In Irish trad there are a few instruments that have issues when it comes to being in tune. The Fiddle, flute and whistle spring to mind. I hear one of our anchors say quite often they have a flute with a weird C (natural or sharp, I forget.) And of course fiddlers know how the fretless thing works–you get to choose where to put your finger and therefore the note that gets played.
I never gave it much thought until I started learning the fiddle, but there’s more than one way to split an octave. In fact there are many that have been used over the centuries. Medieval music’s unmistakable sound, for example, is the result of a certain tuning system called “just intonation.” This involves splitting the octave, say, starting with the note ‘c’, up in even ratios. These ratios tend to be the most pleasing to our ear–if you were tuning something by ear, you would most likely end up with just intonation.
…as Pythagoras discovered, intervals are also mathematical ratios. If you take an open guitar string sounding E, stop it with your finger in the middle and pluck, you get E an octave above. The octave ratio, then, is 2:1. If you stop the string in the ratio 3:2, you get a fifth higher than the open string, the note B. The other intervals have progressive ratios; 4:3 is a fourth, and so on.
One cool (and not-so-cool) thing about just intonation is that not all keys sound alike Because the ratio of a third in C will be different from the ratio of a third in Eb, these keys will have their own personality. I highly recommend the above article as a good primer.
Also this video helps illustrate the differences in sound.
In order to make all the keys sound basically the same, so that music could be easily transposed from one key to another–something we take for granted–musicians started using what’s known as “equal temperament.” This is a way of equally splitting up the octave. Greeks actually came up with equal temperament centuries ago, but it has fallen in and out of favor over the span of time. This is what you play when you play a piano, or my concertina. It can be problematic for some musicians who are used to just intonation–fiddlers for example. Their natural tendency to pick notes that sound best to them has to be put aside so they can make their notes match the piano’s.
Here’s another fun little video demonstrating the differences in certain aspects of just intonation and equal temperament:
Fascinating stuff, if you ask me. Others think so too. Go to any fiddle or violin forum, and even thesession.org, search for “just intonation” or simply “temperament,” and you’ll see what I mean.
So fiddlers–next time you sound a little out of tune, just say, “Don’t sweat it, man–it’s just intonation!”