This is a report of my latest discussions and thoughts about superarrays, following a meeting with theorists and composers at the CUNY Graduate Center, which is now a great hotbed of Babbitt study, with Joe Straus, Jeff Nichols, Zach Bernstein and Daniel Colson all there at the same time.   Joe presides there as the seasoned Babbitt scholar,  Zach and Daniel were among Babbitt's last Juilliard students, who are now becoming major contributors to Babbitt study.  Oren Fader joined me on March 21 for a performance and discussion at the Graduate Center of Babbitt's Soli e Duettini.

I was never clear about what a superarray might be, so I made sure to ask.  Zach and Daniel filled me in, saying that when more than one array is employed in a work, that is a superarray.  My impression was that a superarray is more grand, involving some probing insights into what music does, how arrays work musically, and how multiple arrays can offer a compounding of the riches of the source array.   I now accept the definition of a superarray as the employment of multiple arrays, provided that employment is brilliant, with a deep understanding of what propels music forward, compellingly. 

I see in some seminar notes on Soli e Duettini that hexachordal regions are mapped out--

I want to hear a discussion of the displacements that take place with the arrival at the secondary hexachordal region.  I also understand that Babbitt often uses signatures of the hexachordal regions.  I imagine the signature to be that trichord that contains the potent displacements that best distinguishes the new region.   I want to understand that more.   That regions are identified is a great start.  My understanding is that it is here that 12-tone music and (non-12-tone) interval vector music are both playing the same game, with the 12-tone variant adhereing to a very interesting maximalization in regard to its handling of the complement.

A superarray would hold these musical dynamics as the primary task-- how to intersect the mulitple arrays to accomplish this task meaningfully, dynamically???

[To my ears, the foreground of Soli e Duettini works clearly and beautifully--the unfolding of the aggregates (compounded---enriched--by the multiple arrays).   What is opaque is the background-- which I imagine to be the shift to a different hexachordal region, or shifts to different hexachordal regions, something distantly kindred with what Babbitt describes in his discussion of the 4th Shoenberg quartet.  For my performance to get better, some details about the background would be helpful.  Problem is that the pleasant flow of aggregate-unfolding remains consistently engaging throughout, but the clarity of the background would help a great deal to justify the duration of the piece.  Swan-Song on the other hand is driven much more by what I call background processes in Soli e Duettini.  In Swan song the rhythmic syncopation persists, beautifully and engagingly as the aggregates unfold and until the big rhythmic moments land a contrasting trichord--a dramatic displacement, that is, moreover, probably the potent signature of a new hexachordal regiont.  Swan Song moves with the power of background stuff, and lets the aggregate unfolding serve as a compelling foreground, ever syncopating until the big moment.]

I know that Frank Brickle uses some simple algorithms to generate superarrays, for which he has created some pretty complicated Lisp code.   Yet, his approach to teaching the use of multiple arrays does not begin there.  It begins with his own kind of "simple composition".   I tried to explain this at the CUNY class, and I'm not sure how clear I was, so I'll repeat it here:

A focal collection is extended through its complement.  Ideally, it happens seamlessly, without erasing the quality of the focal collection, providing motion through the complement with a sense, nevertheless, of foregrund continuity, with the aim of setting up a middleground or background dispacement by another collection.   For example--the simplest partition of an array is 4 aggregates each consisting of 3 vertical tetrachords.  Treat the first tetrachord as the focal collection, weight it rhythmically, extend it through the complement in a manner such that its return (inverted) in the next aggregate preserves a sense of long term identity.  In other words, the complement does not erase that essential quality of the focal collection.  This preservation of identity lays the groundwork for a dramatic displacement of the focal collection.   (See Brickle's comment, below.)

If multiple arrays are employed this simple process might be considerably enriched.  And the simple process is an organizing principle regarding how the various arrays will intersect.   It is something like this that might begin to deserve the name, "superarray".  But I believe a superarray is still something more specific.

I imagine Babbitt's approach to the question is characteristically brilliant, nuanced, and highly idiosyncratic.  Moreover, each work will have its own very particular strategies.   I want to delve into how these issues are at play in Soli e Duettini and in Swan Song No. 1, and I am very confident that the CUNY team is onto the answers to these questions.  As the performer, this could help me better appreciate some of the wonderful collections that are so carefully landed, rhythmically.  That rhythmic clarity is there for a reason.  How do these moments relate to the broad trajectory from region to region?  

[Again, what is perfectly clear and plenty rewarding is the pleasant unfolding of aggregates.  Unfortunately, it's not clear to listeners on the first hearing.  What he needed to do is shore up the background, which he did shockingly well in Swan Song--an accomplishment that is truly a quantum leap.  I was always careful to say to Milton, when praising Swan Song, that Swan Song makes the case for deeper study of the earlier works.  So this study of Soli e Duettini is of great importance.]

My Various Roses for violin and guitar uses 4 arrays--a source array, its m5, and 2 arrays where an inversional pair from m5 array happens to form aggregates when combined with an inversional pair in the source array.

Violin arco gets one array; violin pizz gets a second; guitar gets its own array; and guitar tremolo gets the 4th.

The various roses of the title are Es is ein rose entsprungen, Heidenroslein, and a line from Honky Tonk Woman.   The tunes are the focal collection.  And the first two are virtually identical in pitch content.  The interweaving of timbrally distinct m5-infused material expands the time it takes to work back to the focal collection (complete the aggregate).  I never thought of this piece as employing a superarray, and yet now I feel that the decision can be left to the listener.  If it's convincing it's a superarray.  If it's not, then it's mulitple arrays creating confusion.

Many thanks to all of the CUNY scholars for their many valuable insights into Babbitt's music.


Brickle's responses:

This is pretty good. The one major place I'd quibble with your
characterization of my stuff is this: extension into and through the
complement is essentially through what in tonal music we'd call
harmonic motion.


I'm trying to find a sensible way to formulate this -- that
superarrays have to do with the pitch - pitch class distinction. I
know that's very vague right now but I think it's on the right track.

This reminds me that Babbitt did not deny the validity of my observation that specific pitches emerge as significant in later works.  Danci --> E  and G# (Ab);  Swan Song-->  F# and E#.  Specific pitches do not jump to the surface in Soli e Duettini, but maybe I'm missing something.