Analysis of TA TA TEE-TEE TA

 By Robert Caponi

 The three movements of TA TA TEE-TEE TA are related to eachother by
the structural use of two chords comprised of a semitone separated by
a whole tone by a minor third and major third respectively, and a
chord comprised of fourths and tritones that recurs in every movement
for completely different reasons.

 Cell 1: [0146] eg C C# E F#
 Cell 2: [0157] eg C C# F G

 Cell 3: [0167] eg C C# F# G

 Let us first examine the two primary chords. The most striking
commonality between the chords is the presence of both a minor and
major second. The distinction between the two is what gives each
chord its character. Cell 1 is distinctly chromatic,-- in fact the
only permutation of the four groups of three notes that does *not*
yield what I call an "atonal chord" (a three-note chord whose
diatonic spelling results in augmented or diminished intervals
without being a diminished triad) is [146], or, in the given example,
C# E F#. Cell 2, however, is distinctly diatonic; It only contains
one augmented or diminished interval, and yields only one ordered set
comprised of two succeeding "atonal chords,"-- F C# G C. In its
inversion, the chord can be interpreted as a Dom7 with a tonic pedal.

 Cell 3 has a history all its own, one of which I am not prepared to
give. An example I like is Schoenberg's Chamber Symphony #2, in which
melodies descend first by minor seconds and then by fourths. This is
either quoted by Luciano Berio in his Duo Pezzi or arrived at by
similar means, but I suspect the former, as he also quotes
Schoenberg's Violin Concerto in the same piece, along with doubtless
many more quotations that passed under my radar. Notable is the fact
that this chord is a continuation of itself; a minor second a fourth
above a minor second contains the same pitch classes of a minor
second a fourth below a minor second. In atonal music, the immediate
repetition of the same pitch classes in different registers is
generally frowned upon, so such a melodic progression is ideally
terminated soon. As well, the chord can be spelled entirely using
fourths and tritones, which is the ordering I prefer in TA TA TEE-TEE
TA.

 Let us examine the pitch material of the first movement:

 F# 

 A note of explanation; this is not the first note of the piece, but
rather the note *before* the first note of the piece. That is, if the
melody continues as it has, before cycling back to F natural, the
last note will be F#. It is similar to the way a drummer might pick
up the snare on the backbeat *before* the start of a phrase.

F  D  F# C  F  C# G  C
\__ C1I__/  \__ C2 __/

F# C# G  B  F# C  G# B
\__ C2 __/  \__ C1I _/

C  Eb B  F  C  E  Bb F
\__ C1 __/ \__ C2I __/

B  E  Bb F# B  F  A  F#
\__ C2I __/ \__ C1 __/

 Before we examine the coda, let us examine the harmonic and melodic
patterns of the first movement. We have organized the body of the
first movement into eight four-note chords, two of each chord and
their inversion. No tone rows are being used, yet all 12 notes of the
octave are represented in these thirty-two notes. As well, if we
label the first eight notes as "prime", the subsequent groups of
eight notes can be represented as transformations:

        1  2  3  4  5  6  7  8

(P)     F  D  F# C  F  C# G  C

(R6)    F# C# G  B  F# C  G# B

(I7)    C  Eb B  F  C  E  Bb F

(IR11)  B  E  Bb F# B  F  A  F#

 Looking vertically at these transformations, we see that columns 1,
4, 5, and 8 contain orderings of Cell 3,-- B, C, F and F#. As can be
seen on the score, Cell 3 hovers over the melody as a suspended
interval undulating between a fifth (the F and C that start and close
the first two groups of four notes,) and the fourth a semitone inside
it (the F# and B that open and close the second and third.)

 Cell 3 isn't the only harmonic suspension in operation, and here is
where we get to the essence of the first movement. Something that
always impressed me about the music of Boulez (Marteau, Pli Selon Pli
era) is the way notes and intervals hang suspended, though often
opening or closing phrases. The first movement of TA TA TEE-TEE TA
represents my humble effort at simulating the same effect, albeit on
a smaller and humbler scale. The concept is to have succeeding
phrases begin on the same note and end on the same note:

 Three note phrases:

               1          2   1           2          3
 F# F  D  F#  (C  F  C#) (G  (C  F#) C#) (G  B  F#) (C  G# B)

    3          4          5   4           5
   (C  Eb B)  (F  C  E)  (Bb (F  B)  E)  (Bb F# B)   F  A  F#

 Also, note that F D F# is reflected in F A F# at the end. The entire
phrasing of the movement was built around these three-note figures.
Before we examine the coda, mention must be made of the way rhythm
emphasizes harmony in this movement. The sextuple figures jump off
the page at us, upon closer inspection, we see that every occurance
of the sextuplets occurs on a transformation of the chord [015],
which is not one of the germinal chords for this piece. As well, the
semitone interval in the chord is alternately stated vertically as a
semitone and as a major seventh.

 The body of the first movement consists of a single melodic line
broken up and voiced alternately by the tape accompaniment and the
flute. The coda truncates the melodic ideas of the body into a single
6-note melody voiced in unison, the two voices diverging only for a
dyad at the end.

 __ C2 __    __ C2I __
/        \  /         \
B  F# C  E  C# F (F# B)
   \__ C1 __/

 This closing melody not only truncates the melodic material of the
body, but states the four notes of Cell 3 as it has been used in the
first movement. Auditioning the melody as it is written in the score,
it strikes us that the melody is not so astringently atonal as it
might appear. The C E C# sounds as if C is a leading tone for the C#,
and the F natural sounds like it might be the leading tone for the
final F#. This suggestion of tonality reappears in the last movement.

 The second movement of TA TA TEE-TEE TA is frankly my favorite of
the three, and I still believe the underlying musical ideas suggest a
much larger work. None of the movements of the piece are strictly
12-tone serial, but the second movement comes closest, the only notes
unaccounted for being four tubular bell notes that aren't even
notated in the score. As well, two separate rows are used. Let us
examine:

Row 1
        __ C2I __   __ C2 __
       /         \ /        \
 Eb G  F# C# B  F  Bb E  D  A  G# C
 \__ C1I __/ \__ C3 __/  \__ C1 __/

Rov 2
        __ C2 __    __ C2I__
       /        \  /        \
 Eb B  F  Bb F# C  G  C# A  D  G# E
 \__ C2 ___/ \___ C3 __/ \_ C2I __/

 Curiously, Row 1 is comprised of two statements of Cell 1 and 2 in
both their prime and inverted forms "connected" by Cell 3, whereas
Row 2 is comprised of prime and inverted statements of only Cell 2
connected by Cell 3. What is so unique to Cell 2 that Cell 1 isn't
deserving of a row all its own? Remember, Cell 2 only has one
"atonal" ordering of its pitches, and there exists a fundamental
melodic similarity between this ordering of Cell 2 and an ordering of
Cell 3 that is exploited in this movement.

 Let us write out the pitch material for this movement. Notes played
quickly are bracketed whereas notes played slowly aren't.


Row 1P  (Eb G  F#) C# B  F  Bb E  D  A  G# C

Row 2P  (Eb B  F  Bb) F# C  G  C# (A  D  G# E)

Row 2R  (Bb D  G# D#) G  C# F# C  (E  B  F  A)

Row 1R  F# D  Eb G# Bb E  B  F (G  C  C#) A

 The entire emotional drama from this movement comes from the call
and response shared by the flautist (representing man) and the tape
accompaniment (representing machine.) Man and machine imitate
eachother, but both operate in fundamentally different ways. The tape
part plays the notes

 B  F  Bb E

 in slow, plodding rhythms. The flute soon interjects, playing in
excitable dotted-note rhythms

 B  F  Bb F#

 and we can see that man "overtakes" machine. The F# is a "wrong
note," falling a major second *above* where it should have fallen
were it to imitate the tape part, a mistake emphasized by the fact
that the F# falls on the downbeat. Row 2 is then stated in its
retrograde (it should be noted both rows are derived, and that the
retrograde of each row is identical to its inversion.) Note that,
while the inner four notes of Row 2's retrograde are identical to
those of the prime, the retrograde is not a strict one. This is
because it has been transposed by a tritone, Cell 3 remaining
invariant. As well, the D G# in the first four notes of the
retrograde echo those in the last four notes of the prime, B and F
echoing eachother as well. Finally, the ebuillient "overtaking" of
the flute is mirrored towards the end, where the tape plays, in
excitable rhythms

 C  E  B  F

 and the flute "corrects" it by stating dolefully

 Bb E  B  F

 Here, the tape initally plays the first note a major second higher
than it should have been. As we have seen, Cell 3 not only figures
prominently in the second movement, but is essential to the drama.
The fact that this chord can be distorted by whole tones is what
effects the sense of departure and return.

 Movement three was written considerably earlier than the first two
movements. It was initially based on an eight-note row, and
afterwards expanded to a twelve-note row when I discovered the
remaining four notes of the chromatic scale- not harmonically
interesting for our purposes- could be ordered "atonally." 

           __ C1 __
          /        \
 E  G  Eb A  D  Ab C  F#
    \__ C2 __/

 C# F  B  Bb

 Thus we have a broken row of the type commonly used by Schoenberg,
where one segment of the row is used for melody and the remainder
accompaniment. The reason I dusted off this scrap was the discovery
of a commonality between the first two movements and this one: not
only does the row contain four adjacent notes forming C2, and not
only is C1 to be found two notes away, but C3 is nestled between them
in a configuration totally unique to this row.

 For my purposes at the time- purposes I can't be expected to
remember, as this was nearly a year and a half ago,- I had arrived at
this sequence of four eight-note rows:

  P                         RI
 (E  G  Eb A  D  Ab C  F#) (F  B  Eb A  D  Ab E  G)

  I                         R
 (Eb C  E  Bb F  B  G  C#) (D  Ab E  Bb F  B  Eb C)

 Now this is interesting; between rows 2 and 3, we see the notes G Eb
C,-- a C minor chord, the first explicitly tonal reference in the
piece. So unavoidable I found this C minor chord to be that I
expanded on it. I added the notes F and Ab to the end forming an F
minor "tonic" chord, and added a C#, F, F# and A# to the beginning to
form a Neapolitan 7th. "But a C minor chord can't be a dominant," I
can hear you protest, and you're right, but my only other option
would have been to invert the rows to make it a C major chord, only
then my cadence would have been plagal,-- a resolution arguably of
even less finality, though perhaps keeping with the delicate,
religious nature of the movement.

 The logic of Cell 3's deployment in the three movements lies in its
repetition. In the first movement, the chord appears as a melodic
fifth alternating with a melodic fourth; in the second movement it
presented itself as something stated twice, alternating between error
and correction; and in the third movement, as a simple melodic
statement repeating in the center of suceeding eight-note rows. So,
while the small scale musical events center on Cell 1 and 2, the long
term musical happenings are determined by Cell 3 and how its
repetition manifests itself.

 I am a novice composer, and am basically illiterate when it comes to
notated music. For the beginner, I suggest not getting too hung up on
theory, but focus your energies on making music. Imitate what you
hear; not note for note, but if you hear a retrograde in a piece of
music, try writing a retrograde that you would be able to hear. It is
only when you know *how* people listen to music that you can write
music ergonomic to listening. Try playing around with different
themes; being a good composer involves having an instinctive sense of
which themes lend themselves to development and which ones want to
remain static. I have never been wanting for theory, but it took me
years before I was able to finish a piece. I don't know why this is
the case. Anyway, good luck on your compositional endeavours. If you
have any questions or comments about this article, feel free to email
me at tagutcow@nr.infi.net