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!
David
