Contents

Preface

Introduction

Contents

Preface (11-14)

Introduction (17-18)

PART I

MEASURE AND INSTRUMENT MAKING BEFORE THE 18th century

I-1 Preliminary remarks

The role of resources in creation (23-24)

I-2 Concepts connected with the notion of measurement

2.1 Unit and number (25)

Continuous and discrete quantity (25-26)

2.2 What is a difference ratio and a measurement of magnitude? (26-27)

2.3 Proportionality (28)

Means (28-29)

Arithmetic proportion (30)

Geometric proportion (30-31)

Harmonic proportion (31)

2.4 Proportional sections (31-33)

2.5 The symmetrical properties of proportional sections (34-37)

I-3 The measurement of magnitudes in past recipes

3.1 Three examples of recipes from Vitruvius,
Henri-Arnaut de Zwolle and Mathias Roriczer (38-41)

3.2 The myth of the Golden Number (41)

3.3 Proportional geometric drawings and their approximations by number (42-43)

3.6 Approximations and the construction of sequences of converging ratios (43-45)

The geometric progression

The harmonic progression

The subharmonic progression

3.7 The analogical principle and the substitution of measurements (45-47)

I-4 Analysis of measurements in a 15th century technical drawing

4.1 Henri-Arnaut de Zwolle's lute (48-50)

4.2 Drawing the outline: first proportional relations (50-52)

4.3 How proportion generates measurements (52-53)

4.4 The position of the soundhole (54-55)

4.5 The relative nature of the plan (56)

PART II

DESIGN AND OUTLINE OF THE FORMS OF THE VIOLIN FAMILY

II-1 Preliminary remarks
The difficulties of analysing measurements (41)

II-2 Antonio Stradivari's violin moulds

2.1 Relations between the main dimensions of the forms (62)

2.2 Vertical relations (65-68)

2.3 Horizontal relations (68-72)

2.4 Height relations (72-73)

2.5 The length of the neck, the position of the bridge,

the length of the string (73-77)

2.6 Relations between the three dimensions (77-79)

II-3 The proportional archetypes of the violin family

3.1 The square and the organic conception of form (80-81)

3.2 Definition and organisation of the surface (81-83)

3.3 Analogical measurements and an archetypal division in Vitruvius (84-86)

3.4 Some examples of frameworks (86-100)

II-4 Drawing with a compass

4.1 Drawing curves and the principle of the section (101-103)

4.2 Scotia and the reverse curve (103-104)

Drawing a scotia (104-105)

Drawing a reverse curve (105-106)

4.3 Three problems and their solutions (106-111)

4.4 The characteristics of violin curves (112-113)

II-5 Seven models

5.1 Outline of a violin form by Andrea Amati (114-129)

5.2 Andrea Amati violin outline: analysis and commentary (130-138)

5.3 Form of a violin by the Amati brothers (139-147)

5.4 Amati brothers outline: analysis and commentary (148-151)

5.5 Form of an alto viola by Giacomo Gennaro (152-161)

5.6 Form of an alto viola by Andrea Guarneri (162-171)

5.7 Form of a tenor viola by Andrea Guarneri (172-181)

5.8 Form of a cello by Joseph filius Andrea Guarneri (182-191)

5.9 Form of a cello by Domenico Montagnana (192-202)

PART III

Late-period applications of proportionality

III-1 Preliminary remarks
Of arms and legs (207-208)

III-2 Stradivari's inheritance and particularities

2.1 Production of forms and changes in ways of taking measurements (209-216)

2.2 The Turn of the Scroll (217-220)

2.3 Stradivari's proportional principles for placing f-holes (221-223)

2.4 How to draw Stradivari's forms (224-231)

2.4.1 Mould MS 1 MB (232-233)

2.4.2 Mould MS 2 S (234-235)

2.4.3 Mould MS 28 SL (236-237)

2.4.4 Mould MS 21 PG (238-239)

2.4.5 Mould MS 49 G (240-241)

Conclusion (245-246)

Glossary (249-251)

List of subscribers (252-253)

Selected bibliography (254-255)