Bach Chorale Research Articles

Two Cantatas

In a mere six pages of Revolutions in Sovereignty, Daniel Philpott connects John Calvin’s theological writings to the foundations of the sovereign international system, one logical step at a time. It’s like a Bach chorale, moving in bold chord progressions from key to key until it arrives at a place that is both surprising and feels entirely like home.

Consonance, Dissonance, and Formal Proportions in Two Works by Sofia Gubaidulina

Consonance and dissonance are frequently invoked in discussions of Gubaidulina’s music, particularly in terms of the composer’s intentional contrasts between timbres and her golden section-oriented formal planning. In this paper, I use the notion of dissonance to mediate between several competing theories of Gubaidulina’s music and theories of timbre more broadly. Certain passages in her Meditation on the Bach Chorale “Vor deinen Thron tret’ ich hiermit” (1993) are identified as dissonant based on her compositional theories and on sketch material from the Paul Sacher Stiftung, and on further examples drawn from her Am Rande des Abgrunds (2002). Broadly speaking, “dissonant” sounds are closer to white noise than “consonant” sounds, aligning with empirical studies of dissonance perception as well as with spectralist compositional theories. However, Gubaidulina’s music uses this extended notion of dissonance particularly musically; dissonances have specific structural roles in a work and resolve to consonances.

Automated Harmonization of Bass Lines from Bach Chorales: A Hybrid Approach

Abstract In this article, a combination of two novel approaches to the harmonization of chorales in the style of J. S. Bach is proposed, implemented, and profiled. The first is the use of the bass line, as opposed to the melody, as the primary input into a chorale-harmonization algorithm. The second is a compromise between methods guided by music knowledge and by machine-learning techniques, designed to mimic the way a music student learns. Specifically, our approach involves learning harmonic structure through a hidden Markov model, and determining individual voice lines by optimizing a Boltzmann pseudolikelihood function incorporating musical constraints through a weighted linear combination of constraint indicators. Although previous generative models have focused only on codifying musical rules or on machine learning without any rule specification, by using a combination of musicologically sound constraints with weights estimated from chorales composed by Bach, we were able to produce musical output in a style that closely resembles Bach's chorale harmonizations. A group of test subjects was able to distinguish which chorales were computer generated only 51.3% of the time, a rate not significantly different from guessing.

Anticipation-RNN: enforcing unary constraints in sequence generation, with application to interactive music generation

Recurrent neural networks (RNNs) are now widely used on sequence generation tasks due to their ability to learn long-range dependencies and to generate sequences of arbitrary length. However, their left-to-right generation procedure only allows a limited control from a potential user which makes them unsuitable for interactive and creative usages such as interactive music generation. This article introduces a novel architecture called anticipation-RNN which possesses the assets of the RNN-based generative models while allowing to enforce user-defined unary constraints. We demonstrate its efficiency on the task of generating melodies satisfying unary constraints in the style of the soprano parts of the J.S. Bach chorale harmonizations. Sampling using the anticipation-RNN is of the same order of complexity than sampling from the traditional RNN model. This fast and interactive generation of musical sequences opens ways to devise real-time systems that could be used for creative purposes.

Simulating music with associative self-organizing maps

Abstract We present an architecture able to recognise pitches and to internally simulate likely continuations of partially heard melodies. Our architecture consists of a novel version of the Associative Self-Organizing Map (A-SOM) with generalized ancillary connections. We tested the performance of our architecture with melodies from a publicly available database containing 370 Bach chorale melodies. The results showed that the architecture could learn to represent and perfectly simulate the remaining 20% of three different interrupted melodies when using a context length of 8 centres of activity in the A-SOM. These promising and encouraging results show that our architecture offers something more than what has previously been proposed in the literature. Thanks to the inherent properties of the A-SOM, our architecture does not predict the most likely next pitch only, but rather continues to elicit activity patterns corresponding to the remaining parts of interrupted melodies by internal simulation.

Johann Philipp Kirnberger and the Bach Chorale Settings

Johann Philipp Kirnberger and the Bach Chorale Settings Beverly Jerold AsTheTemperedtheArtonlyofClavierworkFuguebysinJohann1801,1752theandSebastianfour-partthefirstBacheditionschoralepublishedsettingsofThebetweenWell-and TheArtofFuguein1752andthefirsteditionsofTheWellTemperedClaviers1801 ,thefour-partchoralesettingsand theircuriouspublicationhistoryhavebeenthesubjectofastorywith manyunresolveddetails.Complicatingthematteristhefactthatmost ofthedocumentationwasdestroyedbywar.ThusArnoldSchering's summary(1918)istheprincipalsourcefortheevents.1Thisessay doesnotpresumetoanswerthequestionsthathavebeenraisedin variousarticles,butmerelytreatsonepieceofthepuzzle.Inbroad outlineform,theprincipaleventswereasfollows: 1765:Aneditionof100chorales"gesammletvonCarlPhilipp EmanuelBach"waspublishedbyFriedrichWilhelmBirnstiel (BerlinandLeipzig),togetherwithalistof59printerrorsand C.P.E.Bach'spreface,whichnotesthatfourchoraleswerenot fromhisfather.2 1ArnoldSchering,"Joh.Phil.KirnbergeralsHerausgeberBachscherChoräle,"BachJahrbuch15 (1918):141-49. 2GerdWachowski,"DievierstimmigenChoräleJohannSebastianBachs,"BachJahrbuch69 (1983),51-79at54.Bach'sprefaceissuppliedinBach-Dokumente(BD)III: SupplementJohannSebastianBachNeueAusgabesämtlicherWerke(NBA),ed.Hans JoachimSchulze(Kassel:Bärenreiter,1963-[2008]),no.723andtranslatedinTheNew BachReader(NBR),ed.HansT.DavidandArthurMendel,andrev.ChristophWolff (NewYork:Norton,1998),379f. 34 Kirnberger and Bach's Chorale Settings 35 1769: Birnstiel published an additional 100 chorales, but without an editor's name or a preface.3 Bach issued a public protest about its defects on 29 May 1769.4 21 July 1769: In a letter to Johann Philipp Kirnberger (who must have indicated his interest in a corrected edition of the chorales and the addition of previously unpublished ones) Bach advised him to proceed on this matter, adding that he [Bach] must be paid in advance.5 1771: C. P. E. Bach conveyed the chorale manuscript (purchased with funds from Princess Amalia of Prussia, whom Kirnberger served as composition teacher) to Kirnberger.6 26 March 1777: The Leipzig publisher Bernhard Christoph Breitkopf died. 10 May 1777: A letter from Kirnberger to Johann Gottlob Immanuel Breitkopf, who had taken over his father's publishing firm, offered the chorales for publication and inquired if an arrangement could be reached.7 7 June 1 777 : Kirnberger wrote to Breitkopf, now offering the chorales "for nothing" and wishing only to have a few copies for Bach and himself.8 19 June 1777: Kirnberger wrote again to Breitkopf, including questionable comments about men with whom the elder Breitkopf had worked closely: 3Wachowski, "Vierstimmigen Choräle," 54. 4NBR, 380. BD III, no. 753. Its errors were "only insignificantly greater" than those in the 1765 portion, according to Frieder Rempp, Choräle und geistliche Lieder, Part 2, Choräle der Sammlung C. P. E. Bach nach dem Druck von 1784-1787 , NBA , Kritischer Bericht , III/ 2.2 (Kassel: Bärenreiter, 1996), 18. 5NBĶ 380f. BD III, no. 754. Achering, "Kirnberger," 148. NBR, 384. BD III, no. 897. Schering, "Kirnberger," 142. NBR, 381. BD III, no. 821. Achering, "Kirnberger," 142f. NBR, 381. BD III, no. 822. 36 Bach But first I must te issued by Birnstiel. miserable and wret with Birnstiel to gi delivery and correct to the sheet. Befor appointed through Birnstiel was forced was still here, to se but demanded for e that a sheet amounte in anxiety and stres Part at this high pri At this point he [B claimed to have bou the corrections. Mr not to get into any not have courage e manuscript being v thereupon Mr. Birn care of the correct various errors; and t himself on Birnstie notice in the Hambu it of being full of chorales were not incorrect, for the m This was so damagi became so much wa Now to come to m chorales by the la Accordingly I req remainder from M demanded 12 louis d'o sent to you for your me, which contai promised him that sion and with my c brought out by Bir Kirnberger and Bach's Chorale Settings 37 But other affairs have hitherto kept me from considering it. Now, however, since it would mean a great deal to me to see them in print . . . and since it is decreed that I am to have no profit in this world for my worries and efforts, I will yield them to you . . . without the slightest payment, only to see them in print to the eternal memory of J. Seb. Bach. . . . If the chorales should be published by you, I will take the corrections upon myself, for I do not trust anybody in Leipzig to understand the matter, not even Mr. [Johann Adam] Hiller - as I conclude from his published things. . . .9 The remainder is a denunciation of Hiller's work, with which the elder Breitkopf had been involved. On 7 August 1778, Kirnberger sent Breitkopf another letter (unrelated to the Bach chorales), bitterly critical of both Hiller and Johann Friedrich...

Valentine: For Piano = Für Klavier , and: Three Character Studies: For Piano Solo , and: Saloon Songs: For Solo Piano , and: 24 Variations on a Bach Chorale: Piano Solo (review)

JAZZ PIANO Fred Hersch. Valentine: For Piano = Fur Klavier. New York: C. F. Peters, 2011. [Composer's note, 1 p.; score, p. 1-3; biog. sketch, 1 p. ISMN-13 979-0-3007-5763-6, pub. no. EP 68328. $9.] Fred Hersch. Three Character Studies: For Piano Solo. New York: C. F. Peters, 2002. [Composer's note on t.p. verso; score, p. 2-15; biog. sketch, 1 p. Pub. no. EP 68046. $12.95.] Fred Hersch. Saloon Songs: For Solo Piano. New York: C. F. Peters, 2005. [Composer's note, 1 p.; score, p. 2-33; biog. sketch, 1 p. Pub. no. EP 68107. $12.95.] Fred Hersch. 24 Variations on a Bach Chorale: Piano Solo. New York: C. F. Peters, 2002. [Composer's note on t.p. verso; score, p. 1-56; biog. sketch, 1 p. Pub. no. EP 68105. $24.] For those of us familiar with the exquisite pianism of Fred Hersch and his formidable improvisational prowess, the publication of his Valentine, Three Character Studies, Saloon Songs, and 24 Variations on a Bach Chorale, handsomely edited by Edition Peters, calls for a big celebration. Those unfamiliar with Hersch's music will find these titles surprisingly refreshing, musically demanding, intrinsically pianistic, and welcoming in the flooded market of often-dubious publications of fully notated piano compositions. Hersch is a pianist par excellence. His elegant sound esthetic, lavish harmonic vocabulary, intricate contrapuntal thinking, effortless musical flow, impeccable sense of musical form, and unconstrained forays into the depths of his boundless creativity can be enjoyed on his many fine recordings. A widely recognizable fixture in the pantheon of jazz pianists, Hersch is a sought-after teacher, composer, bandleader, accompanist, and mentor. As Hersch's followers grow in number and become ever so eager to learn from the master, the publications of these original compositions could not have been better timed. Now, by purchasing any or all of these titles, musical aficionados can experience the magic of Hersch's music in the privacy of their own studios. At times interpretatively and technically demanding, these compositions-full of innate melodic charm, harmonic richness, rhythmic vitality, and structural perfection- ought to be attractive to classical pianists, and thus should provide a delightful addition to their repertoires. Jazz pianists will definitely rejoice at the publication of these titles, as they offer a wealth of crucial information-an encrypted DNA-about the Herschian style: his compositional methods, techniques of improvisation, and different musical influences. A careful study and subsequent performance of these selections can even reveal the mystery of the creative moment that always accompanies Hersch's live performances and captivates his audiences all over the world. In addition to classical and jazz pianists, these publications can also be appreciated by music theorists and musicologists, who can investigate a new repertory, apply their methodologies, and find new ways of speculating about the role of improvisation in composition, sketch studies, and the psychology of the creative moment, among other topics. One of the published pieces, Valentine, received a Grammy nomination for Best Instrumental Composition in 2008. Melodically unrestrained, harmonically rich, and-as always the case with Hersch's compositions-musically challenging, Valen tine provides a fitting introduction to Hersch's pianism at its most intimate. The published arrangement does not significantly depart from a version that Hersch often plays as an encore during his recitals, save the solo section, which is curiously omitted from the printed edition. Three Character Studies is the composer's first set of fully notated piano pieces, each addressing a particular aspect of piano playing. Nocturne for the Left Hand Alone, dedicated to his longtime piano teacher, the legendary Sophia Rosoff, opens the triptych. In that piece, Hersch follows in the footsteps of other composers (Johannes Brahms, Aleksandr Scriabin, and Maurice Ravel) who contributed to the repertory for the left hand alone. …

J.S. Bach's "Meine Seel'erhebt den Herren" (BWV 10) as Chorale Cantata and Magnificat Paraphrase

J. S. Bach's Meine Seel' erhebt den Herren (BWV 10) as Chorale Cantata and Magnificat Paraphrase1 MarkA. Peters At undertook new the church beginning a cantata monumental of his for second each project Sunday year in which in and Leipzig, feast he composed day J.S. of Bach the a undertooka monumental projectin whichhe composed a new churchcantataforeach Sundayand feastday of the liturgical year,forty cantataswritten fromthe FirstSundayafter Trinity (June 11,1724)totheFeastofAnnunciation (March25,1725). The sheervolumeof compositionis impressive, and scholarshave lauded these forty cantatasas exemplary not onlyamong Bach's outputbutalso amongthelarger corpusofchurch cantatacomposition in earlyeighteenth-century Germany.But even beyond the numberof cantatascomposed in such a timeperiod - a practice whichwas in factcommon formanyof Bach's contemporaries, includingsuch major composers as ChristophGraupner,Georg PhilippTelemann, and Gottfried HeinrichStölzel - itis noteworthy thatBachsetforhimself a particular compositional challenge, thatof basingeachofthecantatas inthecycleon a choraletextandmelody. Overthecourseoftheseforty "choralecantatas," as they havecome 1This article isbased onpapers presented atthe biennial meeting ofthe American Bach Society May 2008 atLehigh University and atthe annual meeting ofthe Forum onMusic andChristian Scholarship held February 2009 atthe University ofNotre Dame. Thank you tocolleagues ateach meeting whoresponded tomy work and particularly tomy session chairs, Robin Leaver and Stephen Crist respectively. Thank you also toDonFranklin and Markus Rathey for reading and commenting onearlier drafts ofthe article, toEric Chafe for sharing his yet unpublished research onBWV 243, and toMelUnger andLaura Kennelly for their careful editing. 29 30 Bach tobe known, Bach engageda widerangeofLutheran hymns inways evernewandinventive.2 Considered inrelation tohiscycleofchoralecantata composition, Bach's BWV 10,Meine Seel'erhebt den Herren ,composedfortheFeast of Visitation(MariaeHeimsuchung, July2, 1724), can be seen as typical inmany ways. As a choralecantata, itisbasedon a pre-existent textand its associatedmelody.Furthermore, thistextwas clearly appropriate foritsliturgical occasion,for"Meine Seele erhebtden Herren" - MartinLuther'sGerman translation of the Magnificat, Mary'ssongofpraiserecordedin theGospel ofLuke- is theonly GermantextlistedfortheFeastofVisitation intheLeipziger KirchenStaat , a volumethatsummarizes theliturgical orderforthecity while also serving as a devotionaltextcontaining prayers and hymntexts (theLatinMagnificat textis likewise listed).3 However,itdiffers fromtheotherworksof thecyclesincethe modelforCantata10 is nota choraleperse. It is rather a canticle, a prosebiblicaltextcomposedofthequotationofLuke 1:46-55 plus theGermanversion oftheGloriaPatri, thedoxologicalformula with whichPsalmsandcanticles typically concluded.Nonetheless, Bach's unknown librettist crafted thetextofCantata10insimilar fashion to that oftheother choralecantatas: theopeningandclosing movements and one middlemovement(movements 1, 5, and 7) quote "Meine Seele" direcdy, whiletheinnermovements compriserecitative and aria textsinspiredby the remaining versesof the model. Broadly important studies ofBach's chorale cantatas include Alfred Dürr, "Bach's Chorale Cantatas," inCantors atthe Crossroads: Essays onChurch Music inHonor ofWalter E. Buskin, ed.Johannes Riedel (St. Louis: Concordia, 1967); Friedhelm Krummacher, Bachs Zyklus der Choralkantaten: Aufgaben und Lösungen (Göttingen: Vandenhoek & Ruprecht, 1995); andMarkus Rathey, "Choralkantaten," inBachs Kantaten , BachHandbuch , vol.1,eds.Reinmar Emans andSven Hiemke (Laaber: LaaberVerlag , 2012). ъ Leipziger Kirchen-Staat (Leipzig: Friedrich Groschuff, 1710), 121-22. Inany discussion ofthe relationship between a chorale cantata andthe chorale onwhich itisbased, confusion caneasily arise because both share the same title. Inthis article, I attempt toclarify the difference through terminology (referring specifically to"cantata" or "BWV10"for Bach's setting) andalsothrough type setting (italicÌ2ed Meine Seel * erhebt den Herren for Bach's cantata and"Meine Seele erhebt denHerren" inquotes for the model). Meine Seel'erhebt den Herren (BWV 10) 31 speaking, Bach'scompositional approachissimilar tothat inhisother choralecantatas: inmovements thatquotethe"MeineSeele" text, he employs thetuneassociatedwithit,whiletherecitatives andariasare newly composedwithno reference to thecantusfirmus. Butwhenexaminedmoreclosely, BWV 10 is in factone of the moreunusualexplorations thatBach undertook inthechoralecycle duetotheuniquenature ofhismodel."MeineSeele"isnotbasedon a poeticchoraletext, as areallofBach's otherchoralecantatas, but rather on a Bibleverse.Furthermore, thesetting isnotjustofbiblical quotationbut,even moresignificantly, of one of thebiblicaltexts heardmostoften inLeipzig'schurches. Mary's"Magnificat" waswellknownto Leipzigparishioners bothin itsLatin("Magnificat") and German("MeineSeele")translations. Finally, thetuneassociated with thisbiblicaltextis not a choralemelody, but rathera psalm tone formula. WhileBachemployed compositional conventions associated withhis otherchoralecantatas,he was forcedto findinventive solutions tothechallenges presented bythedistinctive features ofhis model,especially in thosemovements thatquotethe"Meine Seele" textandtune(movements 1,5,and7). Thisarticle addresses theexceptional textual andmusicalfeatures of BWV 10 withinthe contextof theMagnificat's importancein Leipzig.Itarguesthatthesingular nature ofthecantata's model - the GermanMagnificat inbiblical quotation anditsassociatedpsalmtone melody - can help us to understand thecantatain a different way fromhowwe understand theremainder ofBach's choralecantatas, thosebaseduponpoetictextsandmoreelaboratechoralemelodies. Itthusreveals thespecialnature ofthecantata asbothchoralecantata andMagnificat paraphrase, situating BWV 10within richly interwoven traditions ofliturgical, poetic,andcompositional practice. "Magnificat" and'Meine...

The Chorale Cantata in Leipzig: The Collaboration between Schelle and Carpzov in 1689-1690 and Bach's Chorale Cantata Cycle

The Chorale Cantata in Leipzig: The Collaboration between Schelle and Carpzov in 1689-1690 and Bach's Chorale Cantata Cycle

Segmental Pattern Discovery in Music

In this paper we describe a new method for discovering recurrent patterns in a corpus of segmented melodies. Elements of patterns in this scheme do not represent individual notes but rather represent melodic segments that are sequences of notes. A new knowledge representation for segmental patterns is designed, and a pattern discovery algorithm based on suffix trees is used to discover segmental patterns in large corpora. The method is applied to a large collection of melodies, including Nova Scotia folk songs, Bach chorale melodies, and sections from the Essen folk song database. Patterns are ranked using a statistical significance method that integrates pattern self-overlap, length, and frequency in a corpus into a single measure. A musical interpretation of some of the statistically significant discovered patterns is presented.

Of Time and Eternity

This essay discusses tonal ambiguity in the chorale melody “Das alte Jahr” and suggests a poetic interpretation of Bach's chorale. Expressive elements such as the passus duriusculus, the sospiro, and pervasive chromaticism are woven into a radical tonal plan that reflects a multifaceted perspective on time suggested by the change of year. In particular, the chromatic fourth becomes a tonality-defining element that contrasts the essentially diatonic melody. I suggest that the tonal and motivic balances in the piece reflect the duality of regret for the past and hope for the future, as well as a cyclic harmonic plan that reflects the yearly cycle and the notion of spiritual transformation.

Key Structure in “Das alte Jahr vergangen ist”

My discussion of Bach's chorale prelude “Das alte Jahr vergangen ist” centers on its key structure: the hierarchical arrangement of keys in the piece and the relationships between them. In the course of this discussion, I make a number of observations about the nature of key structure and the factors that govern our perception of it. I begin by considering one of Bach's four-part harmonizations of the chorale and then turn to the chorale prelude itself.

Notes on the Opening of the F# Minor Fugue from WTCI

In a recent article I proposed analytic study of this fugue using a graph that lays out various forms of pcset (013) in a certain format.' A version of that graph, somewhat modified for present purposes, is displayed below. Until further notice, graph is be considered as extending indefinitely in all directions. Forms of (013) that are displayed as adjacent vertically include same minor-second dyad. Forms that are adjacent upper-left-and-lower-right include same major-second dyad. Forms that are adjacent lower-left-and-upper-right include same minor-third dyad. In cited article, I point out that the analogous graph for... harmonic triads would illustrate, in its three different directional bondings, Riemann's relations of our relative major/minor, of our parallel major/minor, and of his Leittonwechsel.2 Related matters are studied exhaustively in important recent work by Richard Cohn.3 On graph as given here certain (013)-forms appear using lowercase letter names. The reason for that will become clear later on. At present, one can observe that lower-case forms fill a connected region of graph. My cited article invites its readers to explore how graph is surfed by consecutive forms of Forte-set 3-2 in J. S. Bach's chorale prelude on

Multiple viewpoint systems for music prediction

Abstract This paper examines the prediction and generation of music using a multiple viewpoint system, a collection of independent views of the musical surface each of which models a specific type of musical phenomena. Both the general style and a particular piece are modeled using dual short‐term and long‐term theories, and the model is created using machine learning techniques on a corpus of musical examples. The models are used for analysis and prediction, and we conjecture that highly predictive theories will also generate original, acceptable, works. Although the quality of the works generated is hard to quantify objectively, the predictive power of models can be measured by the notion of entropy, or unpredictability. Highly predictive theories will produce low‐entropy estimates of a musical language. The methods developed are applied to the Bach chorale melodies. Multiple‐viewpoint systems are learned from a sample of 95 chorales, estimates of entropy are produced, and a predictive theory is used to generate new, unseen pieces.

Modal Identity and Irregular Endings in Two Chorale Harmonizations by J. S. Bach

An interesting theoretical problem for chorale harmonization is posed by received cantus firmi that close on pitches other than the modal final. A common irregular melodic ending is on the confinal or dominant.1 Such confinal endings generate unusual harmonic settings, the larger harmonic movement being that of tonic to dominant. In the works of J. S. Bach, a confinal ending has interesting modal and tonal implications when the chorale concludes a larger work. This study considers two examples of irregular endings in Bach's chorale repertoire, his settings of the cantus firmi Christ, unser Herr, zum Jordan kam (the final chorale of Cantata 176) and Durch Adams Fall ist ganz verderbt (the final chorale of Cantata 18.) The paper is organized in two parts. Part I introduces the cantus firmi in question and surveys pertinent historical writings on the sub-

An Expert-Novice Comparison in Musical Composition

The study reported here investigated expert and novice performance on a simple composition task. One Expert and three Novices were given a four phrase Bach Chorale with half of the first phrase and the soprano line provided. They were required to complete as much of the Chorale as possible within one hour. Think-aloud protocols were recorded and retrospective interviews were conducted. The protocols, scores and interview responses were compared. Only the Expert completed the task. The Expert was able to attend to the basic technical aspects of the task and to simultaneously consider part movement, balance and typical features of the genre. The Novices concentrated on chord-by-chord solution, applying the basic rules of harmony and largely neglected the shape and balance of the emerging score. The comparison of the protocols from the Expert and Novice provided evidence of characteristics of expertise found in problem-solving tasks in other domains.

On the Entropy of Music: An Experiment with Bach Chorale Melodies

On the Entropy of Music: An Experiment with Bach Chorale Melodies

IMG/1: An Incidental Music Generator

Computer programs are available to aid musicians in the composition of music-e.g,, Music Mouse (Spiegel 1985); Jam Factory, M (Intelligent Music 1988); and others-but there are circumstances in which a person with little or no specific musical expertise (i.e., not a musician) needs to be able to produce simple musical works fitting a simple set of criteria. For example, a research chemist may want to assemble a videotape presentation showing how some new process works. There may be long sequences with no narration, e.g., while the solution changes color or the chart recorder runs. Perhaps someone is compiling a series of interviews that share a common title/credit sequence. In these sequences, some background or incidental music would be a perfect accompaniment and would lend continuity. The music required need not be very sophisticated or elaborate; it merely needs to have the right and be the right length. However, unless the project has a very large budget, or the person making the video happens to be a musician with recording facilities available, the resulting sound track is likely to be silence or something pirated from a commercial recording. Researchers have been exploring algorithmic composition for many years (Hiller 1970, 1981; Bolognesi 1983; Dodge and Jerse 1985; Loy 1989), but as Kemal Ebcioglu says in a recent article on harmonizing chorales, It seems that musical composition is a hard mental task that requires a substantial amount of knowledge, and any serious attempt to simulate 'noncomputer' music composition on the computer would have to face the task of constructing a formal model of considerable complexity. We have found that even the algorithmic representation of the knowledge underlying the seemingly simple Bach chorale style is a task that already borders the intractable. (Ebcioglu 1988) Recent work at the Bellcore research center (Langston 1986; 1988; 1989a; 1990) has produced short pieces that, although devoid of semantic content, adequately embody the syntactic structures of music and result in acceptable music. IMG/i (Incidental Music Generator number one) is a set of programs built on this work that extend it to address a range of musical styles. The central goal in IMG/1 is to allow musically-naive users to produce pieces of background music of arbitrary length using algorithmic composition techniques. Simplicity was an important design goal for IMG/1; the intended users, computerand music-novices, must be able to compose and play an original piece of music with little or no training. As a result, IMG/1 is extremely easy to use; with a few clicks of the mouse, it can compose and play an original piece of music. The user simply selects a musical style, sets the tempo, and types a length (in seconds) to determine the exact duration of the piece. Most people are more sophisticated in listening than in creating music (I don't know anything about making music, but I know what I like). Since IMG/i can generate arbitrarily-many variations, all different (and, thanks to the built-in musical knowledge, surprisingly pleasant), the user need only pick from among them. The dozens of parameters that provide detailed control of the composition process default to reasonable values if not set explicitly by the user, but may be manipulated as expertise with IMG/1 and its music increases. Melodies are generated by a set of algorithms with expert knowledge of various musical styles. The techniques employed range from probabilistic traversal of graphs to simulation of the mechanics of a specific instrument. In all cases, the melody generation uses some stochastic information (i.e., none of the algorithms are deterministic). Accompaniments are assembled by transforming a set of predefined fragments to fit the progression of the overall harmonic structlre. Although this scheme is deterministic, the gen ration of the harmonic structure is not; thus the accompaniment also changes for each piece (unless the user specifically asks to keep it fixed). Music generated by IMG/1 has been used as background music in videotaped technical demonComputer Music Journal, Vol. 15, No. 1, Spring 1991, C 1991 Massachusetts Institute of Technology.

Using Connectionist Models to Explore Complex Musical Patterns

Music teachers often ask their classes to take musical dictation. The teacher commonly plays a short excerpt, perhaps a phrase from a Bach chorale, and then the students attempt to translate the various pitches and durations into the symbols of standard musical notation. Each resulting symbol can be judged true or false, right or wrong. Music teachers also ask their classes to analyze the musical syntax of phrases from Bach chorales. The resulting answers will likely have varying shades of truth or falsity. Students can have legitimate differences of opinion about how to interpret ambiguous musical events or events that have one meaning in prospect and a second in retrospect. And not only students differ in their assessments of complex musical patterns. Acknowledged experts in eighteenth-century music are known to disagree about how, in a given phrase, the chords, rhythms, contours, melodies, textures, timbres, and counterpoint all interact. Connectionist models offer elegant ways of dealing with multidimensional complexity of the type found in polyphonic, harmonically oriented music. One can, for example, define a musical event as an input pattern of activation that is then transformed by a network of interconnected processing units into an output pattern of activation representing an interpretation of the event. Models that allow for learning often require an explicit teacher prepared to state unambiguously whether, and to what degree, the output pattern is in error (Rumelhart, Hinton, and Williams 1986; Werbos 1988). For relatively low-level musical tasks, like the transcription problem described above, this requirement poses no serious obstacle; but for higher-level tasks, the notion of an explicit teacher becomes problematical. One wonders, for example, if anyone would be comfortable in claiming that one interpretation of a musical phrase is only 69 percent as true as another? An alternative class of connectionist models

Forkel's Letters to Hoffmeister & Kühnel: A Bach Biographical Source Recovered

L an article appearing in the 1932 Peters Jahrbuch, Georg Kinsky described for the first time a series of twenty-six letters written by the early Bach biographerJohann Nicolaus Forkel to the Leipzig publishing firm of Hoffmeister & Kuhnel.' The letters, 549 penned between 1801 and 1814, chiefly concerned the printing of Hoffmeister & Kiihnel'sJ. S. Bach, Oeuvres Complettes, the first attempt at a Bach Complete Works series, for which Forkel served as advisor. But they also touched on a host of other important Bach-related matters, such as the fate of the manuscript scores of Bach's chorale cantatas, the performance of Baroque ornamentation as taught by Bach's eldest son Wilhelm Friedemann, and the Bach materials existing in provincial libraries around 18oo. As the first historian to concern himself with Bach's life and works, Forkel was in a unique position to report on his subject. Although Forkel wrote and published his seminal Uber Johann Sebastian Bachs Leben, Kunst, und Kunstwerke in 1802,2 over a half-century after Bach's death, he had gathered material for the volume a quarter of a century earlier, when it was still possible to confer with those who had known Bach personally. Forkel's principal sources of information were Bach's sons Wilhelm Friedemann and Carl Philipp Emanuel, who supplied first-hand accounts of their father preserved by no one else. A number of letters written by Carl Philipp Emanuel to Forkel in 1774-75, longknown to Bach scholars,3 show how carefully Forkel incorporated