By Andrea La Rose. Used with permission
---------- Forwarded message ----------
Date: Sat, 24 Mar 2007 09:32:46 -0400
From: Andrea La Rose <andrea.larose@GMAIL.COM>
Subject: Re: Intonation
Intonation is a matter of knowing what to listen for, and I've found that hearing beats and difference tones is not obvious or automatic in many people. It helps when both sources of sound (you and a friend, you and some drone, etc) are close in volume and timbre. Those annoying nasally tones produced by tuners are actually pretty good for tuning work; the flute sound is fairly close to a sine wave, so the timbral match is also close.
Here's part of a 'practicing manifesto' I wrote a while back. I've since learned new things about difference tones and tuning systems, so corrections and suggestions are welcome:
*****
While I haven't done this in a while, I do have a regimen for practicing intonation. I had to figure this one out myself. Again, I'm sure someone else has written down suggestions for intonation practice, but I never found it in a normal instrumental method book. Actually, I was rather influenced by W. A. Mathieu's writings in The Listening Book and Harmonic Experience, so someone has written something down. None of my teachers, strangely enough, ever relayed to me a method for working on intonation, other than "work with a tuner."
This is what I've come up with: Get yourself a tuner that drones any pitch you like. An A-440 is useful, but you'll need more. When you tune, you are listening for difference tones: when two (or more) different pitches occur at the same time, their waves interact and create other waves (that's an attempt at keeping the explanation simple). For unisons and octaves you're listening for the absence of difference tones (more likely to be perceived as beats or pulses than an actual pitch), and for any other interval you use the difference tone as the indicator for whether you are in tune or not. Difference tones are easier to hear between like instruments, for example they'll be easier to hear with two flutes than with a flute and clarinet. I have heard people complain that the sound emitted by an electronic tuner with droning capabilities is awful, but I have found that it makes great difference tones with the flute, perhaps because the flute is as close to a sine-wave as you'll get with any pitched instrument (save whistling, apparently). You can also get together with someone who plays your instrument and who can keep their sound very even (this can be an issue with winds, of course). Bowed strings can use an open string as a drone, too.
Set your drone source to any note within the range of your instrument and start by practicing long unisons. Work to eliminate any beating. If you can't hear any beating ever, either you are always amazingly in tune (unlikely), or you are experiencing one of the following: you are not playing at the same dynamic level as your drone, or you just aren't sensitized to it yet. To sensitize your ears to beating, slowly make your pitch higher or lower as much as you can. Listen for that ugly-yet-intriguing wah-wah or buzz in your ears. You may even feel it in your head, more than you seem hear it. As you get closer to matching the drone, the beats will slow down, as you move further away, the beats will speed up, even to a buzz. Practice being in and out of tune; this will build up sensitivity and flexibility. Alvin Lucier has some fantastic pieces based on being in and out of tune with a unison drone. I highly recommend them. Once you are able to match a unison throughout the range of your instrument, then move on to octaves, again working to eliminate beats.
The next interval you should work on is the perfect fifth.
This merits a short discussion. Fifths on the piano are not in tune; in fact the whole piano is "out of tune." Some people prefer piano-tuning (called equal temperament) over "natural" tunings (based on the harmonic series - this has resulted in many tuning systems, because you can't base the piano on just one harmonic series, you always have to compromise between them), such as just temperament or well temperament, in all "classical" music. Some cultures and composers prefer other tunings. I'm a big fan of using anything you can wrap your ears around. Practically speaking, in terms of "classical" music, it is very possible to combine both equal and just/well temperaments. I think just temperaments are easier to hear because the difference tones tune very well; you can (learn to) easily hear them lock into place. Intonation is not about being right; it's about being sensitive and flexible. Anyone who's played with someone (other than a pianist, organist, or percussionist) who insists that they are the only one "in tune" and they are not going to budge, knows how frustrating that can be. By learning just intonation with drones and equal temperament by playing with pianists on a regular basis, you will become duly sensitive and flexible, indeed.
Back to our regularly scheduled program: When you play a perfect fifth above a drone, listen for the difference tone sounding an octave below the drone. For example, if the drone is an A and you play the E above that, you can hear a difference tone an octave below the A. Bend your note and listen for the difference note moving in and out of tune with the drone. Keep working on this until you can hear it and control it.
Next: major thirds. The difference tone will sound two octaves below the drone. Note that if, for example, you play a major third below the drone, the difference tone will be two octaves below you. Major thirds on the piano are sharper than in just intonation.
Minor thirds: the difference tone will sound a major third plus two octaves below the drone, forming a major triad with you and the drone. Minor thirds on the piano are much flatter than in just intonation.
Perfect fourths: the difference tone will sound two octaves below your pitch.
Minor sixths: the difference tone will sound a major sixth below, creating a major triad in second inversion with you and the drone.
Major sixths: the difference tone will sound a perfect fifth below the drone, creating a major triad with you and the drone.
*****
Some caveats: Often, and especially when you work with half steps and whole steps, the difference tones are too low to hear. This sort of tuning regimen would actually be fairly difficult with, say, a tuba, because the difference tones would fall outside our range of hearing. It is helpful, then, to start in a higher register, so the difference tones are more audible.
I could write a lot more, but I have to go grocery shopping. =) (I can talk a little more about tuning major seconds, if anyone is interested.)
One last thing: if you have a Mac, my friend Jim Altieri wrote a little program for figuring out specific intervals. I found that it also works nicely as a drone source (you can ignore all the math). You can download it here:
http://tweeg.net/software.html
cheers,
andrea
