[Compositions 2021]
Composition 2021.01 (Untitled) [26.08] [Nihil Humanum]Composition 2021.01 (Untitled) is based on an eight-note tone-cell of C - D - D# - E - F - F# - A# - B - and consists of fourteen repeating bichords and trichords separated by silence.
Composition 2021.02 (Untitled) consists of a repeating fading tones separated by silence.
Composition 2021.03 (Untitled) is sparsely textured - and consists of repeating fading sounds separated by silence.
Composition 2021.04 (Untitled) is based on tone cells from Arnold Schoenberg’s 1909 composition ‘Three Piano Pieces’ Op.11.
Composition 2021.05 (Untitled) is based on a four-note tone-cell of A2 - C2 - C3 - D#3 - and consists of a drone of C2 and fading tones.
Composition 2021.06 (Untitled) is based on a four-note tone-cell of C - C# - E - F# - from which bichords and tetrachords have been derived.
Composition 2021.07 (Untitled) is based on a two-note tone cell of C3 and C4 - and consists of both repeating and fading tones.
Composition 2021.08 (Untitled) is based on a six-note tone-cell of: C - D# - F# - G - A - A# - and consists of twelve bichords made up of minor thirds - major sixths - and minor sevenths.
Composition 2021.09 (Untitled) consists of overlapping sounds in glacial movement.
Composition 2021.10 (Untitled) is based on the tone row from Arnold Schoenberg's Suite for Piano Op 25 (1921) - and alternates singe tones with bichords. The composition was first performed at Corpora Aliena - Iklectik - London - 20.10.2021. 2021 being the hundredth anniversary of Schoenberg's composition.
[Compositions 2022]
Composition 2022.01 (Untitled) is based on a five-note tone-cell - D2 - F2 - A2 - E3 - G#3 - from Anton Webern’s 1914 composition ‘Three Little Pieces for Cello and Piano’ Op. 11 - and consists of tetrachords.
Composition 2022.02 (Untitled) is sparsely textured - and is based on a five-note tone-cell of C1 - C2 - C#2 - C3 - C4 - and consists of a repeating tone and fading sounds.
Composition 2022.03 (Untitled) is based on Morton Feldman’s Piano Piece (1952) - and incorporates all eighty-nine tones of the original composition. The performance instructions for Feldman’s composition are ‘Slowly and quietly with all beats equal’. Composition 2022.03 uses these instructions as a starting point - but with the tones restricted to a single octave - between C2 and C3. All the tones are of the same length - and alternate with an equal length of silence.
Composition 2022.04 (Untitled) is based on tone-cells from Morton Feldman’s composition ‘Trio for Flutes’ (1972) - and consists of fading sounds separated by silence.
Composition 2022.05 (Untitled) is based on the tone-row from Igor Stravinsky’s Epitaphium (1959). Epitaphium is notable for being Stravinsky's first work where he applied serial techniques to the harmony throughout the piece. Initially conceived as a duet for two flutes - it was later adapted for an ensemble of harp - flute - and clarinet - influenced by the fact that it was to be performed alongside Anton Webern's Fünf geistliche Lieder (1922). Stravinsky began this composition by ear - focusing on a melodic-harmonic phrase before recognising its potential for a serial pattern. For Composition 2022.05 (Untitled) - Stravinsky’s tone-row - of which all twelve transpositions are used - is grouped into trichords.
[Compositions 2023]
Composition 2023.01 (Untitled) is based on a short harmonic sequence from Arnold Schoenberg’s composition Six Little Pieces Op. 19 (1911).
Composition 2023.02 (Untitled) consists of a tone-line moving in semi-tones and minor thirds - within a pitch range between A1 to C3. It suggests never ending permutation and endless movement through time.
Composition 2023.03 (Untitled) is based on a seven-note tone-cell of C - C# - D - D# - E - F# - A# - and consists of bichords and trichords.
Composition 2023.04 (Untitled) is based on tone rows from leading composers of the twentieth century - including Alban Berg - Elisabeth Lutyens - Arnold Schoenberg - and Karlheinz Stockhausen - and consists of fading sounds separated by silence.
Composition 2023.05 (Untitled) is based on a tone cell of C2 - D2 - D#2 - E2 - F#2 - A#2 - C#3 - and consists of repeating bichords and fading tones.
Composition 2023.06 (Untitled) consists of bichords made up of minor thirds and diminished fifths.
Composition 2023.07 (Untiled) is based on seven twelve-tone rows that were generated by an artificial intelligence programme - with the tones within an octave pitch range between C2 to C3. The composition suggests never ending permutation - and endless movement through time.
Composition 2023.08 (Untitled) is based on twelve-tone rows generated by using an artificial intelligence programme - and consists of single tones alternating with bichords.
Composition 2023.09 (Untitled) is based on the chord sequence from John Coltrane’s 1960’s jazz composition ‘Giant Steps’.
Composition 2023.10 (Untitled) is based on nine bichords - and is in the form of a palindrome.
[Compositions 2024]
Composition 2024.01 (Untitled) consists of bichords within the pitch range between G1 and C3.
Composition 2024.02 (Untitled) is based on a five-note tone-cell (E - D# - C - C# - D) from Igor Stravinsky’s composition ‘In Memoriam Dylan Thomas’ (1954) - and consists of a continuous tone line.
Composition 2024.03 (Untitled) consists of a single tone-line moving in semi-tones - minor thirds - and tritones - within a two octave pitch range between C1 to C3.
Composition 2024.04 (Untitled) is based on a six-note tone-cell of C1 - F#1 - F2 - A2 - C3 - D#3 - and consists of continually repeating bichord of C3/D#3 - and fading sounds.
Composition 2024.05 (Untitled) is based on the tone-row from Alban Berg’s ‘Chamber Concerto’ (1925). In the new ‘Composition 2024.05 (Untitled)’ - Berg’s musical ideas have become compressed to a single continuous tone-line.
Composition 2024.06 (Untitled) consists of continually repeating tones and fading sounds.
Composition 2024.07 (Untitled) is based on the tone-row from Arnold Schoenberg’s ‘Variations for Orchestra Op.31’ (1928) - and consists of single tones and bichords.
Composition 2024.08 (Untitled) is based on the ‘Elektra Chord’ from Richard Strauss’ opera ‘Elektra’. This distinctive chord consists of a tritone (an interval of three whole tones) - and an added minor second.
Composition 2024.09 (Untitled) is based on the tone-row (A - A# - E - D - D# - C# - G - F - F# - G# - B - C. ) from Arnold Schoenberg’s opera Moses and Aron (1932) - and consists of single tones and bichords.
Composition 2024.10 (Untitled) is based on twenty tetrachords - all with the root of C2.
Composition 2024.11 (Untitled) is based on a four-note tone-cell of C - D# - F# - A - and consists of an irregular pulsing pedal-note of C1 - and two alternating dyads of D#2/F#2 and A2/C3.
Composition 2024.12 (Untitled) is based on a five-note tone-cell of D - E - A - A# - B - with the tones organised into twenty-seven trichords.
Composition 2024.13 (Untitled) is based on the Ionic scale (the white notes on the piano keyboard from C1 to C2) - and consists of single tones and bichords.
Composition 2024.14 (Untitled) [25.36] [The Story Till Now] Compositions 2024.14 (Untitled) is based on a three-note tone-cell of B1 - C2 - C#2 - and consists of a tone-line and fading sounds.
Composition 2024.15 (Untitled) consists of both major and minor trichords - with AI being used to place the chords within the composition sequence. AI was also used to determine how the trichords entered - either two tones - followed by a single tone (to make the trichord) - or a single tone followed by two tones (to make the trichord). Twelve-tone rows were used to to determine the root tone of each trichord.
Composition 2024.16 (Untitled) is based on short musical events that consist of: an octave bichord - a single tone - and a trichord in which the single tone is common - with the events separated by silence. The tones of the octave bichords are in the range of C1 to C3 - and the single tones are in the range between C2 and C3.
Composition 2024.17 (Untitled) consists of a continually repeating tone and fading sounds.
Composition 2024.18 (Untitled) is based on harmonic and thematic elements from Charles Ives’ composition ‘The Unanswered Question’ (1935). The five-note question from the trumpet in the original - A#1 - C#1 - E1- D#2 - C2 - now appears as in the form of two chords (a trichord and a bichord) - and the increasingly complex ‘answers’ from the flutes in the original - have been condensed to single melodic lines of increasing lengths.
Composition 2024.19 (Untitled) is based on the piano chord sequences and melody from Charles Ives’ ‘The Cage’ - Number 64 of 114 songs (also called ‘In the Cage’). The song was also arranged for small orchestra for ‘Set for Theater Orchestra: I. In the Cage.’ The first seven chords of the introduction are repeated three times - and the chords consist of stacked fourths and fifths.
“ A leopard went around his cage
from one side back to the other side;
he stopped only when the keeper came around with meat;
A boy who had been there three hours
began to wonder, “Is life anything like that?”
Composition 2024.20 (Untitled) is based on harmonic material from Charles Ives’ ‘The Universe Symphony’ (1928). Ives divided the chords used in his symphony into ‘cloud chords’ and ‘earth chords’ - with the chords consisting of stacked fourth -stacked fifths - and polychords in which two or more trichords are overlaid on top of each other - creating complex harmonic structures. Ives described his symphony as ‘a universe in tones’ - and hoped that listening to his music would be like gazing into infinity.
[Compositions 2025]
Composition 2025.01 (Untitled) is based on a set of simple instructions - from which the composition slowly evolves and expands. There are nine trichords - and the root of each trichord comes from the tones of the first chord - C2 / F2 / F#2. The intervals in relation to the root are: perfect fourth - augmented fourth - and their octave equivalents. The chords are sixteen bars in length - and events are separated by four bars of silence.
Composition 2025.02 (Untitled) is based on a set of simple instructions - from which the composition slowly evolves and expands. There are sixteen tetrachords - and the root of each tetrachord comes from the tones of the first chord C2 / F#2 / G2 / A#2. The intervals in relation to the root are: augmented fourth - perfect fifth - augmented sixth - and their octave equivalents. The chords are sixteen bars in length - and events are separated by four bars of silence.
Composition 2025.03 (Untitled) is based on a set of simple instructions - from which the composition slowly evolves and expands. There are twenty-five pentachords - and the root of each pentachord comes from the tones of the first chord C2 / D#2 / G2 / A2 / B2. The intervals in relation to the root are: minor third - perfect fifth - perfect sixth - major seventh - and their octave equivalents. The chords are sixteen bars in length - and events are separated by four bars of silence.
Composition 2025.04 (Untitled) is based on the ‘Thema Regium’ (King’s Theme) from J.S. Bach’s ‘Musical Offering’ (1747). The ‘Thema Regium’ was actually composed by Frederick the Great - the king of Prussia - and was used as a basis for Bach’s composition ‘Music Offering’ which was a collection of fugues and ricecars . The ‘Thema Regium’ is highly chromatic - and uses all the tones of the chromatic scale apart from A# - and - as such - It has some of the qualities of a twelve-tone row - which is a compositional technic developed by the composer Arnold Schoenberg. Anton Webern - who was a student of Schoenberg’s - and also and important exponent of the twelve-tone serial technique in his own right - arranged the ‘Ricercar a 6’ of the ‘Musical Offering’ for chamber orchestra (1934).
Composition 2025.05 (Untitled) is based on the tone-row from Anton Webern’s ‘Symphony’ Op. 21 (1928) - and is in the form of a palindrome.
Composition 2025.06 (Untitled) is based on the four-note theme/leitmotif from the opening of Morton Feldman’s composition ‘For Philip Guston’ (1984). The four notes of the theme/leitmotif are C - G - G# - D#.
Composition 2025.07 (Untitled) is based on tone-rows from Charles Ives’ composition ‘Tone Roads 1’ (1911). Ring-modulaton has been applied to create a higher level of harmonic complexity. The original composition uses contrapuntal and fugal conventions - with the contrapuntal lines representing roads converging in the centre of a town. In the words of Ives ‘‘All roads lead to the centre”. With the new Composition 2025.07 (Untitled) - the complex fugal elements of ‘Tone Roads 1’ have been reduced to a single tone-line.
Composition 2025.08 (Untitled) is based on the permutation of five bichords - C / F# - A / G - F / G# - D / A# - G / A and five durations - with the chords lastings from one - two - three - four - and five bars in length.
Composition 2025.09 (Untitled) is based on twelve melodic fragments from Franz Schubert’s “Der Leiermann” (The Hurdy-Gurdy Man) - which is the last song of the “Die Winterreise” (Winter Journey) song cycle that Schubert composed in 1828. For “Der Leiermann” - Schubert used an eight note tone-cell to compose the twelve melodies that are part of the vocal line. Some of the fragments are repeated - but with minor variations. Composition 2025.09 adheres to the same note order of Schubert’s melodic fragments of the “Der Leiermann” song - and also the same tone-cell - which is E2 - G#2 - A2 - B2 - C3 - D3 - E3 - F3.
“Back of the village stands a hurdy-gurdy man, cranking his instrument with frozen fingers. His begging bowl is always empty; no one listens, and the dogs growl at him. But his playing never stops. "Strange old man. Shall I come with you? Will you play your hurdy-gurdy to accompany my songs?” [From the “Der Leiermann” poem by Wilhelm Müller]
Composition 2025.10 (Untitled) [24.08] [Poetic Truth]
Composition 2025.11 (Untitled) is based on the proportions of the monolith in Arthur C. Clarke’s novel 2001: A Space Odyssey. The monolith - both in the novel and the film - has a ratio of 1:4:9 - corresponding to the squares of 1, 2, and 3 respectively. For Composition 2025.11 the ratios are musically realised has follows:
Part 1: 100 bars in length with a single repeating tone of C2.
Part 2: 400 bars in length consisting of four tones - C2 - D#2 - F#2 - A2 - that have been organised in six bichords.
Part 3: 900 bars in length consisting of nine tones - C2 - D2 - D#2 - F2 - F#2 - G#2 - A2 - A#2 - B2 - that have been organised into thirty trichords.
The use of the squares of the first three integers (1 - 4 - 9) represents a simple yet profound mathematical pattern. This could suggest - in the 2001: A Space Odyssey novel - a message or intentionality from an advanced intelligence - as it reveals an understanding of basic number theory or geometric progression. The ratio 1:4:9 could symbolise perfection or harmony - reflecting an advanced civilisation's understanding of numbers and geometry. This symmetry and simplicity implies a message of order - predictability - or beauty in the universe - themes that are recurrent in Clarke's work.
Composition 2025.12 (Untitled) is based on the twenty-six prime numbers between 2 and 101. Prime numbers are natural numbers greater than 1 that are divisible only by 1 and themselves. The first few prime numbers are 2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - and so on.
Prime numbers are used in the composition to determine the duration of the chords - which consist of trichords - tetrachords - and pentachords. Each of the chords is preceded by an equal duration of silence. Subsequently - the silences and chords get progressively longer - beginning at two bars long - and ending at 101 bars long.
In Carl Sagan's novel Contact - prime numbers play a crucial role in establishing communication with an extraterrestrial civilisation. The first indication of an alien signal comes through a radio telescope detecting a strong regular pattern of pulses. This pattern is not random but structured in a way that suggests intelligence.
By using prime numbers - Sagan highlights how mathematics could serve as a universal language for communication across the vast distances of space - transcending cultural and linguistic barriers. This method of communication through primes is not just efficient but also profoundly symbolic of the shared intelligence between different forms of life in the universe.
Both novels use mathematics as a tool for transcending linguistic and cultural barriers - but Clarke's approach is more metaphysical - suggesting that communication with higher intelligence might not be about understanding words or symbols but about experiencing and interpreting events. Sagan - however, uses mathematics as a clear logical bridge - showing that even across galaxies - certain truths like prime numbers and geometric shapes remain constant - providing a basis for communication. This difference reflects their respective views on science - communication - and the nature of intelligence.
Composition 2025.13 (Untitled) is based on the sixteen tones between A1 and C - and consists of three parts - with each part being subdivided into sixteen sections. The lead tone - one of sixteen - forms a bichord with a secondary tone. Each of the sound events is eight bars in length - with two bars of silence separating the events.
Composition 2025.14 (Untitled) [54.36] [Thinking Aloud] Composition 2025.14 (Untitled) is based on the sixteen tones from A1 to C3 - with the tones being grouped into six three-note tone-cells - and each is in the form of a palindrome. For example: C2 - B1 - C#2 - B1 - C2 : C2 - G#2 - B2 - G#2 - C2 : F2 - C3 - A#2 - C3 - F2.
Composition 2025.15 (Untitled) consists of a continually repeating chord - C2 / D#2 / F#2 / A2 - and is based the first one hundred and fifty decimal places of Pi(π):
3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172 5359408128).
The length of each instance of the chord is based on the decimal number from the pi sequence. For example: 1 equals one bar in length - 5 equals five bars in length - etc. The chords are separated by an equal length of silence.
Pi(π) is an irrational number - meaning it cannot be exactly expressed as a simple fraction - and its decimal expansion (3.14159…) is infinite and non-repeating - with no discernible pattern despite extensive computation (three hundred trillion digits have been calculated). This unpredictability fuels its mystique - as it seems to defy complete human mastery. Philosophically - it raises questions about whether the universe itself is infinitely complex or governed by hidden patterns.
Composition 2025.16 (Untitled) consists of a continually repeating tone - C2 - plus accompany bichords - trichords - and tetrachords.
Composition 2025.17 (Untitled) is based on bichords within a one octave range between C2 and C3. The bichords are eight bars in length - with four bars of silence in between the chords.
Composition 2025.18 (Untitled) is based on two-hundred-unique two note ‘melodies’ within a two octave range between C1 and C3. The tones are eight bars in length - and the pairings are separated by a silence of four bars.
Composition 2015.19 (Untitled) [32.24] [Vita Contemplativa] Composition 2025.19 (Untitled) is based on all the possible bichords between A1 and C3.
Composition 2025.20 (Untitled) [1.09.32] [Vita Contemplativa] Composition 2025.20 (Untitled) is based on the structure of the first thirty rows (from 0 to 29) of Pascal’s Triangle. The numbers from the triangle have been designated a trichord - with the composition growing from one chord in Part One (the fist row of the triangle) - then two chords for Part Two (the second row of the triangle) - and so on. Each part is in the form of a palindrome (which follows the structure of each of the rows of the triangle). Using mathematical structures like this helps to create a sense of form and order for a composition - and helps to push the music into a direction which otherwise may not have been conceived. Each mathematical structure or number pattern helps to create new musical pathways to be explored.
Pascal’s Triangle is a mathematical structure named after the French mathematician Blaise Pascal - though it was known to earlier mathematicians in various cultures. It’s a triangular array of numbers where each number is the sum of the two numbers directly above it. The triangle starts with a single 1 at the top - and each subsequent row is constructed by adding pairs of numbers from the row above.
Pascal's Triangle can increase indefinitely. Each row is generated by adding pairs of numbers from the previous row - starting and ending with 1 - with no limit to the number of rows that can be computed. The triangle expands infinitely as the process continues - with each row having one more element than the last. The only practical constraint is computational capacity for very large rows - as the numbers grow exponentially.
Here are the first five rows: Row 0: 1 Row 1: 1 1 Row 2: 1 2 1 Row 3: 1 3 3 1 Row 4: 1 4 6 4 1 Row 5: 1 5 10 10 5 1
Composition 2021.01 (Untitled) [26.08] [Nihil Humanum]
Composition 2021.01 (Untitled) is based on an eight-note tone-cell of C - D - D# - E - F - F# - A# - B - and consists of fourteen repeating bichords and trichords separated by silence.
Composition 2021.02 (Untitled) consists of a repeating fading tones separated by silence.
Composition 2021.03 (Untitled) is sparsely textured - and consists of repeating fading sounds separated by silence.
Composition 2021.04 (Untitled) is based on tone cells from Arnold Schoenberg’s 1909 composition ‘Three Piano Pieces’ Op.11.
Composition 2021.05 (Untitled) is based on a four-note tone-cell of A2 - C2 - C3 - D#3 - and consists of a drone of C2 and fading tones.
Composition 2021.06 (Untitled) is based on a four-note tone-cell of C - C# - E - F# - from which bichords and tetrachords have been derived.
Composition 2021.07 (Untitled) is based on a two-note tone cell of C3 and C4 - and consists of both repeating and fading tones.
Composition 2021.08 (Untitled) is based on a six-note tone-cell of: C - D# - F# - G - A - A# - and consists of twelve bichords made up of minor thirds - major sixths - and minor sevenths.
Composition 2021.09 (Untitled) consists of overlapping sounds in glacial movement.
Composition 2021.10 (Untitled) is based on the tone row from Arnold Schoenberg's Suite for Piano Op 25 (1921) - and alternates singe tones with bichords. The composition was first performed at Corpora Aliena - Iklectik - London - 20.10.2021. 2021 being the hundredth anniversary of Schoenberg's composition.
[Compositions 2022]
Composition 2022.01 (Untitled) is based on a five-note tone-cell - D2 - F2 - A2 - E3 - G#3 - from Anton Webern’s 1914 composition ‘Three Little Pieces for Cello and Piano’ Op. 11 - and consists of tetrachords.
Composition 2022.02 (Untitled) is sparsely textured - and is based on a five-note tone-cell of C1 - C2 - C#2 - C3 - C4 - and consists of a repeating tone and fading sounds.
Composition 2022.03 (Untitled) is based on Morton Feldman’s Piano Piece (1952) - and incorporates all eighty-nine tones of the original composition. The performance instructions for Feldman’s composition are ‘Slowly and quietly with all beats equal’. Composition 2022.03 uses these instructions as a starting point - but with the tones restricted to a single octave - between C2 and C3. All the tones are of the same length - and alternate with an equal length of silence.
Composition 2022.04 (Untitled) is based on tone-cells from Morton Feldman’s composition ‘Trio for Flutes’ (1972) - and consists of fading sounds separated by silence.
Composition 2022.05 (Untitled) is based on the tone-row from Igor Stravinsky’s Epitaphium (1959). Epitaphium is notable for being Stravinsky's first work where he applied serial techniques to the harmony throughout the piece. Initially conceived as a duet for two flutes - it was later adapted for an ensemble of harp - flute - and clarinet - influenced by the fact that it was to be performed alongside Anton Webern's Fünf geistliche Lieder (1922). Stravinsky began this composition by ear - focusing on a melodic-harmonic phrase before recognising its potential for a serial pattern. For Composition 2022.05 (Untitled) - Stravinsky’s tone-row - of which all twelve transpositions are used - is grouped into trichords.
[Compositions 2023]
Composition 2023.01 (Untitled) is based on a short harmonic sequence from Arnold Schoenberg’s composition Six Little Pieces Op. 19 (1911).
Composition 2023.02 (Untitled) consists of a tone-line moving in semi-tones and minor thirds - within a pitch range between A1 to C3. It suggests never ending permutation and endless movement through time.
Composition 2023.03 (Untitled) is based on a seven-note tone-cell of C - C# - D - D# - E - F# - A# - and consists of bichords and trichords.
Composition 2023.04 (Untitled) is based on tone rows from leading composers of the twentieth century - including Alban Berg - Elisabeth Lutyens - Arnold Schoenberg - and Karlheinz Stockhausen - and consists of fading sounds separated by silence.
Composition 2023.05 (Untitled) is based on a tone cell of C2 - D2 - D#2 - E2 - F#2 - A#2 - C#3 - and consists of repeating bichords and fading tones.
Composition 2023.06 (Untitled) consists of bichords made up of minor thirds and diminished fifths.
Composition 2023.07 (Untiled) is based on seven twelve-tone rows that were generated by an artificial intelligence programme - with the tones within an octave pitch range between C2 to C3. The composition suggests never ending permutation - and endless movement through time.
Composition 2023.08 (Untitled) is based on twelve-tone rows generated by using an artificial intelligence programme - and consists of single tones alternating with bichords.
Composition 2023.09 (Untitled) is based on the chord sequence from John Coltrane’s 1960’s jazz composition ‘Giant Steps’.
Composition 2023.10 (Untitled) is based on nine bichords - and is in the form of a palindrome.
[Compositions 2024]
Composition 2024.01 (Untitled) consists of bichords within the pitch range between G1 and C3.
Composition 2024.02 (Untitled) is based on a five-note tone-cell (E - D# - C - C# - D) from Igor Stravinsky’s composition ‘In Memoriam Dylan Thomas’ (1954) - and consists of a continuous tone line.
Composition 2024.03 (Untitled) consists of a single tone-line moving in semi-tones - minor thirds - and tritones - within a two octave pitch range between C1 to C3.
Composition 2024.04 (Untitled) is based on a six-note tone-cell of C1 - F#1 - F2 - A2 - C3 - D#3 - and consists of continually repeating bichord of C3/D#3 - and fading sounds.
Composition 2024.05 (Untitled) is based on the tone-row from Alban Berg’s ‘Chamber Concerto’ (1925). In the new ‘Composition 2024.05 (Untitled)’ - Berg’s musical ideas have become compressed to a single continuous tone-line.
“ A leopard went around his cage
from one side back to the other side;
he stopped only when the keeper came around with meat;
A boy who had been there three hours
began to wonder, “Is life anything like that?”
“Back of the village stands a hurdy-gurdy man, cranking his instrument with frozen fingers. His begging bowl is always empty; no one listens, and the dogs growl at him. But his playing never stops. "Strange old man. Shall I come with you? Will you play your hurdy-gurdy to accompany my songs?” [From the “Der Leiermann” poem by Wilhelm Müller]
Part 1: 100 bars in length with a single repeating tone of C2.
Part 2: 400 bars in length consisting of four tones - C2 - D#2 - F#2 - A2 - that have been organised in six bichords.
Part 3: 900 bars in length consisting of nine tones - C2 - D2 - D#2 - F2 - F#2 - G#2 - A2 - A#2 - B2 - that have been organised into thirty trichords.
The use of the squares of the first three integers (1 - 4 - 9) represents a simple yet profound mathematical pattern. This could suggest - in the 2001: A Space Odyssey novel - a message or intentionality from an advanced intelligence - as it reveals an understanding of basic number theory or geometric progression. The ratio 1:4:9 could symbolise perfection or harmony - reflecting an advanced civilisation's understanding of numbers and geometry. This symmetry and simplicity implies a message of order - predictability - or beauty in the universe - themes that are recurrent in Clarke's work.
In Carl Sagan's novel Contact - prime numbers play a crucial role in establishing communication with an extraterrestrial civilisation. The first indication of an alien signal comes through a radio telescope detecting a strong regular pattern of pulses. This pattern is not random but structured in a way that suggests intelligence.
By using prime numbers - Sagan highlights how mathematics could serve as a universal language for communication across the vast distances of space - transcending cultural and linguistic barriers. This method of communication through primes is not just efficient but also profoundly symbolic of the shared intelligence between different forms of life in the universe.
Both novels use mathematics as a tool for transcending linguistic and cultural barriers - but Clarke's approach is more metaphysical - suggesting that communication with higher intelligence might not be about understanding words or symbols but about experiencing and interpreting events. Sagan - however, uses mathematics as a clear logical bridge - showing that even across galaxies - certain truths like prime numbers and geometric shapes remain constant - providing a basis for communication. This difference reflects their respective views on science - communication - and the nature of intelligence.
Pi(π) is an irrational number - meaning it cannot be exactly expressed as a simple fraction - and its decimal expansion (3.14159…) is infinite and non-repeating - with no discernible pattern despite extensive computation (three hundred trillion digits have been calculated). This unpredictability fuels its mystique - as it seems to defy complete human mastery. Philosophically - it raises questions about whether the universe itself is infinitely complex or governed by hidden patterns.
Pascal’s Triangle is a mathematical structure named after the French mathematician Blaise Pascal - though it was known to earlier mathematicians in various cultures. It’s a triangular array of numbers where each number is the sum of the two numbers directly above it. The triangle starts with a single 1 at the top - and each subsequent row is constructed by adding pairs of numbers from the row above.
Pascal's Triangle can increase indefinitely. Each row is generated by adding pairs of numbers from the previous row - starting and ending with 1 - with no limit to the number of rows that can be computed. The triangle expands infinitely as the process continues - with each row having one more element than the last. The only practical constraint is computational capacity for very large rows - as the numbers grow exponentially.
Here are the first five rows: Row 0: 1 Row 1: 1 1 Row 2: 1 2 1 Row 3: 1 3 3 1 Row 4: 1 4 6 4 1 Row 5: 1 5 10 10 5 1
