Module Catalogue 2024/25

Pre Requisite Comment

N/A

Co Requisite Comment

N/A

Aims

• To cultivate an understanding of the relationship between numerical and musical ideas;
• To develop awareness of debates surrounding the relationship between music and numbers since Classical Antiquity;
• To instantiate these ideas within specific contexts: historical, architectural, philosophical, technological, or compositional;
• To encourage critical analysis of ideas, commonplaces and misconceptions around music and mathematics;
• To examine case studies relating to number-based or number-oriented musical materials
• To facilitate cross-disciplinary approaches to the subject.

Outline Of Syllabus

This module spans more than two millennia of practice and thought. Historical understandings of sounding numbers have objective origin in the physical sciences: a perfect fifth, for instance, can be expressed through the ratio 3:2, and the perfect fourth 4:3. These numerical ratios can be expressed in physical two- and three-dimensional terms, but musical numbers are are particularly susceptible to metaphysical interpretation. The module is built around a series of case studies which focus upon specific texts, propositions, repertories, places and traditions. Lectures and seminars might be expected to include, for instance:

- Music and numbers in the Pythagorean traditions;
- The case against numbers;
- Instruments, diagrams and scales: representing musical structures according to Claudius Ptolemy;
- Making spaces: acoustics and chant;
- Composing by numbers? Architectonics in medieval polyphony;
- Dufay and Brunelleschi: motet, architecture and the Solomonic Temple;
- The Harmony of the Spheres: classical cosmology and medieval angelology;
- Esoteric notation;
- Bach’s counterpoint;
- Numerological symbolism in Mozart and other classics;
- Composing by numbers in the twentieth century: proportionality, serial matrices, aleatory, stochastics;
- Ars subtilior and rhythmic relationships;
- Bartók, Debussy and the golden ratio;
- Rhythm and pitch transformations in modernism, minimalism and avant-garde

Intended Knowledge Outcomes

By the end of this module, students should be aware of:
• The contexts in which the relationship between sound and numbers has been investigated creatively and philosophically;
• The main debates relating to this relationship since Classical Antiquity;
• Numerical thinking within specific contexts: historical, architectural, philosophical, technological, or compositional;
• Specific works from the relevant repertoire
• Understandings of music-numbers debates from more than one disciplinary perspective.

Intended Skill Outcomes

At the end of this module, participants will be able to:
• Understand key aspects of the relationships between numbers and music;
• Appraise these relationships with reference to specific contexts: historical, architectural, philosophical, technological, or compositional;
• Apply relevant concepts or strategies to creative or analytical practice
• Evaluate ideas, commonplaces and misconceptions around music and mathematics.

Teaching Rationale And Relationship

Lectures introduce new topics, exemplify problems and demonstrate different interpretations; seminars enable students to engage with specific case studies, and prepare presentations based on detailed source readings.

Assessment Rationale And Relationship

The essay enables participants to undertake an extended investigation of key ideas based on secondary or primary sources. The coursework submission enables participants to test their ideas and understanding during the course.

General Notes

N/A