A composition student writes a two-part invention with a strong opening subject but introduces entirely new melodic material in the middle section to create variety. A teacher marks this as a structural error. Why?
AMiddle sections of inventions are required to stay in the relative minor key
BThe invention form requires generating an entire piece from one subject through development, sequence, and register change — introducing new material abandons the economy of means that defines the form
CThe new material creates parallel fifths and octaves with the opening subject
DBach's inventions never modulate, so any departure from the home key is an error
The two-part invention is fundamentally an exercise in motivic economy: one subject generates everything. Sequential episodes, key changes, stretto, and register swaps all use fragments of the subject (or countersubject) — no new material enters. The composer who introduces new ideas has misunderstood the formal constraint. As the explainer notes: 'Every time you hear new-sounding music in an invention, look closely — it is almost always a rearrangement of material you have already heard.' The form's discipline is precisely what makes it pedagogically valuable.
Question 2 Multiple Choice
What is the compositional significance of 'invertible counterpoint' in a two-part invention?
AIt means the subject can be played backward (retrograde) and still work harmonically
BIt means the subject and countersubject are designed so that their registers can be swapped — the countersubject works correctly whether it is above or below the subject — generating variety from existing material
CIt means the invention must be performable on two separate instruments of any combination
DIt refers to the technique of inverting individual intervals within the subject (turning a rising third into a falling third)
Invertible counterpoint is the technical heart of the invention form. The countersubject is not merely an accompaniment — it must be specifically composed to work harmonically in either voice register. When the subject and countersubject exchange positions mid-piece, the ear hears a new texture, but the material is exactly the same, just flipped. This is how an invention achieves ongoing variety without ever needing new ideas. The explainer makes this explicit: 'Every time you hear new-sounding music in an invention, look closely — it is almost always a rearrangement of material you have already heard.'
Question 3 True / False
In a two-part invention, sequential episodes typically introduce new thematic material that contrasts with the opening subject.
TTrue
FFalse
Answer: False
Sequential episodes are built from fragments of the subject or countersubject treated in sequential patterns (the same gesture repeated at successive pitch levels). No new material enters. The sequence is the 'compositional workhorse' of the invention precisely because it can carry the music through multiple keys and generate forward motion using only material already established in the exposition. Contrast in an invention comes from register change, key change, and texture — not new ideas.
Question 4 True / False
A countersubject in a two-part invention must be specifically designed to function correctly in either voice register — not merely to accompany the subject when it appears below it.
TTrue
FFalse
Answer: True
This is the invertible counterpoint requirement. If the countersubject only works harmonically when the subject is below it, the composer loses the ability to swap the voices — which is one of the primary sources of variety in the form. Bach's countersubjects are engineered so that every interval relationship remains harmonically acceptable when the voices exchange positions. This requires composing both parts simultaneously with their inversion in mind, not writing the subject first and adding an accompaniment.
Question 5 Short Answer
Why must the subject–countersubject relationship in a two-part invention satisfy invertible counterpoint, and what would be lost if it did not?
Think about your answer, then reveal below.
Model answer: The subject and countersubject must work in either register because their exchange of positions is the primary source of variety in a form that is otherwise committed to using only one motive. Without invertibility, the countersubject is just a passive accompaniment that can appear in only one position — the composer loses the ability to create new-sounding textures from old material. With invertibility, swapping the voices produces a genuinely different sonic texture while introducing zero new material. This is what allows an invention to remain interesting across multiple key areas and formal sections without ever departing from motivic unity.
Invertible counterpoint is the formal mechanism that makes the invention's economy of means work: one set of ideas (subject + countersubject), but multiple arrangements of them. Without it, the form either stagnates (the same texture repeating) or is forced to introduce new material (abandoning the formal principle). Bach's inventions demonstrate that a single well-chosen motive, properly developed, contains far more variety than it initially appears to hold.