Hello to Moderators and Fellow Members of the Piano Society website,
I felt it might be appropriate to discuss the musical structure of Bach's first Two-Part Invention, because this work is played and studied by amateur and professional pianists and teachers. Too often, I hear this contrapuntal jewel played through as though the pianist is not completely aware of the thematic lines that are going on -- all in the short time of 22 measures! I send my apologies to those, ahead of time, who are annoyed by an essay that takes longer to describe the Invention than it does to perform it.
The style, as usual with Bach, is the so-called imitatory or contrapuntal. The motive for #1 is as follows: C-D-E-F-D-E-C. This original motive is stated first in the right hand and then in the left, and the lines are developed in a great variety of methods and always with wonderful contrapuntal accompaniment.
So, if you would like to have a copy of Invention #1 in hand, let's have a go at this:
Measure #1: The motive (C-D-E-F-D-E-C) appears first in the upper part, and is imitated one octave lower in the left hand part.
Measure #2: The motive is transferred to the dominant (G-A-B-C-A-B-G), again appearing first in the right hand and then one octave lower in the left hand.
Measures #3 and #4: The motive appears four times in succession in the right hand, stated in so-called contrary motion (e.g., upside down) -- (A-G-F-E-G-F-A-g); (F-E-D-A-E-D-F-e); (D-C-B-A-C-B-D-c); and (B-A-G-F#-A-G-B-a).
Also in the above measures, look at the left hand -- too many pianists miss this point: the eighth notes are grouped in fours, and these constitute the first four tones of the motive -- played at one-half speed! (B-C-D-E); (G-A-B-C); and (E-F#-G-A). I believe these left hand phrases should be brought out, rather than simply playing them staccato or simply detached with no apparent connection to anything else going on.
Measures #5 and #6: These measures are devoted to forcing a change of key to G major. But look at them more closely: Measure #5 alone has the left hand played the motive in the key of D (D-E-F#-G-E-F#-D) and the last seven notes of the right hand re-state the motive in contrary motion (A-G-F#-E-G-F#-A). But we are not through! The left hand's balance of Measure #5 breaks up the first four notes of the motive, and Measure #6 right hand plays a succession of the LAST four notes of the motive: (G-B-A-C) and (B-D-C-E). The measure ends with a very nice cadence into the key of G.
Measures #7 and #8: The process of Measures #1 and #2 is repeated, but this time, at the dominant (in the key of G), but here the lower part begins. (G-A-B-C-A-B-G) followed by its octave higher counterpart in the right hand, followed by THEIR dominant counterparts in the key of D.
Measures #9 and #10: The process is repeated, but this time the motives are in contrary motion. (G-F-E-D-F-E-G-f), and its answer is stated at the dominant (D-C-B-A-C-B-D-c). Once again, most pianists fail to see the other subtleties of these two measures. Look at the last three 8th notes of Measure #1 and the first 8th note in Measure #11. Look Closer! (E-F-D-E) constitutes third through the sixth notes of the original motive!
Measures #11 and #12: The motives appear four times in succession in the left hand -- this time, the lower part is written in contrary motion. These measures balance Measures #3 and #4 -- but are inverted, with the upper and lower parts changing places. The right hand resumes playing the first four tones of the original motive -- but at half speed (in 8th notes rather than 16th notes). Restated, compare the symmetry of Measures #11 and #12 with what you see in Measures #3 and #4 -- it is a thing of beauty to see the inverted lines.
Measures #13 and #14: Similarly these measures correspond to Measures #5 and #6, with the lines being inverted with each other. The close of Measure #14 brings the end to the second part of this Invention, with a cadence to the relative minor of C major, namely A minor.
Measure #15: In this measure, the motive appears in the right hand and is imitated in the left hand -- as it is in the very first measure -- but it is now in contrary motion (A-G-F-E-G-F-A), and is imitated in the left hand.
Measure #16: The motive appears in its original direction with the right hand, but in A minor (E-F-G-A-F-G-E), and is imitated in the left hand.
Measures #17 and #18: These two measures are the answer to Measures #15 and #16, precisely as they were at the beginning of the second section.
Measures #19 and #20: There are three more sequences of the original motive -- (C-D-C-F-D-E-C-d); (E-F-G-A-F-G-E-f); (G-A-B-C-A-B-G). Now, notice what the left hand is doing: It is playing, in eighth notes at half speed, the first four notes of the motive, but they are in retrograde motion! (Bb-A-G-F), (D-C-Bb-A).
Measures #21 and #22 prepare for, and complete the final cadence to C Major.
Surely, no design could be more perfect, not only in the balance of the smaller sections and in the corroboration of the various pairs of measures throughout the piece, but also in the never failing variety it exhibits.
Similar perfection of form may be found in nearly all of the remaining Two-Part Inventions. I challenge you to look for them and discover the nuances for yourself.