Friday, January 2, 2015

Quick tour of symmetry

There are basically three types of symmetries that occur in nature and in man made things. 

  1. Reflection symmetry
  2. Rotation symmetry
  3. Translation symmetry

Reflection symmetry is the one that is very obvious to the human eye. Assume that you have a mirror and if you look at the objects to the left of the mirror and the right, they will be identical (Obviously, there is lateral inversion, where left becomes right and vice versa). The mirror is the
plane of symmetry.  Any suspension bridge that most of us have seen does have this reflection symmetry. Musically, you can observe reflection symmetry when you have at least two instruments in a multitude of ways. For example, two instruments can be used alternatively in an interlude and can be argued to have reflection symmetry. However, that will be a boring piece of music and give rise to little interest. Alternatively, when you have three instruments used in an instrument piece that is fully built with C&R arrangement, and the composer manages to create reflection symmetry, it gets very interesting. More on this later. 

Rotation symmetry is something that is not immediately obvious to the eye. You need to get your geometry right in terms of getting the center and the angle of rotation. Once you get that, you will notice that the pattern is repeated as you rotate with appropriate adjustments to the rotation.  A snowflake, a windmill or a wheel have rotational symmetry. However, when it comes
to music, it is extremely hard to get to simple examples of rotational symmetry. The closest you can get to is a pattern that emerges with a duel between two instruments. The other not so perfect example of rotational symmetry is the way instruments are played between left, center and right channels of a stereo system. Raja has played around with symmetry with the same instrument playing initially on the left channel, then the center and finally on the right. The following bars will reverse this by playing right channel first, followed by the center and left channel.

Translation symmetry involves sliding where you start with an object, slide its position and
create a new version of the exact object where all that has happened is a slight shift in position of the object. The double helix structure of the gene is a great example of infinite translation symmetry. While this is a great feature in the world of animation, citing examples in the musical world makes the discussion extremely complex. A number of aptitude tests take advantage of translation symmetry to test the candidate’s spatial abilities.

Our focus on symmetry discussions with Raja’s music will be very simple, looking at mostly reflection symmetries. You can expect some rare occurrences of translation symmetry too.