Symmetry in Music --- Mirror Music

While playing the piano few years ago I wished the left hand would move as nicely as the right hand and suddenly realized a new way of playing music by simply exchanging the finger movement of right and left hands. It was so curious that the new music played by this way sounded somewhat odd but there were certain new taste or flavor in such inverted sounds. Let me call such inverted sounds the "mirror music" and explain here what it is as concisely as possible.

Piano keys are arranged symmetrically with a D key at the center. Hence by rewriting the normal music notes by exchanging the notes as,
D→D, E→C, F→B, G→A , A→G, B→F, C→E, D→D、
a mirror music score can be obtained. (♯must be played as♭and vice versa).

Click below to enjoy the mirror and normal music.

Mirror music score ： Bach-Gounod Ave Maria
Mirror and normal music ： Bach-Gounod Ave Maria

Mirror music score ： Bach Invention 1
Mirror and normal music ： Bach Invention 1

Mirror music score ：Japanese children song: Hato Pot・Pot
Mirror and normal music ：Japanese children song Hato-Pot・Pot

By asking musicians and by surveying on internet, it appeared that this kind of mirror music is not new. However, actual performance of mirror music is not popular at all or in fact not possible to listen to it played.
Mirrored music sounds somewhat odd when one listen to it for the first time but many people who listened to it several times gradually get used to it and start to love the mirrored sound. When the normal and mirrored music are played in succession, the impression of normal music which we know well becomes quite new and fresh. It is amusing to imagine that the songs and music that Alice heard in mirror world must have been ones of this kind.

There is a well-known music piece called Spiegel Musik composed by Mozart.
However, this music piece is composed so as to be playable from the top and from the end of the score to be listened as harmonious music. So this it is not the mirror music presented here.

The explanations of principle of present mirror music can be seen on URL given below.
http://math152.wordpress.com/2008/10/20/symmetry-in-music-pianos-and-keyboards/

We know by seeing through a mirror, figures are quite similar but not exactly the same as real one. Similarly, in mathematics, what are called "inverse functions" are functions which are symmetrical each other with the center of symmetry on the line y = x. For example, y = 1/x vs. x = 1/y (below right) and x = eu vs. u =lnx (below left) are inverse functions. Inverse functions are the same but not the same one another.

The latter example shows basic principle of many physical and sociological phenomena such as the relation of temperature and entropy, the money owned and its utility and etc. Thus looking through a mirror can let us notice the new meaning of what we have in hand. Listening to mirror music seems to expand our way of appreciating the wonderful world of music in similar manner.

Written by Shingu : December 4, 2012 04:33 PM