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minor thirds, perfect fifths, and intro to major-minor (dominant) sevenths

Some new posts extend the intonation work I've begun: for the fifths, and a couple of earlier posts for the thirds and a brief mention (more to come) of the 7th chord.

William Copper
on January 27, 2014 6:59am
This is very interesting. Importantly, I'm delighted to find anyone out there who understands one of the most substantial issues affecting poor intonation, and who is discussing it in serious terms as an issue for standard choral singing. 
The post linked to above and those around it are a well-structured opener to the discussion, but my impression is that the author may have missed the point slightly by making a couple of rather sweeping assumptions:
Is good intonation a case of attempting to sing every single chord in a piece as an exact consonance? - ie exactly in tune with itself?
Is the problem with the chord progression that he mentions (IV-ii-V-I) not also to do with whether you keep the "common" notes (4th, 6th) exactly identical within the two chords?
I'm really interested in teaching skills to big amateur choirs that allow them to sing properly in tune, either for a cappella concerts or to prepare orchestra works effectively. I normally plan to get the following concepts across within the first two rehearsals, (or all at once if it's a woskshop situation).
1) illustrate the perfect fifth between two parts - "wide enough to sound like bagpipes" for example - and get them to sing until they "feel" as well as "hear" the consonance.
2) explain that the major and minor thirds are technically a bit lower than we find them at the piano, but we don't work too hard at this as singers, because so often the music falls to the third, and we don't want to fall too far.
3) try out some properly tempered major and minor chords
4) explain that if we're required to sing the fifith of the fifth (i.e. the second) this will be higher again (double bagpipes!) 
5) Thus singing "Root, second, third" in major (Do-Re-Mi), actually we need the first step to be a bigger wholetone than the second.
    We try singing the second a little higher on purpose in a melodic line - this creates an amazing sense of trying to escape up to the major third.
          ---> important concept - not all tones and semitones are equal.
          ---> another important concept, we can illustrate voice leading with adjusted intonation
6) the 4th of the scale is a bagpipe 5th *lower* than the keynote, so it might have to be a tiny bit lower than we find it at the piano
7) the 6th of the scale is where we might have our first serious conflict - this note can be:
       the third of chord IV (low third on a low root)
OR   the fifth on the second (high fifth on a root that's already 2 increments higher)
So then we try these chords, and get the common note to "move" and change according to its context. Actually I normally find both students and adults love this idea that an apparently fixed note has to wriggle a bit to find its right place in a chord. There are usually some jokes about all those boring Alto lines that don't have to be so boring any more :-D
Regardless of the level of basic theory amongst choir members, the concept that not all steps are equal, that fifths should be bigger, and that notes that look the same might need adjusting can be easily absorbed. I can then at any stage ask for "an extra big tone" or a bagpipe fifth, or a raised second (especially from the basses!), and even if the members don't follow all the reasoning, they can aim for something concrete, and feel the difference when it works.
Now to Tallis... who was likely to have considered the pure fifth to be an ideal to strive for...
A tuning based entirely on fifths is termed Pythagorean, and it seems to me not unreasonable that any chord on ii with the root in the Bass would automatically be expected to be tuned from the Pythagorean bass note (ie a perfect fifth on a perfect 5th), and for the 4th & 6th in a IV - ii - V - I  to adjust themselves upward in the context of an extra small downward minor third on the part of the basses.
Another more radical idea is to suppose that actually singing a piece of Tallis may not just be about the notated dissonances (clashes, suspensions, etc) but may also be a case of making any chord that is not the home chord sound its pythagorean micro-dissonances along the way. This seems to me particularly plausible when we consider polyphonic sections of pieces written originally in partbooks, where adjusting the intonation to illustrate the voice leading might take precedence over the perfectness of the local harmony - except where we move through the home chord. This creates an absolutely special case when a choir can manage this well - if the perfection of the home chord trumps all other "approximate" consonances, the sense of arrival is extraordinary.
Essentially, mistuning passing or leading chords on purpose can create an extra level of contrast and harmonic imperative in our choral music - the extent to which you push this is an open question!
Even if you reject such a concept out of hand, however, I think it is entirely plausible to make an informed choice about which note will function as the tuning note for a chord. Where this note stands in relation to the home note does not neccessarily have to be either equally tempered, or moderated exclusively by the common notes of the previous chord.
I look forward to spirited discussion!!!
Marion Wood
Applauded by an audience of 1
on January 27, 2014 12:48pm
Bravo for the spirited contribution, marion wood!!  
I take issue here and there with what you said, but on the whole, good points. 
One thing, for sure:  a minor third should be HIGHER than the piano minor third, while a major third should be lower.  
The notion of singing everything higher, for Tallis and the like, maybe ... it's a way of staying in tune.   See the recent discussion on major seconds, and Josquin's version of the second scale step, for more on that particular issue.
William Copper
on January 27, 2014 4:49pm
I'll add that in referring to well-tuned fifths, if by 'wide' you mean further apart than one might imagine, I find that to be false in most cases.  I find that the upper note of the 5th is notoriosly sharp, verging on the minor 6th, so I always tell my singers to sit down a bit on the 5ths.  It works.
on January 28, 2014 11:21am
Apologies, William, you are of course right about the Minor third. I got into this area originally through trying to teach Pythagorean tuning, whose minor third is technically a small distance below the equal temperament one, but of course the 5/6 consonance is more useful for "just" intonation, and as you remark, considerably higher than equal temperament.
I very much enjoyed your post about seconds; the Josquin you cite is a lovely example, and your markings a really useful tool to help an ensemble try to explore this sort of thing. I'll round up a few volunteers and try it soonest :-)
Meanwhile... I would like to move to whichever universe Andrew Miller lives in! I have almost never heard 5ths sung sharp, except occasionally in cathedral choirs whose boys or counter-tenors may tend on the high side in any case. Particularly when the chord 5ths are frequent in the Tenor part, which may be inhabited mostly by reluctant baritones in any case, the fifth tends low - at least in England...
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