Composition No. 40K is a medium to medium fast line structure for extended improvisation.  The establishment of this work is consistent with my efforts to solidify an alternative series of line structures for the post-AACM continuum of the music.  Since 1965 I have attempted to contribute at least one structure a year to this medium, and hopefully to future will see fifty to a hundred completions on the effort.  Composition No. 40K is an even line structure that consists almost entirely of eight-note phrase material—to be executed in the phraseology of be-bop.  Long phrase groupings are emphasized in this work—including the use of tutti sections and multiple conceptual focuses.  The work was conceived as a coordinate music platform structure—in conjunction with the composite series of interchangeable and interconnected works that I have composed for that procedure type—as well as an isolated forum with its own special challenges (and secrets).  The idea of Composition No. 40K was conceived separate from any  specific instrumentation (or extended treatment).  This is in keeping with the traditional continuance of Trans African functionalism—where a given focus of material can be executed as a be-bop line, a song or a bossa nova.  In its initial state Composition No. 40K was conceived in conjunction with the performance needs of my touring quartet—having to do with establishing a broad spectrum of different music types as a means for diversity and vibrational dynamics.  I have since performed this work in the duo, trio and quintet context (and the instrumentation on those occasions hase been varied).  The dynamic implications of line structures like Composition No. 40K involved creating phrase contours that give 'lift' to the nature of a 'central way of proceeding' (in the music)—which is to state that the nature of a given tone system is not separate from how it affects its extended interpretation (what it brings to the procedure focus and 'spread' of the music).  Composition No. 40K was conceived to establish several different premises for its extended interpretation—to provide the widest possible basis for exploration.  In this work will be found phrase grouping devices—that can be used as guides into the 'space' of the music—as well as language devices.  Composition No. 40K was conceived as a dynamic forum for extended creativity.  The work is dedicated to the composer/multi-instrumentalist Gunter Hampel.

Composition No. 40K is an atonal line structure that was composed in moment time without any overstructure dictates.  The composite form of the work is A B C (E2) D E and the specifics of that breakdown involve what focus and position a given phrase grouping has in the composite forming of the work.  The sectional implications of Composition No. 40K came about after the actual music was already completely written.  In other words, this is a musical universe that defines its terms, and final shape, from the effects of its composite phrase groupings—rather than the traditional concept of establishing a parameter and fitting the music into it.  Composition No. 40K is a linear perceived soundscape that consists of six phrase groupings of extended be-bop-like concepts.  This is not, however, a musical space of smooth curves—in the manner of diatonic note to note changes that 'round' the contour of a given line, nor does the work rely on great shifts in the shape of its line formations.  Composition No. 40K is constructed as an intervallic structure that contains its own special identity—and challenges.  Section A establishes what this concept means in actual terms.  This section consists of one phrase grouping that extends to include eight full measures of notated music (without any break in its focus of material).

The actual score of Composition No. 40K consists of upper and lower voice parts that attempt to orchestrate the timbral balance of the composite structure.  This material was originally conceived with respect to what it posed for my quartet music performance dynamics.  In composition No. 40K a given phrase grouping takes on several different functions—from single line shapes (that are scored for upper voices only—in either unison line shapes or lines that are voiced in parallel distances of [blank] or tutti line structures that involve the composite ensemble (which for the quartet would mean having the string bass play on the actual line—with open percussion) or repeating line patterns (that are voiced for three voices plus percussion).  The work was conceived as a forum that showed the timbral diversity of the quartet.  Here is a music type whose material nature continually reshifts—rhythmicaly and vibrationally.  Composition No. 40K was conceived to meet the challenge of the next time cycle.

Composition No. 40k also contains a secondary idea germ in its infra-material structure that can be utilized in interpretation.  The work was designed to establish off beat quarter note pivot points as a factor to influence the nature of its extended treatment (interpretation) as well as its structural treatment.  The first appearance of this device takes place in Section E2 and later solidifies as a real 'focus' in Section E.  By the term off beat quarter notes I am referring to the use of up beat emphases to shift the perception nature of the sound space.  What this does is create a feeling that 'something is coming towards ya' in the music.  In the infra-reality of the music the effect of this device is just as real.  This is a music that skips across the sound space—a music that doesn't quite touch the ground (and 'keeps out attention because of its nervousness').  For some reason the quartet seems to use this phenomenon as a wedge to enter the world of dixieland music (not the form but the vibration).  I wonder what this really means?  In the beginning of the work, the secondary idea basis is established on the concert pitch B--.  But as the work opens into the unfolding space of the music, this operative becomes meaningless ('because who knows who's out there!').

Composition No. 40K is a series of interconnected phrase groupings that establishes its own reality basis.  The structural dynamics of the music is consistent with the nature of its idea interchanges and applications.  Section A states the reality and focus of the music; Section B is an eight-bar tutti phrase that repeats; Section C is a six-bar phrase (consisting of a five-note phrase pattern that chromatically ascends one half step each time it repeats); Section D reestablishes the timbral and conceptual nature of Section B; and Section E establishes in depth the use of off quarter note up beat figures as both a secondary idea consideration (that can be used in the open space of the music) and a bridge structure to return to the beginning of the work.  Composition No. 40K is intended as a vehicle for solo and/or collective improvisation—in the tradition of Trans African affinity dictates.  This work is designed to 'get down!'  

Anthony Braxton, Composition Notes C (Frog Peak, 1988: 113-117)