the-rule-of-31

Once the frets are placed, one can tune using the familiar method of tuning unisons between the 5th
fret of one particular course to the next higher open course (except between courses 3 and 4 which
use the 4th fret for the pure major 3rd). Consonances can be checked with octaves between an open
course and the 7th fret of the next higher course. Also, octaves can be checked between the 2nd
fret of courses 6, 5, and 4, and the open courses 3, 2, and 1 respectively. In fact, this tuning method
is exactly what Ganassi recommends, though his errors regarding the placement of frets V and VII
(pythagorean rather than tempered 4ths and 5ths) would have completely fouled up the process 23 .
Conclusions
The debate over whether to tune by geometry or by ear goes back at least as far as Zarlino. For
better or worse, tuning instructions based solely on “hearing” are subject to all kinds of inaccuracies
and misunderstanding, as can be seen in the deeply flawed, but oft cited, method of Robert
Dowland (1610) 24 . On the other hand, the ear is the final judge and the geometrical models must
lend themselves to the sounding result rather than the other way around. With careful calculation
and appropriate choice of disposition, there is no reason why a true 1/4 meantone fretting scheme
cannot be effectively implemented on lutes, viols, and theorbos. Often, performers opt for the 1/6
comma temperament to avoid readjustment of frets for different modes, but as Milan shows us in
El Maestro, adjustment of frets for different pieces was indeed done at the time. It seems that the
choice of 1/6 comma is often made to give one the sense that the finer distinction between
“enharmonic equivalents” may allow one to freely fret an A-flat when a G-sharp is called for, but I
would assert that whether the difference is 1/5th of a semitone, or 1/9th of a semitone is irrelevant:
they’re both out of tune. If one is playing in F minor for example, one must fret the instrument to that
disposition, and not just use a “softer” version of the meantone temperament in order to rationalize
the use of a 1/6th comma G-sharp as an A-flat.
Unfortunately, most fretting guides from the sixteenth-century (as well as modern ones) neglect to
consider the importance of the disposition of the meantone cycle. Even experts such as Mark
Lindley and Eugen Dombois give little or no information on how to adjust the fretting scheme to
handle tonalities other than the so-called “standard” disposition of E-flat to G-sharp. While Lindley
23 Lindley, Mark. Lutes, Viols and Temperaments. Cambridge: Cambridge University Press, 1984. p. 95.
24 ibid. p. 83+89.