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The Musical Offering

January 26, 2023

The Musical Offering (German: Musikalisches Opfer or Das Musikalische Opfer), BWV 1079, is a collection of keyboard canons and fugues and other pieces of music by Johann Sebastian Bach, all based on a single musical theme given to him by Frederick the Great (King Frederick II of Prussia), to whom they are dedicated. They were published in September 1747. The Ricercar a 6, a six-voice fugue which is regarded as the high point of the entire work, was put forward by the musicologist Charles Rosen as the most significant piano composition in history (partly because it is one of the first).[1] This ricercar is also occasionally called the Prussian Fugue, a name used by Bach himself. The composition is featured in the opening section of Douglas Hofstadter's Pulitzer Prize winning book Gödel, Escher, Bach (1979).

History

 
The Flute Concert of Sanssouci by Adolph Menzel, 1852, depicts Frederick playing the flute in his music room, with C. P. E. Bach accompanying him on a harpsichord-shaped piano by Gottfried Silbermann.

The collection has its roots in a meeting between Bach and Frederick II on May 7, 1747. The meeting, taking place at the king's residence in Potsdam, came about because Bach's son Carl Philipp Emanuel was employed there as court musician. Frederick wanted to show the elder Bach a novelty, the fortepiano, which had been invented some years earlier. The king owned several of the experimental instruments being developed by Gottfried Silbermann.[2] During his anticipated visit to Frederick's palace in Potsdam, Bach, who was well known for his skill at improvising, received from Frederick a long and complex musical theme on which to improvise a three-voice fugue. He did so, but Frederick then challenged him to improvise a six-voice fugue on the same theme. Bach answered that he would need to work the score and send it to the king afterwards. He then returned to Leipzig to write out the Thema Regium ("theme of the king"):[3]

 

Four months after the meeting, Bach published a set of pieces based on this theme which we now know as The Musical Offering.[4] Bach inscribed the piece "Regis Iussu Cantio Et Reliqua Canonica Arte Resoluta" (the theme given by the king, with additions, resolved in the canonic style), the first letters of which spell out the word ricercar, a well-known genre of the time.

Possible origin of the King's Theme

Humphrey F. Sassoon has compared the theme issued by Frederick II to the theme of an A minor fugue (HWV 609) by George Frideric Handel, published in Six fugues or voluntarys for organ or harpsichord. Sassoon notes that "Handel's theme is much shorter than the King's, but its musical 'architecture' is uncannily similar: jumps followed by a descending chromatic scale." He also elaborates on their additional similarities, which led Sassoon to suggest that Bach used Handel's A minor fugue as a structural model or guide for the Musical Offering's Ricercar a 6, and that its musical concepts may also have influenced Bach's development of the Ricercar a 3.[5] Nevertheless, the Ricercar a 6 is longer and incomparably more complex than Handel's fugue.

Arnold Schoenberg, in his 1950 essay on Bach, suggested that the Thema Regium was created by Bach's son, Carl Phillip Emanuel, on the orders of the king, as a well-prepared trap to embarrass J. S. Bach.[6]

Structure and instrumentation

In its finished form, The Musical Offering comprises:

  • Two Ricercars, written down on as many staves as there are voices:
    • a Ricercar a 3 (a three-voice fugue)
    • a Ricercar a 6 (a six-voice fugue)
  • Ten Canons:
    • Canones diversi super Thema Regium:
      • 2 Canons a 2 (the first representing a notable example of a crab canon or canon cancrizans)
      • Canon a 2, per motum contrarium
      • Canon a 2, per augmentationem, contrario motu
      • Canon a 2, per tonos
    • Canon perpetuus
    • Fuga canonica in Epidiapente
    • Canon a 2 "Quaerendo invenietis"
    • Canon a 4
    • Canon perpetuus, contrario motu
 
Trio Sonata
1st part: Largo (3:53)
2nd part: Allegro (4:12)
3rd part: Allegro (fin), Andante (4:46)
4th part: Allegro (3:11)
Recorded in 1930, in Paris
Problems playing these files? See media help.

Apart from the trio sonata, which is written for flute, violin and basso continuo, the pieces have few indications of which instruments are meant to play them, although there is now significant support for the idea that they are for solo keyboard, like most of Bach's other published works.

The ricercars and canons have been realised in various ways. The ricercars are more frequently performed on keyboard than the canons, which are often played by an ensemble of chamber musicians, with instrumentation comparable to that of the trio sonata.

As the printed version gives the impression of being organised for convenient page turning when sight-playing the score, the order of the pieces intended by Bach (if there was an intended order) remains uncertain, although it is customary to open the collection with the Ricercar a 3, and play the trio sonata toward the end. The Canones super Thema Regium are also usually played together.

Musical riddles

Some of the canons of The Musical Offering are represented in the original score by no more than a short monodic melody of a few measures, with a more or less enigmatic inscription in Latin above the melody. These compositions are called the riddle fugues (or sometimes, more appropriately, the riddle canons). The performer(s) is/are supposed to interpret the music as a multi-part piece (a piece with several intertwining melodies), while solving the "riddle". Some of these riddles have been explained to have more than one possible "solution", although nowadays most printed editions of the score give a single, more or less "standard" solution of the riddle, so that interpreters can just play, without having to worry about the Latin, or the riddle.

One of these riddle canons, "in augmentationem" (i.e. augmentation, the length of the notes gets longer), is inscribed "Notulis crescentibus crescat Fortuna Regis" (may the fortunes of the king increase like the length of the notes), while a modulating canon which ends a tone higher than it starts is inscribed "Ascendenteque Modulatione ascendat Gloria Regis" (as the modulation rises, so may the king's glory).

Canon per tonos (endlessly rising canon)

The canon per tonos (endlessly rising canon) pits a variant of the king's theme against a two-voice canon at the fifth. However, it modulates and finishes one whole tone higher than it started out at. It thus has no final cadence.

Theological character

Among the theories about external sources of influence, Michael Marissen's[7] draws attention to the possibility of theological connotations. Marissen sees an incongruity between the official dedication to Frederick the Great and the effect of the music, which is often melancholy, even mournful. The trio sonata is a contrapuntal sonata da chiesa, whose style was at odds with Frederick’s secular tastes. The inscription Quaerendo invenietis, found over Canon No. 9, alludes to the Sermon on the Mount (“Seek and ye shall find”, Matthew 7:7, Luke 11:9). The main title, Opfer (“offering”), makes it possible for the cycle to be viewed as an Offertory in the religious sense of the word. Marissen also points out that, canonic procedures often evoking the rigorous demands of the Mosaic Law, the ten canons likely allude to the Ten Commandments. Marissen believes that Bach was trying to evangelize Frederick the Great, pointing him to the demands of the Mosaic Law.

In a recent study[8] Zoltán Göncz has pointed out, the authorial injunction to seek (Quaerendo invenietis) does not only relate to the riddle canons but to the six-part ricercar as well, whose archaic title also means to seek. There are several Biblical citations hidden in this movement, and their discovery is made especially difficult by various compositional maneuvers. The unique formal structure of the fugue provides a clue: certain anomalies and apparent inconsistencies point to external, nonmusical influences.

Among Bach's duties during his tenure at Leipzig (1723–50), was teaching Latin. Ursula Kirkendale[9] argued for a close connection with the twelve-volume rhetorical manual Institutio Oratoria of the Roman orator Quintilian, whom Frederick the Great admired. Philologist and Rector of the Leipzig Thomasschule, Johann Matthias Gesner, for whom Bach composed a cantata in 1729, published a substantial Quintilian edition with a long footnote in Bach's honor.

Adaptations and citations

The "thema regium" appears as the theme for the first and last movements of Sonata No. 7 in D minor by Friedrich Wilhelm Rust, written in about 1788, and also as the theme for elaborate variations by Giovanni Paisiello in his "Les Adieux de la Grande Duchesse de Russies," written in about 1784, upon his departure from the court of Catherine the Great.

The "Ricercar a 6" has been arranged on its own on a number of occasions, the most prominent arranger being Anton Webern, who in 1935 made a version for small orchestra, noted for its Klangfarbenmelodie style (i.e. melody lines are passed on from one instrument to another after every few notes, every note receiving the "tone color" of the instrument it is played on):

 

Webern's arrangement was dedicated to the BBC music producer and conductor Edward Clark.[10]

Another version of the Ricercare a 6 voci was published in 1942 by C. F. Peters in an arrangement for organ by the musicologist Hermann Keller, then based in Stuttgart.[11]

Igor Markevitch produced a realization for three orchestral groups and, for the sonata movements, solo quartet (violin, flute, cello, and harpsichord), written in 1949–50.

The Modern Jazz Quartet used one of the canons (originally "for two violins at the unison") as an introduction to their performance of the standard song "Softly, as in a Morning Sunrise".[12] The Royal Theme is played on the double bass, with Milt Jackson (vibraphone) and John Lewis (piano) weaving the two imitative contrapuntal voices above:

 
Canon from The Musical Offering

Isang Yun composed Königliches Thema for Solo Violin, a passacaglia on the Thema Regium with Asian and Twelve-tone influences, written in 1970.

Bart Berman composed three new canons on the Royal Theme of The Musical Offering, which were published in 1978 as a special holiday supplement to the Dutch music journal Mens & Melodie (publisher: Het Spectrum).

Sofia Gubaidulina used the Royal Theme of The Musical Offering in her violin concerto Offertorium (1980). Orchestrated in an arrangement similar to Webern's, the theme is deconstructed note by note through a series of variations and reconstructed as a Russian Orthodox hymn.

Leslie Howard produced a new realisation of The Musical Offering, which he orchestrated and conducted in Finland in 1990.

The organist Jean Guillou transcribed the entire work for organ in 2005.[13]

Notable recordings

See also

References

  1. ^ Rosen, Charles (18 April 1999). "Best Piano Composition; Six Parts Genius". The New York Times.
  2. ^ David, Hans T.; Mendel, Arthur; Wolff, Christoph (1999). The New Bach Reader. W. W. Norton. p. 224. ISBN 0-393-31956-3.
  3. ^ Gaines, James R. (2006). Evening in the Palace of Reason: Bach meets Frederick the Great in the Age of Enlightenment. Harper Perennial. pp. 9–11. ISBN 978-0-00-715392-3.
  4. ^ New York Philharmonic Notes on the Program, p. 31, December 2018
  5. ^ Humphrey F. Sassoon (2003). "J. S. Bach's Musical Offering and the Source of Its Theme: Royal Peculiar." The Musical Times, vol. 144, no. 1885, pp. 38–39
  6. ^ Schoenberg, Arnold; Stein, Leonard; Black, Leo (1985). Style and idea : selected writings of Arnold Schoenberg. Berkeley: University of California Press. p. 394. ISBN 0520052862. OCLC 12105620.
  7. ^ Michael Marissen (1995). Daniel R. Melamed (ed.). The theological character of J. S. Bach's Musical Offering. Bach Studies 2. Cambridge University Press. pp. 85–106. ISBN 978-0-521-47067-4.
  8. ^ "The Sacred Codes of the Six-Part Ricercar", Bach. The Journal of the Riemenschneider Bach Institute, vol. 42/1 (2011), 46–69.
  9. ^ Kirkendale, Ursula (Spring 1980). "The Source for Bach's Musical Offering: The Musical Offering of Quintilian". Journal of the American Musicological Society. 33 (1): 99–141. doi:10.2307/831204. ISSN 0003-0139. JSTOR 831204.
  10. ^ Vienna: Universal Edition OCLC 461971074
  11. ^ Edition Peters No. 4528
  12. ^ This features on their album Concorde (1955).
  13. ^ Bach, Johann Sebastian, Das musikailische Opfer, transcribed for Organ by Jean Guillou, vol. ED 9804, Schott

Further reading

  • Reinhard Boess: Die Kunst des Rätselkanons im 'musikalischen Opfer', 1991, 2 vols., ISBN 3-7959-0530-3

External links

January 26, 2023
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The Musical Offering German Musikalisches Opfer or Das Musikalische Opfer BWV 1079 is a collection of keyboard canons and fugues and other pieces of music by Johann Sebastian Bach all based on a single musical theme given to him by Frederick the Great King Frederick II of Prussia to whom they are dedicated They were published in September 1747 The Ricercar a 6 a six voice fugue which is regarded as the high point of the entire work was put forward by the musicologist Charles Rosen as the most significant piano composition in history partly because it is one of the first 1 This ricercar is also occasionally called the Prussian Fugue a name used by Bach himself The composition is featured in the opening section of Douglas Hofstadter s Pulitzer Prize winning book Godel Escher Bach 1979 Contents 1 History 1 1 Possible origin of the King s Theme 2 Structure and instrumentation 2 1 Musical riddles 2 2 Canon per tonos endlessly rising canon 3 Theological character 4 Adaptations and citations 5 Notable recordings 6 See also 7 References 8 Further reading 9 External linksHistory Edit The Flute Concert of Sanssouci by Adolph Menzel 1852 depicts Frederick playing the flute in his music room with C P E Bach accompanying him on a harpsichord shaped piano by Gottfried Silbermann The collection has its roots in a meeting between Bach and Frederick II on May 7 1747 The meeting taking place at the king s residence in Potsdam came about because Bach s son Carl Philipp Emanuel was employed there as court musician Frederick wanted to show the elder Bach a novelty the fortepiano which had been invented some years earlier The king owned several of the experimental instruments being developed by Gottfried Silbermann 2 During his anticipated visit to Frederick s palace in Potsdam Bach who was well known for his skill at improvising received from Frederick a long and complex musical theme on which to improvise a three voice fugue He did so but Frederick then challenged him to improvise a six voice fugue on the same theme Bach answered that he would need to work the score and send it to the king afterwards He then returned to Leipzig to write out the Thema Regium theme of the king 3 source Audio playback is not supported in your browser You can download the audio file Four months after the meeting Bach published a set of pieces based on this theme which we now know as The Musical Offering 4 Bach inscribed the piece Regis Iussu Cantio Et Reliqua Canonica Arte Resoluta the theme given by the king with additions resolved in the canonic style the first letters of which spell out the word ricercar a well known genre of the time Possible origin of the King s Theme Edit Humphrey F Sassoon has compared the theme issued by Frederick II to the theme of an A minor fugue HWV 609 by George Frideric Handel published in Six fugues or voluntarys for organ or harpsichord Sassoon notes that Handel s theme is much shorter than the King s but its musical architecture is uncannily similar jumps followed by a descending chromatic scale He also elaborates on their additional similarities which led Sassoon to suggest that Bach used Handel s A minor fugue as a structural model or guide for the Musical Offering s Ricercar a 6 and that its musical concepts may also have influenced Bach s development of the Ricercar a 3 5 Nevertheless the Ricercar a 6 is longer and incomparably more complex than Handel s fugue Arnold Schoenberg in his 1950 essay on Bach suggested that the Thema Regium was created by Bach s son Carl Phillip Emanuel on the orders of the king as a well prepared trap to embarrass J S Bach 6 Structure and instrumentation EditIn its finished form The Musical Offering comprises Two Ricercars written down on as many staves as there are voices a Ricercar a 3 a three voice fugue a Ricercar a 6 a six voice fugue Ten Canons Canones diversi super Thema Regium 2 Canons a 2 the first representing a notable example of a crab canon or canon cancrizans Canon a 2 per motum contrarium Canon a 2 per augmentationem contrario motu Canon a 2 per tonos Canon perpetuus Fuga canonica in Epidiapente Canon a 2 Quaerendo invenietis Canon a 4 Canon perpetuus contrario motu Trio Sonata 1st part Largo 3 53 source source 2nd part Allegro 4 12 source source 3rd part Allegro fin Andante 4 46 source source 4th part Allegro 3 11 source source Recorded in 1930 in Paris Problems playing these files See media help A Sonata sopr il Soggetto Reale a trio sonata featuring the flute an instrument which Frederick played consisting of four movements Largo Allegro Andante AllegroApart from the trio sonata which is written for flute violin and basso continuo the pieces have few indications of which instruments are meant to play them although there is now significant support for the idea that they are for solo keyboard like most of Bach s other published works The ricercars and canons have been realised in various ways The ricercars are more frequently performed on keyboard than the canons which are often played by an ensemble of chamber musicians with instrumentation comparable to that of the trio sonata As the printed version gives the impression of being organised for convenient page turning when sight playing the score the order of the pieces intended by Bach if there was an intended order remains uncertain although it is customary to open the collection with the Ricercar a 3 and play the trio sonata toward the end The Canones super Thema Regium are also usually played together Musical riddles Edit Some of the canons of The Musical Offering are represented in the original score by no more than a short monodic melody of a few measures with a more or less enigmatic inscription in Latin above the melody These compositions are called the riddle fugues or sometimes more appropriately the riddle canons The performer s is are supposed to interpret the music as a multi part piece a piece with several intertwining melodies while solving the riddle Some of these riddles have been explained to have more than one possible solution although nowadays most printed editions of the score give a single more or less standard solution of the riddle so that interpreters can just play without having to worry about the Latin or the riddle One of these riddle canons in augmentationem i e augmentation the length of the notes gets longer is inscribed Notulis crescentibus crescat Fortuna Regis may the fortunes of the king increase like the length of the notes while a modulating canon which ends a tone higher than it starts is inscribed Ascendenteque Modulatione ascendat Gloria Regis as the modulation rises so may the king s glory Canon per tonos endlessly rising canon Edit The canon per tonos endlessly rising canon pits a variant of the king s theme against a two voice canon at the fifth However it modulates and finishes one whole tone higher than it started out at It thus has no final cadence Theological character EditAmong the theories about external sources of influence Michael Marissen s 7 draws attention to the possibility of theological connotations Marissen sees an incongruity between the official dedication to Frederick the Great and the effect of the music which is often melancholy even mournful The trio sonata is a contrapuntal sonata da chiesa whose style was at odds with Frederick s secular tastes The inscription Quaerendo invenietis found over Canon No 9 alludes to the Sermon on the Mount Seek and ye shall find Matthew 7 7 Luke 11 9 The main title Opfer offering makes it possible for the cycle to be viewed as an Offertory in the religious sense of the word Marissen also points out that canonic procedures often evoking the rigorous demands of the Mosaic Law the ten canons likely allude to the Ten Commandments Marissen believes that Bach was trying to evangelize Frederick the Great pointing him to the demands of the Mosaic Law In a recent study 8 Zoltan Goncz has pointed out the authorial injunction to seek Quaerendo invenietis does not only relate to the riddle canons but to the six part ricercar as well whose archaic title also means to seek There are several Biblical citations hidden in this movement and their discovery is made especially difficult by various compositional maneuvers The unique formal structure of the fugue provides a clue certain anomalies and apparent inconsistencies point to external nonmusical influences Among Bach s duties during his tenure at Leipzig 1723 50 was teaching Latin Ursula Kirkendale 9 argued for a close connection with the twelve volume rhetorical manual Institutio Oratoria of the Roman orator Quintilian whom Frederick the Great admired Philologist and Rector of the Leipzig Thomasschule Johann Matthias Gesner for whom Bach composed a cantata in 1729 published a substantial Quintilian edition with a long footnote in Bach s honor Adaptations and citations EditThe thema regium appears as the theme for the first and last movements of Sonata No 7 in D minor by Friedrich Wilhelm Rust written in about 1788 and also as the theme for elaborate variations by Giovanni Paisiello in his Les Adieux de la Grande Duchesse de Russies written in about 1784 upon his departure from the court of Catherine the Great The Ricercar a 6 has been arranged on its own on a number of occasions the most prominent arranger being Anton Webern who in 1935 made a version for small orchestra noted for its Klangfarbenmelodie style i e melody lines are passed on from one instrument to another after every few notes every note receiving the tone color of the instrument it is played on Webern s arrangement was dedicated to the BBC music producer and conductor Edward Clark 10 Another version of the Ricercare a 6 voci was published in 1942 by C F Peters in an arrangement for organ by the musicologist Hermann Keller then based in Stuttgart 11 Igor Markevitch produced a realization for three orchestral groups and for the sonata movements solo quartet violin flute cello and harpsichord written in 1949 50 The Modern Jazz Quartet used one of the canons originally for two violins at the unison as an introduction to their performance of the standard song Softly as in a Morning Sunrise 12 The Royal Theme is played on the double bass with Milt Jackson vibraphone and John Lewis piano weaving the two imitative contrapuntal voices above Canon from The Musical Offering Isang Yun composed Konigliches Thema for Solo Violin a passacaglia on the Thema Regium with Asian and Twelve tone influences written in 1970 Bart Berman composed three new canons on the Royal Theme of The Musical Offering which were published in 1978 as a special holiday supplement to the Dutch music journal Mens amp Melodie publisher Het Spectrum Sofia Gubaidulina used the Royal Theme of The Musical Offering in her violin concerto Offertorium 1980 Orchestrated in an arrangement similar to Webern s the theme is deconstructed note by note through a series of variations and reconstructed as a Russian Orthodox hymn Leslie Howard produced a new realisation of The Musical Offering which he orchestrated and conducted in Finland in 1990 The organist Jean Guillou transcribed the entire work for organ in 2005 13 Notable recordings EditKarl Munchinger Stuttgart Chamber Orchestra Decca 1955 Milan Munclinger Ars Rediviva Stanislav Duchon Karel Bidlo Jiri Baxa Josef Vlach Vaclav Snitil Jaroslav Motlik Frantisek Slama Frantisek Posta Viktorie Svihlikova Supraphon 1959 Karl Richter Otto Buchner Kurt Guntner Siegfried Meinecke Fritz Kiskalt Hedwig Bilgram DGG Archiv Produktion 1963 Milan Munclinger Ars Rediviva Stanislav Duchon Karel Bidlo Vaclav Snitil Jaroslav Motlik Frantisek Slama Frantisek Posta Josef Hala Supraphon 1966 Nikolaus Harnoncourt Concentus Musicus Wien Teldec 1970 Neville Marriner Academy of St Martin in the Fields Philips 1974 Reinhard Goebel Musica Antiqua Koln Archiv Bach Edition 1979 Hans Martin Linde Linde Consort EMI Reflexe 1981 Barthold Kuijken flute Sigiswald Kuijken violin Wieland Kuijken viola da gamba Robert Kohnen harpsichord Deutsche Harmonia Mundi 1994 Jordi Savall Le Concert des Nations Alia Vox 1999 Hanssler Edition Gottfried von der Goltz Petra Mullejans Martin Jopp Daniela Helms Christian Gosses Violin Viola Karl Keiser flute Ekkehard Weber viola da gamba Kristin von der Goltz cello and Michael Behringer harpsichord forte piano BWV 1079 Hanssler Edition CD92 133 1999 Konstantin Lifschitz Orfeo 676071 2008 all movements on piano See also EditList of compositions of Johann Sebastian Bach Perpetuum mobileReferences Edit Rosen Charles 18 April 1999 Best Piano Composition Six Parts Genius The New York Times David Hans T Mendel Arthur Wolff Christoph 1999 The New Bach Reader W W Norton p 224 ISBN 0 393 31956 3 Gaines James R 2006 Evening in the Palace of Reason Bach meets Frederick the Great in the Age of Enlightenment Harper Perennial pp 9 11 ISBN 978 0 00 715392 3 New York Philharmonic Notes on the Program p 31 December 2018 Humphrey F Sassoon 2003 J S Bach s Musical Offering and the Source of Its Theme Royal Peculiar The Musical Times vol 144 no 1885 pp 38 39 Schoenberg Arnold Stein Leonard Black Leo 1985 Style and idea selected writings of Arnold Schoenberg Berkeley University of California Press p 394 ISBN 0520052862 OCLC 12105620 Michael Marissen 1995 Daniel R Melamed ed The theological character of J S Bach sMusical Offering Bach Studies 2 Cambridge University Press pp 85 106 ISBN 978 0 521 47067 4 The Sacred Codes of the Six Part Ricercar Bach The Journal of the Riemenschneider Bach Institute vol 42 1 2011 46 69 Kirkendale Ursula Spring 1980 The Source for Bach s Musical Offering The Musical Offering of Quintilian Journal of the American Musicological Society 33 1 99 141 doi 10 2307 831204 ISSN 0003 0139 JSTOR 831204 Vienna Universal Edition OCLC 461971074 Edition Peters No 4528 This features on their album Concorde 1955 Bach Johann Sebastian Das musikailische Opfer transcribed for Organ by Jean Guillou vol ED 9804 SchottFurther reading EditReinhard Boess Die Kunst des Ratselkanons im musikalischen Opfer 1991 2 vols ISBN 3 7959 0530 3External links EditMusikalisches Opfer BWV 1079 Scores at the International Music Score Library Project The Musical Offering A Musical Pedagogical Workshop by J S Bach or The Musical Geometry of Bach s Puzzle Canons English Schillerinstituttet Danish The Mutopia Project has some of the music of The Musical Offering Das Musikalisches Opfer PianoSociety com Performance of Trio Sonata by The Chamber Music Society of Lincoln Center from the Isabella Stewart Gardner Museum in MP3 format Phillips Tony March 1 1999 Feature Column Math and The Musical Offering What s New in Mathematics American Mathematical Society Johann Sebastian Bach 1685 1750 L Offrande musicale Musical Offering Musikalisches Opfer BWV 1079 ClassicalAlacarte com Portal Classical music Retrieved from https en wikipedia org w index php title The Musical Offering amp oldid 1124987028, wikipedia, wiki, book, books, library,

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