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which was an attempt to overcome the familiar problem that spacings of frets
which are optimal on one string do not suit adjacent strings. The theory underlying
Salmon's Proposal will not be discussed here as the only relevance of the
publication to this article is some tables which will be described below. Part III
of Salmons Proposal explains The tables of proportions, calculated for the viol, and
capable of being accommodated to all sorts of musick (the tables themselves are at
the back of the book). The function of these tables, in Salmons words, is so
that
a man may without thinking perform his Musick in Perfect Proportions;
the Mechanical Workman shall make them ready to his hand, so that he
need only shift the upper part of his Finger-board as the Key requires 38
This means that in order that every fret on every string should be always
exactly in tune, an instrument-maker should equip the fingerboard with staggered
fretting. Salmons Table 1 exemplifies this staggered fretting. For the top
two strings the first fret is about 39.5 mm from the nut, for the third string 44
mm, for the fourth and fifth 35 mm, and for the sixth string it is 39 mm from
the nut. Salmon realises this will not work for different keys so he gives
a Table of Proportions in every Key, that the Mechanick may accordingly
make a sett of Finger-boards for each instrument, according to its
particular length; the Proportions ever remaining the same though the
size be various. 39
In all, Salmon calculates fret spacings for fourteen keys, which will require
seven fingerboards, so he provides seven tables. He is not totally committed to
swappable fingerboards, and suggests that 'Makers of Instruments may find out
some other way much more convenient'. Appended to the Proposal is a long
commentary by the extremely distinguished mathematician John Wallis. Wallis
suggests, as an alternative to swappable fingerboards, separate frets for each
string 'to slide up and down in a Groove' with coloured-coded markings on the
[23] fingerboard to show where they should be set. 40 Nevertheless, viol-players'
hearts will sink at the thought of swapping the fingerboard or adjusting the
frets whenever they play a piece in a different key. Salmon therefore adds an
eighth table called Lyrick Harmony which he claims can be used for many keys
by 'any person that uses a fretted instrument, either Lute, Viol, or Gittar'. 41
For all the tables, the size of the pages in the Proposal means that spacings
can be shown only for the first five frets, but calculations are given for the
sixth and seventh. 42 The relevance of Salmons Proposal to this article is that his
38 T. Salmon, A proposal to perform musick, in perfect and mathematical proportions (1688), 17.
39 Ibid., 17-18.
40 J. Wallis, Remarks on the Proposal (1687), 41. Players may be interested to know that
Salmon demonstrated his system to the Royal Society, and Frederick and Christian Steffkin
performed on instruments fitted with his stagger-fretted fingerboards, in June/July 1705: see
L. E. Miller, 'John Birchensha and the Early Royal Society: Grand Scales and Scientific
Composition, Journal of the Royal Musical Association 115 (1990), 63-79, at p. 78, n. 50. This
would be an interesting experiment to repeat, perhaps on its 300th anniversary, at the same
time comparing the swappable fingerboards with Wallis's alternative suggestion or new ideas
from contemporary Mechanical Workmen.
41 Salmon, Proposal, 25.
42 Ibid., 27.