Thursday, March 08, 2007


Network Slammer is a composition for amplified flute and electronic sounds, by Zack Browning. Its structure is based on the magic square of Venus:

A magic square is an arrangement of the numbers from 1 to n^2 (n-squared) in an n times n matrix, with each number occurring exactly once, and such that the sum of the entries of any row, any column, or any main diagonal is the same. Therefore, the simplest magic square is 1. The next simple square is:

8 1 6
3 5 7
4 9 2

Eight plus one plus six equals fifteen, which equals three plus five plus seven, four plus nine plus two, eight plus three plus four, and so on. As you can see, there is nothing of the supernatural, although ancient Romans and early Christian mystics believed Sator-Rotas magic squares to ward off evil spirits and protect the bearer from disease and misfortune.

Network Slammer is based on seven routes through the magic square of Venus, which looks like this:

22 47 16 41 10 35 4
5 23 48 17 42 11 29
30 6 24 49 18 36 12
13 31 7 25 43 19 37
38 14 32 1 26 44 20
21 39 8 33 2 27 45
46 15 40 9 34 3 28

Browning calls the set of numbers from left to right “routes”, and each of the numbers as “cells”. Hence, the first route is the numbers 22, 47, 16, 41, 10, 35, and 4. 22 is the first cell of route one, 47 is the second cell of route one, and so on. Each cell represents a section of a route and decides how many quarter notes the section has. For example, the first section of the first route is 22 and therefore 22 quarter notes long. At quarter note equals 160 beats per second each quarter note is 0.375 second. Hence, route 1.1 is 8.25 seconds long. The sum of each route is 175 and consequently each route takes 60.625 seconds. With the 44 second intro and the 42 second coda, the piece is approximately 9 minutes and 12 seconds. This is essentially the extent to which Browning uses the magic square in Network Slammer.

By using a constructively organized set of numbers as the compositional model, Network Slammer sounds erratic yet structured. Each cell is predicated an anatomy of ideas and voices. The first cell of each route is a solo of one idea by either the flute or the tape. The second is a trio of two ideas, by flute and tape. The third is a duo of one idea, by flute and tape. The fourth is a duo of two ideas, with tape alone. The fifth is a trio of two ideas by solo tape. The sixth is a duo of two ideas with alternating orchestration, and finally, the seventh is a trio of three ideas and alternating orchestration. Hence, the first cell of every route is always the simplest, and the last cell is always the most complex, although not consistently progressive.

There are six main themes used in Network Slammer, represented by letters. The ideas are as follows:

A. Eighth notes centered on D
B. Quarter note chords
C. Triplet eighths
D. Glissando
E. Sixteenth note line always with flute and tape unison
F. Syncopated eighths centered on D flat

As you can see, the ideas are rhythm based save for one. The following chart shows which ideas are used in each of the cells:

Cell 1 Cell 2 Cell 3 Cell4 Cell5 Cell6 Cell7
Route I 22C 47BC 16A 61BC 10BC 35AB 6ABC
Route II 5A 23FC* 48B 17AF 42AC 11C* 29ABE
Route III 30F 6AC 24AD(B)* 49C,D 18C* 36CF 12BCE
Route IV 13C 31AD 7ADB* 25ED 43CD 19C* 37FBD*
Route V 38B 14AB(B)* 32C 1DBC 26DB 44AC 20CDEF*
Route VI 21(A) 39AF 8C EF(B) 2FB 27BD 45ACD
Route VII 46C 15BD 40AD* 9AB 34AFD* 3C* 28ACE

Letters = ideas
Numbers = number of beats
* = irregularity
( ) = shadow of idea

Clearly, there is no obvious pattern as to how and when the ideas are used. There are only subtle consistencies: The six ideas are gradually stated within the first three routes of the piece. Once an idea is first stated, it reoccurs throughout all remaining routes to the end of the piece, never leaving the music for too long. . Ideas A, B, and C, stated first in route 1, reoccur in routes 2 to 7. Ideas F and E, first stated in route 2, are again stated in routes 3 to 7. Idea D occurs first in route 3, then throughout the remaining routes. After an idea is first presented, it comes back as variations of the original idea. And when all the variations are stated, the variations and the original ideas are stated simultaneously, with different ideas, or with variations of other ideas, resulting in a new composite sound as we experience each new cell.

Let’s take Idea C as an example. First stated in 1.1, it is essentially a triplet line with a bass. The main pitches are centered at G and F diminished. In 1.2, it keeps the jumpy triplet feel of 1.1 but the pitches are changed to E flat major and D flat major. 1.4 is a mirror image of 1.1; same pitches but the bass and treble lines are flipped. 1.5 is a combination of 1.1 and 1.2, literally repeated but this time stated simultaneously. 1.7 is like 1.1, but with only the bass line of G and F. In 2.2, we have the rare occurrence of a literal repetition of 1.5 but of course the composite sound is different as this time it is stated with a new idea; idea F. In 2.5 we have the variation from 1.4 plus a slimmed down version of 1.2 (same pitches, more rests). Cell 2.6 is another literal copy of 1.2 but for the first time in the piece, the flute is allowed to play the idea with the tape. The pitches in the flute part resemble that of cell 1.1 with the common tones G, F, C# (D flat in 1.1), and B. Next, in 3.2, the original theme from 1.1 is back again as a duo with idea A as heard in cell 2.5 and this time the spice comes from the flute part which plays a variation of idea A, which until now has yet to be heard. 3.4 for is another replica of 1.1, but again, stated in a new combination; this time with the glissando idea D. Cell 3.6 is cell 2.2 minus treble line from 1.1 and the variation from 1.2 resulting in just the bass line with G and F but still with idea F. Cell 3.7 has this idea as heard in 1.2 but of course, again, with different combinations of other ideas. Route 4 starts with flute alone on idea C, as heard previously in 2.6. Both are two 4/4 followed by an odd meter (3/4 and 5/4) and both have the accents, tenutos, and staccatos marked in the same notes, but the order of the notes are a mixed up, as if they have been patched up differently. Cell 4.5 is cell 2.5 with the idea from 1.2 without as many rests. In cell 4.6 a fresh sounding variation occurs. The flute and tape play similarly to 1.1 but instead of a monophonic line with a bass it is now chordal, and the 1.1 variation is playing all the while. After taking a break for 3 cells idea C comes back, again alone, with the 1.1 and the first flute variation. It is sonically transparent as there are only two notes playing at a given time, building up the mystery, and handing it off graciously in the one beat long cell 5.4, to cell 5.5 which answers the mystification with a cry of glissandos. Then in 5.6 the mystery continues, idea C being at its bare minimum of the G and F bass note octaves and the clock like controlled force of idea A. Finally, after 44 beats of this subdued anxiety it reaches cell 5.7 which is a jack in the box of ideas C, D, E, and F. After much mixing of ideas A and F, C comes back and dominates cell 6.3, combining the second flute variation with the tape in chordal unison, and the original variation from 1.1. C takes another 3 cell like break until the burst happens again in cell 6.7, stating the second variation again but this time with ideas A and D. For the third time idea C starts a new route; the second variation, heard first alongside the first variation, then eight more times in combinations of other ideas, but now stripped from its accomplices. Next we hear the second flute and tape variation for three beats in 7.6 and interrupted boldly by the first variation and ideas A and E. After 28 beats of this organized chaos, the coda comes in and takes the piece to its end.

Aesthetically, this building up and increasing variety of ideas gives Network Slammer a sense of adventure, much like the classical sonata allegro form. The ideas (or themes) are given, explored, and ends similarly to the beginning. Gross generalization: the only difference is that Network Slammer has many themes that mix and match, instead of developing two or three ideas based around its key centers. It mirrors the original, pieces patched sets of notes, and combines ideas to explore its composite relationships.