With audio examples. HUZZAH!

Adam, they are in the order listed in the article: harmonic, Pythagorean, equal temperament. You should be able to hear the "beats" (sort of like a flutter in the sound) of the Pythagorean and equal temperament examples.

and how does YOUR choir sing thirds?!

O ... and I meant so say this, too:

If you are an organist, you might think your thirds are fixed, and maybe most of them are, BUT: you have the resources of touch, timing, and duration to modify the perception of the thirds you play. Consider it ...

Exactly so, Henry ... Sullivan's problem, that the third in the accompaniment is hard to tolerate against the third in the voice, is one of the influences that set me on this exploration of intonation.

and how does YOUR choir sing thirds?!

to an accuracy of +/- 100 cents. :-(

Mr. Copper:

String players and singers have three thirds for every note - one for rising scales, one for falling scales and one when the note stands on its own.

Pipe organs and pianos cannot ever choose between them, unless keys are split into three sections.

Your "pure" thirds fail miserably. If you are singing "pure" thirds, there is only one chance in three that you are singing one that fits the music.

BUT: you have the resources of touch, timing, and duration to modify the perception of the thirds you play

This is truly bizarre, to be as polite as I can be. Playing a note on the organ is like lighting the fuse on a firecracker in a mail box, watching the fuse burn down to northing and seeing the local policeman turn the corner and find you standing there. There is nothing you can do to change what's imminent.

There is NOTHING that you can do to change the perception of the tuning of a note on an organ except by tuning it. Your touch, timing and the duration don't affect the waveform in any way.

If you do not believe that string players adapt each pitch they play to just intonation, and do believe that organ note pitch sounds different when it is played earlier or later you remind me of:

Friend viewing the earthly remains of a recently deceased atheist friend, clad in his favorite designer suit, tie in a windsor knot turns to the funeral director and says, "all dressed up and no place to go..."

Mr. Copper, heresy in music, I do not find welcome on this list. There are many on this list thirsting for knowledge and we all should work to avoid confusing them.

If you can provide scientific proof of any of this go for it...for example, pipes are known to "pull together" in pitch but that has nothing to do with playing them early or late.

TCC, would you take a minute to review the Forum Etiquette Guidelines?

Mrcropper,
This has been a fascinating discussion for me. I need to learn more about tuning, no doubt about it.

As a trained singer, I have learned how to tune over time, and especially after I figured out how to use resonance of my instrument, I was able to sing in tune alone and with other singers and a variety of instruments. As music director, I insist on training volunteer singers to find their own resonance and be responsible for their own tuning. Takes a lot of time with some, and very little time with others, notably children.

Pertinent to this discussion of thrids, I wonder if the reason why so many chant accompaniments grate on my ears is the (often needless and anachronistic) use of triads on notes of length. The pastiche of 19th cent harmony on top of Gregorian melodies really bugs my ears, and perhaps it has to do in large part with the tuning of thirds. What do you think about that?

I've also noticed that many, many keyboard players sing slightly out of tune. Several I've known judge intonation by the last note of a phrase and don't seem to hear sourness within the line. I suppose it stands to reason that their aural impressions may have been formed by the type of tuning they most often hear?

Thankfully, our organist is open to exploring different ways of accompanying chant when needed, and mostly avoiding triadic harmony. Do you have ideas on effective ways to do that?

MaryAnn, thanks very much for raising this point: I've hesitated to criticize exactly what you describe, but I hate it. The gregorian masses are splendid, and then there are these 'canonical' accompaniments that, to put it politely, do not really work.

IMHO, often Gregorian accompaniments have a tendency to force the modality into either a modern major or minor key, without respect to the elasticity of the modal system. I have found the NOH accompaniments to be the best.

I have recently noticed in my own accompanying of chant propers (always improvised from the Graduale, SEP, or whatever) that I tend to use primarily open fifths, octaves, and fourths; then 'dissonant' intervals like seconds and sevenths; but very rarely thirds or sixths.

Yes, CharlesW: I've admitted elsewhere I'm no organist, but I have been, long ago, an organ tuning assistant, and have sat beside a big reed pipe trying to adjust the tongue to tune the fundamental while ignoring the wild swirl of harmonics from the room, from the reference pipe, and from manufacturing defects. Perhaps that's why organ is still a satisfying musical instrument, despite its many flaws: the ear works with the organ to make sense of all the sound.

This is an excellent thread and I've learned quite a bit from all of you, but while "pulling" the third in a chord might delay the discomfort that I feel upon hearing it sound, I find that omitting it altogether in the accompaniment is better. In addition, the temperatures in most the churches I've been able to play in vary so much over the course of the year that I doubt that any of the organs are actually in tune. Finally, would your theory apply to electrical organs and to pipe organs? We have a few refurbished ones in Brooklyn and Queens and tuning is a big problem with them since the sound is produced by the original pipes.