Monday, August 13, 2007
Reflection and Translation
Symmetry on the Guitar

Last Monday we talked about two kinds of symmetry on the kalimba: reflection and translation symmetry. This week we look at symmetry on the guitar.

If you learn a riff on the guitar, it is easy to shift this riff up a half step, i.e., to symmetrically translate the riff - you just shift everything up a fret. OR you could shift it up a fourth by shifting everything to a thinner string. Of course, the 2nd string breaks this symmetry slightly, as every guitarist knows.

What would reflection look like on a guitar? OK, we can reflect in different directions, but the only direction that really makes sense is to reflect from low strings to high strings, and from high strings to low strings. You can do this, but it doesn't always result in music that makes sense.

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