Mr. Birchensha's Ear

(Full text)

It is the afternoon of Wednesday 10 August 1664. We're in London, at a meeting of the Royal Society. The Society is about four years old, as is the reign of Charles II: Oliver Cromwell has been dead for nearly six years. The meeting includes Robert Boyle, Robert Hooke and Christopher Wren: it does not include Isaac Newton, who is still an undergraduate in Cambridge, nor Samuel Pepys, whose diary is well underway but who will not join the Royal Society until next February.
     William, Viscount Brouncker, presides, armed with a judge's mallet to keep order. It doesn't seem to be needed very often: the Fellows disagree frequently and violently over the fundamentals of how the world works, but order is maintained pretty well at the meetings.
     The secretary is Henry Oldenburg. He has a Europewide network of correspondents, and publishes everything he can in his privately-funded journal, the Philosophical Transactions, which some say is the heart of the society. The meetings themselves are frequently more like a weekly entertainment for the fellows, many of whom are dilettante aristocrats. Robert Hooke, the overworked, underpaid Curator of Experiments, talks them through four or five or more spectacular demonstrations each week. He is an intense, wiry little man, and he keeps up a stage magician's patter as he works the equipment. Recently he has been slacking, since he is working on a book. Micrographia, published in 1665, will become one of the most celebrated scientific books of the century.
     Oldenburg is reading out a letter to the society from John Beale. Beale is a wondrous eccentric, and it's rather a shame he has fallen out of history. His rambling prose, innocent of a full stop for seemingly pages at a time, his frequent digressions, and slightly alarming fixation with the improvement of cider, probably irritate the Fellows as much as they will his (few) 21st century readers. But he comes up with some novelty worth hearing often enough to be tolerated. This is not the sort of thing they find greatly entertaining, though. In a few decades time they will drop glass balls filled with mercury from the top of St Paul's dome to investigate gravity. Another time they will put Robert Hooke in the vacuum pump. A letter about cider is rather tame.
     Mercifully the reading is cut short. A visitor has arrived, who they have been awaiting since the spring. Beale is postponed until another meeting, and the newcomer called in.

John Birchensha, composer, music theorist and teacher of lute, voice and composition, was the only professional musician to be invited to a meeting of the Royal Society in the 17th century. By this time he was about 50. Born in Ireland, he spent the inter-regnum in England writing books about the end of the world - scheduled for around 1660. After the Restoration, in 1660, he performed the considerable feat of rehabilitating himself as a music teacher and theorist, tirelessly networking with important royalists. His system of composing by rules was a welcome home-grown alternative to similar continental systems: the Pepys archive contains songs written under Birchensha's tuition, as well as a mechanical 'composition box' devised by the Italian Jesuit Athanasius Kircher. Birchensa's overcharging eventually caused a disagreeable split with Pepys but the musician went on to teach the Duke of Buckingham, and his star was still rising when he got in touch with the Royal Society early in 1664.
     The idea of a musical science interested the Fellows. Three months before our interruption in medias res, anticipating his arrival, they began an intriguing series of musical experiments.

6 July 1664. Robert Hooke has excelled himself. After weeks of demands from the Fellows he has devised an experiment on sound: a brass wire so long that it vibrates only once every second. So long, in fact, that they have to perform the experiment out of doors. Passers-by jeer at the useless toy: the pointlessness of the Royal Society's activities is already threatening to become proverbial. (Shadwell later wrote a comedy in which 'the Virtuoso' weighed air, swam on dry land and read by the light of a decaying fish. Poor Hooke went to see it and 'people almost pointed'.)
     One hundred and thirty-six feet long, Hooke tells them. One thirty-second of an inch thick. Stretched horizontal by a weight of five pounds six ounces. Pendulum in hand to time the vibrations, he plucks the middle of the wire. The Fellows can see the vibration speeding from one end to the other, so that the centre of the wire flicks from side to side every second. The demonstration is spectacular, the sort of thing that satisfies everybody. It is copied from a similar experiment done in the 1630s by a French monk, Marin Mersenne, but no-one mentions the fact.
     When the Fellows have had enough of this he shortens the wire to 72 feet, and shows them that the vibrations are twice as fast. Someone asks for a wire twice as long, and Hooke promises to provide one next week. Finally he shortens it to one foot: the vibrations are invisible now, but they can be heard. Some of the more musical Fellows sing the note. Someone calls it a G. Since a wire 136 times shorter vibrates 136 times faster, that makes G a vibration of 136 strokes per second: knowledge in the making.
     In fact, the frequency is badly wrong - probably because Hooke was careless about the length of the pendulum that measured the time. In private he is meticulously precise, but maybe the details don't matter so much for Society showpieces.
     The next week Hooke repeats the experiment, with the promised longer wire. They also use the wire for a different experiment, striking it at one end to see if a person listening to the wire at the other end can detect any delay before the sound reaches him. He can't, even with the longer wire.
     The experiments go on throughout the summer, confirming scientifically some well-known correlations between musical pitch and the length and tension of a string. Finally, on 10 August, the musician himself appears.

Birchensha is ushered in: he's quite amiable, if a little dour, and very aware that the Fellows are his betters and his potential patrons (they are the Royal Society, after all, which makes them potentially very useful to anyone with an idea to promote). The atmosphere at the society makes him nervous. Hooke beckons him over: they've set up an instrument called a monochord. He tries to appear at ease with the strange device. Monochords are rather archaic in musical circles, and the Royal Society's specimen is clearly the work of a scientist, not a musician. Still, he assumes a confident air.
     Despite the name, the monochord at this period seems to have had two strings. It is something like a two- stringed guitar, about four feet long: one of the strings always stays the same length, but the other has a moveable piece of wood underneath it, a 'bridge', like a violin's, to vary the length of the string allowed to vibrate. If the string is stopped in the middle it is half as long as the other string and the two sound an octave apart; if it is made two-thirds as long, they sound a perfect fifth, and so on. It is possible to mark out an entire scale along the length of the instrument, and this was traditionally how different kinds of scale were described by music theorists.
     The president explains something that had not been quite clear in their invitation: that they expect Birchensha to tune certain musical intervals on the monochord by ear, and Hooke will then measure the lengths of the strings. This will enable them to determine how closely the current practice of music corresponds to the ancient theory of harmony, in which musical intervals correspond to simple numerical ratios. Birchensha's role is to submit to testing to produce data for the Society. The precise mathematical definitions of harmonies in his writings have made them think he can reproduce them by ear.
     He tunes the monochord to make a perfect fourth, from G up to C. Easy. But before Hooke takes his measurement, someone (Hooke himself perhaps, sceptical of musicians' boasts since his time as a Christ Church choral scholar?) nudges the bridge slightly. Plucks the string: is it still a fourth? Birchensha looks worried. He moves the bridge again. And now?
     It emerges that for none of the musical intervals under consideration can Birchensha detect even a halfinch displacement of the bridge. Some of the Fellows snigger. Hooke doesn't look pleased: a failed experiment reflects badly on him, too. The musician is dismissed, more or less in disgrace, and Hooke tries to save the situation by promising to bring along next week a keyboard instrument, precisely tuned, to replace the defective Birchensha. They can tune the monochord against that and make their measurements. The meeting moves quickly on to other matters.

Reading the Society's minutes, it's very disappointing when the experiment fails. It would be extremely valuable for early-music performers if they had a scientific record of the musical tuning that sounded 'right' in 1664. But if the monochord was four feet long Birchensha failed to distinguish between intervals as much as half a semitone apart. He seems to have been a competent music teacher, out of his depth when faced with the Royal Society's demands.
     The promised experiment with a keyboard instrument never took place. Possibly Hooke realised on reflection that its tuning relies on the judgment of another musician's ear, so that using it merely displaces the problem rather than removing it. At the next week's meeting an offer was relayed to the Society from Birchensha of a bass viol to replace their monochord. He suggested that gut strings would make it easier to distinguish differences in sound than wire strings. Birchensha tacitly acknowledged that his appearance had been a failure, but implied that the blame lay not with his musical ear but with the experimental equipment. The Society accepted the implication - at least, it accepted the viol - but Hooke, overworked, disappointed by Birchensha and embarrassed by his failure, was not asked to do any more musical experiments.

What was all this about? Why did the Royal Society think a music teacher had something to offer them in the first place, and why does his failure matter?
     A recurring belief in 17th century science was the notion that reliable knowledge is produced by the senses: the Royal Society's motto, Nullius in Verba, is roughly equivalent to 'take no-one's word for it'. In practice, only vision tends to produce the kind of exact numerical data we associate with science. Smell, touch, and taste only give qualitative information. Hearing is more complicated: the ancient association of musical intervals with mathematical ratios gave some promise of using ears to produce numerical data, but it wasn't at all obvious how that could be made to work.
     Changes in musical practice during the Renaissance had rendered the ancient Greek theory, which identified musical intervals with exact numerical proportions, obsolete; and 16th-century attempts to patch the theory up didn't match reality convincingly either. At the same time, the invention of decimals and logarithms around 1600 had made it possible to describe less pure but more practical methods of tuning.
     This in turn implied a loss of confidence in the ear's ability to recognise exact ratios expressed in sound. For an old-fashioned theorist the mathematical proportions were inscribed on the human soul, and when they were manifested in sound the soul would recognise them and respond, just as a wine glass rings when a singer sings a particular note. But exact ratios were gone from mathematics, replaced by decimals, and they were increasingly ignored by musicians. Decimals could also be used to express inaccuracies or approximations, and it was often said that the ear would tolerate quite large deviations from exact tuning.
     So problems existed with the relationship of hearing to knowledge, and with the capability of the ear to make exact judgments - and with the relationship of tuning theory to both of those questions.
     One of Hooke's many obsessions, and the force behind his work with microscopes, was a wish to expand the 'empire of the senses'; to increase the domain of reliable knowledge by increasing the reach of our senses. Telescopes and microscopes apply this idea to vision: perhaps the ear could be improved using precise instruments like the monochord, which potentially allows the conversion of aural experiences into numerical data and vice versa. For this, not just an ear but a musicallytrained ear is necessary. One week the Fellows had tried to tune a whole tone (e.g. the interval from A up to B) by ear, and found that the measurement it corresponded to wasn't what they expected: hence the need for Mr Birchensha and his, supposedly, highly sensitive ear.
     This chance to bring the ear into the lab was not what Birchensha had in mind when he sought patronage for his theories about composing and tuning. He was probably rather baffled by his appearance before the Royal Society. About a year later he gave a talk in which he claimed that one of his mathematical charts would enable its user to test the accuracy of any monochord: possibly an attempt to revenge himself on the instrument which had defeated his ear and his chance of patronage.
     The ear does not appear again as a source of accurate knowledge in the minutes of the seventeenth-century Royal Society. A full-scale quantification of music had to wait until the 19th century when mechanical devices were invented to convert sounds into visual diagrams: because only the eye could make sufficiently accurate judgments. Birchensa's failure on 10 August 1664 was decisive.
     And what happened to Mr Birchensha? Later the same day he played in a concert at the nearby post office hall, attended by Brouncker and others from the Royal Society. Pepys was also there, but 'found no pleasure at all in it'.
     Birchensha's career never seemed to recover from the incident at the Royal Society. He appeared a few more times: writing about composition in the late 1660s and later soliciting subscriptions of one pound per copy for a book he promised to write. A year after the book's deadline had gone by he reappeared, unembarrassed, at the Royal Society, but this time he did no more than talk and was sent away with an 'encouragement', but no tangible assistance. And despite his scientific unhelpfulness he earned a peculiar distinction also conferred on Robert Hooke: an unflattering reference in a Shadwell comedy.
     On 14 May 1681, a 'John Birchenshaw' was buried in the cloisters of Westminster Abbey.