How to Study the Two-Voiced Inventions of Bach

By Ernest Hutcheson

Probably no single work known to teachers and students of the piano is more constantly used than the inventions of Bach. The lapse of time since they were written has served but to enhance our recognition of their musical and technical value; no substitute for them has been found or even suggested. The beginner may sometimes, in his haste, deny Bach and heatedly call them “Inventions of the Devil”; on the other hand, the teacher is abidingly grateful for a work which he can hear endlessly and often execrably repeated without loss of the interest and admiration it inspires.

Yet few persons thoroughly understand the Inventions. To do so is to have made a significant step toward real musicianship, and no student should be content to rattle through these masterly miniatures without seriously trying to grasp their meaning and appreciate the beauty of their workmanship.

I may begin by pointing out that the two-part and three-part Inventions each consists of fifteen pieces written in a particular series of keys. These keys are C major and minor, D major and minor, E flat major, E major and minor, F major and minor, G major and minor, A major and minor, B flat major and B minor. The reason for the omission of the other keys is an interesting one.

At the time the pieces were composed the method of tuning the piano by what is called “equal temperament” had not been introduced. By the older method, not all keys could be equally well tuned, and naturally those least often used, namely those with many sharps and flats, were sacrificed in favor of the others. Bach, therefore, avoided all keys having more than four sharps or flats, and also F sharp minor, C sharp minor and A flat.

Later, when equal temperament was suggested, Bach threw the weight of his influence solidly behind the innovation. His propaganda work had an immortal results in the well-tempered (i.e., the well-tuned) clavier, a double series of preludes and fugues in all twenty four keys.

Bach gave to the Inventions a quaint and lengthy title. As few take the trouble to read it, it is worth translating:

“An honest guide whereby is shown to lovers and especially to students of music a clear way not only of learning to play two parts accurately, but with further progress to handle three obbligato parts correctly and well; at the same time not only to acquire good ideas (“inventions”) but also to develop them properly; above all, however, to cultivate a cantabile style of playing, besides gaining a real foretaste of the art of composition.”

We see from these words of Bach that the volume was intended as a set of studies in two and three part counterpoint for the benefit alike of players and composers. It is essential, therefore, that at the outset we should understand the main features of polyphonic writing. The following simple definitions and explanations will suffice for the uninitiated:

  1. Counterpoint or polyphony is the art of combining melodic parts or “voices” usually of a stated number.
  2. Double counterpoint is the art of writing such parts so that they can be “inverted” without injury to the effect. If you compare measures 1-4 of the sixth Invention with measures 5-8 you will see that either passage is a contrapuntal inversion of the other. Better still, take the trouble to invert the entire first Invention, playing the bass an octave higher with the right hand, and the soprano two octaves lower with the left hand. Almost all the Inventions are written in double counterpoint.
  3. The recurrence of a melodic figure or motive in different parts constitutes “imitation.” See the first two measures of the first Invention, etc. The Inventions all abound in imitation.
  4. A canon is a composition written throughout in strict imitation between two or more parts. A popular example, familiar to every child, is the tune of Three Blind Mice. Actual canons do not occur in the Inventions, but we shall find several instances of canonic structure.
  5. A stretto occurs in the imitation of a theme or motive when a second part enters before the first is complete. An example will be mentioned in discussing the fourteenth Invention.
  6. Thematic or melodic inversion, not to be confused with the contrapuntal inversion already explained, is best shown by an example. In Invention No. 4 the direct form of the theme (a) is varied at measures 22-23 by the thematic inversion (b).

two-voiced-inventions17. In a contrapuntal composition there is usually a leading idea called a theme or subject, often very short, which recurs frequently in the different voices. The other parts accompanying this subject are usually referred to as “counterpoints” and when a counterpoint persistently attends a theme throughout the composition it is called a “counter-subject.”

So much for the general features of polyphony. Let us now examine some of the Inventions in detail, in order to observe their wide variety of style and structure.

No. 1, in C major, is based entirely on a short motive of eight notes, the final note being variable.


Cadences at measures 6, 14 and 20-21 divide the piece into three sections, and the first two of these cadences are the only places in which the theme is absent. This is an unusually closely-knot structure; more often, in polyphonic composition, the various entrances of the theme are separated and relieved by “episodes” kindred in style but not identical in motive with the subject. In measures 3-4 the theme appears four times in melodic inversion:


Here the counterpoint in the left hand should be noted; it recurs frequently, and consists of an augmentation of the first four notes of the theme. From this point on the theme occurs almost as often in its inverted as in its direct form.

Other instances of this general type are Inventions 4, 7, and 15.

No. 2 in C minor, is quite different in plan. The upper voice begins with a subject (A) of two measures in length. When the lower voice repeats this the upper adds a counterpoint (B). The lower voice now proceeds to (B) and the upper voice again presents a new counterpoint (C). The process continues until, in all, five melodies or counterpoints have been introduced. The whole scheme is then repeated in the contrapuntal inversion. The lower part beginning and the upper part following. Finally, after an imitative episode of two measures the counterpoints A and B are alternated in both parts to form a coda. The whole plan might be graphically shows as follows, each vertical line except the last representing a section of two measures:


At (f) a new counterpoint will be found, but this is merely to preserve the continuity of the upper voice, and there is no recurrence. This particularly interesting form has no counterpart in any other Invention.

No. 3, in D major, looks very simple, yet it might easily puzzle a novice. The theme is:


It is seldom given, however, in its complete form. Whole passages (e.g. measures 5-10) contain only the measu8re I have marked a. Occasionally the longer fragment, b, occurs alone. Most frequently, however, we find b with a prefix of three notes, as at the twelfth measure:


There is also a euphonious little phrase, continued from a, which is used in all the cadences (see measures 9-12, 21-24, etc.). Finally, the first notes of the theme are once or twice subjected to a slight variation.

Bach follows the main plan of the D major Invention in many others. That is to say, there is often a theme which is occasionally or frequently curtailed, only the chief motive or figure being quoted. See, for instance, No. 5, in E flat. Here there is a comparatively long theme of four measures, the first of which announces a striking motive often used alone in the development. This piece also shows a persistent counter-subject in sixteenth notes. No. 14, in B flat, is another case in point, and a quite remarkable one. The thematic announcement is spun out by repetition to three measures, but the subject proper is contained in one. This subject itself consists of a motive a, followed by its melodic inversion b:


And the motive is again sub-divisible, the figure c playing a very prominent independent part in the course of the piece. In the first half of the Invention there is a counter-subject in eighth notes, which afterward disappears as the imitations become more closely crowded. Toward the end Bach uses a clever stretto; I quote the beginning of it for convenience on a single staff.


Other examples in which the theme is often quoted in part only are Nos. 9, 11 and 12. These three Inventions are all characterized by distinct counter-subjects. The whole group (3, 5, 9, 11, 12 and 14) is also conspicuous by the absence of thematic inversion, the figure c in No. 14 being a solitary exception.

Invention 6, in E major, is an excellent illustration of double counterpoint. It is constructed of two melodies or counterpoints of equal importance, used simultaneously. One of these concludes with a strongly rhythmic figure:


Which is used independently, sometimes in thematic inversion. This is the only invention divided by Bach into two repeating sections. The student is strongly recommended to make a careful comparison of the first twenty measures with the final twenty; except for some trifling variations resulting from the change of tonality, the two passages are written in strict inversion.

No. 8, in F major, is probably the most popular of the inventions. Harold Bauer has not hesitated to introduce it on his recital programs. The piece may most accurately be described as being written in canonic imitation. It has, in fact, all the effectiveness of a canon without the stiffness almost inseparable from an extended strict adherence to that form. In this connection it may well be emphasized that Bach always displays the utmost freedom in handling all polyphonic forms and devices. He treats the medium with consummate mastery and easy, disdaining all rigidity of rule where musical effects are in question.

I should be observed that the second Invention, already referred to, might also be regarded as canonic in structure. To me it seems preferable to consider it as merely a series of counterpoints, but the difference is purely technical. There is again a well-defined semblance of canon in No. 13, in A minor. At a casual view, this Invention may seem rather loosely put together, with little relation to its main theme, a.


Two longer phrases (b and c in the example below) are used later; the first of them is treated in close imitation (stretto).


These phrases seem new, but their essential identity with the original theme is disclosed by the rhythmical similarity of the three examples at a and the prevalence of progression by thirds. They are, therefore, simply variations of a single leading idea. No. 10, in G demonstrates the same use of varying figures easily recognizable as derived from the main subject.

I do not pretend to have given, in the above remarks, anything resembling an analysis of the Inventions. This could be done only by quoting and appropriately marking the entire text. I have been content to indicate general lines of structure, in the hope of stimulating interest toward a more exhaustive study.