What I Learned Today

An A note is a vibration at 440 Hz — but it wasn’t always so. Prior to 1939, musical conventions varied by location, which must have caused some interesting results if musicians from different areas tried to play together (the A note is commonly used for tuning, the set point from which all other notes are created). In 1939, an international treaty was signed fixing A on 440 Hz, not only to enable musicians to play together, but to standardize the creation of musical instruments. A clarinet creates notes based on its length, so its physical construction is influenced by the standard frequency chosen for A.

This standard, the basis of music tuning, is an example of a convenient yet arbitrary choice for a constant reference value. Some values we use commonly are dictated by physics: in free fall towards the Earth, objects accelerate at 9.8 m/s^2; the location of 0 latitude is the equator. But others, like the location of 0 longitude, are more like the A note. While the equator is defined by the spin axis of the planet, there’s no physical reason to prefer one location over another to serve as the reference point for longitude calculations. It is, however, awfully convenient for us all to agree on the same location!

Our temperature scales fall somewhere in between. The establishment of 0 or 100 degrees is arbitrary, but an effort was made to associate them with physical phenomena, like ice freezing or water boiling. The length of the meter (also arbitrary) was originally set to be “one ten-millionth of the distance from the Earth’s equator to the North Pole (at sea level)” in an attempt to tie it to a physical property, but since 1983 it has been instead defined as the distance light travels in a vacuum in 1/299,792,458 of a second (!). But that’s really just convenience too, since light travels at 299,792,458 m/s… too bad we didn’t just decide that light travels at 300,000,000 m/s and get the length of the meter from there! I imagine that any such change would be a nightmare to implement, though.

These values influence our everyday life: how much gas in a gallon? How much flour in a cup? How many atoms in a mole? It can be useful therefore to know which ones were derived from physical constraints and which ones were obtained from consensus!