All this Invention's basic materials are set out in the first couple of measures; as the left hand trots up and down a stair-step figure, the right plays a tiny motif consisting of a trill and an unornamented note, repeated once and creating a skipping rhythm. The right hand then follows this with a more extended trill before taking up the stair-step material, whereupon the left hand has a go at what the right hand has accomplished so far. Soon that third trill is shed, and the full melody, which passes back and forth between the hands, is assembled by joining the stair-step pattern to the initial pair of skipping trills. And so it continues, the two lines imitating one another but not with absolute strictness. The material of greatest melodic interest finally settles into the treble, with the bass ultimately relegated to accompaniment mode for the final measures.

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This invention remains in constant motion through its brief duration; the main line, in the right hand, is perky and chattering, while the left hand repeats everything just a few steps behind throughout. One of the problems this happy little canon presents is finding the right tempo; a beginner is likely to be laboriously slow, but a professional may be inclined to take it at such a fast, exhibitionist clip that the piece can sound more like clacking, windup toy teeth than music.

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The first of Bach's famous little finger exercises begins with the right hand playing a generally upward-lifting melody that hardly ever pauses, while the left hand provides a steady but obviously simpler accompanimental melody in the bass. Near the end, however, Bach writes a brief call and response passage, the two hands gently tossing back and forth the half-bar motif that pervades this entire invention, before joining forces again for the final measures.

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Bach's third exercise for his son Wilhelm Friedemann eases into the not terribly challenging key (only two sharps) of D major, but away from the strict counterpoint of the C minor invention. Here, the two voices are complementary but generally not canonic, except for an explicitly imitative middle section. Otherwise, the right hand presents a busy, wandering theme that the left hand supports with material that is initially simpler, but ultimately as complex as the treble tune.

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Unusually, Bach begins this Invention with the left hand having very little to do—a tiny four-note accompaniment figure spaced between long rests, while the treble line twirls gently up and down the staff. But soon a brief call and response passage confuses the issue, and the main melody emerges in the bass, with the right hand now playing accompaniment. The right hand regains control of the melody, but the left, reluctant to relinquish the spotlight, maintains a steadier accompanying line and eventually joins the right hand in a closer canonic relationship through the piece's final bars. In a minute and a half, Bach has managed to survey the development of a student's left-hand facility, from rudimentary support for the melody line to fully equal and integrated partnership with the right hand.

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"A proper guide, by which lovers of the harpsichord, and especially those who crave instruction, are shown a clear way of learning not only to play cleanly in two voices but also, after further progress, to deal correctly with three obbligato voices, and also to create and properly develop good musical ideas; but, above all else, to acquire a true cantabile style of playing, and, with it, to get a good foretaste of the art of composition."

Thus reads J.S. Bach's own description, provided in a paragraph-long preface to the volume that contains the final 1723 versions of the pieces, of his Two- and Three-Part Inventions for keyboard. His purpose in writing them could not be made more plain—and, indeed, it was not as instructional material in some general sense that he first conceived the pieces, but rather as exercises specifically designed for his 12-year-old son Wilhelm Friedemann (the first versions of the pieces are to be found in the 1722 Clavier-Büchlein for Wilhelm Friedemann). There are 30 pieces altogether, 15 Inventions in two voices and 15 Sinfonias in three.

The 15 Two-Part Inventions are written in the 15 keys that were at the time considered to be standard for keyboard use (remember that the Well-Tempered Clavier, which explores all 24 keys, was a novelty made possible only by the advent of more sophisticated tuning systems). The original order of the pieces was rather different than is the order in which one today finds them—it was Bach himself, however, and not modern editors, who rearranged the pieces. The final key scheme is as follows: 1. C major, 2. C minor, 3. D major, 4. D minor, 5. E flat major, 6. E major, 7. E minor, 8. F major, 9. F minor, 10. G major, 11. G minor, 12. A major, 13. A minor, 14. B flat major, 15. B minor.

The Two-Part Inventions are perfectly suited for the development and maintenance of finger dexterity (they are often used specifically as preparation for the Well-Tempered Clavier), and one will find them on the pianos of not only young students and their teachers, but also many accomplished pianists who have realized that simpler is not always easier. But these 15 short pieces—only a few break the 30-bar mark by an appreciable amount—are also phenomenally well-composed; they are miniature specimens of ingenious motivic development.

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The treble line dominates this Invention, with the bass accepting a subsidiary but hardly dull role. The bass tends to echo the treble's rhythms and melodic contours a few beats behind, without precisely duplicating the melody. So although Bach here works with a greater variety of note values and rests than is common in his Inventions, he achieves a sense of constant forward motion by having one hand continue to chug away when the other is elongating a note or pausing for a beat.

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Here, Bach introduces the keyboard student to two-part canonic writing more strictly yet imaginatively than he does in his first, C major invention. The right hand alone announces an unsettled two-bar theme hovering high in the treble, which the left hand then picks up. The two hands then meander through a bit of contrapuntal writing, each checking in with the original motif again at the middle and end of the piece.

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This is one of Bach's most elegant-sounding yet more simply constructed inventions. A stately, well-ornamented theme rises and develops in the right hand, the same material then passing to the left hand as the right engages in a long section of passagework. The piece repeats this pattern several times, the theme shifting to slightly different registers but hardly changing otherwise, moving from one hand to the other and always accompanied by the busy but aurally undemanding passagework.

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This invention's bass line at first seems to combine with the treble into an imitative, two-voice canon, but within a few bars the left-hand role becomes quite independent, more given to phrases punctuated by a trill and a rest, or to maintaining a flatter melodic line while the treble part wanders more freely around the staff. Overall, this is a bucolic piece, pleasant country music in which the opening figure suggests a hunting horn.

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This is an exercise in contrary motion, one hand picking its way up the scale while the other descends, off the beat. The theme then essentially repeats the same pattern, but now mostly in triplets, providing a bit of contrast. Bach recycles these two segments several times, always starting from a different point on the scale, perhaps pushing the piece—at about three and a half minutes, the longest of the inventions—beyond the capacity of its modest material.

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Despite its minor key, Bach's fourth invention has a pleasant, swaying feel thanks to the smoothly rolling, up-and-down contour of its right-hand melody. The left hand picks up the theme, but supports it with independent though related material rather than mimicking it in strict canon. Long, imposing trills intrude upon each part. The "two-part" designation here applies not only to the voicing but to the structure; the piece falls into two halves, the second both a commentary on and prolongation of the first.

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Bach produces one of his finest examples of counterpoint-in-miniature with this invention. The grim, determined primary theme in the right hand progresses over the out-of-step inversion of its chromatic countersubject. The piece requires absolute clarity of voicing and independence of the two hands, simultaneously serving as an excellent introduction to the art of counterpoint.

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The right hand plays and expands upon a hesitant, questioning figure; the left hand occasionally echoes the main motif, but otherwise lies at rest through the first section of this invention. The left hand's role becomes far more active in the remainder of the piece, delivering an accompaniment line that is similar but by no means identical to the treble part.

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This final Invention starts off as a sort of grim, moderate-tempo court dance with a rather Eastern European feel. But within seconds it becomes almost, but not quite, a two-voice fugue, the little dance figure embedded in busy passagework and emerging now in the bass, now in the treble. Bach manages an impressively complex weave of the two lines in an exercise that lasts little more than a minute.

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Initially, the bass part of this invention gives the impression of being a carbon copy of the treble, just a few beats behind. Actually, although it closely imitates the rhythmic values of each measure of the primary theme, at phrase ends the bass line tends to veer in a direction opposite the path the treble has taken. Thus, the player can't merely synchronize the two hands to play the same line out of phase; it's always necessary to realize that the left hand has its own distinct melody.

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