Parallax Orionis MMXVI
string trio on Orion
2016
5’
the score is constructed from the geometry of the constellation
players travel between stars (noteheads), over a plane on which, like in a conventional score, the x-axis represents time and the y-axis pitch
volume/dynamic is determined by apparent magnitude (brightness as seen from Earth), represented by notehead size
durations between noteheads are determined by the real distances between stars (information absent from the 2-dimensional constellation), calculated through astrometry using the coordinates of right ascension, declination, and distance from Earth.
original performance notes:
This work sees the performers make a trip around the constellation Orion. Each instrument follows a path through the stars (which take the form of noteheads) as they are connected in the constellation, with some crossing and divergence.
Duration
The distances as they appear in the score are proportional to the distances between the stars as they appear in the constellation Orion (on the two-dimensional plane). The note durations, however, are extrapolated from the actual distances between the relevant stars (calculated in three dimensions, using the trigonometric coordinates of right ascension, declination, and distance from Earth), and are given in seconds. The term ‘parallax’ is
used simply to refer to the general idea of differing perspectives (in this case, 2D and 3D). A timeline is given to show the instruments’ progress in context with each other (red lines join multiple appearances of stars). A stopwatch should be displayed in order to assist the players in their counting, and its start should coincide with theirs.
When moving from one note to the next, there are two options. Either the initial note can be sustained consistently for the entire duration, with its pitch changed upon reaching the next (as in the conventional fashion), or a slow, proportional glissando can be made from one note to the next. The player may alternate between methods according to their preference, though a balance of the two between players is encouraged. When playing double-stops
(the secondary line is notated in green, with durations in brackets), the player may use both methods simultaneously. Cues are shown in grey. The final note may be held as long as desired, or as though marked by a regular fermata.
Bowings and string changes (during glissandi) are left to the discretion of the player, but should be coordinated with other players in order to maintain a sense of continuum.
Variables
Volume: The size of each note is equivalent to its dynamic, where larger is louder. These sizes correspond to the apparent magnitude of the stars; their brightness as seen from Earth. Betelgeuse is a variable star (in that its brightness fluctuates), so it may waver slightly (though its dynamic should stay towards the louder extreme). The change in dynamic between notes should reflect the chosen duration method; crescendi/diminuendi alongside glissandi, with sudden changes otherwise.
Pitch: The starting pitch is chosen by the player, and all subsequent pitches should be reached based on their position relative to the previous (associating pitch with the y-axis, as in conventional notation); the degree of separation between pitches is chosen by the player, but should remain consistent throughout. Notes marked with accidentals should be pitched relative to both adjacent notes. Vibrato may be used on and off throughout a note‘s
duration, but its limits should not exceed a quartertone. Players are encouraged to choose microtonal pitches on occasion (in contrast to the instruments’ traditional string tunings, and relative to the other players).
Articulation: Accents can be as pronounced as desired, but still should affect only the attack of the note. Sections marked con sordino and sul ponticello are executed normally. The duration of the note prior to that which is to be muted may have its duration shortened slightly to facilitate the mute’s attachment.