6:36pm // My thesis composition is a concert in four movements for piano, vibraphone and cello. Movement three is based on a 24-pitch tone-row derived from the Fibonacci Sequence. The Fibonacci Sequence is based on a recursive mathematical formula: tx = t ( x -1) + t ( x -2)

t represents the term’s numerical value, and x represents the term’s position in the sequence. The first 12 values of the sequence are therefore 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144. I use these values to represent the pitch class on the 12-tone chromatic scale. However, to keep the values of the sequence below 12, the math function “Modulus” must be used. This function divides a number X by a divisor Y and generates the remainder, called the modulus. X represents the Fibonacci number we’re working with. For example we’ll use the Fibonacci number 21. Y is the number of pitches in our scale, 12 in this case. So, for example, 21 ÷ 12 = 1 Remainder 9. The Modulus is therefore 9, which is the pitch A in conventional pitch-class theory. So that’s the pitch class we use to represent that particular Fibonacci number.

In going through this process for all the Fibonacci numbers, I serendipitously found that there is a repeating pattern of 24 values, which is very useful when used in composition of music. The end result is a cyclic pattern of pitches that uses Db and Ab most often, giving the whole sequence a sense of tonality. After all of this number crunching, decided it would be fitting to give the most theory heavy movement the lightest character of the concerto. This works well because the inverse of the tone-row outlines the blues scale, which is used as a playful second theme.

– Mark DeSimone


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