Many of us have gravitated towards a system of "just" intonation, rather than the tempered scale that's used for tuning pianos. You may not have even thought about this and simply accepted that the piano is the arbiter of what's in tune and what's not. However, equal temperament is really a compromise tuning system (and all systems will have their pros and cons). However, if one tunes according to the natural harmonics present, one gets a very different tuning for particular intervals (especially the major third) than with equal temperament.
On a keyboard, of course, one has to choose a tuning system and deal with its pros and cons, since once tuned, it's fixed (until you tune again). There are examples of organs with split sharps that allow for a different D# than Eb, for example, but that need not concern us here (you're unlikely to have one available!).
However, with a choir (or instrumental group that can be flexible with pitch) one can sing or play pure thirds, for example, no matter what the root of the chord. This is, in essence "just" intonation. This wikipedia article can give you a start if this is new. Barbershoppers use just intonation all the time and I'll have a guest post soon about that approach.
To show the differences in cents (remembering that there are 100 cents in a half step), here is a chart of chords in just intonation with the difference in cents between just and equal temperament.
As you can see, the major third is 14 cents lower in just intonation than in equal temperament. And the dominant seventh chord includes the same lower third, but 31 cents lower for the seventh (which is a chord used constantly in barbershop)!
There's much more I could say about science, but I think it's more important to get to practical matters! How do I use this in my choirs? How do I teach them to do this?
First, you have to train your own ears to hear the difference between a tempered and pure major third. This will take some work if it's totally new to you. I still remember an interview with David Willcocks, after his choir participated in the Bach cantata series on Telefunken with Gustav Leonhardt. He was asked if he accepted the lower tuning of the thirds and responded that he felt it was surely correct, but that his ear still heard and wanted a "brighter" third.
Most of us were trained at some point to sing the third "high" because otherwise in a dominant chord (where the third is the leading tone) the tonic chord that follows will be flat. I can say that doesn't have to be the case, but can't deal with that yet--patience!
With my choirs I often do an exercise early in the year to help them hear a pure third. This requires a group who can sing accurate unisons/octaves and a room which is resonant enough to be responsive to overtones. I have them sing a chord in A or Bb with voicing B2 root (near the bottom of staff), B1 fifth above, T2 octave, T1 fifth above, A root above that, and S the fifth above that (i.e. near the top of the staff). They need to sing very pure and unified pitches with a clear, ringing fifth. I usually use an "ah" vowel and it needs to be a very bright, forward (and unified) "ah." And they need to sing senza vibrato with a fairly loud dynamic (I ask them to breathe frequently and keep the air flowing). In other words, they only sing root and fifth, no third. If they can do all of this and the room is reasonably responsive, you (and they) will start to hear the third appear in the room as a harmonic. Sometimes it takes a while, or my singing the harmonic lightly as an example after they've cut off, for them to hear it. But normally it will start to become clear and in the right room can be quite loud (you may have had the experience of a harmonic appearing that no one is singing when your group sings particularly well in tune).
If I can get them to hear this, then I can ask sopranos or tenors, for example, to match the third they hear in the room. If they can do this and learn to feel/hear the restful nature of this pure third (because it is in "harmony" with the natural harmonic system, there are no beats), I can then re-voice the chord in different ways with different parts singing the third. It's very interesting then, if they've really settled into this tuning, to play the same chord/voicing on the piano, which now sounds very "jangly" (OK, that's a vague and perhaps invented term, I know! but to my ear the beats in the thirds on the piano strike me that way!) and out of tune. I wrote something about this in my blog after the last NCCO conference in reference to how my ear has changed over time.
This is just an opening exercise, but then I have to work on tuning chords in vocalises at the beginning of rehearsals, and as we begin to work repertoire, to do the same, particularly on any chord that is held for any length of time. Most often, if they aren't tuning the third well, I remove the third from the chord (so that only parts with root and fifth sing) and then sing the third for them myself. Then I have the part which sings the third match my intonation. It takes time to do this and skill builds gradually, but it's very possible. If barbershop quartets and choirs can do this, there's no reason your choir cannot as well. But it takes consistent effort.
This has already gone on a bit too long--and might be too esoteric for some! I promise I'll get around to more basic issues of teaching good intonation and fixing various intonation problems.
Until Memorial Day I'll be posting twice a week, Thursday and Saturday, so I can cover more ground on a fascinating and important topic before the summer hiatus. Next, a guest post about barbershoppers's methods of teaching tuning, then next week, how I use (and don't use) piano in rehearsals.
If you have the chance to try the exercise I give above with your choir, let me know the results!