Rule-based Music Composition

using Cantus Firmus

Daniel Alarcón

Supervisors:

Ian Davies & Dr. Shayne Flint

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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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