Chorales in J. S. Bach s Pedagogy: Recasting the First Year Undergraduate Music Theory Curriculum in Light of a New Source

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1 Chorales i J. S. Bach s Pedagogy: Recastig the First Year Udergraduate Music Theory Curriculum i Light of a New Source DEREK REMEŠ spired by ew evidece about J. S. Bach s teachig method, this article offers a historically iformed perspective o teachig part writig while strivig to achieve the College Music Society s curricular goals of itegratio, creativity, ad diversity. The key is a emphasis o trasferrable skills, which are hoed i the simplified cotext of hym tue harmoizatio ad the applied to more diverse settigs through aalysis ad model compositio. Trasferrable skills sharpeed i this method rage from basic (figured bass, chord spellig, voice-leadig, harmoic aalysis, ad vocal ad keyboard experiece) to more advaced (formal ad cadetial aalysis, orametatio, compositio with compoud melody, ad reductive aalysis). The resultig method is historically iformed, pedagogically appropriate, iterally cosistet, fudametally musical, ad always cotextualized. Ý troductio Log-stadig curricular assumptios i music theory ad musicology have bee icreasigly questioed i recet decades i favor of a more culturally iclusive ad less techical curriculum. We see such cocers raised i the 201 College Music Society (CMS) maifesto (Myers et al. 201), umerous articles, 1 ad i recet curricular chages at Harvard. 2 Part writig, ofte described as uecessary ad outdated, is oe of the most commo targets i this debate. For istace, the CMS maifesto states that both the effectiveess of [four-part, Bach-style part writig] ad the arrow horizos toward which it aims eed to be carefully assessed from a cotemporary, creative vatage poit (Myers et al. 201, 3). Ad Kulma ad Naxer (201) write that musicias i the past cetury have moved beyod part writig as the oly model of good music makig. [A moder] view of music history ad style requires a more geeral approach, ad de-emphasizes the cetrality of eighteethcetury part writig. Clearly part writig ad other traditioal music-theoretical 1 See Schubert (2011), Freema (201), Covach (201), Kulma ad Naxer (201), Lowe (201), ad Richards (201). 2 As of fall 2017, the traditioal theory ad history sequeces at Harvard are o loger required of music majors. See Leifer (2017) ad Robi (2017).

2 Joural of Music Theory Pedagogy olume 31 (2017) topics lay i the crosshairs of curricular reform. So, Why lear part writig? What use, if ay, does it serve today? To aswer these questios, let us begi with the CMS maifesto s laudable pillars of itegratio, creativity, ad diversity (Myers et al. 201, iii). accordace with these goals, propose a method of teachig part writig that aims to itegrate various basic skills i order to eable creativity later i diverse cotexts. roically, this ew method does ot take a more geeral approach, as Kulma ad Naxer propose, but istead has its roots i the most traditioal of sources: J. S. Bach s chorales. argue that chorales are ideal tools for teachig trasferrable skills. A focus o trasferrable skills is amog the best strategies for preparig studets to succeed i our pluralistic musical culture, because o sigle curriculum ca teach everythig that each studet eeds. But before a cocept ca be trasferred to a ew cotext, it is helpful to itroduce the idea first i a simple eviromet. This eviromet fuctios like a coceptual home base agaist which to uderstad other styles. 3 However, this pedagogical strategy, which relies o a stable stylistic referece poit (chorales), works agaist the importat goal of curricular diversity. To couteract this, supplemet my part writig method with the aalysis of a diverse rage of music. this way, aalysis defied here as the recogitio of a patter i a ew cotext is the studet s first act of trasfer. Similarly, model compositio is aother, more creative act of trasfer. Therefore, at the ceter of my proposed curriculum is the iterplay betwee part writig, aalysis, ad compositio as tools for promotig itegratio, creativity, ad diversity through trasferrable skills. Example 1 outlies this iterplay more specifically. Hym tues (i.e., moder chorale melodies) ad the aalysis of a wide rage of repertoire form the axis aroud which umerous other toal theory topics revolve. Like J. S. Bach s teachig, this first-year curriculum begis with figured bass, show here at the 12 o clock positio. But the more sigificat similarity with Bach is the use of outer-voice frameworks (as described below), together a harmoic outlook iformed by eighteeth-cetury Germa figured-bass theory. Begiig at 12 o clock i Example 1, my two-semester curriculum proceeds clockwise through progressively more advaced topics, 3 My itet is ot to suggest that Bach s chorales are the fout from which all other styles ad geres sprig (as his studet Kirberger believed). Rather, i my experiece, studets beefit from cosistet, cocrete poits of referece, ad chorales are useful tools i this regard. t should be oted that the CMS maifesto was i part respodig to the chagig eeds of music curricula which ofte serve o-musicias. The method proposed here is iteded for the professioal traiig of future musicias (be it at a coservatory or elsewhere), ot for music appreciatio courses.

3 Derek Remeš Chorales i J. S. Bach s Pedagogy 7 Formal aalysis Figurated Textures No-chord Toes Modulatio (Commo chord/direct) Model Compositio Figured Bass HYMN TUNES & ANALYSS Sequeces (Harmoic/Melodic) Applied Chords Outer-voice Frameworks/Cos. vs. Diss. Harmoic Fuctio/Sytax Harmoic aalysis (RNs) oice Leadig/Ted. Toes Cadece Types Harmoic Paradigms Example 1 Hypothetical First-Year Toal Theory Sequece Revolvig Aroud Hym Tues ad Aalysis. cocludig with model compositio. Some readers may feel a year is too log to wait for compositio, especially i a curriculum which supposedly values creativity. My persoal experiece, however, has bee that studets are too ofte asked to be creative before hoig the techical parameters to eable creativity i the cotext of model compositio. The results are ofte mediocre, i part because of a lack of restrictig guidelies. Hym tues, which act as a curricular through-lie i my method, are a ideal eviromet for itroducig the techical parameters ad guidelies to eable creativity, because hym tues are simple, sigable, playable, complete pieces of music that evertheless coform to pedagogical eeds. That is, hym tues are like miiature laboratories where itroduce theoretical cocepts first i a simplified cotext, later applyig ad developig these cocepts i the aalysis of at times drastically differet repertoire. Though this article focuses primarily o my part writig method, aalysis also occurs i tadem with part writig throughout my oeyear curriculum. Aalysis ca ecompass ay kid of music the guidig idea is simply that the hym tues itroduce the aalytical parameters. sum, my curriculum takes Bach s outer-voice part-writig method as its startig poit ad uses hym tues to cosolidate may basic theoretical topics i a itegrated way, later applyig these cocepts more creatively i aalysis ad compositio. Thus far have made strog claims for what may seem like a rather uorigial method. As we will see, my approach borrows ideas from may sources, but it also differs have tried to list the topics i Example 1 i order of icreasig difficulty, but aturally oe may choose to order them differetly. The reader may woder why a method that claims to be rooted i J. S. Bach s pedagogy does ot use the same chorale melodies that Bach used. describe my reaso for preferrig more moder hym tues i Part below.

4 8 Joural of Music Theory Pedagogy olume 31 (2017) from curret part writig methods i at least seve importat ways: 1) my approach uses hym tues, which are toally closed, complete pieces of music, ot fragmets; 2) ulike Bach s chorale melodies, the hym tues use lack o-chord toes ad are ever modal, which simplifies the harmoizatio process; 3) ulike Bach s chorales, hym tues are ofte periodic or setetial, allowig for simple formal aalyses; ) ulike may part writig exercises today, hym tues are especially desiged for sigig ad are simple eough to play at the keyboard sigig ad playig keyboard are both importat trasferrable skills; ) i my method, studets work either from a outer-voice structure or a melody, ad are ever asked to simply compose a chord progressio out of othig; ) my hym harmoizatios costatly recycle five voiceleadig patters which serve as chuks (see Exx. 13 ad 1), ecouragig patter recogitio; ad 7) my method borrows from eighteeth-cetury Germa figuredbass theory by focusig o bass scale degrees as harmoic determiats. Therefore, the resultig method is cotextualized (1), relatively simple (2), coducive to formal aalysis (3), fudametally musical (), cocrete (), iterally cosistet (), ad historically iformed (7). The impetus for the developmet of this ew method was the recet re-idetificatio of a source from Bach s studets. Part : Bach s Method ad a New Source Harmoic aalysis of Bach s published vocal chorales ad harmoizatio of chorale melodies have bee maistays of theory ad compositio classrooms for ceturies. However, a recetly rediscovered source suggests that we ca come closer to imitatig Bach s method (Leaver 201). 7 The aoymous mauscript, held i the Eastma School of Music s Sibley Music Library, likely origiates from Bach s studets i Dresde from about 170. The Sibley Choralbuch cotais 227 figured-bass chorales ad may be a copy of the chorale book Bach used with his studets (Leaver 201, 31). This fidig implies that Bach bega his studets ot with the harmoic aalysis of orameted chorales, as we ofte do today, but with the realizatio of figured-bass chorales i a simple, uorameted, homophoic maer that call the Choralbuch style. This term is iteded to differetiate the homophoic, keyboardorieted style from Bach s more orameted vocal chorale settigs, or Choralgesäge. 8 7 The Sibley Choralbuch was already kow to Has-Joachim Schulze (1981), but Schulz idetified it as ot comig from Bach s studets. See Remeš (2017). 8 C. P. E. Bach uses the word Choralgesäge i his publicatios of his father s vocal chorales. stead of Choralbuch ad Choralgesag, Leaver (2001) calls these styles keyboard ad vocal because of the settigs i which they occur i Bach s writigs. prefer the former ames because do ot wish to

5 Derek Remeš Chorales i J. S. Bach s Pedagogy 9 describe the Sibley Choralbuch ad Bach s pedagogy i greater detail i Remeš (2017), which is summarized below. We kow figured-bass chorales featured promietly i Bach s teachig because of Emauel Bach s descriptio of his father s pedagogy: compositio [J. S. Bach] started his pupils right i with what was practical, ad omitted all the dry species [i.e., decotextualized exercises] of couterpoit that were give by Fux ad others. His pupils had to begi their studies by learig pure fourpart thoroughbass. From this he wet to chorales; first he added the basses to them himself, ad they had to ivet the alto ad teor [Stage 1]. The he taught them to devise the basses [ote the plural] themselves [Stage 2]. He particularly isisted o the writig out of the thoroughbass i parts [Aussetze der Stimme im Geeralbasse]. [Presumably later,] teachig fugues, he bega with two-part oes, ad so o. / The realizatio of a thoroughbass ad the itroductio to chorales are without doubt the best method of studyig compositio, as far as harmoy is cocered. 9 This descriptio suggests that Bach used chorales i two stages, as outlied i Example 2. Stage 1, the studet receives a chorale melody, basslie, ad figures, ad supplies the ier voices. Later, i Stage 2, oly the chorale melody is give ad the studet supplies the basslie, figures, ad ier voices, ofte supplyig multiple basslies to a give chorale melody. 10 STAGE 1 STAGE 2 STUDENT RECEES STUDENT PRODES PEDAGOGCAL FOCUS TYPES OF SOURCES Chorale, Basslie, ad Figures er voices Texture Sigle-Bass Sources Chorale oly Basslie, Figures, ad er voices Harmoy & Two-oice Couterpoit Multiple-Bass Sources Example 2 Overview of J. S. Bach s Two-Stage Pedagogical Method ad Source Types. imply that each style is ecessarily boud to a specific istrumet, though it ofte is. 9 Wolff (1998, 399), commetary added by the author of this article. terestigly, C. P. E. makes o metio of chorales i his ersuch über die wahre Art das Clavier zu spiele (173/2). Heirich Christoph Koch, however, describes may styles of settig chorales i the sectio titled O Couterpoit i his ersuch eier Aleitug zur Compositio (1782, ). 10 Sarah McCormick (201) surveys the majority of kow multiple-bass sources from Bach s studets.

6 70 Joural of Music Theory Pedagogy olume 31 (2017) As already metioed, we ca geeralize two styles of chorale harmoizatio. 11 The Choralbuch style (homophoic, keyboard-orieted) correspods to that of the Sibley Choralbuch, as show i moder trascriptio i Example 3. geeral, the Choralbuch style is more triadic, cosoat, disjuct, diatoic, vertically orieted, has a half-ote pulse, is ofte improvised at the keyboard, ad is used for orga cogregatioal accompaimet where oly the chorale is sug. cotrast, Example presets Bach s Choralgesag settig (orameted, vocal-orieted) of the same chorale from Catata 1. The Choralgesäge use more dissoat figures, suspesios, ad faster values, are more cojuct, chromatic, horizotally orieted, have a quarterote pulse, ad are writte out for cocerted music where all four voices are sug. Choralbuch Style (homophoic) Example U Tue Source: Selecker's (Leipzig, 187) U # w # w & # # C # w w U C w w # # Nu laßt us Gott, dem Herr e, - Dak sag - e ud ihm ehr e?# # Ë B # # 7 7 # # U U # w w w w & # #?# U # # w w # w o weg e - sei er - Gab e, - Die wir emp fag - e - - hab e. # # # Ä2 # U w U w "Now let us give thaks to the Lord ad hoor him o accout of his gifts which we have received." 3 Nu laßt us Gott dem Herre for Keyboard from the Sibley Choralbuch (ao. ms., likely Dresde, ca. 170). Choralgesag Style (orameted) S. A. T. B. Origial Key: G major. Text replaced for compariso with Ex & # # # U U U U c Nu laßt us Gott, dem Herr e, - Dak sag - e - ud ihm ehr e - o weg e - sei er - Gab e, - Die wir emp - fag e - - hab e. & # # # c U U U U j j # # # Nu laßt us Gott, dem Herr e, - Dak sag - e - ud ihm ehr e - o weg e - sei er - Gab e, - Die wir emp - fag e - - hab e. # # U U U U & # c # # J J Nu laßt us Gott, dem Herr e, - Dak sag - e - ud ihm ehr e - o weg e - sei er - Gab e, - Die wir emp - fag e - - hab e.?# # c U U U U # # # # Nu laßt us Gott, dem Herr e, - Dak sag - e - ud ihm ehr e - o weg e - sei er - Gab e, - Die wir emp - fag e - - hab e. Example J. S. Bach s ocal Settig of Nu laßt us Gott dem Herre from Catata BW 1, O heilges Geist ud Wasserbad. 11 Ulrich Kaiser (2002) makes a similar pedagogical divisio betwee Katioalsatz (homophoic, as exemplified by Heirich Schütz) ad Choralsatz (orameted, as exemplified by J. S. Bach s vocal chorales).

7 Derek Remeš Chorales i J. S. Bach s Pedagogy 71 sum, Bach s two-stage method begis with a outer-voice figured-bass structure while studets supply the ier voices. Later, studets write multiple basslies ad harmoizatios to a give chorale melody. The goal of each stage was likely to provide a pedagogical bridge betwee Choralbuch to the Choralgesag styles through icreasigly embellished realizatios. Part : Adaptig Bach s Method for Today s Classroom To adapt Bach s method for the today s classroom, preset hym tues i five ways. 12 They form a sequece of icreasigly difficult part-writig activities i order to build creative idepedece o a small scale. begi with a complete harmoizatio, which acts as a model. Each subsequet type removes a support, first omittig the ier voices, the the harmoic aalysis, ad fially, the basslie. Thus, the five ways imitate Bach s Stages 1 ad 2. This sequece requires the studet to take o first more aalytical ad the more creative decisio-makig resposibility. Creative freedom culmiates i the still relatively restricted eviromet of the model compositio project (Part ). Later compositio projects i year two are of course ecessary. The fifth ad fial way of presetig hym tues is the solutio with full realizatio ad aalysis. Example outlies the five ways of presetig hym tues i the classroom, which desigate Types. The types progress through the preparatory model (Type 1), the easiest activity (Type 2), the itermediate activity (Type 3), the target activity (Type ), 13 ad fially the solutio (Type ). Studets receive a variety of differet hym tues at each stage use the same tue i the followig examples oly for demostratio purposes. Teachers might itroduce a hym tue i Type 1 durig class ad assig it as homework to aalyze, play, ad sig. Later, whe studets are ready, they ca begi Type 2 ad so o. At each stage, the aswer (Type ) ca provide quick correctio ad a poit of departure for discussio, though there are sometimes multiple correct solutios. 12 My website provides a freely accessible database of hym tues for use i my proposed curriculum ( All tues are orgaized ito five types ad employ the same set of harmoic paradigms ad cadeces throughout with slurs idicatig phrase divisios (i order to simplify harmoic aalysis). 13 Oe reaso that Type is a appropriate target activity is that the additio of a basslie to a give melody is the mai compoet of the Free Respose Questio 7 o the Advaced Placemet (AP) Music Theory Exam.

8 72 Joural of Music Theory Pedagogy olume 31 (2017) TYPE DFFCULTY STUDENT S GEN STUDENT PRODES 1 Preparatory Four voices oly Figures ad Roma Numerals 2 Easier Outer voices with Figures ad Roma Numerals er voices 3 termediate Outer voices with Figures Roma Numerals ad er oices Target Activity Soprao oly Alto, Teor, Bass, Figures, ad Roma Numerals /a (solutio) Four voices, RN s, figures, formal labels Nothig (for modelig, correctio, ad sigig) Example Five Ways of Usig Hym Tues i Today s Udergraduate Theory Classroom. Examples through 10, all of which use the same hym tue (agai, merely for demostratio purposes), correspod to the five types i Example. Example demostrates the preparatory Type 1, where studets are give a four-voice realizatio as a model ad supply oly the figures ad Roma umerals. Here the studet becomes familiar with hyms through sigig, playig, ad harmoic aalysis (figured bass plus Roma umerals). A formal aalysis is optioal i Type 1. Example 7 illustrates the preparatory Type 2, i which studets compose oly the alto ad teor voices to a give outer-voice framework that icludes a harmoic aalysis. Phrases, which are always marked with slurs, begi with give complete, four-voice chords. By startig i the same positio, studets solutios are more likely to correspod with the give aswer, streamliig both realizatio ad gradig. 1 Example 8 shows Type 3, the itermediate activity, which resembles the give outer voices ad figures i Bach s Stage 1. Type 3 differs from Type 2 oly i that the Roma umerals are ot give. Here studets supply the ier voices, Roma umerals, ad formal aalysis themselves. Example 9 displays Type, the target activity, ad is similar to Bach s Stage 2, i which he oly provides the chorale melody. ( describe the process of addig a basslie to a give chorale melody i Part below.) Example 10 gives the full solutio, or Type. 1 Admittedly, the solutios are 1 Some may object that givig the startig chord of each phrase makes it too easy. f this is the case, the simply assig more exercises or bump studets up to Type 3 or. My philosophy is to to make tasks easier i the begiig stages so that studets perceive their progress more readily. 1 The solutios for Type iclude fuctio symbols because believe they are helpful to studets whe combied with the idetificatio of the bass scale degree, show as a superscript. The dual fuctio of a harmoy i a commo-chord modulatio is show with two adjacet symbols. would ot require that studets add fuctio symbols i Types 1 ; iclude them i the aswers simply for referece.

9 Derek Remeš Chorales i J. S. Bach s Pedagogy 73 somewhat cluttered, but this is a byproduct of their aalytical comprehesiveess. Evetually studets ca describe every aspect of each hym a miiature compositio usig figured bass ad Roma umerals, 1 as well as labels for cadeces, harmoic paradigms (see Example 13), sequeces, modulatio, ad form. Most importatly, studets gai a ituitive sese of these cocepts through the physicality of sigig ad playig keyboard. Both are ivaluable because they provide studets with immediate aural feedback, helpig to match a harmoic pheomea with a aalytical label. also advocate for self-accompaimet at the keyboard i private. 17 HOMOPHONC &b j J j J Tue: j MORGANSGATE J? b j J j J j J 9 &b j J #? j 13 J j J # j b J j J j J Example Type 1 Studet supplies figures ad Roma umerals (optioal: form aalysis). Tue: MORGANSGATE & b j j j? b J J J F Major: 7 vi 3 3 vi &b j j j? b J J J # # ii Example 7 Type 2 Studet is give outer voices, figures, ad RNs; studet supplies the ier voices (optioal: form aalysis). 13 ii iii vi ii vi vi C: vi ii vi ii 8 7 F: 1 use a arrow to poit to a secodary domiat s resolutio. This is problematic, however, i the case of a deceptive resolutio. the latter case would use slash otatio (e.g., /vi). 17 My harmoizatios are i chorale style, where the teor is writte i the bass staff ad is geerally lower tha i keyboard style, where it is writte i the upper staff. Chorale style is difficult for o-

10 7 Joural of Music Theory Pedagogy olume 31 (2017) &b j j j? b J J J Tue: MORGANSGATE &b j j j? b J J J # 3 # 7 Example 8 Type 3 Studet is give outer voices ad figures; studet supplies RNs ad ier voices (optioal: form aalysis). &b j j j? b &b j j j? b (setece) 9 A &b? b a Dec. Motio 7 Example 9 Type Studet is give the melody oly ad supplies the lower three voices, figures, ad RNs (optioal: form aalysis). Stepwise- Bass Cad. Pedal / a' HC j J j J A2 sequece j J j J b Tue: MORGANSGATE 8 7 Tue: MORGANSGATE Cad. / PAC i j J j J Fuctio Symbols: T1 D7 D TS D7 (setece) oice Exchage 9 vi T1 T1 10ths Log Way Parallel 10ths vi D7 TS D (reversed) PHC i vi A' a'' HC & b a''' j J j J #? b j J j J 3 ii # T3 S ii iiii vi # j J j J vi 13 A2 sequece # S vi b' ii S2 D C: 7 T1S vi vi ii S2 D ii F: T1D PAC i T1 S S T1 D T1 S T3 D2 T1 SS D T1S S S D7 D T1 S S D T1 Example 10 Type Full solutio (for modelig, correctio, sigig, ad playig). keyboardists to read ad to play, which is a hidrace to self-accompaimet. Should chorale style prove too difficult, studets ca sig oe voice while playig two others.

11 Derek Remeš Chorales i J. S. Bach s Pedagogy 7 Part : Summary of Supportig Topics The outer rim of Example 1 icludes what call supportig topics. These aalytical topics form the studets itroductio to the techical parameters which eable creativity i the cotext of model compositio: vocal rages, / chords, harmoic paradigms, the Big 2, cadece types, o-chord toes ad oramets, ad formal aalysis. Before explai these further, wish to emphasize that my defiitios outlied below do ot claim applicability for all styles of music. Rather, they hold true most of the time i the artificial pedagogical cotext of my origial hym harmoizatios. However, as will show at the ed of Part, the ed goal of aalysis is evetually to break out of this artificial system so that studets ca grapple with the ways i which composers depart from expected orms, thereby producig expressive effects. 1) ocal Rages: Though the outer voices are give i Type 3 (i effect reducig the chaces studets will exceed vocal rages), still cosider it importat for studets to kow the rage of each voice part. Example 11 proposes a simplified model of SATB rages that makes them easier to memorize: each rage is a octave plus a sixth, ad the soprao/teor ad alto/bass pairs relate by octave. (For this simplicity am willig to sacrifice a alto rage that goes too low ad teor that goes too high.) & Soprao: Alto: Teor: Bass: &?? Example 11 Simplified ocal Rages for Part Writig. 2) / Chords: Example 12 illustrates types of / chords. focus o the same three types that Nadia Boulager taught her studets: eighborig (i.e., pedal), passig, ad cadetial. 18 All of my hym harmoizatios use oly these three types. recommed that studets practice writig, sigig, ad playig these three /-usages i isolatio i a few differet keys as a preparatory activity to Type 1 exercises, i which studets ca later practice idetifyig these / chords i Type 1 exercises. Note that the upper three voices of Example 23 are ivertible at the octave. 18 Nadia Boulager s teachig is preserved to some extet by her log-time studet, Narcís Boet. See Boet (200, ). For a thoughtful recet reassessmet of / chords, see Temperley (2017).

12 7 Joural of Music Theory Pedagogy olume 31 (2017) &? 3 C Major: Upper three voices (S, A, T) are ivertible. Neighbor (Pedal) oice Exchage/Passig Cadetial order to help studets uderstad the harmoic sytax outlied i this curriculum, the teacher should emphasize that / harmoies rarely receive their ow Roma umeral (or fuctioal symbol) because they are dissoat cotraputal elaboratios. 19 This is also true of the cadetial /; eve though the Roma umeral is placed uder the / figure, it actually applies to the /3 harmoy. The iterval of a fourth i the cadetial / is always some kid of o-chord toe: either a suspesio, passig toe, or appoggiatura (i.e., icomplete eighbor). 3) Harmoic Paradigms: The passig / also serves as oe of the three voiceleadig paradigms i Example 13, the other two beig Parallel 10ths 20 ad 10ths the Log Way. Like schemata, paradigms idetify commo voice-leadig patters. 21 Together, the five patters i Examples 12 ad 13 help simplify the harmoizatio process because they occur over ad over i my collectio of hym tue harmoizatios. f studets ca recogize the outer-voice scale degrees, keepig i mid the possibility that the upper voices are iverted (but usually ot i my harmoizatios), it becomes easier to fill i the ier voices through the process of chukig. 3 Example 12 Three Types of / Chords (Boet 200, ) Advaced studets may be curious to kow why this is so. Without goig ito the cotroversial status of the fourth throughout music history, have foud it helpful to explai that fourths that iclude the bass are cosidered primary ad therefore dissoat, whereas fourths betwee uppervoice are cosidered secodary ad therefore are tolerated. 20 While the Parallel 10ths paradigm icludes a dissoat /, make a exceptio to my abovestated rule ad do iclude a Roma umeral ad fuctio symbol for this chord. Note also the ostadard figured-bass symbol for the cadetial / resolvig to a /2 chord i Example 1. have foud that studets struggled to compose upper voices to this progressio because of the chage of bass. For this reaso, prefer the otatio: /-//2. The two horizotal lies (- ad -) idicate the motio of idividual voices above the bass ad clarify the uusual circumstace that the dissoat fourth resolves to aother (augmeted) fourth. 21 Paradigm is roughly equivalet to schema i its focus o outer-voice scale degrees, but lacks the latter s cogitive cootatios.

13 3 &? 3 oice Exchage/Passig C Major: Derek Remeš Chorales i J. S. Bach s Pedagogy 77 Upper three voices (S, A, T) are ivertible. Parallel 10ths Example 13 Three Primary oice-leadig Paradigms. 3 10ths the Log Way ) The Big 2 : Example 1 presets the Big This table aims to simplify the harmoizatio process by limitig the available chords. As i Heiiche s 1728 treatise, Geeralbass i der Compositio (which Bach kew), the scale degree of the bass voice provides the primary orgaizig factor i this table (give across its top row). 23 Yet ulike Heiiche, Example 1 also categorizes each harmoy ito rows accordig to harmoic fuctio. Studets may use this table as a referece FUNCTON Best Progressios: 1. T - S - D - T 2. T - D - T 3. T - S - T (but ot ii-) TONC (T) (, iii, vi) SUBDOMNANT (S) (ii,, vi) DOMNANT (D) (, vii o ) * the mior mode, oly chord qualities chage. --, 3--3, iii vi ii 2 BASS SCALE DEGREE ii, ii 7 ii,, ii vi,, ii3,, vii o, 3 2 Example 1 The Big 2 (Primary chords i commo practice style model compositio is limited to these i Step 3, Ex. 21). -, 7, , borrowed the idea of restrictig studets harmoic vocabulary from Seth Moaha s Big 18 as taught at the Eastma School of Music. thak the aoymous reviewer who poited out the similarities betwee Example 1 ad Figure 1.1 i Gauldi (1988, 11), the ow-dated zig-zag model of Roma umerals. While both Example 1 ad Figure 1.1 use Roma umerals ad label fuctio, the orgaizatio of Example 1 by bass scale degree fudametally chages how studets iteract with the table. Example 1 is therefore less abstract tha Figure 1.1 ad more closely coected with figuredbass theory, specifically the rule of the octave. 23 Bach sold Heiiche s treatise out of his home. Joha David Keller s treatise, Treulicher Uterricht (2 d ed., 1737), borrows much from Heiiche ad icludes a table similar to Example 1 (9 97). The first Eglish traslatio of Keller s treatise is forthcomig (Remeš ad Leaver, eds. 2018).

14 78 Joural of Music Theory Pedagogy olume 31 (2017) whe composig their ow basslies i Type ad durig the compositio project, discussed below i Part. The top left corer of the table idetifies three fuctioally ormative progressios: 1) T S D T; 2) T D T; or 3) T S T (but ot ii ). 2 ) Cadece Types: Studets ofte ask What is the differece betwee toicizatio ad modulatio? The table i Example 1 provides a brief (albeit overly simplified) aswer to this questio that have foud pedagogically appropriate. t shows eight commo cadece types o a cotiuum of varyig degrees of fiality. The faded color i the left-most colum shows that the differece betwee toicizatio ad modulatio is oe of degree ad ot kid. Four cadeces perfect authetic, imperfect authetic, plagal, ad stepwise-base result i a modulatio whe they occur i a o-toic key. additio, a toicized half cadeces are stroger (or more coclusive) tha applied chords, which typically occur mid-phrase ad therefore do ot form cadeces. ( defie cadeces here as phrase-edig evets.) exclude the deceptive cadece/deceptive motio from the cotiuum, as its effect is ambiguous regardig toicizatio. would ecourage studets to use this table (as with Example 1) as a CADENCE TYPE PHRASE ENDS WTH FNALTY Modulatio (whe i a ew key) Perfect Authetic (PAC) (7) - with 1 i soprao More coclusive (geerally) mperfect Authetic (AC) (7) - with 3 or i soprao Plagal Cadece (PC) () - Stepwise-Bass Cadece (SBC) (7) - with either chord i iversio Toicized Half Cadece (To. HC) (7) (applied chord may be iverted) Toicizatio Phrygia Half Cadece (PHC) iv - Half Cadece (HC) (7) (precedig chord ot specified) Applied Chords *? Deceptive (DC) / Dec. Motio (DM) (7) - ot (usually vi) (7) Less coclusive (geerally) *Not actually cadeces because they occur withi phrases. Example 1 Categorizatio ad Descriptio of Cadece Types. 2 practice, these three models are over-simplificatios that admit may exceptios. Moreover, they are secodary to the cotraputal motio of the bass voice whe it comes to determiig ier voices. Lastly, the theory of harmoic fuctio arose i the late ieteeth cetury with the work of Hugo Riema ad thus is ahistorical i a study based o Bach s teachig. Despite all this, evertheless thik the idea of fuctioally ormative progressios is useful, so log as studets do ot become boud to it.

15 Derek Remeš Chorales i J. S. Bach s Pedagogy 79 referece whe idetifyig cadece types i Types 1 3, writig their ow basslies i Type, ad aalyzig pieces. For istace, i Type, studets might first determie the cadetial otes ad the fill i the remaider of the basslie. ) No-Chord Toes ad Oramets: Example 1 outlies four types of ochord toes: eighbor (N), passig (P), suspesios (SUS), ad pedal poits (PED). Chordal leaps (CL), which are by defiitio chord toes, are icluded as additioal embellishmets. aryig factors are show o the right, providig some otio of the sheer variety of o-chord toe types. These cocepts will be applied i the compositio project. NON-CHORD TONES / EMBELLSHMENTS ARYNG FACTORS Neighbor (N) Acceted/ Uacceted Diatoic/ Chromatic Complete/ complete Upper/ Lower Passig (P) Suspesio (SUS) Pedal Poit (PED) Chordal Leap (CL) Acceted/ Uacceted Cosoat/ Dissoat Diatoic/ Chromatic Prepared/ Uprepared (usually) toic or domiat /a Upward/ Dowward Resolvig /a soprao, ier, or (most ofte) bass voice (By defiitio these are chord toes, but are icluded as embellishmets.) Example 1 Types of No-Chord Toes & Oramets. 7) Formal Aalysis: Example 17 sketches a three-tiered formal hierarchy usig the phrase as the primary formal uit. 2 this curriculum, defie a phrase as a 2- to -bar groupig edig with a cadece. To simplify aalysis, always idetify phrases usig slurs i my harmoizatios. Therefore, the primary aalytical activity regardig form i my method is ot the determiatio of phrase boudaries, but rather i determiig how phrases combie ito larger formal uits like periods, seteces, or phrase groups. Periods are defied as cosistig of two phrases (either + or bars) i the patter a + a' or a + b. Seteces have three phrases (either or bars), usually displayig the patter a + a' + a'' or a + a' + b. A phrase group usually has three phrases ad acts as a catch-all term for sectios that are ot periods 2 recogize that my defiitios of setece, period, ad phrase group will ot satisfy everyoe. my opiio, clarity ad cosistecy are overridig cocers i a pedagogical cotext.

16 80 Joural of Music Theory Pedagogy olume 31 (2017) or seteces. 2 each category, the last phrase is usually the strogest, accordig to the hierarchy give i Example 1. Phrases may be also broke dow ito (usually melodic) sub-uits that may ot ed with a cadece. Each level of the hierarchy has its ow labelig scheme, which the reader will recogize from Example NAME SZE LABEL DESCRPTON Primary Formal Uit Period, Setece, or Phrase Group Phrase Larger A, A, A, B, C a, a, a, b, c Sub-phrase Smaller x, x, x, y, z Period: 2 phrases; usually + or 2+ 2; a + a (at. + cos.) or a + b Setece: 3 phrases; either or Phrase group: 3 phrases (i.e., either of above) Periods, seteces, ad phrase groups: last cadece is usually the strogest ariats: Double Period ( phrases) ad Nested Seteces 2- to -bar groupig edig with a cadece ( idetify phrases with slurs.) (Melodic) sub-uits withi phrase that may or may ot ed with cadece (ofte 1 or 2 bars) Example 17 Three-Tiered Form Hierarchy for Hym Tue Aalysis. Part : Sythesis through Compositio ad Aalysis The model compositio project is the capstoe of my two-semester curriculum. t aims to itegrate all the precedig cocepts outlied i Example 1 i a creative, yet still appropriately restricted, cotext. The compositio project has seve steps which progress from a sigle-lie melody to the harmoizatio of that melody ad, fially, to the orametatio of this four-voice texture i a variety of ways. Although created this method, it mirrors Bach s pedagogical strategy by progressig from homophoy to orametatio. Oe importat differece, however, is that tried to make this approach more applicable to the average studet today by tailorig it specifically to sigle-lie istrumetalists. Example 18 presets a hypothetical prompt as a 1-bar rouded biary form, similar to eighteeth-cetury miuet-trio istrumetal movemets (except that the texture is chorale-like). Studets fill i the missig bars with a sigle-lie melody (Step 1). Begiig with a sigle lie provides the opportuity to address basic melodic issues of cotour ad gap-fill (the priciple by which a leap is followed by a step i the opposite directio). By defiig the last pitch of each phrase, melodies are guarateed to coform to the prescribed cadeces. Moreover, the first, secod, ad 2 May of these ideas are borrowed ad adapted from Laitz (201). 27 idetify mm. 1 8 ad 9 1 as seteces i my formal aalysis of Example 10. At a higher formal uit the etire hym tue could be iterpreted as a parallel period cosistig of two 8-bar seteces.

17 Derek Remeš Chorales i J. S. Bach s Pedagogy 81 fourth phrases all begi with scale degrees three-four-five, esurig a sufficiet degree of similarity to warrat the formal labels a, a', a''. Example 19 is my realizatio of the give prompt. Studets may write multiple melodies, choosig the most sigable ad iterestig oe for the ext step. A a & # HC a # B & # 9 # must toicize ii,, or vi i this phrase b Example 18 Hypothetical Model Compositio Prompt (Miiature Rouded Biary Form). Example 19 Hypothetical Realizatio of Ex. 18 (Step 1). Step 2 is to add a basslie, as show i Example 20. First, studets should complete the cadeces, sice these are predetermied. Secod, studets should look for soprao scale degree patters that match the five paradigms i Examples 12 ad 13. For istace, the successio 3 allows for both Parallel 10ths ad 10ths the Log Way. Lastly, studets should use cosoat itervals (3,,, ad 8) to fill i the remaider of the basslie. 28 Note the strig of four parallel -chords i mm. 7 8, which is usually ot allowed i species couterpoit: like Bach s, my approach does ot subscribe to species couterpoit methodology. HC Available rhythmic values: q, h, iq, q. e A & # a HC a # J J # B & # 9 b HC a 13 # J must toicize ii,, or vi i this phrase PAC i Studets should be aware that cosoat/dissoat status is idepedet of diatoicism/chromaticism. That is, cosoace ca be chromatic ad dissoace diatoic. f studets choose to use dissoace, it must be oe of the figures i the Big 2 ad exhibit correct resolutio of tedecy toes (Ex. 20, m. 3). terval idetificatio helps idetify parallel ad direct fifths ad octaves. t also aids studets 28 Aother useful idea may be the PP priciple begi with a perfect cosoace, use imperfect cosoaces i the middle, ad ed with a perfect cosoace. The PP priciple was coied by Markus Jas, who exteded a idea by Klaus-Jürge Sachs [Sachs (197, 121)]. practice, its applicability to hym tue harmoizatio may be limited because it was origially developed to describe Reaissace duets. 13 a PAC i PAC i PAC i

18 82 Joural of Music Theory Pedagogy olume 31 (2017) A & # HC HC # J?# # B & # AC i ii HC PC 13 # J i uderstadig that figured bass idicates itervals ad ot chord-toes (a commo source of cofusio i my experiece). a imitatio of Bach s multiple-bass method, where multiple basslies are writte to a give chorale melody (Stage 2), studets could write at least three basslies ad choose their favorite oe for the ext step. Studets might eve patch together the best passages from their various basslies to make a superb oe. oly dissoace?# # # # j 1, 3,,, 8 are cosoat; 2,, 7, 9, aug./dim. are dissoat Toicized HC cosecutive s allowed J # J # j must toicize ii,, or vi i this phrase Example 20 Basslie ad tervals Added to Ex. 19 (Step 2). Example 21 adds ier voices, figures, ad Roma umerals (Step 3). 29 This is equivalet to Type 3, except here, studets harmoize ad aalyze their ow basslie without figures provided. This is where the Big 2 is especially useful i arrowig dow the possible chords available for a give bass scale degree. The fact that the soprao lie is also give restricts chord choice eve further, simplifyig the task. PAC i PAC i A B D Major: ii vi vi A: ii vii (Hidde) D2 sequ. AC i ii 10ths the Log Way HC Parallel 10ths PC 9 13 & # #?# # e: Parallel 10ths - i iv # ii D: HC i ii - HC vi 10ths the Log Way & # # #?# # # # (Direct modulatio) j J j J Example 21 Middle oices, Figures, ad RNs Added to Ex. 20 (Step 3). 3 t To. HC Dec. Motio j # # J # J 7 # # PAC i j j J j J PAC i # vi 29 Example 21 omits a aalysis of fuctios to coserve space. As metioed earlier, iclude fuctio symbols i Type solutios, but would ot ormally require studets to produce them.

19 Derek Remeš Chorales i J. S. Bach s Pedagogy 83 Now we begi to add orametatio, as show i Example 22 (Step ). Studets follow a simple procedure, as show i the box above the staff: 1) Fill i ay iterval of a third with a passig ote; 2) Tie over ay ote that desceds by step, creatig a suspesio; 3) Tie ay repeated ote. my opiio, this method of writig suspesios is sigificatly easier tha that i species couterpoit. Give a cosoat structure, almost ay voice ca be suspeded by delayig descedig stepwise motio, allowig the teacher to skip complex discussios about the three evets i a suspesio (preparatio, suspesio, resolutio) ad their cosoat/dissoat status. Still, the three steps outlied above may result i parallel fifths or octaves (for istace, whe direct motio is filled i by step), requirig some additioal proofreadig. The kid of simple orametatio illustrated i Example 22 proves ideal for both sigig as a choir or performace by a brass esemble. Studets might also add text to their hyms if they wish. A & # #? # # Ay third:...adds a passig ote. Ay dowward step:...becomes a suspesio. Ay repeated ote:...is coected. 1 & ( ) 2 & 3 & j J j J # # j J # j J Example 22 Simple Orametatio (Step ). P S R etc. The ext step icreases creative idepedece by itroducig more complex istrumetal textures. Example 23 adds yet more orametatio to Example 22, creatig a istrumetal trio. This step is more difficult because it is less restricted, but therefore also offers more creative possibilities. As show i the box above the score, there are four ways a suspiras figure ca oramet a give pitch. applied these patters to the soprao lie of Example 22 while orametig the other voices i a similar style. The middle voice i Example 23 combies the alto ad teor voices i Example 22. This type of texture is ideal for a strig or woodwid trio, providig a opportuity to egage sigle-lie istrumetalists, hopefully icreasig their buy-i as to the value of hym tue harmoizatio.

20 8 Joural of Music Theory Pedagogy olume 31 (2017) A Alterate Orametatio Possibilities The ext three examples (Exx. 2 2) outlie a alterate, simpler method of orametig Example 21 specifically for a sigle-lie istrumet. First, studets traspose their harmoizatios ito a suitable rage ad key for their primary istrumets (Step ) Example 2 is for cello. 30 (Note that the slurs here are rewritte to occur every two bars istead of every four; a alterate formal aalysis is give.) Note the alterate formal aalysis with 2-bar phrases compared to previous versios. (Double a HC b a To. HC c PAC i Period) HC A?# # # Cello j J j # J Out of rage d AC i ii d B HC A a PC b 9 PAC i 13?# # # # # j J Out of rage Example 2 Traspositio of Ex. 21 to Suit Studet s Primary strumet (Step ). Example 2 gives five hypothetical patters for the sigle-lie embellishmet of a chord, show i the lower ad upper staves, respectively. The patters use eighbor toes, passig toes, ad chordal leaps, which are described i Example 1. Studets may first fid it helpful to determie the overall cotour of the figure they wish to use, as show by arrows beeath the staff i Example 2. With Example 2 (Step 7) we fially reach both the culmiatio of the compositio project ad the fruitio of my two-semester curriculum. Each chord from Example 2 ow takes up the space of oe measure, which is repeated i the style of a Baroque prelude. 31 The specifically Bachia cotributio that my method makes available is that, This:...could become ay of these (suspiras figure): & 3 & # etc. # J J J J Œ?# # Example 23 Complex Orametatio Figurated strumetal Trio from Ex. 22 (Step ). 30 Strig players will prefer sharp keys, while brass ad woodwid players will prefer flat keys. Sigle otes or etire passages may be trasposed if rage is a issue. 31 Some chords are omitted to make the phrase flow more aturally. t is ot ecessary to use the

21 Derek Remeš Chorales i J. S. Bach s Pedagogy 8 Origial: Orameted: (a) (b) (c) (d) (e)? # 12 w w w w ww?# Cotour: Example 2 Patters for Sigle-Lie Orametatio usig N, P, ad CL s (see Ex. 1) applied tot he first chord of Ex. 2. while other curret theory textbooks make similar paradigms ad harmoic cocepts available to studets, they do ot streamlie them as a vehicle toward model compositio where virtually ay cofiguratio of istrumets ad textures is available. Aother advatage of my method is that the etire seve-step compositio project is prescriptive eough for those without prior experiece composig, yet also flexible eough to allow for a eormous rage of possible orametal figures; thus creativity is fostered withi guidelies. Oe importat trasferrable skill especially targeted i the project is to show the immese variety possible from a limited stock of uderlyig patters. Aother skill is a uderstadig of how a sigle melodic lie (Example 2) ca project multiple voices that obey voice-leadig orms (Example 2). This coectio is crucial because the majority of music studets (at least the performace majors) play sigle-lie istrumets. 32 deally, studets would perform their compositios i a public cocert at the ed of the year. This kid of public accoutability is a strog motivator for producig excellet work ad masterig cocepts. Although the compositio project eds with a Baroque prelude, my itet is that studets would cotiue to compose i less restricted cotexts i the secod year of theory. Origial: Orameted: Allego q = 0?# 3?# 3 mf?# etc.?# Note that some chords are omitted. Example 2 Fial Result: Hypothetical Applicatio of a Orametatio Patter to Ex. 2 (Step 7). etire excerpt of Example 2, sice the resultig piece would be quite log. The first two ad last two phrases could suffice. 32 ocalists ca also perform origial orameted compositios that resemble Example 2, albeit with simpler figures that will allow for more time to breathe (compare Example 2). The same priciple applies to wid ad brass players.

22 8 Joural of Music Theory Pedagogy olume 31 (2017) Aalytical Applicatio Up to this poit have largely igored the aalytical applicatios of my method. t is importat to emphasize, however, that my curriculum applies the aalytical tools developed with hym tues to diverse toal styles throughout the two-semester sequece. This could iclude Baroque suites ad chamber music, Classical symphoies ad soatas, ad Romatic character pieces ad Lieder, as well as the Great America Sogbook, jazz, Broadway, rock, blues, electroic music, folk, Top-0 charts, film music, or miimalism. Though o oe example will please every reader, offer Example 27, the Sog of the Eveig Star from Wager s Tahäuser, to show oe possible aalytical applicatio. Advaced studets could create their ow reductios, but would supply oe (or portios thereof) to the average studet. The, would ask studets to supply the harmoic, cadetial, o-chord toe, ad formal aalyses. this aria, theoretical cocepts easily support questios for discussio, such as: Could the five deceptive cadeces symbolize Wolfram s urequited love for Elizabeth? Are the parallel fifths i m. 28 wrog? (ad ca music be wrog?) s the dowbeat of m. 3 a modally distorted cadetial / chord or flat- i first iversio (or both)? s the / chord o the dowbeat of m. 30 cadetial, passig, or does it chage? Does Wager use a As ad Bb o the last eighth of m. 30 to suggest the eharmoic reiterpretatio of the dimiished seveth? Such topics make this aria ideal for about the third semester of a two-year sequece.

23 Example 27 Wager, Tahäuser Sog of the Eveig Star (Act, Scee 2, 2 bars after reh. A) Derek Remeš Chorales i J. S. Bach s Pedagogy 87 Hym-like Four-voice Reductio Wolfram (Baritoe) Reductio A & # (Double Period) a ( ¼)?# 8 m vii grü 8 G: p?# 8 & #?# # b O! pp strigs pizz./harp 8 7 H N B N ii E D 3 E D b ii vii b chr. P P pp SUS p SUS > (# ) P > J ( J ) b ( ) N J J J j Œ ( ) J ( J ) ( ) B a' ( ¼) du mei hol der - A bed - ster, - wohl grüßt ich im mer - dich so ger; vom Her ze, - das sie ie 8 3 vi vi 7 (Period) c DC (o mixture) AC 29 H 3 ii 7 # 9 SUS ( ) Em: iv Am: i SUS p ( ) - ße sie, we sie vor - bei dir zieht, we sie et-schwebt dem Tal der Er - de, ei sel' 7 3 vi SUS ( ) J SUS ( ) p P ( ) J dort zu wer de, - we b' b # b b ii vi # sie et- schwebt dem 8 # C # m: (direct modulatio) più p j G i Tal der Er de, - ei sel' ger - - E gel D iv ii vii H H b7 T T vii vii chr. P p dim. b > # ( ) J 8 dort ver - riet, - ger E - ic. N gel zu wer de. u poco ritard. ppp poco cresc. più ritard. Leto cross relatio cross relatio a tempo arco/trem. DC (with mixture) DC (o mixture) # b b b G: Am: AC # # # # b # # b # b b PHC # DC (with mixture)?# P ( ) J ic. N (appoggiatura) chr. N T # J J Œ ( ) J J J ( ) ( ) J & # b?# ## C & # DC (o mixture)?#?# & # 8?# 8 Œ Œ Œ b Œ G: Em: # # (Setece) b b b b Œ b b# b PHC Œ # Œ # # # # # # # # P s! E: u Promise of E Major...dashed! & # # # # pp # # # # j # j j J J?# Œ Œ # # # # Œ Œ P s! pizz. # # # # j Œ # J Œ Œ # # Œ Œ G: -bar (exteded) cosequet b J b # # b b b Œ # j j Œ j Œ b # # # # # J SUS ( ) J Œ Œ U SUS d b G: Œ iv ii # (Oly!) PAC J ( ) J Œ Œ Œ U Œ Œ Example 27 Wager, Tahäuser Sog of the Eveig Star (Act, Scee 2, 2 bars after reh. A).

24 88 Joural of Music Theory Pedagogy olume 31 (2017) Summary ad Coclusio My goal has bee to defed part writig by clarifyig its goals ad revitalizig its methods. The goal of part writig is ot to perpetuate itself; rather, like all good pedagogy, its aim should be to teach trasferrable skills. Amog these skills is a uderstadig of how embellished textures, ad especially sigle orameted lies, ca project multiple implied voices (i.e., compoud melodies). This kowledge opes the door to simple reductive aalysis (like Example 27), which asks whether pitches that are ear i register yet separate i time are related, ad if so, what this might mea i performace. Other more basic trasferrable skills hoed i my method iclude chord spellig, tuig oe s voice withi a chord, hearig multiple voices simultaeously, perceivig modulatio, acquirig basic sigig ad keyboard skills, recogizig melodic similarity betwee phrases, assessig degrees of cadetial closure, ad haressig the expressive potetial of o-chord toes (especially suspesios) i compositio. My method, which recasts Bach s outer-voices plus figured bass approach i a ew light, itegrates these skills ad other music-theoretical topics withi the simplified cotext of hym tues. This simpler pedagogical eviromet lays a solid foudatio so that studet ca apply cocepts creatively i more diverse aalytical ad compositioal settigs. Thus, rather tha throwig out part writig, we ca use this time-hoored traditio to promote itegratio, creativity, ad diversity i a historically iformed way. With this article hope to have rebuked the CMS maifesto s claim as to the arrow horizos of part writig whe taught properly, part writig ca i fact help us defie the horizo by givig us a cocrete stylistic ad coceptual vatage poit.