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The Latin magic square shown above (which means roughly "countryman Arepo runs a wheel shop") might seem like a strange way to describe a piece of music, but in the case of Anton Webern's Symphony it is entirely apt.
This piece, a work I first heard in my teens and love just as much today, is as close to the perfect piece of music as I am ever likely to hear. Anyone coming to this work with any sense of what a conventional symphony sounds like (from classical through romantic and into the more conservative 20th manifestations of the form) will scratch their heads, for it sounds nothing like anything that came before. Nor has much followed it (despite the cult of serialism that developed in the 1950s and 1960s) – it really is a work sui generis.
That is where the Latin 2D palindrome comes in. Webern constructed his symphony from a 12-tone row that was designed both to avoid tonal implications and to contain as much palindromic interrelation between the notes as he could muster. Consequently, hearing this piece is somewhat akin to looking at the Latin palindrome, only far more difficult to divine immediately because of the effort of needed to comprehend such a structure woven in musical notes.
Webern helps a lot by giving the work a canonical structure that allows us to follow the musical line more easily than we might. Furthermore, he uses a compelling palette of instrumental color that serves to draw the listener into the work. That was the hook that caught me. Only after repeated hearings did I begin the discern the incredible framework beneath it.
I am listening to it again right now. It is wonderful.