PRELUDE FOR THE SI SYSTEM AND TWO PIANOS

The collection of preludes and fugues The Well-Tempered Clavier (Das wohltemperierte Klavier, 1722) was Johann Sebastian Bach’s expression of a desire for a unified tuning system — we could even say a calibration of the keyboard — that would allow performance in all musical keys without retuning. Today, we take it for granted that pianists do not re-adjust strings between two pieces, but just like the Metre Convention, such tuning is in fact a historical compromise.

 

The idea of a global system of units began to take shape only about forty years after Bach’s death, in the mind of Louis XVI, who commissioned a group of scientists led by Lavoisier to realise it. Louis XVI soon lost that head — and a year later Lavoisier lost his. After several revolutionary governments, Napoleon Bonaparte created the conditions for the path toward standardisation, culminating in the Metre Convention on 20 May 1875.

 

Imagine a science-fiction scenario: we perform the First Prelude from The Well-Tempered Clavier together with Johann Sebastian Bach — we play the left hand, and Bach plays the right hand, transported from his year 1722. Since no standardised units of measurement existed in 1722 (not even the metre), differences in performance between him and us are inevitable. Listen to what that might sound like.

 

 

The Second

Bach does not know what a “second” is, so when he plays with his right hand, his timing is slower than ours. His unit of time is 1%, 2%, or 5% longer than our second.

 

The Metre

 

Bach does not know what a “metre” is, so the lengths of the strings (and therefore the frequencies of the tones) on his piano differ from those on ours. His unit of length is 1%, 2%, or 5% shorter than the metre.

(Differences in frequency could also arise from not knowing the kelvin, since temperature affects several physical properties of a string.)

 

Measurement Uncertainty

 

Because of the difficulties of transmitting information through time, the difference between the pitch (frequency) of the two pianos changes continually. The frequency uncertainty during transmission amounts to 1%, 2%, or 5%.