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TRANSCRIPT
Rule-based Music Composition
using Cantus Firmus
Daniel Alarcón
Supervisors:
Ian Davies & Dr. Shayne Flint
2/14
Contents
1. Introduction
– Background
– History
– Examples
2. Scope of Work
3. Results
– Illustrative output
4. Future Work
5. Conclusion
6. Questions
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Introduction
• Problem definition – Computer Aided Composition (CAC)
– Interdisciplinary project: Music + SE/CS (formal analysis methods)
– Cantus Firmus/Counterpoint
– Rule-based music composition; sets guidelines → “universal aesthetic”
– Species Counterpoint – originally a teaching method
• These rules have a rich history– They are over 400 years old – first defined in 1610
– Well-established in 1725 by Johann Joseph Fux (Fuxian Method)
– Algorithmic history
• Athanasius Kircher 1650 – poems translated into music using cypher
• Mozart 1787 – Musikalisches Wuerfelspiel
• Illiac Suite 1956 using Illinois Automatic Computer – using some variation on
the Fuxian Method
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•1st Species is "note-against-note"
•2nd Species is "2-against-one"
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•4th Species is "suspensions (tones held across harmonic changes)"
•3rd Species is "4, 3 or 6 notes against one"
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•5th Species is a combination of the other 4 (also known as "florid" counterpoint)
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J.S. Bach’s Well Tempered Clavier, 1, Prelude XXIV.
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STRIPPED:
ORIGINAL:
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Introduction (2/2)
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• Motivation
– Express the rules of Fuxian Method formally – for coding and analysis
– Work towards a powerful semi-automated composition tool
• Sample rules:
– Each line Shall have a single "highest note”.
– And between these lines, these Shall not coincide.
– Rules relate to distances between tones both consecutively and simultaneously.
They also relate to the way that motion must occur – the “shape” of the music.
• Most notable related work
– ANTOR – FuX (Android): Variable Search Neighbourhood
– ANTOR vs. Us – Number of rules considered: 33 (15/18) vs. 75 (27/48)
– Why didn't ANTOR use them all?
– Generally, CAC ignores the rule-based approach. Usually employing:
mathematical, random, statistical and probabilistic methods.
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Scope of Work
• Focus is on the theory – aided by implementation (SE)
• Implement the rules of the Fuxian Method
– 1st Species Counterpoint
– Diatonic scale
– Essentially a predicate logic
• Develop a stable, parameterised Java tool
• Modelling of music in data structures in a way that
facilitates rule-applications and analysis
• Algorithm: Constrained Depth-first Search with
Backtracking
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Results
• Planned scope was entirely fulfilled
• Unbiased algorithm
• All rules, and only the rules, relating to the diatonic were
implemented
• What did we learn about the rules? – There can exist a condition of unsatisfiability/deadlock of rules: due to
having been drawn for many sources
• Outputs– Pleasant music – audible at run-time and a MIDI file
– MIDI files then become…
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1. Seed 101634465655517
2. Seed 195299903456534
3. Seed 196406845204745
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Future Work• Analyse the accuracy of the rule-definitions (need to reconcile the
multiple sources). More careful disambiguation is also needed.
• Other scales: quarter tone scale, Phrygian scale, Persian scale,
Mixolydian mode, Dorian scale, blues scale.
– Different rule-sets? The software can manage this
• Implement the remaining 4 Species
• Support for more than 3 voices
• Rich GUI – interface perhaps through gestures or vocalisation
• Propositional Logic and FOL (c.f. Report 6.1.1)
– This can help to fix unsatisfiability problems
– Some indication on how to achieve this has been started
• The dream is Reverse-Reverse-Engineering…
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J.S. Bach’s Well Tempered Clavier, 1, Prelude XXIV.
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SOURCE:
TARGET:
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Conclusion
• The project fulfilled its scope
• Could lead to breakthroughs for the Fuxian method
• Could be exciting for CAC and composers
• Completed tool envisioned would be extremely powerful
• This vision has never been fully realised
Thank you for listening to this overview.
Please refer to the Report for more detail.
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QUESTIONS?
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