FUNDED
Trichords, Permutation and Concatenation
vol. 42 2021-06-29 0
Music Analysis (7) Trichords - Permutation and Concatenation
The pitches organization of the music composition Hyakunin Isshu no tame no Chushaku for Soprano, Baritone, Alto Flute, Vibraphone and Piano employ a serial system organized with trichords. The identity of a trichord consists of 3 notes considered as a configuration of the same unit. The 3 notes of a trichord are here united by the identical interval of a major second, same as the kind of trichord used by the composer Francesco Valdambrini, inventor of the compositional technique of Tricordale Music.The trichords of this composition are aligned in 2 distinct rows combining 12 permutations, each applying 4 trichords conjoined by 2 hexachords and covering a concatenation of 121 pitches in total. In 1 single hexachord are conjoined 2 trichords by an interval of a minor second, and the 2 hexachords are conjoined together by the same note, that as unison is intended to be an internal pivot in between the 2 hexachords. Therefore, the 2 hexachords are corresponding to the total amount of 11 pitches by sharing one same pitch as an internal pivot in between 2 groups of 5 notes. The last pitch of each permutation of 2 hexachords corresponds to the first pitch of the next permutation. Those pitches are considered the external pivots linking the 12 permutations, and for this reason, the concatenation corresponds to a total of 121 pitches. Thus, the notes of the original hexachord are creating the 2 parallel rows of pitches originally ordered with 2 hexachords appearing in 2 scales by contrary motion. The permuted intervals of the concatenation 121 pitches aligned in the row a also appear as inverted in row b.A similar configuration of trichords is also employed in the composition by Alessio Silvestrin: 31 Tanka for harpsichord and fortepiano.
In the next 2 pages, follows the 2 tables displaying the concatenation of 121 pitches by the 12 permutations aligned in rows a and b classified in 12 system next to the respective scales of 2 hexachords. The prime numbers encompassed within such concatenation are marked above the respective pitch with p.
The next 3 pages are presenting the music score, from bar 1 to 12, corresponding from bar 1 to 10 with the first poem of the collection: Tenji Tenno (Segment 1 on p. 17), followed in bars 11 and 12 with the beginning the second poem; Jito Tenno (Segment 2 on p. 18). In the 10 opening bars of Section 1, it is observed the use of the concatenation of 121 pitches - row a in the vibraphone part. In this occurrence, the octave of the intervals transposes according to the instrument痴 extension. At the end of bar 10, the concatenation played by the vibraphone arrives to pitch 118. The alto flute instead transposes the same concatenation by an alternation of the pitches from the permutation of the row b with notes values of 1/16. From bar 11, vibraphone and alto flute are rhythmically aligned, maintaining the distinct rows a & b with the pitch 119 of duration 1/32, pursuing with the pitches 120 and 121 composed by two different accentuated values of 6/32 (3/32 x 2) and 21/32 (3/32 x 7). Therefore, one rotation of the concatenation concludes in bar 12 on the first sub-measure with time signature 2/8 by pitch 121 pivoting in correspondence with pitch 1. From bar 1 to 7, the piano penetrates the concatenation conferred to vibraphone and alto flute, through the use of 1 trichord in each hand. Then, the piano continues from bars 7 to 10 by marking the beginning of the bars, steadily with trichords in note values of 1/32. Therefore, alto flute, vibraphone, and piano initially intercalate with the rhythmic scansion given by the soprano and baritone. Both singers at the beginning appear with the reciting voice and incorporate the use of singing gradually through the composition. Follows the next example with an extract from the beginning of the music score, from bar 1 to 12:
