Bach : Toccata and Fugue in Dm

Bach : Toccata and Fugue in Dm (For Organ)

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In 1974, Robert Morris and Daniel Starr famously enumerated every all-interval twelve-tone row. 

Inspired by their work, and in around 1979 in unpublished works, I generated an analogous catalog of what one might call the all-trichord rows, meaning rows, which together with two of their untransposed rotations, and in "first-species counterpoint," produce a sequence of all twelve distinct trichord classes.  By the standards of the day, this 
involved very substantial computational search.  But lately I have vastly expanded that calculation, now allowing transposition, retrograde and inversion of the rotations. Some of these new rows provide the basis of my recent pieces.   

The catalog of all-trichord rows runs to about 300 more or less, depending upon the accounting for symmetries.  That makes these rows quite rare among all the twelve-tone rows.  This rarity suggests my original compositional conception but unrealized at the time: a museum-like installation where a listener might walk in a large space from sonic exhibit to sonic exhibit, and experience the different ways these rows fit together and do their thing.  

So here are just three typical exhibits, realized now as works for chamber orchestra.  In each, the basic row first gets a plain but lapidary statement, and then the rotated forms fade in, statistically speaking, and eventually the rows likewise fade out in the order in which they entered, leaving finally a statement of the basic row.  By design, this treatment could loop seamlessly as one "display," as per my original conception.

0    1    9    4   10    5    2    8    7    6    3   11

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Bach : Toccata and Fugue in Dm (For Organ)

Anthony Hamilton