Did Kirnberger invent Kirnberger III?

I am reading a book by the visual artist David Hockney called Secret Knowledge. It deals with the use of camere obscure and mirrors as aids to painting. Although there is no definite confirmation of this practice in historical writings, and art historians are reluctant to accept it for that reason, as a practical artist who has spent a decent amount of time using these aids, Hockney makes a convincing case for their use by Cavaraggio, Holbein, Leonardo, Canaletto and many others, based on clues in their work, including lack of preliminary drawings. The visual evidence he brings is impressive. One of the reasons he adduces for lack of evidence in contemporary writings is that it was a trade secret, although widely practised, and would have attracted the wrath of the Catholic Church. At the time, the Church was very against the use of mirrors and lenses generally (think Gallileo) and, in fact, the first use Hockney has found is in the Protestant Netherlands.

So I began to wonder about tuning and temperaments. I suspect that the major triad of pure intervals was much prized by the Catholic Church (Trinitarian connections), and this may explain the Church’s lesser interest in instrumental music, as opposed to vocal music, in which pure intervals are commonly sung. Meantone was used in Italy for a long time: it has pure thirds.

Forward to the 17th and 18th centuries, and in Protestant Germany we have people like Werkmeister and Kirnberger. It is the latter that I want to concentrate upon and his temperaments, called nowadays Kirnberger II and Kirnberger III.

I dont think it was beyond the wit of an ordinary keyboard player who tuned his instrument to have discovered and experimented with these “Kirnberger” temperaments before he was born. The progression is Pythagorean tuning with perfect fifths, written about by Arnout van Zwolle in the early 15th century (Netherlands), then the less limited Meantone with perfect thirds (described by Salinas and Zarlino in the 16th century), and it requires little imagination to try combining them: tune C-E pure and fit the fifths in between as for meantone, and then tune as many as possible of the remaining fifths pure, the one that completes the circle being arranged to be where it least offends.

I am talking about practical musicians, not people who write books, but who just get on with tuning and playing. I think it quite likely that they invented this tuning and Kirnberger came along in the 18th century and codified and wrapped theory around it. Of course, by that time, Werkmeister and others had already proposed more sophisticated alternatives, which was unfortunate for Kirnberger.

But I think that the simplicity of Kirnberger III has a lot of commend it. I dont expect the theorists here to approve, but those with an open mind should try tuning it (in secret!) and playing real music – not just playing awkward intervals and chords and wincing!

Start by tuning C-G-D-A-E as for meantone, then tune pure fifths C-F-Bb-Eb-G#-C# and E-B-F#. Done with care, the remaining F#-C# should be an Equal Temperament fifth, or this ET fifth can be placed elsewhere, if desired.

According to Charles Padgham (The Well-Tempered Organ), quite a few organs in Germany and the UK have been tuned in K-III.

Chag Pesach Sameach, or Happy Easter, whichever you celebrate!



Well, excellent topic David. I have studied painting for a long time and have an interest in the Dutch Golden Age and Vermeer in particular. I’m familiatrwith the Hockney Falco theory, and I read rhat about 50% of art specialists agree. But since then it’s been fairly soundly debunked by more careful examination of the matter.

Here’s a discussion rather than a complet debunking but useful all the same:

[An excellent Vermeer site by the way.]

There’s a great documentayr called Tim’s Vermeer on this issue.

Well worth watching, even if it may be fundamentally wrong.

I think I am going to have to create a new Category for The Jackrail called Vermeer. :slight_smile:

As to Kirnberger, I completely agree. I don’t think practical musicians necessarily álwasy followed theoreticians recipes. It’s easy to sit down and come up with a workable tempering for what you need by noodling around with the tuning hammer combined win an understanding of what you are doing. And entirely possible that people like Kirnbeger who srikes me always as a practival sort of man simply codified and refined various common practices. I don’t think that all temperaments sprang solely from the forehead of Athena or similar! Perhaps people foillowed texbook meantones, as the theory is so simple to grasp, but by the time you get to well tempering and circualting tunings things become very msurky indeed, so I am not surprised that musicians would cook up their own recipes.

I think Vermeer is on topic for The Jackrail as he painted so many keyboard instruments!

Andrew: Perhaps you might want to create a new thread for this.

The major part of Hockney’s study does not concern Vermeer, whom others have concentrated upon. His thesis studies paintings from 1500, and I think he warrants consideration, given that, as a highly competent artist, he knows what is difficult to paint (he gives the lute as an example), and moreover, he has spent months using optical aids, to discover how they were used. The vast majority of art historians, particularly those who disagree with his claims, do not draw or paint.

I see a comparison here with the performing musician who is also a composer, and who therefore is able to bring deeper insights into the analysis and “interpretation” of the works he or she plays or conducts.


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