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Full Orchestra
String Orchestra
Wind Ensemble
Vocal
Chamber
Solo Instrumental
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Gamma was commissioned by Katie Lombardi for Shahen Mirzoyan
Gamma (γ) represents a mathematical constant that was discovered by Leonhard Euler and refined further by Lorenzo Mascheroni in the 18th century. Known as the Euler constant or the Euler-Mascheroni constant, it is a mysterious number that we don't fully understand to this day, but it shows up in many seemingly unrelated places in analytic number theory and calculus and has been dubbed by some as the third most important constant behind pi and e. It is defined by the relation between the natural logarithm function and harmonic numbers (eg. 1, 1/2, 1/3, 1/4, etc.) and the first few digits are as follows:
γ=0.57721566490153286060651209008240243…
To represent this fascinating number musically, this piece uses a couple of different approaches. The first is to take the series of digits and translate them directly into a series of pitches. Each number represents a scale degree in the key of c minor. The number zero turns into the leading tone B natural to distinguish itself from 7, which is represented by B flat, and the numbers 8 and 9 represent scale degrees 1 and 2 respectively to become C and D.
This melody becomes the basis of this piece, stated early by the first violin above a mysterious undulation of morphing chords. Throughout this piece, this idea is fragmented and developed, finally screaming out like a rock music electric guitar solo at the close.
The idea of harmonic numbers is also vital to the construction of this piece, manifesting itself in the frequent use of harmonics and harmonic glissandos, techniques that take advantage of the natural harmonic nodes that divide the instruments' strings by half, in thirds, in quarters, etc. The structure of the music is also built on harmonic numbers. After an extended slow opening, the second much faster section lasts half as long as the first section. The third section returns to the slow music of the opening and lasts one third as long as the first section. The fourth section is fast again and lasts one quarter as long as the first section. Two more sections follow this pattern, and the slow melody from the opening finally merges with the driving rhythmic texture of the fast sections.
Duration: ca. 6'
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