Johann Sebastian Bach - The Musical Offering

The Musical Offering (German: Musikalisches 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).

This ricercar is also occasionally called the Prussian Fugue, a name used by Bach himself.

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.

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"):

Four months after the meeting, Bach published a set of pieces based on this theme which we now know as The Musical Offering.

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.

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

A Sonata sopr'il Soggetto Reale – a trio sonata featuring the flute, an instrument which Frederick played, consisting of four movements:

Largo

Allegro

Andante

Allegro

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.

J. S. Bach - Triosonata in C minor from the 'Musical Offering', BWV 1079 Nr. 8.webm

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Photo: Johann Sebastian Bach, The Musical Offering, BWV 1079. (Canon 1, and 2 violini in unisono)  Wikipedia

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Music cancrizans

Contrapuntal forms

In the canonic forms, the earliest known in music as an independent art, the laws of texture also determine the shape of the whole, so that it is impossible, except in the light of historical knowledge, to say which is prior to the other.

The principle of canon being that one voice shall reproduce the material of another note for note, it follows that in a composition where all parts are canonic and where the material of the leading part consists of a pre-determined melody, such as a Gregorian chant or a popular song there remains no room for further consideration of the shape of the work...

The resources of canon, when emancipated from the principles of the round, are considerable when the canonic form is strictly maintained, and are inexhaustible when it is treated freely.

A canon need not be in the unison; and when it is in some other interval the imitating voice alters the expression of the melody by transferring it to another part of the scale.

Again, the imitating voice may follow the leader at any distance of time; and thus we have obviously a definite means of expression in the difference of closeness with which various canonic parts may enter, as, for instance, in the stretto of a fugue...

The close canon in the 6th at the distance of one minim in reversed accent in Bach’s eighteenth Goldberg variation owes all its smooth harmonic expression to the fact that the two canonic parts move in sixths which would be simultaneous but for the pause of the minim which reverses the accents of the upper part while it creates that chain of suspended discords which give harmonic variety to the whole.

Two other canonic devices have important artistic value, namely, augmentation and diminution (two different aspects of the same thing) and inversion.

In augmentation the imitating part sings twice as slow as the leader, or sometimes still slower.

This obviously should impart a new dignity to the melody, and in diminution the expression is generally that of an accession of liveliness.

Neither of these devices, however, continues to appeal to the ear if carried on for long.

In augmentation the answering part lags so far behind the leader that the ear cannot long follow the connexion, while a diminished answer will obviously soon overtake the leader, and can proceed on the same plan only by itself becoming the leader of a canon in augmentation.

Beethoven, in the fugues in his sonatas op. 106 and 110, adapted augmentation and diminution to modern varieties of thematic expression, by employing them in triple time, so that, by doubling the length of the original notes across this triple rhythm, they produce an entirely new rhythmic expression.

This does not seem to have been applied by any earlier composer with the same consistency or intention.

The device of inversion consists in the imitating part reversing every interval of the leader, ascending where the leader descends and vice versa.

Its expressive power depends upon such subtle matters of the harmonic expression of melody that its artistic use is one of the surest signs of the difference between classical and merely academic music.

There are many melodies of which the inversion is as natural as the original form, and does not strikingly alter its character.

Such are, for instance, the theme of Bach’s Kunst der Fuge, most of Purcell’s contrapuntal themes, the theme in the fugue of Beethoven’s sonata, op. 110, and the eighth of Brahms’s variations on a theme by Haydn.

In such cases inversion sometimes produces harmonic variety as well as a sense of melodic identity in difference.

But where a melody has marked features of rise and fall, such as long scale passages or bold skips, the inversion, if productive of good harmonic structure and expression, may be a powerful method of transformation.

This is admirably shown in the twelfth of Bach’s Goldberg Variations, in the fifteenth fugue of the first book of his Forty-eight Preludes and Fugues, in the finale of Beethoven’s sonata, op. 106, and in the second subjects of the first and last movements of Brahms’s clarinet trio.

The only remaining canonic device which figures in classical music is that known as cancrizans, in which the imitating part reproduces the leader backwards.

It is of extreme rarity in serious music; and, though it sometimes happens by accident that a melody or figure of uniform rhythm will produce something equally natural when read backwards, there is only one example of its use that appeals to the ear as well as the eye.

This is to be found in the finale of Beethoven’s sonata, op. 106, where it is applied to a theme with such sharply contrasted rhythmic and melodic features that with long familiarity a listener would probably feel not only the wayward humour of the passage in itself, but also its connexion with the main theme.

Nevertheless, the prominence given to the device in technical treatises, and the fact that this is the one illustration which hardly any of them cite, show too clearly the way in which music is treated not only as a dead language but as if it had never been alive.

All these devices are also independent of the canonic idea, since they are so many methods of transforming themes in themselves and need not always be used in contrapuntal combination.

EncyclopaediaBritannica, 11th Edition, Volume 7

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The great Netherlands school

At the period of musical history which we have now reached, the Dutch, as I have had occasion to say in another work, "led the world in painting, in liberal arts, and in commercial enterprise.

Their skill in mechanics was unequalled, and we naturally expect to see their musicians further the development of musical technic."

The Dutch musicians at first revelled in the exercise of mechanical ingenuity in the construction of intricate contrapuntal music.

In the first period of their great school they acquired by such exercise so great a mastery of the materials of their art that in the second period they began to make serious attempts at writing beautiful music for beauty's sake.

In the third period the possibilities of writing something different from church music began to be developed, and we find the Dutch masters attempting the description in tones of external phenomena by the process called tone-painting.

This period also saw secular music taken into the fold of art, and began the production of madrigals and other secular songs.

In the fourth period the dry old science of counterpoint was so completely conquered that the composers of the time were able to make it the vehicle of the purest expression of religious devotion the world has yet found, and church music passed through its golden age.

On account of these facts let us consider this great school, which had more influence on the development of music than any other school in the history of music, under the following heads:

Netherlands School (1425-1625 A. D.).

First Period (1425-1512).—Perfection of contrapuntal technics. Chief masters: Okeghem, Hobrecht, Brumel.

Second Period (1455-1526).—Attempts at pure beauty. Chief master, Josquin des Prés.

Third Period (1495-1572).—Development of tone-painting and secular music. Chief masters: Gombert, Willaert, Goudimel, Di Rore, Jannequin, Arcadelt.

[Pg 40]Fourth Period (1520-1625).—Counterpoint made subservient to expression of religious feeling. Chief masters: Orlando Lasso, Swelinck, De Monte.

The reader will note that the division of these periods is not based on chronological, but artistic grounds; and hence, in respect of years, they overlap.

The most famous writer of the first period was Johannes Okeghem, born between 1415 and 1430, in East Flanders.

He studied under Binchois, a contemporary of Dufay, at Antwerp, was a singer in the service of Charles VII. of France in 1444, was made by Louis XI. Treasurer of the Cathedral of St. Martin's at Tours, and died there about 1513.

A considerable quantity of his music has been preserved.

It is notable chiefly for its technical skill; and during his life Okeghem was the most famous teacher of his day.

His most noted pupil was Antoine Brumel (1460-1520), whose personal history is lost, though many of his masses and motets are preserved.

Jacob Hobrecht (1430-) achieved great celebrity.

Eight of his masses are extant.

As I have said in another account of the Netherlands school, "It is the prevailing influence of one or two masters in each period that marks its extent. Its character was formed by that influence, and salient features of the style of each period may be fairly distinguished. The first period was marked by the extreme development of the 'canon."

I have already endeavored to explain the nature of canonic writing.

If the reader will bear in mind that it is the most rigid form of imitation, requiring the original melody to be imitated throughout in the subsidiary parts, he will not go astray.

Okeghem and his contemporaries completely explored the resources of canonic writing.

They invented all kinds of canons.

They originated the 'crab' canon, in which the part sung by the second voice was the first voice part written backwards.

You can sing or play this through forward and then backward, and its counterpoint remains correct.

They had also the inverted canon, in which the second part consisted of the first part turned upside down.

The canon by augmentation makes the melody appear in a subsidiary part in notes longer than those in which it appeared in the principal part; and the canon by diminution is formed on the opposite principle.

These old musical puzzle-workers had other forms far more complicated, and they took great delight in writing "riddle" canons.

In these only the subject was given, with the motto, "Ex una, plures," meaning that the musician must work out the other parts from the one; and then some hint as to the manner of working them out would be given, as, "Ad medium referas, pauses relinque priores."

The working out of these riddle canons became a mania with Okeghem and his immediate successors; and the result was that they acquired an immense command over the technics of contrapuntal writing.

But "the highest praise that can be awarded to their works is that they are profound in their scholarship, not without evidences of taste in the selection of the formulas to be employed, and certainly imbued with a good deal of the dignity which would inevitably result from a skilful contrapuntal treatment of the church chant."

It is, however, of singular significance in the history of this period that some of the works of both Hobrecht and Brumel show a tendency toward some conception of chord harmonies.

W. J. Henderson, How MusicDeveloped (A Critical and Explanatory Account of the Growth of Modern Music), New York, 1898.

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Crab canon

A crab canon (also known by the Latin form of the name, canon cancrizans; as well as retrograde canon, canon per recte et retro or canon per rectus et inversus) is an arrangement of two musical lines that are complementary and backward.

If the two lines were placed next to each other (as opposed to stacked), the lines would form something conceptually similar to a palindrome.

The name 'crab' refers to the fact that crabs are known to walk backward (although they can also walk forward and sideways).

It originally referred to a kind of canon in which one line is played backward (e.g. FABACEAE played simultaneously with EAECABAF).

An example is found in J. S. Bach's The Musical Offering, which also contains a table canon ("Quaerendo invenietis"), which combines retrogression with inversion by having one player turn the music upside down.

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