It sounds pretty simple when someone says that a singer, an orchestra or a piano is in or out of tune.
But the search for the right tone lowers the drawbridge on a world of physics and fashion that has, for centuries, been the preserve of the most diehard musical geeks inhabiting a hothouse of jealousies, intrigues, and infighting.
I’m prompted to write about this because of articles trumpeting the computer advances designed to make the human piano tuner obsolete.
If only the world of tuning were that simple.
First, everyone needs to agree on a common note to use as a reference point.
Pitch: Concert A
When concertmaster Jonathan Crow stands up in front of the Toronto Symphony Orchestra at Roy Thomson Hall, he will ask principal oboe Sarah Jeffrey to play an A on which the whole orchestra will tune.
Simple enough — except that, at nearly the same moment, Charlotte Nediger will play a different A for the Tafelmusik Baroque Orchestra at Trinity-St. Paul’s.
That’s because the actual pitch of that A has varied over the centuries. Official modern concert pitch is an A that produces sound waves measuring 440 Hz. But many musicians are tempted to cheat, because a fractionally higher pitch makes for a brighter sound (some orchestras, like the New York Philharmonic, tune at 442 or 443 Hz).
Baroque pitch is lower — and all over the map. Scientists couldn’t measure the amplitude and duration of sound waves until 150 or so years ago, so people relied on the craftsmen who made tuning forks and pitch pipes. At the extreme, these tuning standards could be two or even three full tones apart.
Each period-performance ensemble sits down — sometimes before each new concert program — to decide what frequency they will use as their tuning standard (for example, if they are building a concert around a historical organ, which is difficult to tune, they will tune themselves to that instrument).
The official modern concert pitch standard of A=440 Hz was only confirmed in 1939, by the ISO.
If you listen to the organ at the University of Toronto’s Knox College, then walk down the drive to listen to the same piece of music on the organ at Convocation Hall, it will sound different. That’s not only because the instruments are tuned to a different pitch, but also to a different temperament, which sets up the intervals, or gaps, between notes from one end of the keyboard to the other.
The Laws of Physics, inconveniently, don’t allow for equal increases in frequency when going up the Western halftone scale. If anyone were to try that, the instrument would, ironically, end up sounding completely out of tune. This means that all instruments have to cheat some intervals as they go up and down the scale.
The codified, modern system of cheating is called equal temperament — made famous by J.S. Bach in his two books of Preludes and Fugues for all 12 possible major keys and their minor-key relatives.
Until the 18th century, keyboards were tuned using a number of alternate tuning systems that focused on solving problems with thirds or fifths, usually in particular keys. (Still today, wind-instrument players find it very difficult to play in certain keys for tuning reasons, so sympathetic composers try to avoid writing in those keys.)
The Knox College organ is tuned using a mean-tone temperament, which goes back to Pythagoras, the Greek geek who, besides figuring out musical intervals, gave us the key to measuring the length of the sides of a right triangle.
What Does this all mean?
What we hear as in-tune is really a combination of traditions and habits that our ears interpret as being correct.
Leonardo da Vinci, should his time machine send him to Roy Thomson Hall, would find the sound strange, if not alien.
Think this is all about splitting hairs? Here are Frédéric Chopin’s 24 Préludes played by Michele d’Ambrosio on a piano tuned in an unspecified variation of unequal temperament: