Five Bagatelles for Solo Piano — MP3
The most important and audible subset relationship in my piece are most notably the use of perfect 4ths and fifths i.e. interval class 5 as well as major and minor seconds i.e. interval class 1 and 2. Predictably, sets 016, 018, 019 and 027 are quite prevailant throught the work. The other most striking feature of the piece from a harmonic standpoint was the pitch relationship for the first half and the last half of the row. While constructing my matrix, I became aware of a rather striking division between the first six notes and the last six notes of my row. When I examined Pt, (G C B E D A, Ab Eb BbGb F Db) I noted that the pitches conspicuously grouped into two hexachordal structures, approximating a diatonic modal pitch relationship. When arranging these two subclasses in ascending order, this relationship was much more apparent. (C D E G A B, Db Eb F Gb Ab Bb) The result is that two hexachords exist, each one approximating a diatonic mode missing one scale degree. i.e C ionian missing an F and Db ionian missing a C. This revelation guided me as I set about choosing my row forms. Rather than using a form of P and I followed by R and IR, I decided to use two transpositions of P followed by two transpositions of I. For instance, in measures 1 and 2 of the piece I use P0 in the right hand and P6 in the left hand. The result is that 'D major' hexichord in the right hand melody is combined with the 'Ab Major' hexichord in the left hand accompaniment for the first 6 notes. Then the modal relationship shifts to Eb major superimposed over A major. The end result was a successful obsuring of any strong sense of tonality that may have resulted because of the construction of this row.
For the second two measures of the piece, I used I5 (right hand) and I1 (Left Hand) drawing on a similar (if not so forceful) harmonic relationship between my two row forms. Of course when I'd gotten 4 measures into the piece I would have been content to leave it be, but then I made the mistake of hitting the playback in finale. I liked what I heard so I finished the piece The distant transpositions between the parallel row forms continued through the length of the piece only becoming less parallel at the very end of the piece. mm 5, 6 have IR6 and IR 6, mm 7, 8 has rows RT in the left hand and rows R5 followed by RT in the right hand. Lastly, for mm 9, I use P2 and P7, followed by I6 and I2. In the end all four forms of the row are used in a number of transpositions.
In this piece, there are strong traditional motivic, formal and development elements present. For instance the piece is grouped into 4 2 bar rhythmic themes. The first two bars state the theme and the rest of the piece is spent variating on it. Futhermore, there is the presence of a monophonic line which is accompanied by a polyphonic line. Which hand the monophonic line occurs in is structurally important to the piece, as are the dynamic indications. In the end, we end up with a rounded binary piece with 2 4 bar phrases and a single bar cadential gesture at the conclusion of the work. Even though this piece is 12 tone and all twelve tones are used in each instance of the row, there are repeated pitches. From a theoretical standpoint, the repeated pitches exist for two reasons: 1) they exist in an accompanimental figure. i.e. the pitches are part of an accompanimental figure which serves to counteract the natural decay envelope of a piano. 2) they are the result of a chordal inversion. The notes are rearticulated more for the percussive effect than for the harmonic implications from this sort of usage. The most odd usage of pitches will be where some pitches are reused in a chord where others are changed. A possible example of such an occurance would be GAD ADC, DCE from a GADCE pitch class set. This system was adopted to maintain the horizontal relationship between rows. i.e. having the Row in the Left hand and in the Right hand begin and end at the same time. This methodology was adopted for formal reasons.
Lastly, the use of texture and register are employed to create a sense of progression and opening up throughout the piece. The texture begins legato and the register span small. By the end of the piece, the register span is large and the texture is disjunct. The purpose of these elements in the piece were to create a strong sense of forward motion and progression, something that would not have been possible from a strictly harmonic standpoint.
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Here I'll present my matrix. The Prime form (P) is read left to right. Retrograde (R) is read Right to Left. Inversion (I) is read top to Bottom and Retrograde Inverstion (RI) is read bottom to top. This results in all possible combinations of pitch material being available to me. The result is that I create a harmonic world in which my piece can exist. P0 is in the top row. All other rows are enumerated in ascending order based on the semitone relationship between thier starting pitches.
A D C#F#E B A#F C G#G D#
E A AbDbB GbF C G Eb D Bb
F BbA D C G GbDbAbE Eb B
C F E A G D DbAbEbB BbGb
D G GbB A E EbBbF DbC Ab
G C B E D A AbEbBbGbF Db
AbDbC F EbBb A E B G AbD
GbB BbEbDbAbG D A F E C
BbEbD G F C B GbDbA Ab E
B E EbAbGbDbC G D BbA F
EbAbG C BbF E BGb DDb A
When creating a row, P0 i.e. the original row, is written out across the top of the matrix from left to right.
A D C# F B A# F C G# G D#
The Inversion is then written out from top to bottom on the leftmost side. The A is obviously shared by both forms of the row like a crossword puzzle. For a tone row, inversions are performed as follows. If the distance between the first two notes is an ascending 5 semitone interval, the distance between the first two notes of the inversion are an interval of 5 descending semitones. Down is up and up is down so to speak.
You then write out the prime forms left to right. they are all transpositions of the inversion. You transpose the intervals up by the number of semitones that exist between the prime form and it's transposition.