publication of )zerny's $ art d improviser , in


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.hich ummel, oscheles, ?al6brenner and Bies are upheld as models, although the studentis also advised to study ozart's 635#R*==a, )lementi's variations on the same theme in the

finale of a < 4onata, and


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- more thoughtful typology from .ithin the 4chumann circle .as published in 18EF by the ># .hileadding fantasy$variations


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finale and the plagal maMor conclusion of 4chubert's 9 minor Cuartet 79er !od und dasYdchen !he slo. movement of op 3E, on the other hand, uses a floating, chromatic treble

theme .ritten much earlier %dedicated to )lara in a little poc6et noteboo6 of )hristmas ve185#, and sent to her t.o months later+ .hich fluctuates bet.een minor and maMor, opens

.ith a se:uence on " and V"", and opposes rising #ths and descending chromatic figures "n

short, the theme is sufficiently 7free for it to be varied strictly and still suggest fantasy, as inthe first variation, .hich sounds li6e a continuation of the theme .hile actually incorporatingaugmentation, diminution and a ne. bass line -fter t.o sets of paired variations %1A*, 3A#+,the second resembling the aggressive counterpoint of 3+ to the )larinet 4onata in op 1*F no * %18=#+, reveals ne. preoccupations and older

models of a different 6ind; finale variations .hich :uote the theme of the first movement to

bind the .or6 together %4tring Cuartet in < op E>, )larinet Cuintet op 115+ or serve to

conclude the .or6 .ith a slo. movement li6e E no Eand 4chubert's 7 anderer (antasy slo. movement %-dagio of the 4tring Cuintet in 0op 111+ !he 74t -nthony or 7 aydn Variations %the chorale theme .as not .ritten by

aydn+ .as probably the first independent set .ritten for orchestra and is .idely vie.edtherefore as and musette **+ )haracteristic variations, li6e thescherzando %5+ and siciliano %>+, are fe. !he embellished varied repeats of variation 3

contrast .ith the repeats in invertible counterpoint in # and .ith the added countermelody in


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8 "n the passacaglia finale, progressive diminution and e panding registers articulate theclose of this novel form "n the finale of the (ourth 4ymphony, on the other hand, .hich bearsa :uite different 6ind of .eight,


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#1 reaches a climactic level of scoring and dynamics !he &oco -dagio of his (ourth4ymphony, on the other hand, dra.s more on the variation groupings of + and the variations by Beger on themes by iller%op 1FF, 1=F>+ and ozart %op 13*, 1=1#+ 2thers, recalling such earlier .or6s as )hopin's

op *, add a featured solo instrument, such as !chai6ovs6y's Variations for )ello and2rchestra on a Bococo !heme %18>E+, (ranc6's4ariations s mphoniKues %.ith piano, 1885+or 9elius's Appalachia %18=E+, or adapt variations to a programme, as in 4trauss's +onQui?ote %also .ith prominent solo cello, 18=EA>+, d'"ndy's *star %18=E+ and lgar's 7 nigmaVariations %18=8A=+ 9vo 6 begins in


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theme is mar6ed simplymaggiore and its status .ith respect to the first and primary theme isunclear both are fully 7thematized versions of melodies heard in the introduction %9ulcinea,also heard there, returns in variations 1, 3, 5 and E+ .hich subse:uently appear varied bydivision and by other sorts of rhythmic and harmonic transformation as the programmere:uires /nli6eTill Eulenspiegel , a rondo in .hich the pran6ster's theme peeps out unvaried bet.een episodes of mischief$ma6ing, in +on Qui?ote the themes are incorporated into thesometimes precisely delineated action, from the adventures .ith the .indmills %variation 1+and sheep %*+, ending .ith Cui ote's death ore ruminative sections include theintroduction, .hich details Cui ote's process of derangement after reading 6nightly romances,and variation 3, a mad conversation bet.een 9on and s:uire

!he attention given to lgar's Variations on an 2riginal !heme op 3E has focussed primarily on the 7enigma contained therein, a .ord authorized by the composer to be placedin the score, alluding possibly to an un.ritten theme that goes 7through and over the .holeset , as .ell as a 7dar6 saying that 7must be left unguessed )ommentators on the .or6s,.hile assessing lgar's .ords and subse:uent theories, have also made clear %as did lgarhimself, and !ovey+ that the piece should be evaluated on its o.n musical terms %see Bushton,1===+ ach variation is a character portrait of someone close to lgar, including himself, andthe initials and other cryptic references that serve as headings to the variations have all been

identified !he ternary structure of the 0 minor theme, .ith a # section in the parallel maMor,loo6s ahead both to the fre:uent appearance of variations in the maMor %3, 8, 1F, 13, 1#, as

.ell as EA> in ) maMor and = in + and to the relatively greater importance of the melody of

the A section as a virtualid(e fi?e !hat melody, appearing in a variety of rhythmictransformations, in different registers, metres, tempos and instruments, has been the focus ofintense scrutiny both because of the contrapuntal possibilities suggested by the enigma and

because of its similarity to other melodies by lgar and to the second theme of the slo.movement of ozart's &rague 4ymphony "ts prominent chains of 3rds and ascending bassline have also dra.n comparisons .ith


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depression .ith a conversation about


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figurations in the !elemann set %on a theme from the MusiKue de ta!le+ seem stri6ingly

derivative, .ith


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4choenberg's contributions to the history of variation emerge from his .ritings andteachings as .ell as his compositions e identified variation as an important ingredient incompositional techni:ue generally %7developing variation +, and variation form seemedcongruent .ith the techni:ues of serialism "ndeed, his earliest set of variations, in the thirdmovement of his 4tring Cuartet in 9 %18=>+, reveals a progressive te ture already in thetheme, .hich begins .ith a single line opening out into t.o$part counterpoint %bars 5A8+ !histe ture, described as 7uni:ue in the variation literature %(risch,The Earl 6or5s of Arnold

choen!erg: =NL NO=, 1==3, p #3+, appears to conMure both .ith the chromatic lament bassin its initial iambic semitone descent and the tetrachord span of its first incise and .ith thecontrary$motion dynamic of the variation theme in the third movement of


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three notes %e A g A e + radiating through the te ture, first in minims, then in :uavers, sometimes

transposed and usually countered by chromatic scales !he singer has only one e posedstatement of the motif, in minims %bar 1F+, ironically to the te t 7versch.iegen %silently+ it

also begins her final phrase %bar *3+ &erhaps the note$based subMect foreshado.s the note$ based serial structures to come, first in the 7Variationen third movement of the 4erenadeop *#, .ith its 1#$note theme !hat the theme contains both the ro. and its retrogradeimmediately reveals the tension bet.een the ro. and the theme 4choenberg describes thevariations as using 7inversions and retrograde inversions, diminutions and augmentations,canons of various 6inds, and rhythmic shifts to different beats A in other .ords, all thetechnical tools of the method are here, e cept the limitation to only t.elve different tones

%7 y volution ,t le and *dea, ed @ 4tein, 1=8#, p =1+ !he variations in the 4uite op *=e acerbate the ro.Atheme issue by using a tonal melody, 4ilcher's Aennchen von Tharau

9uring the composition of the4ariationen f r 'rchester , op 31, 4choenberg .rote the!hird 4tring Cuartet op 3F %1=*>+, the -dagio of .hich still provo6es controversy -fter

r.in 4tein's published analysis of it as a theme .ith variations and alternations %fore.ord tothe &hilharmonia score, 1=*>+, 4choenberg asserted that the movement .as really a rondo2degard %1=EE+ supports the variation model, lin6ing it to aydn's alternating variations and

the contrasts of rhythm and mood in


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rhythms that remain memorable !he cellos begin the theme %the prime, of five bars, is givenin e 1Ea it is follo.ed by a transposed retrograde inversion, seven bars and a retrograde,five bars+, and for the last phrase they are Moined by the violins %transposed inversion, seven bars+ .hile they return to the transposed prime, thus lending a three$part construction .ith asense of return to the relatively symmetrical four$phrase theme !he focus is on finding motifsconnected to the theme and a play of topics relating to genre, mood or dance$type %variation *is 7chamber$music$li6e , 3 7stormy , # 7idealized .altz ;e 1E! + !he


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solilo:uy becomes more and more over.rought, but the theme, by contrast, is an eerily tonaland consciously archaic melody, in imitative te ture and .ith a hollo. 5th, to underscore the


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is repaid in a mature and compelling .or6 %!he passacaglia finale of emlins6y's 4ymphonyno *, 18=*A3, is clearly also indebted to


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variation to a part in a sonata structure; theme introduction, variation 1 main theme, * transition, 3 second theme, # reprise of main theme, 7ho.ever in the manner of adevelopment %7for it is an andante form , i e slo.$movement sonata form+, 5 7repeatingthe manner of the introduction and transition , E coda %see 3+ % e similarlydescribed the first movement of the 4tring Cuartet op *8 as variations in an adagio form +"ndeed, the 7first theme is the closest thing in the piece to accompanied melody, .hile the7second theme after a chordal transition presents the tiny motifs slightly more lyrically thanthe theme !he ro. itself %e 1>+ forms pitches EA1* as the retrograde inversion of 1AE, and

ebern identified the first si pitches %four in the double bass, t.o in the oboe, immediatelyretrograded so that t.o four$note motifs sound+ as the source of all the rest of the material %the70estalt to be subMected to 7metamorphoses , that is, variations but the theme itself is alreadya variation, itself a metamorphosis of the basic shape; letter to Ione, *E ay 1=#1+ `etdespite this s6ein of motivic development in formally recognizable groupings, eberndescribed the variations as in 7a :uite different style .ith an 7affinity .ith the type of presentation one finds in the Netherlanders , thus forging a ne. path .ith elements of anarchaic constructive principle

(ii) tra'ins y, "inde ith, !ritten.

4travins6y's eight variation movements on original themes are framed by the 70avotte

e due variazioni in Pulcinella and the orchestration of


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the final fugato variation 4imilar elements appear in his ballet scores % Jeu de cartes, 1=3E +anses concertantes, 1=#FA#*+ and other instrumental .or6s %)oncerto for !.o &ianos,1=3*A5 4onata for !.o &ianos, 1=#3A# E!on .oncerto , 1=#5+, even the serial 4eptet%1=5*A3+, a relatively strict passacaglia on 1E notes in the second movement !he oscillating3rds of the final movement of the E!on .oncerto appear unpromising material for a theme,yet al.ays stand apart rhythmically from the surrounding te ture only in the third and finalvariation are they treated .ith diminution, and the repeated chords of the theme'saccompaniment also become a subMect for variation 4travins6y's later variations increasinglyfeature disMunct themes, but from the beginning he treated his themes .ith octavedisplacement and instrument dispersal to recast the melody 4ometimes a fragment of thetheme appears as an ostinato during a variation %)oncerto, variation # +anses concertantes,variations 1 and 3 4onata, variation 1+ or becomes the subMect of a fugal variation %2ctet,variation > 4onata, variation 3+ !he )oncerto for !.o &ianos dra.s on aydn's model ofalternating variations in its third movement, though different melodic shapes obscure therelationships bet.een the first theme and its variations using the first theme as a subMect forthe fourth$movement fugue brings to mind


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pieces 7Vom !ode ariY -nother early .or6, the Viola 4onata op 11 no # %1=1=+, seems tohave a surfeit of variations; the movements are (antasie, !hema mit Variationen, (inale %mitVariationen+ !he (antasie acts as an improvisatory introduction and the finale introduces ane. theme .hich alternates .ith variations continuing from the second movement &erhapsthe connection of the fantasy .ith variations gave rise to indemith's more rhapsodicvariations of the 1=3Fs, such as the Philharmonisches @on)ert %1=3*+ and the finale of theviola concerto +er chwanendreher %1=35+ - stricter strand of melodic$outline variation.riting is evident in the variations on ozart's lied @omm: lie!er Mai that conclude the

onata Es ist so schCnes 6etter draussen8 op 31 no * %1=*#+ for violin indemith's mostimportant variation .or6, +ie vier Temperamente for string orchestra and piano %1=#F, also.ell 6no.n .ith


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is best$6no.n set of variations, theoung Person s "uide to the 'rchestra %Variations and(ugue on a !heme of &urcell+ op 3#, is, in the felicitous .ords of &aul 0riffiths %7Variations ,"roveH +, 7at once a tour of the forces and a tour de force @i6e the


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development section of the second movement the theme of the first movement appears 7inverYnderter 0estalt that the theme of the fourth movement is alluded to there as .ell that inthe recapitulation of the same movement the *R# rhythm of the e position is changed into 3R8and that in the finale the theme of the first movement is 7e tended from its original chromaticform into a diatonic one%e *F+ artmann .as similarly concerned .ith variation proceduresand presented large$scale forms as variants of each other is 4ymphony no E %1=51A3+, fore ample, concludes .ith a 7!occata variata of three fugues, in .hich the second t.o arevariants of the first 4hosta6ovich's variation movements include the passacaglia slo.movements of his string :uartets nos 3 %1=#E, unusual in that the theme is a lyrical melody,rather than a frame.or6+, E %1=5E+ and 1F %1=E#+ as .ell as the Violin )oncerto no 1 %1=#>A 8+ !he finale of 4tring Cuartet no * %1=##+ is a variation movement beginning .ith aconstant$melody build$up, .hich ma6es the remaining variations seem developmental in fact,all the movements of the :uartet are thematically connected and the variation movementalludes to the others -t the level of individual movements, ho.ever, it is unclear ho. todifferentiate bet.een cyclic procedures and variation techni:ues "f .e have managed toavoid the temptation to see variations in the thematic transformation of developmental andcyclic forms of 1=th$century music, then there is no reason to succumb to it for that of the*Fth

2ther notable variations of the second :uarter of the *Fth century include )opland'sastringent &iano Variations %1=3F, orchestrated in 1=5>+, about .hich the composer .rote 7it.as not composed in the consecutive order of its finished state J " .or6ed on the variationsindividually, not 6no.ing e actly .here or ho. they .ould eventually fit together 2ne fineday, .hen the time .as right, the order of the variations fell into place %)opland and V&erlis,.opland , i; NOO through N G, 1=8#+ the si th movement of emlins6y's 4tringCuartet no #, op *5 %1=3E+, subtitled 7


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variation .hile ac6no.ledging that 7sectional repetitions are interrelated solely through a fe. prominent motivic and rhythmic

+, in .hich the first painting isalready a variation 13 of the ne t 1= variations focus on the central figure, the "nfanta in a


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.hite dress, and one can see her face progressively dissociating in #A11 !he vista broadens before a 7theme reprise in **, .hich inaugurates a series of four variations on the entire picture !he rest of the variations concern the secondary figures, .ith the "nfanta returningonly as part of a larger ensemble %3EA8+ !his engagement .ith an earlier 7te t that createsvaried 7vie.s , and different perspectives of a model may be at .or6 in &aul @ans6y'si? Fantasies on a Poem ! Thomas .ampion %1=>8A=+, an electronic piece in .hich each fantasyuses the te t of the poem %7Bose chee6t @a.ra, come + read in its entirety to very differenteffect the .hole has an e traordinary overall shape and impact 5+, .hich gives the players instructions on ho. to use selected parts of the %unplayed+ theme so that each of the three variations unfolds as a process, a 7self$regulating and self$generating system "n the first %7(ullness of ind +, each player's tempois decreased, .ith the rate of decrease governed by the instrument's register %bass slo.+ "nsome respects this resembles -rvo &Yrt's.antus in memoriam #en7amin #ritten %1=>>A8F+, in.hich all the strings ine orably descend the - minor scale .ith the upper strings moving

much faster than the lo.er, and each progressively slo.ing Bochberg's variations on&achelbel's canon in his Cuartet no E %1=>8+, by contrast, maintain the structure of the themeeven .hile moving far a.ay from and then bac6 to.ards its style -n entirely differentapproach to the historical sense of 7Variations on J animates auricio ?agel's4ariationenohne Fuge for orchestra %1=>1A*+, a peculiarhommage & #rahms that 6eeps the phrasestructure and rhythm of the andel Variations .hile changing their harmony and ordering %*,1=, *1, 3 etc + the effect is rather li6e a smear of sound over a distanced but recognizable

original -s in -le ander 0oehr's Variations on the 4arabande from E+, .ith its mi of 18th$ to *Fth$century styles in different characteristicvariations the theme, a ballade, is in the centre of the set

!he idea of repetition in combination .ith gradual change ma6es problematic the

relationship bet.een the minimalist musical style of the 1=>Fs and 8Fs and variations Verytiny ostinatos produce the feeling of pulsations rather than structures to be varied 4ome


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pieces in a minimalist style or aesthetic do reveal a more structural approach, ho.ever,especially .hen governed by a te t, as in 4teve Beich'sTehillim %1=81+, .hich sets four psalms !he first presents strophic variations at each te t repetition, .ith canons, elaboratevocal overlapping and interplay and increasing comple ity, then d.ells almostdevelopmentally on t.o$ or three$line segments, finally returning to the entire te t in a set ofrecapitulatory variations !he last psalm uses incantatory canonic repetitions .ithin eachstanza .hile retaining the strophic form until the coda Beich's4ariations for 6inds: tringsand @e !oards %1=>=+ ma6es three increasingly comple statements of a long harmonic progression into a stretched chaconne

"ndeed, contemporary progeny not only of variations but of its older forms continue toe ert fascination, as they did in the early *Fth century ario 9avidovs6y's.hacona forviolin, cello and piano %1=>1+ is based on a regularly recurring pattern of durations 0eorge

d.ards's +raconian Measures %1=>E+ and.)eched wing %1==#+ maintain an element ofharmonic structure in each variation, .hile in the latter, as in Mazz, the bars may be variable inlength but every variation has the same number of bars ovements in larger .or6s alsoadopt an updated 7constant$harmony chaconne type; the slo. movement of !ippett's &iano4onata no 3 %1=>*A3+ varies 1> chords in Iohn arbison's 2boe )oncerto %1==1+, the&assacaglia middle movement maintains a sarabande$li6e tread and harmonic structural

elements especially in the tutti sections, .hile the solo sections are either connected to thesubstructure or more freely rhapsodic in !homas -dUs's.oncerto conciso for piano andorchestra %1==>+, a seven$bar chordal theme underlies theciaconetta slo. movement 2thercomposers interested in older forms of repetition include +,4chnitt6e %passacaglia+ and ?ernis %7ground + llen .ilich's &rologue and Variations %1=8#+uses 7prologue in place of 7theme %e **a +, in the sense of the introduction to the

7characters in a drama, here represented by different musical motifs and te tures over E= barsof -ndante misterioso the four variations develop no. one, no. another of these aspects.ithout maintaining a structural resemblance %1F*, *E, 8E, #* bars respectively, at -llegro%e **! +, @ento, &resto, !empo "+ - loo6 at these and other remar6s composers ma6e abouttheir variations suggests a self$consciousness about claiming 7true variation status, especially.hen the structure of the theme is changed, even .hen they use the title !his reveals thetenacity of the model both as a sense of limitation and as a testing$stone for the compositional

imagination


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