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Reflection

The harmonic reflection of a tonal composition leads to the creation of a new piece of music -- through the strict inversion of all intervals. It is a process somewhat similar to melodic inversion. Just as a mirror image to the right of a score reverses left and right to produce the retrograde form (temporal reflection), so an image from a mirror placed underneath a score reverses top and bottom, treble and bass, revealing a subtly different view of the original object. However this procedure, as used by J.S.Bach in the 'mirror fugues', is not rigorous in the inversion of intervals. In contrast, through the strict inversion of all intervals, the original harmony may be precisely 'reflected' to create a new piece of music consisting of the same raw information content, yet sounding different: effectively giving every piece of tonal music a matching 'harmonic reflection' or companion piece. The process is related to 'harmonic dualism', a line of thought stretching back to the theorist Zarlino (1588) and most fully developed by Arthur von Oettingen (1836-1920). Ultimately, treating chordal sequences upside down and backwards, can be viewed as analogous to the techniques of extension used in mathematics to broaden the scope of operations and processes. From this perspective, the chords of tonal music may be viewed, more or less, as numbers in material form, and musical phrases, as mathematical statements or number processing -- though generally of a limited and incomplete character. These ideas are explored in the articles and essays Journey to the Heart of Music.

The concept of 'reflection' is based on the supposition that chords are, in effect, incomplete harmonic and arithmetic series. However, as the human ear only natively understands 'ascending' harmonic relationships, chords which have a 'descending' arithmetic structure (i.e. the minor triad) are interpreted by the ear as consisting of somewhat more complex ascending relationships rather than the simple descending structures they intrinsically are. It is the human processes of aural cognition which 'break the symmetry' between the major and minor triads, so as to yield two different aural experiences from what is the same information load. Overall, the process of reflection turns simple harmonic compositions into pieces of greater 'complexity' and 'interest'; and pieces already complex and interesting, into something convoluted, lacking tonal focus, and on occasions, weird. The Gavotte by Henry Thornowitz (No.8 below) is a reasonably clear example of this process of 'complexification' producing a new and more 'interesting' view, from a relatively simple original piece.

Diagram: Dual Symmetry




Preface to the Rosebay Music Archive

Below is small archive of examples of reflected music, arranged principally for solo keyboard or baroque trio/solo sonata ensemble. Scores are in PDF format and suitable for printing on both A4 and US letter paper sizes - an A4 score is centered left-right but not top to bottom and US letter vice versa. MIDI files are also provided with most scores.

Most pieces are 'simple' reflections, that is, exact applications of the principle of reflection; while a few others are somewhat more elaborate. The sequence of some pieces -i.e. the order of normal and reflected portions - is left to the performer and in others is built into the score.

The art of reflection is very much that of bringing out the light and shade inherent in the contrast between the 'normal' harmonic version of the composition's information content and the often strange (perhaps 'abnormal') twists of harmonic and melodic progression produced through reflection.




No. 1 Vater unser im Himmelreich - Johann Krieger, 1652-1735
No. 2 Chorale Variations based on J.S.Bach's setting of Nun komm' der Heiden Heiland
No. 3 Fugue IX/II from 'The Well-tempered Klavier' by J.S.Bach
No. 4 Gavotte in C Major - G.F.Handel, 1685-1759
No. 5 Vom Himmel hoch da komm' ich her - Johann Pachelbel, 1653-1706
No. 6 Ricecar dopo il Credo - Girolamo Frescobaldi, 1583-1643
No. 7 V'adoro, Pupille, Saette D'amore - G.F.Handel, 1685-1759
No. 8 Gavotte by Henry Thornowitz, circa 1720's
No. 9 Loth to Depart - Giles Farnaby, c.1560-1600
No. 10 Fugue VII/II from 'The Well-tempered Klavier' by J.S.Bach
No. 11 Reflection upon 'Greensleeves to a Ground' - Anon. (from The Division Flute)
No. 12 Gavotte from the French Suite No.3 - J.S.Bach, 1685-1750
No. 13 Gavotte - Jean-Philippe Rameau, 1683-1764
No. 14 Menuet - G.F.Handel, 1685-1759
No. 15 Study: based on Prelude No.1 from the Well-tempered Clavier - J.S.Bach, 1685-1750
No. 16 Gavotte - G.F.Handel, 1685-1759


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Copyright Notice

While all material on this page is copyright © P.J.Perry it is intended that the scores may be freely downloaded, distributed, copied, printed and used in any non-commercial situation such as private study, education or amateur performance. Permission for professional live performance is also granted. However, the professional and/or commercial recording or printing of this music is not permitted without permission.

Created 10July2005.
Updated 30Nov.2009.