Constants by consensus

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!

1 of 2 people learned something from this entry.

  1. Terran said,

    July 4, 2011 at 11:51 am

    (Knew it already.)

    Sadly, “A 440” isn’t even a constant. Apparently, a lot of orchestras tune a bit sharp — say, A=442 Hz or A=443 Hz — and sometimes marching bands tune a bit flat (or so I am told). I think the idea is that the orchestras want things to sound a bit “brighter”. My digital tuner has a fiddle to reset the basis for A by a few Hz in either direction in order to accommodate such locality preferences, but I’m not sure I can hear the difference.

    I don’t know clarinets, but I do know a bit about flutes at this point. A flute is fundamentally a half-open pipe, so it supports odd-half wavelengths ((2n+1)*pi). When you assemble the flute, the “head joint” (bit with the embouchure hole) fits into the “body” (bit with most of the keys) via a snug-fitting friction joint. That joint gives you a reasonable amount of play, however, which allows you to alter the effective length of the pipe by inserting the head further or less far. So, although the flute is “designed” to an ideal A 440, you can tune it to a different A by fiddling that length. (This is actually a crucial feature, even if everybody accepted A=440Hz, because an orchestral flute, being metal, is subject to significant thermal expansion, which can change its fundamental frequencies quite noticeably — enough that even I can hear it. You have to be able to re-tune it for different ambient temperature conditions, and even as you play for a while and the flute literally “warms up”!)

  2. Kiri said,

    July 4, 2011 at 3:14 pm

    Interesting — a quick browse on clarinets also suggested that they have some fiddle room for changing the length of the tube a bit, probably for the same reasons. Good to have that flexibility!

  3. Kiri said,

    July 4, 2011 at 3:15 pm

    So, I wonder if tuning your orchestra a bit sharp means you’re violating an international treaty? ;)

  4. Susan said,

    July 4, 2011 at 6:40 pm

    (Learned something new!)

    Ha! I didn’t know about the international treaty, but I do know that that there was once a lot of variation on A.

    As a violist, I’m on the opposite end of the tuning spectrum. Since open strings (strings without a finger pressed on them to raise the note) tend to sound different when played than strings you have pressed your fingers on, the goal is often to never play an open string in a piece of music. It’s the open strings that are tuned against A. And since orchestral strings are not fretted, one tends to be tuning unconsciously to the orchestra all the time while playing. So I probably wouldn’t even notice a variation on A unless it was glaring.

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