Friday, March 29, 2019

A Summary and Overview of Main Results from My Research


Many of the ‘rules’ amount to collections of ratios
traditional to a feature


So for example, the basic width and length for
instrument bodies follow a simple rule:

 Make the body length
 ‘a part less than’
 twice the width.
This rule yields the tradition body ratios:
9::5    7::4    5::3    3::2
All the bouts relate similarly through traditional ratio options.

4 by 7 body in a
1525 Lira from Giovanni Maria of Venice

3 by 5 body in a
1580c Viola from Zanetto of Brescia

2 by 3 body in a
1607 Gamba from the Brothers Amati of Cremona


The rules give repeatability and a structured way to create variations   

The Neck length or ‘neck stop’ gets related to ‘body stop’, which is based on the bridge line.

 Make the neck stop
 2/3 the body stop,
or ‘a part’ of the ‘stop unit’
shorter or longer
The ‘stop unit’ is the ‘unit’ of the normal 2::3 unit, or 1/3 the ‘body stop’. (Fingerboards were then proportioned from the resulting neck length from the nut. And scroll heights were proportioned from the ‘stop unit’.)

Neck length taken as the normal 2/3 ‘body stop’
1742 violin ‘Lord Wilton’ from Guarneri Del Gesu

Neck lengthened by ¼ the ‘stop unit’ in a
1613 piccolo violin from the Brothers Amati

Neck shorten by ¼ the ‘stop unit’ in a
1793 Tenor Viola from the Brothers Mantegazza


Some rules determine the actual execution of the work, others only guide the makers’ choices   

The width across the upper eyes of the soundholes has two ‘guide’ rules, but is actually ‘executed’ by a third rule

 Guide the upper eye span
by 3rds of the upper bout
and 4ths of the center bout,
but make the span equal to or
‘a part less than’ the stop unit.
The upper eye diameter is than taken as ‘a part’ of the span.

Here we see the interplay of such guide and execution rules in
Strad’s 1715 ‘Soil


Classical Cremona makers took some freedom and flexibility by varying the application of rules rather than breaking or ignoring them

Do we measure from the center or edge of a circle? 
Do we measure from the outer edge of the outline, or from the pufling?  
Classical makers varied their answers to such questions as it suited their purposes. Sometimes such choices help define one instrument type versus another.

 For Violins and Violas,
Take the Upper Eye Span to Include the Eyes.
  For Cellos,
Take the Span as the Space Between the Eyes.
(The soundholes are complicated features.  Many rules work together in sizing and positioning the soundholes.  Additional traditions then govern the actual shaping of the eyes.  Every detail has traditional rules and constructions for executing the work, and many have further traditional guides.)

Eye span is 7/8 a stop unit across the eyes
Strad’s 1721 violin, ‘Lady Blunt’

Eye span is 5/6 s stop unit between the eyes
Strad’s 1673 cello ‘Dupre’


Besides rules for positioning and sizing,
the tradition includes geometry constructions for all the shapes,
using just compass and straight edge

Full geometry for the head of Strad’s 1690 tenor viola, ‘Tuscan-Medici’

Principle body outline geometry for G. Maria’s 1525 lira


Even the most complex of these constructions boil down to smoothly joined lines and circle arcs.      

Tangency gives smooth joins.

If the radii centers and point of connection lie in a line, arcs will join smoothly.

The upper and lower bout shapes are based on overlapping circles, called vesici.

Arcs centered proportionally across the vesici takes us toward the corners

A long arc connects the vesici circles in violin family bouts.  These long arcs are generally centered on 3rds or 5ths of the body length.


All the differences between individual instruments, makers, regions, and generations turn out to be variations using a consistent traditional toolkit of methods.
By ‘reading’ the choices in historical instruments,
we can follow the tradition’s evolution, as features and preferences develop.  This evolution is highly conserving – always within the traditional kit of methods

(Soundholes developed actively during the Classical Cremona period, providing an excellent example of the traditions evolving in their characteristically highly conserved way.)

1580c Zanetto viola

Some very early Andrea Amati examples follow this same geometry structure.

1560c Andrea Amati violin  ‘Kurtz

However, in most examples, Andrea Amati develops the arcs extending from the eyes, and the wing treatment.

1620c Brothers Amati viola    RAM

The brothers make many experiments developing the soundholes 

1645c Nicolo Amati violin treble and bass compared
Nicolo Amati largely settles on the final 'Amatese' soundhole.

Strad soundholes change some sizings and proportions,
but actually they continue using the very same geometry structure

Del Gesu experimented with greater extension of the curves beyond the eyes. 
He continued this past the point the standard geometry structure could accommodate.
In a number of late examples, Del Gesu adds an extra arc in the curves above the upper eyes.


The 3D shapes of the arching are governed by various control points and curves, then completed by smoothly connecting the shapes between these bounds. 
This approach parallels boat building of the time.

The long arcs of Alard’s 1715 Strad

Between the main control points, arching follows a simple rule: 

1/2 Fall in 2/3 Run

This rule can be used recursively to provided as many
additional control points as desired.
And the notion of ‘smooth’ is rooted in boat building’s concept of ‘yar’ or ‘fair’ –
based on the curve of bent splines or wood slats across the control points.

Illustrated work sequence to form a cross arch shape:


CTscan maps reveal that classical makers
 did not share modern notions of ‘graduations’. The plate concept is more of a loosely even
diaphragm thickness,
with an extra mass in the center back

Note the smooth but randomly drifting thickness variances of about +/- .3mm for violins

Del Gesu top thicknesses

Strad top thicknesses

Del Gesu back thicknesses

Strad back thicknesses

Composited from Anders Buen data points, and Smithsonian Institute Scan maps.  Blue shows thinner, yellow thicker.


Classical design methods can be
worked directly on the wood,
or transferred by template and similar means. 
But the features of classical examples mainly appear to be characteristically
sized, placed, and worked ‘in situ’

It appears that as early as the Brothers Amati, templates were probably used at times, especially for complex shapes.  Templates can also be used to document shapes.  We see Strad left many paper templates.  Some may have been for documenting, and some for transfer of shapes.  However, the norm for classical making seems to have been direct unique working of shapes in context. 

The patterns of asymmetries and variances in classical work, and the uniqueness of actual sizing, positioning, and shapes between instruments – and even from treble to bass side of a single instrument; these seem easier to understand if we assume direct working out of shapes, with design choices made interactively and uniquely with each build. 

However, making and executing such design choices directly is highly skilled work, and time consuming. Augmenting direct design work with templates would have always helped in making good use of assistants and apprentices.   And if a master maker wanted to keep a few secrets, templates allow good use of assistants – without having to reveal all about the designs and principles.

It seems likely that the economic pressures emerging in the 2nd half of the 18th century would have pushed makers toward greater time saving through templates.  This also would mean that more people could significantly help manufacture instruments without having full the knowledge of a master.  In this way, template work may have been a major factor in the breakdown and loss of traditional knowledge as violin making greatly expanded economically and dispersed geographically.

Some typical remnant design marks:


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