January 2004
Science and Music	Show Menu

Adrian Somerfield, St Thomas, Mount Merrion, Co. Dublin

Knowing that I was a teacher of Physics, Randal Henly asked me to write an article for the Irish Science Teachers’ Association. “Was it not remarkable”, he said, “that so many scientists (e.g., Borodin, Galileo, Einstein) were also musicians?” Many teachers commonly find science pupils whose interest and skills include music, though the reverse is rarer. I duly wrote such an article and he published it in SCIENCE in 1997. This is a much shortened version. By music I am thinking mainly of "classical" rather than "pop".

Why should we find it remarkable? Is this not a manifestation of our "two-cultures" concept which has surely only developed since about 1800?. Galileo, the mathematician and astronomer, played the lute. Would his contemporaries have found this odd or would it seem reasonable that an educated person would have wide interests spanning natural philosophy and culture? We now tend to think of music as an art, and science as something else, but I want to consider the proposition that music is an intensely mathematical subject, and therefore appeals to the scientific mind even if it plays to the emotions too.

Consider rhythm: what is rhythm but arithmetic? The march, the waltz, the jig. And is not the person with the mathematical bent soon going to be fascinated by the complex rhythms of Stravinsky or Dave Brubeck or Monteverdi? Nobel physics laureate Richard Feynman was an expert on percussion instruments, especially the bongos, and a formidable exponent of rhythms. Those early observers of nature will have been aware of rhythm; day and night, the seasons, tides, swinging things, the motions of the Moon and planets, the beating heart; perhaps they wondered if Nature were a musician too? Astronomers referred to "the music of the Spheres" in describing the regularities of heavenly motions and the ratios between them.

Secondly, tone and pitch. We easily accept that pitch is an expression of frequency. Indeed in older physics textbooks the treatments of wave-motion and sound are inextricably mixed. I suspect that ancient people were aware that as frequency rose, so did pitch. Felix Savart may have proved this in the early nineteenth century using a toothed wheel and card, but one would only have to watch and listen while ropes were tautened to realise this.

From time immemorial, humans must have known that by blowing through reeds or plucking strings, one produced tones, which you could also sing. At an early stage the idea of two notes being the same, in unison, would arise, and I suspect that someone would have discovered beats, and probably the concept of what we call the octave. Soon, perhaps beside the Nile or Euphrates, somebody may have discovered the concordant intervals we call the fifth, fourth, sixth and major and minor thirds. Makers of pan-pipes and stringed instruments must soon have associated these intervals with ratios of lengths (less obviously tensions). Although Pythagoras in ancient Greece left no written records of his work, he is credited with having laid the arithmetical foundations of harmony. One can illustrate the idea by plucking or bowing a stretched string. If you "stop" it halfway along, both halves sound the octave. If you stop it one third of the way along, the shorter length will sound two octaves above the "fundamental", and the longer the fifth (3 : 2). Stopping a quarter of the way along gives the fourth (4 : 3) and so on.

Following such ratios the Greeks seem to have developed a system of harmony from which arose the mediaeval modes and the scales we take for granted. Would not any student with a mathematical bent be fascinated by finding that music depends so much on ratios; by finding reasons why the keyboard has its shape with "black" notes between some but not all the "white" ones; might he not be fascinated by the compromises needed to "temper" the natural diatonic scale to allow easy changes of key. Would not that marvellously mechanical instrument the pipe-organ, with the lengths of its pipes describing beautiful "reciprocal" curves and its stop keys ornamented with numbers like 32, 16, 8, 4, 2 and mystical fractions such as 22/3, and the ability to produce different tone colours with different shapes of pipe at least be interesting? Years ago I found it so.

The analytical mind may also be attracted to music by learning that many pieces have a structure to be unravelled; the fugue, sonata, symphony, variations; or a story or scene to be interpreted; tone poems by Sibelius. Many people attracted into music by the theoretical route may well develop an interest in the

"theoretical" music of more modern times associated with such composers as Debussy, Schoen-berg, Webern and Stockhausen. Let us remember that Bach was an innovator and mechanic too! (Think of his "Well-tempered Clavier".) There is no harm in reminding "pure" musicians that much "scientific" work has been done to improve musical instruments and make music possible by "mechanicals" such as Renatus Harris, Stradivarius, Boehm or Cavaille-Coll.

In the 1960s as developments in electronics led to the possibility of producing music electronically, Robert Moog originated the "synthesiser". Working in conjunction with him, Walter Carlos, a physicist who "was content to write operas and string quartets for his own amusement and that of his friends", produced the first music played entirely electronically in 1968. The record "Switched-on Bach", became a classic and was followed by others. Electronics also makes it practicable to experiment with unconventional scales; it is no longer necessary to retune the whole harpsichord!

In conclusion, I suggest that the fact that many scientists develop an interest in music, and from there may go on to develop performing skills, is not as odd as first appears but is perfectly natural, and music, by its mathematical structure, can well be expected to appeal to the enquiring mind. We might also reasonably expect that many musicians will be interested in the physical foundations of their art without being less "artistic" for that.

And finally, a completely unrelated observation — Leap Years and Sundays

Organists, and Parish Treasurers, may have noticed that 2004 is one of those unusual years in which there are five Sundays in February. This can occur only in Leap Years, and then only if New Year’s Day falls on a Thursday. The last such year was 1976 and there are only three more in the twenty-first century, in 2032, 2060 and 2088. It might be expected that these should occur at intervals of 28 years, but since 2100 will not be a Leap Year, the one following will be in 2128, which is unlikely to affect most of us.

The superstitious will note that such a February will contain a Friday the Thirteenth, and lovers will find St Valentine’s Day on a Saturday.

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