Brou Mlr u;nc r Tx sannr of Fine Arts to you by the ASU Ss-$l{, Anr Musrum rwex Presented in repertorY, Chekhov's The Cherry Orchard and Lanford Wilson's Fifth of luly - Feb.19'29 New Ploys Festival - APril t4-25 Prints lrom M.A.R.S. - through May zz Landscope in the Fireploce: Paintings by Pedro Alvarez -teb.7 - June t9 Mrursncr Dlncr $$-$$e New Danceworks ll - March 4-7 Humor,lrony and Wit: Ceramic Funk from the Sixties and Beyond - Feb. z7 - June 5 Spring Dance Collection - March Blue Memory: Paintings by Tron Trong Vu * Feb. 7 - MaY z z5-28 MAlnsrncr Lvnlc Oprnl Tn:lrnr Ss-$.',s Once Upon a Mottress - Feb. z7-March 7 Mozart's Die Zauberfliite - April z3-May z illnrrsrnc: Oncnu S$*S{e The Transcriber's Art - )an. z5 !.5. Bach,The Consummate Musician Mathematical Music - Feb. zz Bach & the North German Ttadition Gurnn Corcrnrs $le"Sts Turkish born guitarist Cem Duruoz Violin/guitar duo Finn Svit and Jochen Brusch - March 3 Flcurw Anrlsr - Feb. 8 The Long Day: Sculpture by Claudette Schreuders - March zo - June 19 kusrlrurt Fon SruDlEs llu IHE Antl Miranda luly- screening of July's films, discussion of her work - Feb. t9 Inside Informati on - visual tra n slation pxss and three-dimensional display of numerical data streams * March z5 - MaY t4 Shelter Against Violence - resea rch - March 7 engaging art, media and engineering for a social cause - April z9 - Feb REClralJ $5 14 classical, jazz or contem Potary choices 5 Mustc Eru3rmglrs Fmse Concert of Soloists - Feb. 9 With Strings Attached * Feb.'t7 Grand ond Glorious - March to Dreams and Fancies - APril 8 Beloved Masterpieces - APril z8 Scxoor oF Ant resx Around the Wortd in Eighty Minutes Harry Wood Gallery, Northlight Gallery Step Gallery and the Art Gallery Shows change weekly. TICKETS: - April z9 Herberger College Box Office can: {8o -g6S'6447 -4:crberqerCollese Dof Fine Artso MnTHEMATTcAL MUSrc: NuMBER rN THE CoNcEPTToN oF BAcH's OncnN Musrc Kimberly Marshall, Organ School of Music Herberger College of Fine Arts Arizo na State University February 22, 2004, 2z3O p.m. Organ HaIl Music Building ffilfil"'.8iltP" Pnocnann Prelude in E-flat Majoa B\fV 552a. . . . . Johann Sebastian Bach (r685-1750) Adesto/Firmissime/Alleluia. . . .Anonymous, Robertsbridge Codex, c. 1360 Pavenne/Galliarde Pavana . published by Pierre Attaingnant, Paris, 1531 lachrimae . . Jan Pieterszoon Sweelinck (c. r562-r62t) Fantasia chromatica Das alte Jahr vergangen ist, BWry 614 (Orgelbtichlein) . J. S. Bach Wir glauben all' an einen Gott, B\Xry 680 (Clauier-Ubung.III) Passacagliain D Minor, Bux\X/V' 161 . . . . .Dieterich Buxtehude (1637_r707) CanzonainDMinor,BWry5BB.. Excerpts from Fiori musicali,1635 ....J.S.Bach . Girolamo Frescobaldi (1583-1543) . . . . . . Johann Sebastian Bach Canzona Ricercar Bergamasca Fugue in E-fat Major, B\Xry 552b Pnocnnnn Norrs Much has been made recently of the links benveen musical study and test scores in mathematics. This is no surprise to musicians, of course, because of the many links between the two disciplines. Musical intervals are aural reflections of mathematical proportions, and the pipe lengths of the organ are physical manifestations of these. In addition, every piece of music has a structure composed of metrical units that contain a certain number of beats. In todayt program, we will explore the ways in which composers have manipulated musical meters and proportions, sometimes with symbolic intent. Of great importance to musical numerology are the triangular numbers, derived from adding numbers in their natural order: 1, 7 + 2, 1 + 2 + 3, I + 2 + 3 + 4, etc. This creates a triangle, the simplest geometrical figure that can be made by joining lines: o Os oo OOO to oooo ooooo zr 6 15 OOOOOO 28 The triangle symbolized the Divine for the ancient Greeks, and the Trinity for Christians. The triangular numbers were imbued with great significance, and they are reflected in nature, with 3 and 6 forming the basis of the duodecimal system (12 signs of the zodiac, 12 months of the year), and 10 the decimal system (10 fingers and toes on the human body). Several of the selections on today's program will demonstrate how these triangular numbers were incorporated into musical composition. Mathematical proportions often govern musical structure and meter, where the speeds of various sections are calculated as proportions of a basic pulse, or tactus. Such proportional relationships are exploited in Frescobaldi's Bergamasca, while his Canzona presents a theme first in duple meter and then modified in triple meter. This proportional shifting benveen two and three is fundamental to much early music, as heard in the figures decorating the medieval motet, and in the Pavenne and Galliarde dances. Bacht E-flat Major Fugue features subdivisions in2 and 3 that change between the 3 sections of the work. He also uses the old technique of hemiola to emphasize the half-point and conclusion of the second fugue. A hemiola shifts from 2 subdivisions of 3 to 3 subdivisions of2, thereby adding one accent to each group of6 beats and intensifying the cadence. A ratio known as the Golden Section was used in classical art and archirecture to create balance, and this too finds musical equivalents. In this proporrion, a line is divided into two parrs so that the ratio of the longer part (a) to the shorter part (b) is the same as rhe rario of the entire segment (a + b) to the longer part; alb = (a + b)/a. This works out to be about 1.618, and although musical strucrures cannor be so exactly measured, the Fantasia by Sweelinct and the Ricercar by Frescobaldi both introduce the contrapuntal technique of augmentation, where a theme is presented in long nores, ar roughly this point in the work. A mathematical relationship that Bach exploited was rhe numerical derivationofhisname: B=2,A= 1, C= 3, H = B BACH = 14. Thecareful study of his music reveals his mathemarical "signature" in 14 entries of a theme, or a significanr occurrence in the 14th measure of a piece. \x4rile this type of interpretation is purely speculative, it sometimes seems ro explain particular features in Bacht music and is very much in keeping with the arcane complexi ries of counrerpoi n r. The program is framed by Bachs rnagisterial prelude and Fugue in E-flat Major, tsv/V 552, the opening and closing works of his clauier-[Jbung, Part III (1739). This was the first organ music that Bach published, and a close scrutiny of the score reveals numerical aspects related to his Lutheran faith. The complete clauier-Ubungrrr contains 27 pieces (3 x 3 x 3), perhaps mirroring the 27 books of the New Testament. The number 3, which represents the Thiniry is paramount to both the Prelude and the Fugue. The choice of E-flat major, a key with three flats, underscores the tripartite srructures: the prelude has three main rexrures while the Fugue is in three large sections. Musical characteristics also seem to reflect aspects of thetiniry. In the prelude, the Father is represented by stately chordal sections with dotted rhythms in overture style. These alternate with galant echo effects (no pedal) ro represent Christ, and contrapuntal trearment of a rapid theme that suggests the Holy spirit. Medieval theorists considered the number 3 to be complete, or "perfecr." Because of this, the earliest surviving polyphony was always subdivided into rh1'thmic units of 3, and it was not until a "new art" (ars nova) was introduced in the early 14th century, that subdivisions in 2 were explored. The keyboard arrangemenr of the ars nova morer Adesto/Firmissime/Alleluya demonsrrates the repetitive use of triplet figuration, occasionally interrupted by pairs of notes in the new style. In the spring of 1531, Pierre Attaingnant published seven small books of music in keyboard tablature, and these constitute the only French sources surviving from the Renaissance. The Pavenne and Galliarde were the most popular dances of the time, and sometimes the same musical material is treated in duple and triple metet as in the example performed today. The pavenne is a stately processional, while the Galliarde is robust, as its name implies, with a demanding choregraphy of jumps and rurns. Although Bach had no direct contact with him, the Dutch organist/ composer Jan Pieterszoon Sweelinck was a seminal figure in the development of the north-German style. Major 17th-century organists such as Jacob Praetorius, Samuel Scheidt and Heinrich Scheidemann came to Amsterdam to study with Sweelinck, and upon returning to Germany, rhey applied his figurative contrapuntal style to the large organs over which they presided. The Pavana Lachrimae is an arrangement of John Dowland's famous song, "Flow my tears." The simple structure heard in the previous Pavane is expanded here, with embellished repetitions of the three main sections. The Fantasia chromatica is a marvelous work that is structured according to the Golden Section: at this point a6out 213 through the piece, Sweelinck introduces the descending chromatic subject in augmentation in the lowest voice. The theme is then developed in diminution and stretto, leading to a dramatic close. Sweelinckt ingenious keyboard figurations foreshadow those ofBach a century later. "Das alte Jahr vergangen ist" (The old year has passed away) presents a concise numerological depiction of its subject, the calendar year. Despite its brevity, the piece is full of symbolism: it contains 12 bars, one for each month of the year; there is a rising motive of 6 semitones and a falling one thar mirrors it, suggesting the changing seasons, and if you count rhe number of notes and symbols on the page, you arrive at 365, one for each day of the year. "'Wir glauben all an einen Gott" (\7e all believe in one God) is a fugal treatment of the chorale melody over an independent pedal motive that is 6 measures long and enters at different pitches 6 times during the piece. As shown above, 6 is a triangular number and has symbolic significance as the sum of the Tiinity: I + 2 + 3 = 6. It is also the first "perfect" number, where the number equals the sum of its factors. In this chorale setting, rhe number 5 may represent the six days of creation, to illustrate the continuation of the text, "Schdpfer Himmels und der Erden' (Creator of heaven and earth). The 14 entries of the chorale theme in the manuals may correspond to the numerical equivalent of Bach's name, suggesring a personal prolession of fairh. Buxtehudet Passacaglia in D Minor may be based on the second "numerus perfectus," 28, which is the sum ofits factors (l + 2 + 4 + 7 + 14) as well as of the first seven cardinal numbers (l + 2 + 3 + 4 + 5 + 6 + 7).The factors of 28 define the piecet strucrure, with two halves each containing 14 statements of the passacaglia theme, and 4 sections each with 7 statements. The statements can be further subdivided into groups of 2 and 1. The Dutch organist Piet Kee goes even further with his interpretation to suggest that the number 28 also refers to the cycles of the moon, and that the 4 sections reflect the moon's phases as follows: o o o o new moon (D minor, first presentation of theme) first quarter (move to F major, intermediate point to A; addition of a 5th voice part) full moon (A minor, with low pedal entries, full chords) last quarter (return to D minor, waning intensiry triplet figures) Bacht Canzona in D Minor may stem from his study of Italian forms' particularly the canzoni of Frescobaldi, which are based upon rePeated-note themes, with lively imitation of short motives in all parts and a sectional form based on the change from duple to triple meter. The excerpts from Frescob aldi's Fiori musicali refect the early Italian style that Bach studied. The Canzona was intended to be played after the reading of the Epistle. Its Iively sryle derives from the French chanson, a song containing spirited imitation of a repeated-note motive. Characteristic of the genre is the shift from duple to triple meter. A precursor of the fugue, the Ricercar (from the Italian verb "ricercare" meaning "to search out") is based on contrapuntal manipulations of a subject. Like Sweelinck, Frescobaldi introduces the subject in augmentation about 213 of rhe way through the piece, using the Golden Section to create a balanced structure. The Bergamasca is an exercise in metrical proportions, with each section featuring a different meter that must be calculated in relation to the others. Frescobaldi was well aware of this challenge to the performer, for he prefaced the piece with this remark: "\Thoever plays this Bergamasca will not have learned little." The E-fat Major Fugue, BWy 552, is a masterpiece of design and expression. The subject of rising fourths (identical to the first phrase of the chorale tune "O God our Help in Ages Past," although Bach would not have known it as such) is presented in three sections to symbolize the Thinity. The first section, a stately 5-voice Fugue depicts the Father; the second, where the chorale is combined with a running motive, the Son; and the third section' with its dense counterpoint and fiery pedal fourishes, the Holy Spirit. This work displays Bacht contrapuntal mastery, his ingenuity in treating simple themes and combining them with diverse countersubjects in different meters' The Fugue is an apogee in Bach's writing for the organ, transcending the techniques of composition to symbolize the divine. Kimberly Marshall Brocnapnv Kimbedy Marshall maintains an active career as a concert organist, performing regularly in Europe and the US. She presently holds the Patricia and Leonard Goldman Endowed Professorship in Organ at Arizona State Universiry having previously held teaching positions at the Royal Academy of Music, London, and Stanford University, California. \Tinner of the St. A-lbans Competition in 1985, she has been invited to play in prestigious venues and has recorded for Radio-France, the BBC, the ABC, and numerous American statl0ns. Dr. Marshall has been invited to play throughout Europe, including concerts in Londont Royal Festival Hall and \Testminster Cathedral; King's College, Cambridge; Chartres Cathedral; Uppsala Cathedral; and the Dormition Abbey in Jerusalem. She has also performed on many historical organs, such as the Couperin organ at Saint-Gervais, Paris, the Gothic organ in Sion, Switzerland, and the Cahmann organ in Leufstabruk, Sweden. Dr. Marshall especially enjoys tailoring programs to the sryles of the instruments she plays, as is evident from her recordings of Italian and Spanish music on historical organs. Her playing is informed by research into obscure repertoire and knowledge of performance practice, although she does not limit herself to early music. \flhile at Stanford, she gave performances of organ works by Ligeti in the presence of the composer, and during her time at the Royal Academy of Music she premiered a new work commissioned by Madame Messiaen. She is attracted to the organ by its vast possibilities of timbre and by the instrument's complex development since its invention in the third century BCE' Her work reflects this enthusiasm for musical creativity and historical awareness. In 1986, Dr. Marshall received the D.Phil. in Music from the University of Oxford. Her thesis, Iconographical Euidence for the Late-Medieual Organ, was published by Garland in 1989. More recently, she has developed this work in several articles and lecture/presentations; a CD recording ofthe earliest surviving keyboard music is in press. She has lectured on her research for the American Musicological Sociery the Berkeley Organ Conference, and the organ course in Romainm6tier, Switzerland. In recognition of her work, Dr. Marshall was awarded a Fulbright Scholarship to continue her research and teaching during 1991 at the Sydney Conservatorium in Australia. Northeastern University Press published her edition of articles on female traditions of music making, Rediscouering the Muses, in 1993, and she has contributed entries for the Groue Dictionary ofMusic 2000. Her anthology of late-medieval keyboard music was published by Wayne Leupold in 2000. Dr. Marshallt compact disc recordings feature music of the Italian and Spanish Renaissance, French Classical and Romantic periods, and works by J. S. Bach. Loft Recordings has re-issued a number of her recordings, including Diuine Euterpe, works for organ by female composers, and How Excellent is Thy Name, Jewish liturgical music for cantor and organ. Dr. Marshall was a recitalist and workshop leader during four recent National Conventions of the American Guild of Organists (Dallas, 1994; NewYork, 1996; Denver, 1998; Seattle, 2000) She has been a Project Leader for the Organ Research Center in Goteborg, Sweden, where she teaches and performs frequently. During the summer of 2001, she appeared in Seoul for the Korean Association of Organists and in Toronto for the Convention of the Royal College of Canadian Organists. Her recording of Chen Yi's organ concerto with the Singapore Symphony was released last year on the BIS label. Her itinerary for 2004 includes appearances playing the famous Fisk organs at Stanford University and House of Hope Presbyterian Church, St. Paul, Minnesota; the newly restored Tannenberg organ in OId Salem, North Carolina; and the new dual-temperament Pasi organ in St. Cecilias Cathedral, Omaha, Nebraska. G-n=nlr lrronnnnrron Emergency Mesiaget Physicians and other patrons expecting calls during a performance are asked to give their seat locations and paging devices to the house manager. All checked paging devices will be monitored throughout the performance and afterward can be picked up from the house manager. Patrons who need to make an emergency phone call should contact an usher or the house manager for assistance. Box Office Serving Mainstage Dance, Lyric Opera Theatre, Theatre and Organ series; Faculty Artist Recital series; and Cuitar Concert series. PaulV. Calvin Playhouse/Nelson Fine Arts Center, 48o-965-6447. Hours: 1o:30 a.m.-6 p.m., Tuesday-Friday; noon-4 p.m., Saturday. 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Go to ! 2 herbergercollege.asu.edu/eventssignup.html E-mail events-subscribe@asu.edu ,on oeE aE2e = American Express Beyo n d Broa dw ay Body Power JANFBI Sat., - Breaking Musical Bou n d aries DANITL EERIUARD RO{JMAIN Fagaala Feb.7,?A04,7 pn Back by popular denand! fhe dancers of Jant-Bi surge with enotion. style and sheer verve. -withRockestrs guest very strrecir:l DJ RADAR Sat., Feb.21,20A4.7 pm (6 pm pre-party) Art meets entertatnnent everything yau feel about and changes -nusic! * Lend Me QUASAR YCIur Eyes * :'"$' Sat., Feb. 28, 2004 Through the ' 7 pm af video use projection, high-energy techno music and co ntem pora ry d a n ce, Qu a sa American audiences to r expases the fascrnations of Erazilian culture, Meet the rilmmaker TREftIIBtlruG trEFORT S"P Thurs.. March 1i,2004 pm (6 pm pre-party) / fh i s i nte rn at i an a I praject d estroys assunptions abaut falth, sexuality and religious function and challenges the meaning of religiaus identity and tradition in a cantenporary world. BAT's*{HVA SAruET Decn Sgmee - Tues., lVlar. 23. 2004 / pm (6 pm pre-party) Regarded as one of lsrael's cu ltu ra { trea sures, Batsheva Danrc explores world issues using a blend af poweful, physica! mavenent and familiar sangs. Tickets available at ASU's Gammage Box 0ffice 4S0-965"3434 www.asuga m mage.c0m and all Ticketmaster locations 50% 0f{ for sludentslkids \N . Use your American fxpress Card and a recieve a $3 discountl o Groups, 480-965-66/B NATtoNAL ENDowMENT FoR THE ARTS \p lb;i t:,:r:r,;q:' [)ublii' li'crrts