The 1885 book by Ed. Heron-Allen is well-known to the curious violin makers. While certainly not a modern reference, it is interesting in its historical picture of the world of violin making. It also teaches us there is nothing new under the sun; on page 133 he refers to the vibration modes 2 and 5, and nodal lines. The book is now available from the open library project online, here.
In this book Heron-Allen provides a geometric way of producing a violin outline, taken from Jacob Augustus Otto book “ueber den Bau der Bogen-instrumente” from 1817 [Otto] also available in English [Bishop] here. I decided to try reproducing the outline in a CAD program and came up with the following outline. I can offer it to anyone interested. Heron-Allen described it as: “though terribly complicated, the most ingenious piece of mechanical drawing I have ever come across”. He does not give any method for choosing the dimensions, so I would classify this as more of a ‘curiosity’, then a sound reference.
Here is an excerpt from the book and the instructions for generating the diagram (Ed. Heron-Allen, Violin-Making: As it Was and Is Being a Historical; Theoretical and Practical Treatise on the Science and Art of Violin-Making for the use of Violin Makers and Players, Amateur and Professional, 2nd edition (Ward, Lock & Co. Ltd: London, New York, Melbourne, 1885) pp136-139):
To trace an independent outline mathematically on a given, graduated, perpendicular straight line, you must proceed as follows. And I beg, before commencing the explanation of this operation, which is illustrated by Fig. 79, to record my indebtedness to Mr. John Bishop, by whose courtesy I am enabled to reproduce this diagram and descriptive letterpress from his translation of Otto’s work on the construction of the violin (vide note p. 20)  :—
Draw a perpendicular line down the middle of a sheet of paper or of the flat side of the piece of wood intended for the back, of the exact length required for the body of the instrument (without the button b, Fig. 79), and divide it into 72 equal parts, as shown in the figure. This must be done with the greatest accuracy, for on it depends the correctness of the whole.
Then intersect this perpendicular, by 20 horizontal lines at the points named below.
|Line (1) A at the point 8
||Line (11) L at the point 33
|Line (2) B at the point 14
||Line (12) M at the point 34
|Line (3) C at the point 16
||Line (13) N at the point 37
|Line (4) D at the point 20
||Line (14) O at the point 39
|Line (5) E at the point 20 ¼
||Line (15) P at the point 40
|Line (6) F at the point 22
||Line (16) Q at the point 44 ¼
|Line (7) G at the point 23
||Line (17) R at the point 48
|Line (8) H at the point 27
||Line (18) S at the point 55
|Line (9) I at the point 28
||Line (19) T at the point 56
|Line (10) K at the point 31
||Line (20) V at the point 65
This being done, open the compasses to an extent of 9 parts of the perpendicular, and describe the two arcs a a from the point b.
Then place the compasses on the point 24, and opening them to b, draw the curve a b a.
Next set off 2 parts c, on each side of the perpendicular, on the horizontal line C. Place the compasses on the point c, and opening them to a, draw the curves d d, from a to the horizontal line A.
Now set off one part e, on each side of the perpendicular on the line B. Place the compasses on these points, and opening them to the line A, where the curve d ends, draw the curves f from the line A to that of D. This completes the draught of the upper portion of the instrument without the corners.
For the middle or narrow portion proceed thus :—On the horizontal line L set off 11 1/3 parts from the perpendicular to the point g; and then 11 other parts, from g to h, from which latter point draw the curve from the line L to that of P.
Next set off 23 ¾ parts on the line K, from the perpendicular to k ; open the compasses to the point where the curve i intersects the line M, and draw the curve from the line M to that of H. The little angle formed by the curves between the lines L and M, must be worked off so as to bring the sides into proper shape.
The lower portion is obtained as follows :—Open the compasses 11 parts, and describe the two arcs v v from the point r r. Then place the compasses on the point 35, and opening them to r r, draw the curve v w v.
Next set off 6 parts x on each side of the perpendicular on the line S. Place the compasses on the point x, and opening them to v, draw the curves y y from v to the line V.
Now set off 4 parts z on each side of the perpendicular on the line T. Place the compasses on these points, and opening them to the line V, where the curve y ends, draw the curves a a from the line V to that of R.
For the upper corners, set off 24 ½ parts on the line G, from the perpendicular to o, and placing the compasses on this point, open them to the line D, where the curve f ends, and draw the curve from the line D to that of F.
Then on the line I set off 14 2/3 parts from the perpendicular to m. Place the compasses on this point, and opening them to line H where the curve ends, draw the curve from the line H to s.
Now on the line E set off 22 parts from the perpendicular to q. Place the compasses on this point, and opening them to where the curve meets the line F, draw the curve from the line F to s. Again place the compasses on the point 20, and opening them 16 1/3 parts mark off the length of the corners s s.
For the lower corners set off 24 parts on the line Q from the perpendicular to b b, and, placing the compasses on this point, open them to the line R, where the curve a a ends, and draw the curve from the line R to d d.
Then on the line N set off 16 ½ parts from the perpendicular to t. Place the compasses on this point, and, opening them to where the curve meets the line P, draw the curve from the last-named line to d d.
Lastly, place the compasses on the point 49, and, opening them 19 ¾ parts, mark off the length of the corners d d,d d.
This completes the entire model, and the belly can now be marked from the back thus traced.
To obtain the proper rise or height for the back or belly, take a thin piece of bard wood, about 2 inches broad, and a little longer than the violin you propose to make (Fig. 79a), and mark it in the middle at the point A, which must be three ” parts ” (of the foregoing scale) distant from the edge, shown here by the dotted line. Then, placing a large pair of compasses on the point A, open them 216 parts, or three times the length of the body of the instrument, and with this radius describe the arc shown in the figure, which, by being sawed out, will serve as a guide for the height or rise required.
The small semicircular piece seen at the top of Fig. 79 is the ” button,” which is part of the back, and made in one piece with it, to which is glued the shoulder when the neck is fixed to the body.
This method of tracing an outline (which has been given by more than one author) is, though terribly complicated, the most ingenious piece of mechanical drawing I have ever come across. Nowadays any one can get access to a good outline, which may be copied as before set down, but I have given the above method as it is extremely interesting, and clever in construction.
Jacob Augustus Otto, “ueber den Bau der Bogen-instrumente,” etc., 1st edition (Halle and Leipsic, 1817); 2nd edition (Jena, 1828),
John Bishop, of Cheltenham, “A treatise on the Structure, etc., of the Violin, etc.” (London, 1st edition 1848; 2nd edition 1860; 3rd edition 1875), Translation of Otto’s “ueber den Bau der Bogen-instrumente”