Iconic Sections (2015)
for
alto sax, trumpet, cello and tuba

by
Robert Morris

Program Notes

TEXT I wrote Iconic Sections to be played at the USF New-Music Festival (March 4-5, 2016) at the University of South Florida at Tampa. The perhaps unconventional instrumentation of alto sax, trumpet, cello, and tuba was determined by which players were available for the performance.

I chose the title "Iconic Sections" to give the piece a mathematical ring. But "Primitive Roots" would have been a better title since the pitch and rhythmic material of the work are based on the primitive root concept in number theory. This idea occurred to me in the late 1970s, since the twelve-tone row of my composition, Not Lilacs (1973), is based on the same concept, but it took me until 2016 to work out the way I could compose with it.

The series for Iconic Sections is a ring or cycle of 36 notes long:

B Bb A A C Ab Eb Ab G B F G C D Bb G E F# C Bb C# E G# F# C# B F C# D A D F# Eb Eb E F


or in pitch-class numbers

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


This series is the result of the isomorphism between the multiplication group of mod-37 and the addition group of mod-36. Then the mod-36 is mapped many-to-one (epimorphism) onto the familiar mod-12 addition group (transposition).

So the ring has the following property: transpositions of the ring are found in itself in order separated by n notes. For instance, 

T0:  0BAA1949806813B8571B259720623A374456 0BAA1949806813B8571B259720623A374456 etc.
TB:   B A 9 9 0 8 3 8 7 B 5 7 0 2 A 7 4 6 0 A 1 4 8 6 1 B 5 1 2 9 2 6 3 3 4 5  etc.
TA:     A   9   8   8   B   7   2   7   6   A   4   6   B   1   9   6   3   5  etc.
T9:         9       8       7       7       A       6       1       6       5  etc. 

(A = 10 and B = 11 to save space)


Nine streams of material interleave each other to produce the 73 short sections of the work, differentiated by instrumentation and contrapuntal voices. To this a coda is appended that concisely presents the basic ring without interruption. The relation of this structure and its elaborations to the experience of the work is everywhere. Certainly, the cross relations of pitch and rhythmic motives are easy to hear, but a certain boldness of articulation and emotional intensity are equally apparent.