The Musical Concept: Bilateral Keyboard Symmetry
The human body possesses bilateral symmetry: our hands are physical mirror reflections of one another (thumbs inward, pinkies outward). In contrast, the traditional piano keyboard is strictly linear (frequencies ascend toward the right for both hands).
In Symmetrical Inversion, the keyboard is reflected across a geometric symmetry axis—traditionally centered around D or A♭ / G♯, where the acoustic piano's black and white key arrangements are naturally symmetrical:
- When one hand ascends, the opposing hand descends in exact mirror pitch intervals and physical gestures.
- Fingerings become 1:1 identical between hands: Thumb mirrors Thumb, Index mirrors Index, Pinky mirrors Pinky.
- Practicing symmetrically inverted scores develops bilateral motor balance, unlocks equal dexterity across non-dominant hands, and synchronizes neuro-muscular pathways across cerebral hemispheres.
The Four Mirroring Modes
- Mode 0 (Normal): Johann Sebastian Bach's original two-part counterpoint, available transposed across all 12 musical keys.
- Mode 1 (Left Hand Inverted): Voice 1 (Right Hand) remains authentic, while Voice 2 (Left Hand) is inverted across the D/A♭ axis (physical mirror ascent).
- Mode 2 (Right Hand Inverted): Voice 1 (Right Hand) is inverted across the axis (physical mirror descent), while Voice 2 (Left Hand) remains authentic.
- Mode 3 (Full Symmetrical Mirror): Both voices are inverted simultaneously, rendering the entire invention into a complete bilateral mirror reflection.
Bach's Dedication (1723)
"Forthright instruction, wherewith lovers of the clavier, especially those desirous of learning, are shown in a clear way not only 1) to learn to play two voices clearly, but also after further progress 2) to deal correctly and well with three obbligato parts, moreover at the same time to obtain not only good ideas, but also to carry them out well, but most of all to achieve a cantabile style of playing, and thereby to acquire a strong foretaste of composition."
Credits & Technology
Engineered by Benjamin Pritchard (Kundalini Software) as an application of the Mozart Transposition Engine. Typeset with GNU LilyPond and Python. Autograph manuscripts provided via IMSLP / Staatsbibliothek zu Berlin.