Bach: the Greatest Composer and Teacher (15 Inventions and their Parallel Sets)
In this section, we briefly analyze Bach’s fifteen 2-part Inventions (from simple structural points of view) in order to explore how and why he composed them. The objective is to better understand how to practice and benefit from Bach’s compositions. As a by-product, we can use these results to speculate on what music is and how Bach produced such incredible music out of what (we will demonstrate) is basic “teaching material” that should be no different from Czerny or Cramer-Bulow. Clearly, Bach used advanced musical concepts in harmony, counterpoint, etc., that music theoreticians are still debating to this day, while others wrote “lesson music” mainly for their finger training value. Here, we only examine the Inventions at the simplest structural level. Even at this basic level, there are some educational and intriguing ideas that we can explore and arrive at the realization that music and technique are inseparable.
There is a nice essay on Bach’s Inventions and their history, etc., by Dr. Yo Tomita of Queen’s University in Belfast, Ireland. This is one of the best analysis of the Inventions and what they contain. The name “Inventions” does not seem to have any specific meaning in terms of the contents of the Inventions. Each Invention uses a different scale (in ascending order by key) that was important in the Well Temperaments favored during Bach’s time. They were initially written for his oldest son Wilhelm Friedemann Bach when Friedemann was 9 years old, around 1720. They were subsequently upgraded and taught to other students.
The single most striking feature common to all the Inventions is that each one concentrates on a small number of parallel sets, usually less than three. Now, you might say, “That’s not fair -- since practically every composition can be decomposed into parallel sets, of course, the Inventions must be all parallel sets, so what’s new?” The new element is that each Invention is based on only one to three specific parallel sets that Bach chose for practice. To demonstrate this, we list these parallel sets below for each Invention. In order to concentrate entirely on simple parallel sets, Bach completely avoids the use of thirds and more complex chords (in one hand), that Hanon uses in his highest numbered exercises. Thus Bach wanted his students to master parallel sets before chords.
Single parallel sets are almost trivial from a technical point of view. That is why they are so useful -- they are easy to learn. Anyone with a some piano experience can learn to play them pretty fast. The real technical challenges arise when you have to join two of them with a conjunction in between. Bach obviously knew this and therefore used only combinations of parallel sets as his building blocks. Thus the Inventions teach how to play parallel sets and conjunctions -- learning parallel sets is of no use if you can’t connect them. Below, I use the term “linear” parallel set to denote sets in which the fingers play sequentially (e.g., 12345), and “alternating” sets when alternate fingers play (132435). These joined parallel sets form what is normally called “motifs” in these Inventions. However, the fact that they are created using the most basic parallel sets suggests that the “motifs” were not chosen because of their musical content, but were chosen for their pedagogical value and the music was then added with the genius of Bach. Thus only Bach could have achieved such a feat; this explains why Hanon failed. Only one representative combination of parallel sets is listed below for each Invention; Bach used them in many variations, such as reversed, inverted, etc. Note that Hanon based his exercises on essentially the same parallel sets, although he probably accomplished this by accident, by extracting these motifs from Bach's works. Perhaps the most convincing evidence that Bach knew about parallel sets is the beautiful progressive complexity of the sets he chose with increasing Invention number.
List of the parallel sets in each Invention (for the RH):
#1: 1234 and 4231 (linear followed by alternating); in a later modification of this Invention, Bach replaced the 4231 alternating set with two linear sets, 432,321. This change is logical because it converts this Invention from one that teaches two different types of parallel sets to one that concentrates on only one, since these inventions are arranged in order of increasing parallel set complexity. Thus the alternating parallel set 4231 was out of order for the first Invention. However, the order of difficulty of each Invention may not follow the same order as parallel set complexity for most people, because the structural simplicity of the parallel sets does not always equate to easier playing.
#2: Linear sets as in #1, but with a wider variety of conjunctions. An added complexity is that the same motif, appearing at different times, requires a different fingering. Thus the first two inventions deal mainly with linear sets, but the second one is more complex.
#3: 324 and 321 (alternating followed by linear). A short alternating set is introduced.
#4: 12345 and 54321 with an unusual conjunction. These longer linear sets with the unusual conjunction increase the difficulty.
#5: 4534231; full blown alternating sets.
#6: 545, 434, 323, etc., the simplest example of the most basic 2-note parallel sets joined by one conjunction; these are difficult when the weak fingers are involved. Although they are simple, they are an extremely important basic technical element, and alternating them between the two hands is a great way to learn how to control them (using one hand to teach the other, section II.20). It also introduces the arpegic sets.
#7: 543231; this is like a combination of #3 and #4 and is therefore more complex than either one.
#8: 14321 and first introduction of the “Alberti” type combination 2434. Here, the progression in difficulty is created by the fact that the initial 14 is only one or two semitones which makes it difficult for combinations involving the weaker fingers. It is amazing how Bach not only knew all the weak finger combinations, but was able to weave them into real music.
#9: The lessons here are similar to those in #2 (linear sets), but are more difficult.
#10: This piece consists almost entirely of arpegic sets. Because arpegic sets involve larger finger travel distances between notes, they represent another progression in difficulty.
#11: Similar to #2 and #9; again, difficulty is increased, by making the motif longer than for the preceding pieces. Note that in all the other pieces, there is only a short motif followed by a simple counterpoint section which makes it easier to concentrate on the parallel sets.
#12: This one combines linear and arpegic sets, and is played faster than previous pieces.
#13: Arpegic sets, played faster than #10.
#14: 12321, 43234; a more difficult version of #3 (5 notes instead of 3, and faster).
#15: 3431, 4541, difficult combinations involving finger 4. These finger combinations become especially difficult to play when many of them are strung together.
The above list shows that:
(i) There is a systematic introduction of increasingly complex parallel sets.
(ii) There tends to be a progressive increase in difficulty, with emphasis on developing the weaker fingers.
(iii) The “motifs” are, in reality, carefully chosen parallel sets and conjunctions, chosen for their technical value just as in the Hanon series. However, Bach succeeded where Hanon failed because Bach understood the difference between music and noise, and that music and technique cannot be learned separately.
The fact that motifs, chosen simply for their technical usefulness, can be used to create some of the greatest music ever composed is intriguing. This fact is nothing new to composers. To the average music aficionado who has fallen in love with Bach’s music, these motifs seem to take on special significance with seemingly deep musical value because of the familiarity created by repeated listening. In reality, it is not the motifs themselves, but how they are used in the composition that produces the magic. If you look simply at the barest, basic motifs, you can hardly see any difference between Hanon and Bach, yet no one would consider the Hanon exercises as music. The complete motif actually consists of the parallel sets and the attached counterpoint section, so-called because it acts as the counterpoint to what is being played by the other hand. Bach’s clever use of the counterpoint obviously serves many purposes, one of which is to create the music. The counterpoint (which is missing in the Hanon exercises) might appear to add no technical lessons (the reason why Hanon ignored it), but Bach uses it for practicing skills such as trills, ornaments, staccato, etc., and the counterpoint certainly makes it much easier to compose the music and adjust its level of difficulty.
Thus music is created by some “logical” sequence of notes or sets of notes that is recognized by the brain, just as ballet, beautiful flowers, or magnificent scenery is recognized visually. What is this “logic”? A large part of it is automatic, almost hard-wired brain data processing, as in the visual case; it starts with an inborn component (newborn babies will fall asleep when they hear a lullaby), but a large component can be cultivated (e.g., Bach versus Rock and Roll). But even the cultivated component is mostly automatic. In other words, when any sound enters the ears, the brain instantaneously begins to process and interpret the sounds whether we consciously try to process the information or not. An enormous amount of this automatic processing goes on without our even noticing it, such as depth perception, eye focusing, direction of origin of sounds, walking/balancing motions, etc. Most of that processing is inborn and/or cultivated but is basically out of our conscious control. The result of that mental processing is what we call music appreciation. Chord progressions and other elements of music theory give us some idea of what that logic is. But most of that “theory” today is a simple compilation of various properties of existing original music. They do not provide a sufficiently basic theory to allow us to create new music, though they allow us to avoid pitfalls and extend/complete a composition once you have somehow generated a viable motif. Thus it appears that music theory today is still very incomplete. Hopefully, by further analyzing music from the great masters, we can, slowly, step by step, approach that goal of developing a better understanding of music.
Finally, it is clear that the Inventions were created for technique development. However, Bach’s music has not been utilized as much as they should have been in the past because of the difficulty of learning to play them for students unfamiliar with effective practice methods. The methods of this book should eliminate those difficulties and allow more widespread use of this most valuable resource for healthy technique acquisition. Hopefully, this section illustrates the synergy between Bach’s teachings and the methods of this book which will allow more students to benefit from the world’s greatest music composed by the world’s greatest teacher.