About this project

Andrea Amati (1505-1577), who lived in Cremona, made the world’s first violin. In homage to him, the `Digital Amati` project seeks to advance our understanding of fundamental geometric structures in the design of classical string instruments. Like classical architecture, the design of these instruments is founded on geometric principles. We can bring to light computational aspects of that artistic history, using a new programming language vernacular that describes traditional methods of design.

We explain seventeenth-century knowledge of these artistic and inherently computational structures in software, using a *domain-specific programming language.*

*Computational thinking*
is an accepted way of understanding complex, constructional processes;
programming languages---a form of writing---provide a medium for us to
express *to each other* what we know how to do.

Here is a simple geometric problem: given points *p,q,r* in the plane
that are not collinear, what is the unique circle where the points lie
on the circumference of the circle?
The "analytic geometry"way of solving this problem is to plug the
three points into that equation, and you get three
equations in three unknowns. Solve this set of equations, and you get
the equation for the circle.
The "Euclidean geometry""'' way of solving this problem is to draw,
with a straightedge and compass, the line *pq* bisecting *p* and *q*,
where every point on *pq* is equidistant from *p* and *q*; similarly,
draw the bisecting line *qr* of points equidistant from *q* and *r*.
(See the picture below.) Because *p,q,r* are not collinear (all on a
straight line), the lines *pq* and *qr* intersect---at a point *c*
equidistant from *p,q,r*. That's the center of the circle. The
radius is the distance from *c* to *p*. There's no *
calculating*---only *drawing*.

A suite of straightedge and compass constructions are what are used to design instrument forms based on geometric principles. An instrument outline is composed of an ensemble of circular arcs and straight edges, composed together in a precise arrangement.

Here's an example: given the**Traite de Lutherie: The Violin and the Art of Measurement**, pp. 114--129), a violin by Andrea Amati. The geometry engine
outputs full-scale PDF of the instrument outline. This drawing can be
modified and elaborated in various ways. The additional arcs and
lines elaborate the straightedge and compass constructions that are
used to assemble, as an ensemble, the instrument outline.

Internal forms for the Stradivari *Cristiani* violoncello, made
for a reduced-size instrument that is 740mm long, with bout widths
commensurate with a classic Stradivari *forma B* instrument. The
first was made from a full-size drawing, and cut out on a band saw.
The second (made in a lot of 40 at the Oberlin Violin Workshop in
summer 2015) was made using the PDF of the drawing to drive a CNC
router.

Here is an internal form made by a CNC router for the drawing: