Music
Presenter(s): Olivia Mello
Advisor(s): Dr. Vera Ivanova
“1089” is an aleatoric piece written for solo piano. Each line contains simple mathematical equations that are palindromic. Each digit is assigned a pitch as defined in musical set theory (ex. C=0, C#/Db=1, D=2, etc.). Each system ultimately produces ‘1089’ by a three-digit number, a subtraction of its reversal, and the addition of its own reversal. Any three-digit number (abc) where a > b > c that is reversed and the result subtracted, and that answer is then added to its reversal; the answer will always be 1089. To prove this, solve for (100a + 10b + c) - (100c + 10b + a). Every possible answer is a multiple of 99. I utilize arch form in this piece by using seven possible combinations of multiples of 99. Herein referred to as “segments.” In total, there are 84 possible three-digit combinations where a > b > c. Each multiple of 99 shows up a certain number of times for the respective first digit, and the total of appearances is palindromic in nature. I used this information to create the organization of the segments. To choose the equations to showcase in each line, I examined the largest segment produced with the smallest three-digit a > b > c number. Section B (which occurs in between Sections A1 and A2) consists of every possible three-digit combination where a > b > c. Furthermore, when each digit within a three-digit number is added to each other within each segment used in the form, it will always equal 18. I used this information to create 18 specific articulations or dynamic markings for each occurrence of the segment. I used all possible combinations with their reversals for each segment to show how different pitches (or numbers) can create the same sound at the end. Exploring mathematics as inspiration for music composition produces endless new ways to create sound. Studying mathematical phenomena has the potential to highlight how to view music in the abstraction. It allows listeners to gain a deeper appreciation and understanding of musical compositions from Baroque until the 21st century.