The initial idea of composing a series of pieces based on a specific technical development – transposition – came as a lucky result of one of my improvisations. The first of these ètudes was born out of a Bachian premise: the aural journey over a concise rhythm of sixteenth notes that evoked a serene continuum. In a general sense, the pieces must be interpreted with dynamic freedom. The deliberate choice not to include special annotations on intensity or volume came from wanting to relieve pressure from the player, and not fill them with the predisposition to obey a certain set of instructions on dynamics: I wanted to give the player the freedom to assess, control, and decide on the agogic nuances.

“12 Circles” exists as a recreation of Johann Sebastian Bach’s Prelude in C major (BWV 846), which was the first piece my son played before an audience when he was 6 years old. The imitative component of my composition stems out of the Prelude’s inalterable and continuous movement of the sixteenth notes, as well as the duplication of each motif resulting in a repetition of each measure. The ètude’s harmony is what shifts away from Bachian baroque norms, coming closer to a conjunction between Keith Jarrett’s improvisational style and Maurice Ravel’s constructivism based on sevenths and ninths, as well as a varying rhythmic meter across consecutive measures – though this meter always conserves the pulse of the shorter notes. The continual downward modulation toward the immediate degree below, which characterizes “12 Circles,” owes itself to the successive modulating bridges ascending by thirds, beginning in measure 33 (tonal center: E) and eventually arriving at A flat in measure 40. By extension, measure 60 is the same as the first measure, yet transposed downward by a single semitone. Therefore, all fifty-eight succeeding measures (following the sixtieth) are repetitions of the initial model, with the shared characteristic of being transposed one semitone down. In this way, twelve repetitions occur using the same structure, each one 59 measures int total. Thus, the structure empowers the player with the freedom to change the piece’s dynamics and phrasing over the course of its harmonic and phraseological development.

“12 Circles” also offers improvement for the player’s manual dexterity. Their hands’ posture may improve gradually over the course of practicing this ètude, creating greater finger independence and strength. The transposition of the piece also works as a technical exercise in fingering. Playing the piece through all twelve transpositions at once can be especially rewarding: through practice, the player may attain an evenness of strength and skill across all fingers, building up their endurance. Comparatively, Marguerite Long’s piano exercises are similar in that the fingering of the individual patterns remains the same across different keys. With “12 Circles,” the seeming awkwardness of the same finger-placements is beneficial to the player’s agility – in particular, the differences in striking distances between black and white keys forces the player to practice their finger coordination, so that figurations sound balanced even though their physical distances have been transposed and changed.

“Onde” (‘waves’ in Italian) is a variation on the characteristics mentioned above, however with an entirely different essence. Here, repeated arpeggios are used no longer and chordal transformations occur in the second half of each measure, instead. This new metric scheme is not structured by traditional numbers, but rather by bar lines that follow the piece’s harmonic design, irrespective of the amount of notes in each measure. These harmonic structures reflect an ostensible dramatic tension that is different in nature from the first ètude. The piece is divided down the middle at measure 18, where a fermata resolves. The apparent conclusion of the piece occurs in measure 34, given that measure 35 transposes the first measure by a full ascending tone. As a result, it would take the piece six iterations to conclude and finally reach the seventh, which would result in the same as the first, only one octave higher. On a technical level, “Onde” is a good exercise in dynamic control and expressivity, wherein the player can vary their dynamics according to the pieces’ harmony. The player may use a crescendo to precede a cadential figure or motif, a diminuendo in the same instance, or an entirely sudden and unexpected change in dynamic instead. Ultimately, the harmonic and spatial challenges of this piece make one’s dynamic control more refined and graceful.

“Melody and Triads” is a posthumous homage to Gerardo Gandini, the only composition professor I ever had, who, bringing me under his tutelage -an adolescent student who incessantly presented virtuosic pieces in the styles of Liszt and Ravel, camouflaged by morbidly fast harmonies- finally instructed me to write a piece based on certain restrictions that I found abysmal at the time. With this assignment, I would have to limit my composition to a single melody accompanied by chords of a maximum of three voices, which would prioritize intervals of major or minor thirds – in the style of Debussy. At first, these restrictions acted as an almost insurmountable obstacle but eventually became the surprisingly rich grounds on which to create something musically fulfilling that was both concentrated and expressive. The final product was a piece called “Oppositions,” and I remember it as the best example of my first personal style. In “Melody and Triads” the ‘exposition’ is made up of 37 measures, wherein the final one successively repeats the two consecutive major thirds from the first measure, by way of an interval of a descending minor third. Consequently, the piece can be transposed thrice, with the fourth one being a direct transposition of the first version, but one octave below.

“Mordents” uses the ‘orographic’ musical adornment as its title. Formally speaking, the piece is a ‘fugue in three voices’ where the subject of the fugue lasts three measures (4/4, 3/4 and 2/4) and is built upon augmented fourths which conclude in a final cadence. The fugue’s development is carried out through the exchange of the subject between the right and left hands, constantly materializing as transpositions of descending fifths: B flat, E flat, A flat, C sharp, F sharp, B, E, and ending in a coda that concludes with a triple octave A cadence (measure 27, fermata). Starting on measure 28, the piece is transposed by a semitone, downwards. After which the subject’s exposition begins with A. Thus, the piece could be transposed eleven times before arriving to the original, one octave below.

“Diabolus in Musica” alludes to the tritone, which in former times was considered a terrible dissonance and in direct opposition to the concept of beauty in music. In this ètude, the tritone is used throughout in both micro-structures and the piece’s generative macro-structure, which informs the only iteration present in “Diabolus,” and converting the tritone into an augmented fourth. The ètude’s sentimental atmosphere is charged with anxious expressivity, underscored by the omnipresent pedal in F sharp, which lasts 24 measures. Following a modulatory bridge, which is elaborated upon in an apparent and transfigured passus duriusculus, several cadential passages lead to a new tonal center located an augmented fourth away – the second iteration could be performed an augmented fourth up or down, or otherwise the left hand lower and the right hand higher by the same interval.

“Glassiana,” as its name indicates, is an homage to Philip Glass, manifesting minimalist and repeating structures. However, the motifs of said repetitions are stylized in Bartokian turns of phrase. The formation of its tonal centers are ambiguous: the rapid tempo of “Glassiana’s” chords implies tonics are occurring, whereas they are actually not clearly defined. A new chordal structure signals harmonic changes, counterposing the repeating structure which came before. Said shift is similar to an abstract movement from white to black keys and back. This structural constant culminates in measure 37, which anticipates the new iteration into an exact fourth above the original iteration. The length to which this piece may extend depends upon the amount of ascending transpositions that are possible, based on the sound quality of the instrument being used and the player’s own technical adaptability.

While the ètudes present useful pedagogical material for learning transposition, they may also be performed in concert. It would be impractical to perform all iterations of each ètude, so the performer may choose what key to end in. For example, “12 Circles” may be performed as three iterations in D, D flat, and C, with successive iterations transposed down a semitone. Because of the particular technique employed in each one of the ètudes, each one of them has a verifiable maximum extension (and therefore duration) given by its individual rendering. “Onde” could be played six times before becoming the original again, transposed an octave above. “Melody and Triads” will take three transpositions before becoming its original again one octave below. “Mordents” must be played eleven times before arriving one octave below the original. “Diabolus in Musica” was designed to be reproduced only once: it could either expand once – an augmented fourth up for the right hand and an augmented fourth down for the left hand, or else be played one augmented fourth down by both hands – while the second iteration would simply be the original, but an octave lower. Conversely, it could be taken an augmented fourth up, under the same terms.

In all cases, the freedom to choose dynamics for each one of these iterations and phrases implies the invention of a new rendering based on the player’s sequential decisions, congruent to the piece’s architecture.