[Compositions 2026]
Composition 2026.01 (Untitled) is based on Scheherazade numbers - which are a set of numbers identified by the architect - philosopher and mathematician Buckminster Fuller in his book ‘Synergetics’ (1974). The term is inspired by Scheherazade - the legendary storyteller from the ‘One Thousand and One Nights’ - who used her narrative skills to delay her execution by captivating the Persian king with stories over 1,001 nights. Fuller drew this analogy to describe numbers that exhibit remarkable symmetry or memorable patterns - much like the tales that unfolded over that symbolic span.
Fuller specifically highlighted ‘powers of 1001’ (with 1001 being a prime number) - as Scheherazade numbers - noting that 1001 itself is the product of the primes 7 - 11 and 13 (( 7 times 11 times 13 = 1001 )) - which aligns with the primorial condition starting from ( n = 13 ). The storyteller’s 1,001 tales symbolise an infinite narrative - mirroring Fuller’s vision of numbers as infinite - harmonious structures.
Composition 2026.02 (Untitled) is based on a mathematical pattern that emerges when squaring numbers composed entirely of the digit "1." - which results in a palindromic number.
Each line follows the pattern where the base number is a string of ( n ) ones (e.g., 1, 11, 111, 1111, etc.) - and its square forms a palindromic number with a symmetrical sequence of digits. The pattern expands by adding one more "1" to the base number for each subsequent line - and the resulting square reflects this growth with an increasing number of digits in a mirrored structure in the form of a pyramid.
The pattern begins with the first line consists of a single digit - 1
1^2 = 1 11^2 = 1 2 1 111^2 = 1 2 3 2 1 1111^2 = 1234321 11111^2 = 123454321
The pattern is a subtle reminder of the interplay between order and symmetry in mathematics - and consequently in music - a kind of poetry written in numbers - with the composition exploring this order in musical form. Following this mathematical structure - a new chord (number) is introduced to each part (line of the pyramid) - with the composition getting progressively longer as the composition develops. The composition consists of twenty parts - with each part representing each line of the pyramid. Two twelve-tone rows were used to determine the root tone of each chord. The chords are four bars in length - and there is a silence of four bars that separates the parts.
Composition 2026.03 (Untitled) is based on a sixty-one-digit prime number - and consists of a repeating tone and a four-note chord. The prime number is also a palindrome - with the first thirty digits being the number one - the thirty-first digit is the number four - and the following thirty digits are also the number one: 11111111111111111111111111111111411111111111111111111111111111111
To put this sixty-one digit number in context - one trillion consists of thirteen digits (1,000,000,000,000). - and so the sixty-one digit number is astronomically large. This number is a rare find given that only about 1 in 300 numbers of this size are prime - as estimated by the Prime Number Theorem - highlighting its mathematical uniqueness.
This number’s symmetry - with a single four embedded in a sea of ones - mirrors properties of palindromic primes - though its odd length and central four make it an unusual case not fitting the typical pattern where even-digit palindromes.
Composition 2026.04 (Untitled) is based on Joseph Rozhenko’s ‘Inventory Sequence’ - and consists of repeating bichords.
The ‘Inventory Sequence’ is a mathematical sequence where the terms represent a running count of how many times each number has appeared in the sequence so far - with a new "inventory" triggered whenever a zero is recorded. Each number of the ‘inventory’ is assigned to a bichord - zero being silence - with the music slowly changing and evolving over time.
The sequence grows in a way that’s not easily captured by a simple formula - and the frequency of zeros - silence in the case of composition 2026.04 - creates an almost chaotic pattern. The "lead" number (the most frequent number in a segment) changes unpredictably over time. The growth is irregular and complex - defying simple predictive formulas.
Fuller specifically highlighted ‘powers of 1001’ (with 1001 being a prime number) - as Scheherazade numbers - noting that 1001 itself is the product of the primes 7 - 11 and 13 (( 7 times 11 times 13 = 1001 )) - which aligns with the primorial condition starting from ( n = 13 ). The storyteller’s 1,001 tales symbolise an infinite narrative - mirroring Fuller’s vision of numbers as infinite - harmonious structures.
Each line follows the pattern where the base number is a string of ( n ) ones (e.g., 1, 11, 111, 1111, etc.) - and its square forms a palindromic number with a symmetrical sequence of digits. The pattern expands by adding one more "1" to the base number for each subsequent line - and the resulting square reflects this growth with an increasing number of digits in a mirrored structure in the form of a pyramid.
The pattern begins with the first line consists of a single digit - 1
1^2 = 1 11^2 = 1 2 1 111^2 = 1 2 3 2 1 1111^2 = 1234321 11111^2 = 123454321
This number’s symmetry - with a single four embedded in a sea of ones - mirrors properties of palindromic primes - though its odd length and central four make it an unusual case not fitting the typical pattern where even-digit palindromes.
The ‘Inventory Sequence’ is a mathematical sequence where the terms represent a running count of how many times each number has appeared in the sequence so far - with a new "inventory" triggered whenever a zero is recorded. Each number of the ‘inventory’ is assigned to a bichord - zero being silence - with the music slowly changing and evolving over time.
The sequence grows in a way that’s not easily captured by a simple formula - and the frequency of zeros - silence in the case of composition 2026.04 - creates an almost chaotic pattern. The "lead" number (the most frequent number in a segment) changes unpredictably over time. The growth is irregular and complex - defying simple predictive formulas.
