Equal Temperament

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Notes Cut from The Violin Lover

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            The rustling of leaves is rated at ten decibels, a whisper at twenty, an ordinary conversation at sixty-five, a moving train at one hundred. Any sound over one hundred and twenty decibels is experienced as pain, not sound. Too much of anything, even something beautiful, is experienced as pain.

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            The decibel is one tenth of a bel, a measurement of amplitude named in honour of Alexander Graham Bell, who also invented the phonograph, and taught the deaf. Like Beethoven, only in reverse. Beethoven wrote music he couldn’t hear for the pleasure of others. Bell, who could hear, made a language for those who couldn’t. Translating sounds to signs, or electrical impulses, in the ear or along a wire, into voices, into music. Vibration—simple vibration—is what makes all bodies sound. And at the lowest register, sound waves are felt on the skin, the body itself resonating like a drum.

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            To sing you need to breathe deeply and hold your breath for longer than the ordinary four-second speech interval, then generate as much power as you can. The human voice is a more efficient transformer than a musical instrument, yet only one per cent of the energy a singer puts out is transmitted as sound waves. On the other hand, ordinary conversation is so weak that it would take two million people talking at the same time to run a fifty-watt light bulb.

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            The first public concert in England did not take place until 1672, organised by a violinist named John Banister who wanted to offer the public an experience previously reserved for the aristocracy: music outside the walls of a church, music for its own sake. Music as art, not as a practical aid to everyday life. Not to lull an infant to sleep, or inspire soldiers on the march, or set the tempo for oarsmen or labourers; music unconnected to public spectacles of dancing or feasting. A separate world.

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            Unaccustomed to their role, early audiences were appreciative but noisy, treating the concert hall no differently than they did the theatre. They talked and ate and shouted to their acquaintance; clapped or booed or hissed spontaneously and frequently; demanded favourite encores. Not until the late nineteenth century did concerts become decorous affairs. Wagner was the first conductor to turn off the lights, sheltering each listener in private reverie; Mahler the first to lock out late-comers and forbid applause between movements. Now we have come to rely on these conventions to help us listen. In a world saturated with sensory information, we require an absence of all other distractions to focus on sound.

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            There are those who contend that musical tones, like mathematical symbols, have no reference to anything outside themselves. They inhabit a platonic dimension of ideal forms: there is no way of representing them except through themselves, no shortcut to understanding their meaning. They simply are, B flat or the square root of fifteen, π or a minor seventh. They do not signify toothbrush or rhododendron; they cannot evoke the Napoleonic Wars or the Birth of Venus.

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Others insist that musical tones participate in the patterning – the relationship of part to part and parts to whole – that is innate in human consciousness. For example, whether their local musical scale consists of three notes or five or eight or more, every person on this planet can hear and recognize the intervals of the fifth and the octave. Mean-tone tuning derives from this innate human ability. A frequency is selected and given a name: let’s call it “A”. It is doubled to form an octave, then halved to form a fifth, which we call “E”. The process is repeated with “E” and its fifth, “B,” and so on, all around the circle of fifths, the rainbow of sound that makes up the “Pythagorean” scale.

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This mathematically generated scale dominated Western music for two thousand years, in part because philosophers cherished its implication that music simply made audible humanity’s innate perfection. But every system has its limitations; the limitations are what make it a system. And the limitation of mean-tone tuning is perplexing both philosophically and practically: it only works in one scale at a time. Beyond that scale lies dissonance or, if you will, chaos.

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This is a minor difficulty for the solitary musician but a disaster for the ensemble, constrained to retune a whole flock of discordant strings every time they play a new piece. Luckily, around 1700, a method was invented according to which this built-in dissonance could be distributed evenly – almost inaudibly – throughout every scale. In The Well-Tempered Clavier, Bach demonstrated the versatility of the new tuning, known as “equal temperament”, by composing two pieces in each of the twelve major and twelve minor keys, all of which are to be played consecutively, without re-tuning the instrument. There was no looking back.

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The “gravicembalo col piano e forte” – keyboard instrument with soft and loud – was presented by Bartolommeo Cristofori of Padua to Prince Ferdinando dei Medici in 1709. It replaced the quiet plucked-quill action of the harpsichord with a hammer action, allowing for much greater control. The first instruments had four-and- a-half octaves; over time, both their range and volume increased until, by 1800, the very loud, seven-and-a half octave forte-piano we still use today had supplanted its more modest ancestors.

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When the pianist’s finger touches a key, the far end tilts up, raising a lever that, in turn, hits a felt-tipped hammer. This hammer lifts a damper, allowing the string beneath it to vibrate. As the key is released, the lever lowers the hammer so that the damper touches the string and impedes the vibration. Unless, of course, his foot hits the sustaining pedal, which lifts all the dampers off the strings, leaving them free to resonate to infinity (or at least far beyond human apprehension).

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Both the piano and the violin make music by causing strings to vibrate. Perhaps an ancient archer heard the thrumming of the string after his arrow had taken flight.  Perhaps he duplicated this phenomenon while idly plucking his bow. Was it because of such inadvertent discoveries that Apollo, god of music, is twinned with his sister Artemis, goddess of the hunt?

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The piano uses more than 200 strings to play its 88 notes. The long, thick bass strings run singly; the shorter, thinner tenor strings doubly; the slender trebles in threes, like schoolgirls arm-in-arm on a busy street. Piano strings are wire lashed to an iron frame; their tension can be adjusted by a series of pins. It is a laborious job, requiring the services of a professional. By contrast, all violinists tune their instruments often, even compulsively, by themselves. Another contrast: the violin has only four strings and yet can attain a seven-octave range. The pull on each violin string is 70 pounds, 280 pounds in total. The combined pull of the strings on an upright piano is 16 tons; a concert grand will be closer to 23 tons.

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Some musicians remain haunted by nostalgia for the Pythagorean scale with its concurrence of divine and earthly mathematics, and resent the modern insistence on compromise for the sake of the ensemble. They try to discriminate between a C sharp and a D flat; a B sharp and a C natural. Theoretically, this should be possible, especially on a fretless instrument like the violin from which one can coax many fractions of a tone. But in practice, our ears have grown too lazy for such fine discriminations.

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The ear collects sound as a flower does dew; channels it along the auditory canal to brew a secret honey. The air flutters, the air is alive with wings; sound waves drum against the ear and set its architecture humming. Sensation is transformed into energy like dew into nectar. And then (but this is no explanation, this is just the map of a mystery) the mind gives meaning to what it hears.

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