interval madness

String players have both the benefit and curse of being able to play more than one note at a time.  This technique is known as double-stopping (i.e. putting fingers down (stopping) two strings at once, and bowing the two strings simultaneously).  Unlike other instruments with strings (the piano or guitar for example), we don’t have either fixed pitches played by keys, or frets on our fingerboards.  So there is much gnashing to teeth and rending of garments when we are forced to fix intonation on two notes that sound at the same time.  It can take on a surprising amount of complexity.

Let’s look at the first measure of the Penderecki Cadenza for solo viola:

We’ve got an A-flat against a G-natural.  On the viola, the G is one of the open strings, i.e. the second string from the bottom, when plucked or bowed without any fingers down sounds G in the octave below middle C.  Then you’ve got the A-flat.  To get the two to sound together, you’ve got to play the upper sounding note on the string below (since you can’t sound two notes at once on the same string at the same time). The interval is a half-step (or two adjacent keys on the piano keyboard), otherwise known as a minor second.  It’s a very dissonant interval, and one that our ears (well, most ears) want very badly to resolve downward to a unison (the same pitch sounded at the same time on two strings).

The amazing thing about this, especially when you have relatively sausage-like fingers like me, is that there is a whole world of intonation adjustment possible in this smallest of chromatic intervals (we’ll ignore micro-tones for now, until I start working on the Ligeti Sonata).  A very dissonant interval can be in or out of tune – there is an acceptable level of dissonance which can be crossed.  However, here enters the subject which is the cause of bitter disputes between string players and almost all other musicians: expressive intonation.  A wind player, for example, might say that a minor 2nd is a acoustically measurable phenomenon, and it should be tuned in a certain way – and always that way.  Say, like the interval sounds on a modern piano, which is in equal temperament, which is to say, every interval is equally out of tune in order to make the instrument playable in all keys without being re-tuned.  However, the tradition in string playing is that you expressively nudge the pitch upward or downward in response to the destination where the note resolves the tension of the interval.  In the example above, I would tend to lower the A-flat just a hair, so that it is especially dissonant and really pulls into the G, leading to an interval even more fraught with tension than it would be otherwise.  See how complicated this can get?