page forty-seven

The Spinet

Forty-six rooms, and nothing in any of them ever had to be in tune. Today's number shows you up to a music room in a Georgian town, where an instrument has drifted since the last visit and the owner wants it in a particular temperament by tonight. You have a fork, a tuning hammer and the tuner's book. The book never gives you a number to aim at. It tells you how fast each interval should beat.

—

—

—

The bearing, string by string round the circle of fifths

—

—

Right tightens the string and raises it. If tightening makes it beat faster, you are on the sharp side of pure. The book also says which side the interval belongs on, and the beats look the same on both.

Spinet
—

The arrow keys walk to other days. Every day is a different house, instrument, fork and temperament.

What is real here and what is not

The temperaments, the commas, the beats and the bearing are real. The houses, the owners and the drift are the day's number.

  1. 01

    Twelve fifths will not go into seven octaves

    Climb twelve pure fifths from C and you arrive about a quarter of a semitone above the C seven octaves up: the Pythagorean comma, 23.46 cents. Four pure fifths overshoot a pure major third by the syntonic comma, 21.51 cents. A keyboard with twelve keys to the octave has to lose these somewhere, and a temperament is just a decision about where.

  2. 02

    Why tuners count beats

    A plucked string sounds its harmonics as well as its note. In a fifth the third harmonic of the lower note and the second of the upper nearly coincide; when they differ by a few vibrations a second you hear the sound swell and fade that many times a second. A pure interval does not beat. A tuner sets a tempered one by its beat rate, which is why the book here gives beats and never cents.

  3. 03

    The bearing

    One octave in the middle of the keyboard is set first, from the fork, by a chain of fifths and fourths that runs sharpwards from A to G sharp and flatwards from A to E flat. Every other string is then tuned in octaves from it. Each string is tuned from the one before, so a small error early on is carried all the way round, which the page lets you find out for yourself.

  4. 04

    What the page simplifies

    The strings here have perfectly harmonic overtones, where real wire is slightly stiff and its upper partials run sharp. Pitch was not standard: forks from the period that survive range from below 410 to above 430 vibrations a second for A. The six temperaments are worked out exactly from how their authors divided the commas among the fifths.

Forty-seven rooms, and one number doing all the work. Today it lets a keyboard go out of tune, picks the temperament its owner was brought up on and hands you the fork.