VISION OF EQUINOX FOR ORCHESTRA

The artistic play of light seen on a pyramid in some Mayan ruins located in Cancun, Mexico provided the inspiration for Vision of Equinox. On both the spring and autumn equinox days, the sunlight projected on the pyramid forms a shape which looks like a serpent moving on the stairway of the pyramid. Vision of Equinox was composed with an image of light as the model for the artistic transfiguration of sound. The light image of sound changes its shape in each stage of the piece, using the orchestra in different ways - sometimes like a chamber ensemble, sometimes like one big instrument. The image of light casting on a pyramid is expressed by descending melodic lines that can be heard several times in the piece. At the final climax of the work, a complete and embodied artistic figure is formed and stated, expressing the appearance of the Mayan god Quetzalcoatl, the serpent, in my own imagination. The light and shadow which comprise this pyramid art are treated as two contrasting elements in my composition and become the two main motives in this piece. To express these two contrasting elements, I picked the numbers "5" and "2," and used them as "key numbers" in this piece. As a result, the intervals of a fifth and a second (sometimes inverted as a seventh) are the two main intervals used in the structure. The interval of a fifth was taken into account for the construction of the pyramid, which has five points of contact. The interval of a second was selected as a contrasting sonority to the fifth. Further, the numbers "5" and "2" are used as the number of notes which form the main motives in this piece; quintuplets are used throughout this piece, and the short motive made by two sixteenth notes is used as one of the main motives in this piece. Moreover, the shape of the pyramid provided a concept of symmetry, which is expressed by the setting of a central point of the music (pitch center) as well as the use of retrograde and inversion in this piece.

Lament for String Quartet

This piece explores the changing nature of emotion focusing especially on the feeling of sorrow. The opening and ending parts of the first movement represent the overall motive of sorrow. The first movement opens with an augmented chord G-C#-F-B and from this chord the first violin expands upwards while the cello moves downwards towards the C chord (p.2). As the melody alternates between each part, there is a subtle change in harmony which creates tension and release and changes the sound color. In addition, ornamentation in each part reinforces the movement towards the C chord. This progression represents the inner emotion of lament. Sostenuto e largamente section (p.2) uses heterophony in order to express a feeling of chaos. Section Scherzando (p.4) uses the interval relationship M7 and m2, and is a respite from the overwhelming feeling of sorrow. The ending of the first movement (p.12) returns to create a second tension by every instrument ascending slowly, and the viola produces a distinctive melody derived from the previous chaotic section that ends on an Ab. The second movement contrasts with the first movement in order to express a concealed, not explicit, sorrow, and differs in both tempo and texture. The tempo is a waltz that is faster than the first movement. This produces a light, playful figure and a simple melody without much ornamentation. Imitation and canonic structure emphasize the individuality of the strings. The third movement merges material from the first movement rhythmic figure and the second movement pizzicato (p.17). It shows timbral change through con sordino, pizzicato arpeggio, and sul ponticello to display string techniques. An Allegro section (p.19) especially contrasts with Misterioso in rhythm and dynamics. In the Grazioso (p.22), random beats are accentuated by pizzicato arpeggio to de-emphasize the meter. Finally, there is a return to the ending figure of the first movement with con sordino (p.23) and sul ponticello in viola that articulates the internal tension and the timbral change to return to a voice of sorrow.

Motivic Decomposition of Projective Pseudo-Homogeneous Varieties

Let G be a semi-simple algebraic group over a field k. Projective G-homogeneous varieties are projective varieties over which G acts transitively. The stabilizer or the isotropy subgroup at a point on such a variety is a parabolic subgroup which is always smooth when the characteristic of k is zero. However, when k has positive characteristic, we encounter projective varieties with transitive G-action where the isotropy subgroup need not be smooth. We call these varieties projective pseudo-homogeneous varieties. To every such variety, we can associate a corresponding projective homogeneous variety. In this thesis, we extensively study the Chow motives (with coefficients from a finite connected ring) of projective pseudo-homogeneous varieties for G inner type over k and compare them to the Chow motives of the corresponding projective homogeneous varieties. This is done by proving a generic criterion for the motive of a variety to be isomorphic to the motive of a projective homogeneous variety which works for any characteristic of k. As a corollary, we give some applications and examples of Chow motives that exhibit an interesting phenomenon. We also show that the motives of projective pseudo-homogeneous varieties satisfy properties such as Rost Nilpotence and Krull-Schmidt.