Two-part Inventions by J. S. Bach, Thematic Hypostases

: Johann Sebastian Bach can be considered the greatest pre-classical composer for keyboard instruments, respectively piano, his works being universally present in concert programmes. Also, due to his experience as a teacher, the creation of J. S. Bach also has a great pedagogical importance: among the compositions intended for musical education we mention: Two-and Three-part Inventions (1723). The invention is a small free-form polyphonic composition, written in an imitative style, with a pronounced improvisational character. The two-part inventions that we have focused on (the first six), true jewels in terms of perfection of form, Bach's fundamental works for the piano, do not contain features of outward virtuosity, but music full of content and depth, the various thematic hypostases emphasizing their emotional substance. Another important aspect is the didactic function of this music, Bachian inventions constantly accompanying the training and improvement of pianists, being ideal due to their complexity, for deepening musical thinking.


Introduction
Even today, more than 250 years after the death of the last representatives of European musical Baroque, the works of Haendel, Bach and Scarlatti remain universally present in concert programmes."Johann Sebastian Bach (1685Bach ( -1750) ) was the heir of the polyphonic art of the past.He is the culminating figure of Baroque music and one of the titans in the history of art" (Machlis 1991, 110).
Although his vast work also includes works in the field of orchestra, chamber music, cantata and oratorio, Bach can be considered the greatest pre-classical composer for keyboard instruments, respectively piano.Also, thanks to his experience as a teacher, Johann Sebastian Bach's work also has great pedagogical importance: among the compositions intended for musical education, we mention: Orgelbuchlein (1717), the 6 Small Preludes (1720-1722), Klavierbuchlein fűr Wilhelm Friedemann (1721), Da Notenbuchlein fűr Anna Magdalena (1722-1725), The Well-Tempered Harpsichord (1722-1744), and Two-and Three-part Inventions (1723).
In the following, we will refer to the two-part inventions, (G.Ricordi and C. Editori, Milan), more precisely to the first six of them.

The invention
The invention is a "polyphonic form with 2 or 3 voices, dedicated to a keyboard instrument (harpsichord, piano) " (Teodorescu, 2014, 235), having a pronounced improvisational character.A two-part invention presents an "elegant displacement in two, with unequal speeds; they are sometimes aligned and, then, the procedure serves to mark important sections of the musical form" (Bălan 1975, 118).Apparently a pedagogical exercise, "an invention, a prelude, a fugue are for Bach not only an opportunity for lyrical externalization but also a logical act, an intellectual elaboration" (Bălan 1966, 62).In the Riemann Musik Lexicon, Mainz, 1967, it is stated that the invention is a principle of composing, being an example for the art of musical invention.The introductory words that form the basis of the score of the 15 two-part inventions are: "A benevolent introduction in which it is shown to lovers of the piano, but especially to lovers of learning, that not only two voices can be played at the same time, with clarity, but, after the necessary progress, even three.Subsidiarily, one can learn from him not only how good inventions can be invented, but also how they should be executed in order to achieve the interpretation similar to the human voice and thus to sense the true taste of music."(Bach 2007, 73).
3. Invention no. 1 in the key of C major constitutes the prototype of the "school example" (Toduță 1975, 12), where, in a limited framework, the polyphonic valences of a single musical idea, namely the theme, are exploited.This has, in its composition, two motives, the sixteenth and the eighth, which together form a well-knit idea, developed in a single measure (Figure 1).At the same time, it is worth noting the presence, within the first motif, of the folded ascending tetrachord, which, as we will see later, is a characteristic often encountered in Bacchian creations.
The thematic exposure is achieved by imitation at the octave, within the first two measures, fixing the tonality by means of the tonic and the dominant, fifth step (Figure 2).The hypostases in which the of the invention is found are: transposition, the theme being taken at a distance from the fifth, and inversion, a procedure achieved by stating a fragment compared to the standard fragment, in the opposite sense or like in the mirror.
Invention no. 2 in C minor asserts its particularity, within the cycle, through a constructive spirit, which gives the musical expression an internalizing character and, at the same time, through its resemblance to a fugue (because the thematic beginning, both within the fugue and within this invention is not accompanied by the countersubject, but enters alone).The theme is procatalectic, having two measures; at its base, there are two primary melodic elements: the melodic oscillation (x) and scale fragments, ascending or descending (y): (Figure 3).The theme of the invention no. 3 in D major, the anacrusic theme, is limited to a fifth ambitus, for the purpose of an easier interpretation, with the fingers fixed on the five keys of the space between the tonic and the dominant, not requiring a change of hand position.Again, it is noted, as in the previous invention, the nonexistence of the counter-subject within the first thematic exposition.(Figure 4).The thematic idea of invention no. 4 in D minor represents a typical and widespread melodic contour in Bach's creation; the gradual ascending hexachord and descending pentachord, separated or linked by the leap of the diminished seventh.This is a specific aspect of the Baroque, and implicitly, of Bach.(Figure 5).The interruption of the linear development by the leap gives the theme the appearance of latent polyphony; the range evolves in the two directions (ascending and descending), being interrupted by a melodic oscillation on steps I-VII, which gives it a special intonation.The theme promotes a unitary melodic drawing, being a crustic one and having, in the composition of the ascending hexachord, the sounds of the arpeggio of the tonality.In subsequent occurrences, the theme is reversed, yet retaining the same rhythmic values.It is also transposed to other keys than the original one (Figure 6).Invention no. 5 in E flat major focuses on the tetrachord principle, also found in the theme of 4 measures, the widest extension in the entire cycle of inventions.
The theme begins with an eighth rest, followed by a melodic oscillation, linked to the ascending tetrachord.
The repetition of this drawing a higher level inscribes a slight trend of evolution and tension (Figure 7).In the framework of the invention no.6 in E major, we find the coexistence of two thematic ideas, of four measures each, consisting of: a) the gradual upward pace, extended over an octave distance, in contrast to b) the gradual descending pace, projected an octave from the first theme (Figure 9).Through the collaboration of the the complementary rhythm is born, an alternation of dissonant delays, prepared and resolved.
The themes (the first, a crustic one; the second, procatalectic) arise from a gradual octochordic pace, both ascending and descending, the latter being complemented by some ornamental melodic oscillations.

Conclusions
The Two-part Inventions that we have focused on, true gems in terms of perfection of form, Bach's fundamental works for the piano, contain no outward virtuosity, but music full of content and depth, the various thematic hypostases emphasizing their emotional substance.Another important aspect is the didactic function of this music, Bachian inventions constantly accompanying the training and improvement of pianists, being ideal due to their complexity, for deepening musical thinking.