East Midlands Branch

THE INSTITUTE OF MATHEMATICS

AND ITS APPLICATIONS

A performance by

Professor Kevin Jones

School of Music, Kingston University

The Music of Numbers, Keyboards and Calendars

Friday 3 May, 2002

starting at 7.30pm

Repton School, Derbyshire

Abstract

The pattern of white and black notes on the piano keyboard matches the pattern of long and short months in the calendar (with January equivalent to the note F). Is it significant? Musical tuning is a compromise between producing sweet sounding, harmonic intervals between notes, and establishing a system of “joined-up” harmony which can move seamlessly through related musical keys. This problem of musical temperament gives rise to the design of the ubiquitous, contemporary keyboard. Mathematically - speaking, in simple terms it reflects the fact that although no power of 2 is ever the same as a power of 3, there are some close matches at very significant points as the power-cycles move in and out of phase. These points themselves form a Fibonacci-type sequence as they converge to reduce the gap after cycles of order 5, 7, 12, 19, 31 etc. - numbers which have special significance in music theory and keyboard design. The juggling necessary to temper musical harmony is similar to that required to reconcile the mismatched cycles of the sun and the moon in the design of the calendar. Remarkably, the same series of numbers appears, but here resulting from the phase relationships of the celestial “spheres”. This fortuitous match between cosmic and musical phenomena has helped to shape cultures east and west, resulting in special religious or symbolic significance being attached to numbers from this sequence. In a cross-disciplinary quest, supported with musical demonstrations, Kevin Jones will explore some of the musical, mathematical, and cultural issues which attach to these intriguing number patterns.

The 2002 Branch AGM will be held during the Evening starting at 7.00pm

For further details of this event or other East Midlands Branch activities consult the Web Site http://science.ntu.ac.uk/ccb/html/ima.html or by contacting the Branch General Secretary:

Dr Stephen Hibberd, email: Stephen.Hibberd@nottingham.ac.uk or Tel. (0115) 9513841