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MATH6050 - Mathematics and Music

Title:Mathematics and Music
Long Title:Mathematics and Music
Module Code:MATH6050
Duration:1 Semester
Credits: 5
NFQ Level:Fundamental
Field of Study: Mathematics
Valid From: Semester 2 - 2013/14 ( February 2014 )
Module Delivered in no programmes
Module Coordinator: David Goulding
Module Author:  
Module Description: This module is an exploration of some of the many links between Mathematics and Music. The learner should contact the module coordinator to ensure they have the appropriate level of mathematics and music knowledge prior to registering for this module. Maximum class size of 20, arising from the interactive nature of this module and the substantial practical content.
Learning Outcomes
On successful completion of this module the learner will be able to:
LO1 Describe and analyse horizontal and vertical structures in music.
LO2 Describe and manipulate mathematical waveforms and their relationship to musical sound.
LO3 Describe the relationship between analogue sounds and their digital counterparts, and carry out calculations related to their conversion.
LO4 Describe and calculate various tuning methodologies.
LO5 Develop simple melodies using algorithmic methods.
Pre-requisite learning
Module Recommendations

This is prior learning (or a practical skill) that is strongly recommended before enrolment in this module. You may enrol in this module if you have not acquired the recommended learning but you will have considerable difficulty in passing (i.e. achieving the learning outcomes of) the module. While the prior learning is expressed as named MTU module(s) it also allows for learning (in another module or modules) which is equivalent to the learning specified in the named module(s).

Incompatible Modules
These are modules which have learning outcomes that are too similar to the learning outcomes of this module. You may not earn additional credit for the same learning and therefore you may not enrol in this module if you have successfully completed any modules in the incompatible list.
No incompatible modules listed
Co-requisite Modules
No Co-requisite modules listed

This is prior learning (or a practical skill) that is mandatory before enrolment in this module is allowed. You may not enrol on this module if you have not acquired the learning specified in this section.

No requirements listed

Module Content & Assessment

Indicative Content
Horizontal and vertical structures
Time signature, tempo, pitch, modular arithmetic. Circle of fifths, row charts.
Periodic functions, amplitude, frequency, phase. Harmonics, elementary treatment of Fourier Series, from sine waves to square, triangular and sawtooth waves.
The digital domain
Indices, binary, decimal and hexadecimal conversion, A-D and D-A, bit depth, sampling frequency, dither.
The power of 2. Musical intervals and scales. Ratios and logarithms. Just temperament and equal temperament. Application to instrument design.
Algorithmic composition
History, random composition, Guido's method, algorithmic methods. Elementary treatment of fractal music. Practical content: Wolfram Tones.
Assessment Breakdown%
Course Work100.00%
Special Regulation
Retake is by special exam.
Course Work
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Short Answer Questions In class: Short answer questions on horizontal and vertical structures. 1 20.0 Week 3
Short Answer Questions In class: Short answer questions on periodic functions 2 20.0 Week 6
Multiple Choice Questions Online multiple choice test on digital arithmetic. 3 20.0 Week 8
Multiple Choice Questions Online multiple choice test on intervals and scales. 4 20.0 Week 11
Project Submit a short piece of music composed using algorithmic methods 5 20.0 Sem End
No End of Module Formal Examination
Reassessment Requirement
Repeat examination
Reassessment of this module will consist of a repeat examination. It is possible that there will also be a requirement to be reassessed in a coursework element.

The institute reserves the right to alter the nature and timings of assessment


Module Workload

Workload: Full Time
Workload Type Workload Description Hours Frequency Average Weekly Learner Workload
Lecture Classroom interactions 2.0 Every Week 2.00
Lab Weekly lab using software relevant to course 1.0 Every Week 1.00
Tutorial Weekly worksheet sessions 1.0 Every Week 1.00
Independent Learning Self directed work, including elements of group learning 3.0 Every Week 3.00
Total Hours 7.00
Total Weekly Learner Workload 7.00
Total Weekly Contact Hours 4.00
This module has no Part Time workload.

Module Resources

Supplementary Book Resources
  • David Wright 2009, Mathematics and music, American Mathematical Society Providence, R.I. [ISBN: 9780821848739]
  • Gareth Loy, Musimathics (Volume 1) [ISBN: 9780262122825]
  • James S Walker, Gary W Don 2013, Mathematics and Music: Composition, Perception and Performance, CRC Press [ISBN: 9781439867105]
This module does not have any article/paper resources
Other Resources

Cork Institute of Technology
Rossa Avenue, Bishopstown, Cork

Tel: 021-4326100     Fax: 021-4545343
Email: help@cit.edu.ie