in C major — "Meta-Generativo"
Wolfgang Amadeus Mozart concluded his symphonic journey with the great triad of Symphonies №39, №40, and №41 "Jupiter." The Jupiter Symphony represents the pinnacle of polyphonic mastery, yet does not close the system of functional harmony as such.
This project hypothesizes that a Symphony №42 could exist not as an emotional continuation, but as a meta-composition grounded in the combinatorial principles that fascinated the composer (see Musikalisches Würfelspiel — "Musical Dice Game"). We generated this music using a strict stochastic algorithm layered upon statistical analysis of all 41 preceding symphonies and the topology of the chromatic pitch space.
Duration: approximately 13 minutes
The exposition maintains strict diatonicism (dice sum 7), creating the fanfare character typical of Jupiter. The development activates the "Ophiuchus Event" — a chromatic pivot modulation into B major, a tonality foreign to Mozart's symphonic output.
Harmony remains static while the dice govern timbre and register. Sums below 7 activate low register (cellos, bassoons); sums above 7 activate high register (flutes, violins). The texture density follows a probability sine wave. A single chromatic passage marks the golden ratio.
An astronomical clock: 12 phrases traverse the complete circle of fifths with enharmonic pivot, returning to C (C→G→D→A→E→B→G♭→D♭→A♭→E♭→B♭→F→C). The Trio in G minor pays homage to Mozart's minor symphonies, with a hemiola creating the illusion of 4/4 within 3/4 — a shadow within the dance.
Sonata-rondo with fugato. Module density doubles (changes every 2 bars). The coda executes "Spectral Synthesis" — rapid modulations spanning the full frequency range. The final chord: unison C across all octaves, with an almost imperceptible F♯ overtone — the tritone ghost of the "13th sign."
This reconstruction relies on a synthesis of two systems: Pitch Space Topology (Theory 88) and Stochastic Composition (Dice Theory). Below is a detailed analysis of each.
This theory treats the piano keyboard (and orchestral range) not as a set of notes, but as a mathematical model projected onto astronomical cycles.
The number 88 appears throughout the universe as a fundamental constant of harmonic systems. The standard piano keyboard contains exactly 88 keys — a number that emerges not from arbitrary design, but from the physical constraints of human hearing (20Hz to 20kHz) mapped onto the logarithmic spiral of musical pitch. This same number appears in the 88 recognized constellations of the celestial sphere, the 88-day orbital period of Mercury, and the approximate number of keys required to span the practical orchestral range from the lowest contrabassoon note to the highest piccolo overtone.
In esoteric numerology, 88 = 8×11, combining the symbol of infinity (8) with the "master number" of intuition (11). More practically, 88 represents the intersection point where human physiology (cochlear frequency response), physics (overtone series), and culture (12-tone equal temperament) converge into a single unified system.
Classical Western music (and astrology) is based on a 12-system: 12 semitones per octave, 12 zodiac signs, the Circle of Fifths with 12 stations. When we superimpose this 12-system onto the 88-key range, a mathematical conflict arises. This is resolved through Euclidean division with remainder:
Where: 12 — Number of sectors (Signs/Tonalities). 7 — Number of complete cycles (Octaves). This is the "Harmonic Norm." 4 — Remainder. This is the "Anomaly" — the mathematical proof that our 12-tone system does not perfectly tile the acoustic spectrum.
Within this theory, the entire sound range is divided into 12 equal sectors (7 keys each, 12×7=84). Each sector corresponds to one tonality of the Circle of Fifths (C, G, D, A...).
Musical meaning: These are zones of stability. When music stays within a sector, it sounds diatonic, pure, and "Mozartean."
The remaining 4 keys (the Remainder) belong to none of the 12 sectors.
Astronomical parallel: In the ecliptic, there exists a 13th constellation (Ophiuchus) through which the Sun passes, but which is excluded from the classical zodiacal circle to preserve the symmetry of 12.
Musical realization: In our symphony, these 4 units (sounds forming a diminished seventh chord or tritone pair, e.g., {F♯, A, C, E♭}) constitute the "Chaos Zone."
Function: These sounds are forbidden in the symphony's main texture. They are used exclusively as "wormholes" (pivots) for instant modulation to distant tonalities. This is mathematical proof that the 12-tonality system is not closed.
This theory is based on Mozart's historical fascination with combinatorics (K. 516f) and applies the laws of statistics to musical form.
In 1787, Mozart composed his "Musikalisches Würfelspiel" (Musical Dice Game, K. 516f) — a system for generating waltzes through dice rolls. The game contained 176 pre-composed musical measures arranged in tables. By rolling two dice 16 times, a player could select measures to assemble a complete waltz. The system could theoretically produce 11^16 (approximately 45 quadrillion) unique compositions, all sounding authentically Mozartean.
This was not mere entertainment. Mozart understood that musical coherence emerges from statistical constraints, not individual note choices. The dice game proved that "style" is a probability distribution — a fingerprint of which progressions appear frequently versus rarely. Our Symphony №42 extends this principle from 16 measures to a full symphonic form.
Unlike a random number generator (RNG), which gives uniform distribution (all numbers appear equally often), the mechanics of two dice (2d6) create a non-uniform, dome-shaped probability distribution.
Total possible combinations: 6×6=36.
| Sum | Combinations | Probability | Role in Symphony №42 |
|---|---|---|---|
| 7 | 1+6, 2+5, 3+4... | 16.67% (Max) | Norm (Tonic) |
| 6, 8 | ... | 27.78% | Development (S/D) |
| 2, 12 | 1+1, 6+6 | 5.56% (Min) | Anomaly (Ophiuchus) |
In a conventional symphony, the composer relies on "inspiration" or narrative. In Symphony №42, dramaturgy is governed by statistics.
Center of the Dome (Sums 6, 7, 8): Since these numbers appear most frequently (almost 45% of the time combined), the symphony automatically becomes tonally stable, harmonious, and "classical." The listener perceives this as Mozart's style.
Edges of the Dome (Sums 2, 12): These appear extremely rarely (once every 18-20 bars). In our theory, this triggers an "Ophiuchus Event."
Thus, Symphony №42 is the result of a collision between two mathematical models:
This transforms music from "the art of expressing emotions" into "the art of expressing the structure of the Universe," where Order (7) and Chaos (2/12) coexist in strict proportion.