Your programme is made up of credits, the total differs on programme to programme.
| Semester 1 Credit Value: | 10 |
| Semester 2 Credit Value: | 10 |
| ECTS Credits: | 10.0 |
| European Credit Transfer System | |
• 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.
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
| Category | Activity | Number | Length | Student Hours | Comment |
|---|---|---|---|---|---|
| Scheduled Learning And Teaching Activities | Lecture | 10 | 2:00 | 20:00 | N/A |
| Guided Independent Study | Assessment preparation and completion | 1 | 60:00 | 60:00 | N/A |
| Guided Independent Study | Directed research and reading | 1 | 100:00 | 100:00 | N/A |
| Scheduled Learning And Teaching Activities | Small group teaching | 8 | 2:00 | 16:00 | Combining seminar discussions and student presentations |
| Scheduled Learning And Teaching Activities | Drop-in/surgery | 1 | 4:00 | 4:00 | 20-minute sessions |
| Total | 200:00 |
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.
The format of resits will be determined by the Board of Examiners
| Description | Semester | When Set | Percentage | Comment |
|---|---|---|---|---|
| Essay | 2 | M | 80 | Essay or project. Approx. 3,200 words or agreed equivalent |
| Written exercise | 2 | A | 20 | 1,000 critical evaluation of one of the key source readings discussed during the module. |
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.