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Journal of Cultural Heritage 27S (2017) S26–S33

Available online at

ScienceDirectwww.sciencedirect.com

ooden Musical Instruments Special Issue

ritical study of the use of a length unit in the design of 16th to 18thentury Italian violins

imone Regina Zopf ∗

TBLA Hallstatt, Lahnstrasse 69, 4830 Hallstatt, Austria

a r t i c l e i n f o

rticle history:eceived 27 February 2015ccepted 14 April 2016vailable online 21 June 2016

eywords:eometrical analysis of musical

nstruments

a b s t r a c t

Until now, the question of geometrical construction (or: reconstruction) of the violin form has beenthe subject of numerous hypotheses. Without doubt, instruments were designed using the tools of thatperiod, namely, a ruler and a compass and applying the ideas of Pythagoras or Vitruv, to achieve a perfectlybalanced instrument. In particular, the question of a “standard unit” is of importance. Previous researchmostly dealt in geometrical construction and not in a “standard unit”. Based on our recent discoveriesof tools and drawings, we suggest that instruments of the Brescian and Cremonese schools might haveused a standard length unit that could have been the Roman oncia. This unit was applied to the Stradi-

remonaeasurements of violins

matitradivariutherie

vari instruments, later to all Cremonese violins. But initially, the relationship between the proportionsdid not emerge, until a completely, new construction system, using concentrical circles, was applied.Consequently, all necessary markers for the construction and the radii of the outline can now easily bedetected. The construction might be also applicable to violas, violoncellos and even the smaller violins,too. Also the violin scrolls were successfully analyzed.

© 2016 Elsevier Masson SAS. All rights reserved.

. Research aims

The main aim of this study is to propose and discuss the rel-vance of a historical unit, named the Roman oncia, that mightave been used by some violin makers to design their instruments.he design of the Italian violin is a well discussed topic and manyifferent approaches have been used over the last two hundredears. To understand the way of constructing an instrument, thenowledge of the used measuring unit is essential. Although sev-ral researchers have been looking for this unit, no persuading oneas yet to be found. Based on the information Najmon [1] has givenegarding investigations on brass rulers of A. Stradivari, a unit of8.66 mm was chosen. Subsequently, this unit was identified ashe Roman oncia, a unit used by architects, engineers and craftsmenrom the Renaissance to the beginning of the 19th century. Anotherim, was to find a possible method to construct the outline of theiolin based on this unit and using the tools of that period – rulernd compass. Furthermore, the construction should be compared

o existing instruments and other items such as templates andorms.

∗ Tel.: +4369912194249.E-mail address: simone.zopf@gmx.at

http://dx.doi.org/10.1016/j.culher.2016.04.012296-2074/© 2016 Elsevier Masson SAS. All rights reserved.

2. Introduction

How were objects designed in the 16th to 18th century?There are plenty of writings dealing with beauty and pro-

portion in architecture, based on the ideas of Pythagoras. Thisconcept states that beauty lies in the perfect balance of numbersand proportions, common in all arts and crafts, even in beautifulsounding music with ratios like the fifth or the fourth. Also, themost famous painters of that time, Leonardo da Vinci, AlbrechtDürer were discovering and publishing ideas about the relation-ship between harmonics, ratios & the aesthetic, beauty to be foundin the architecture of human beings. The use of numerical propor-tion is well documented for buildings, paintings, furniture and eventhe construction of cities [2]. However, with musical instruments,being the most obvious objects related to musical proportions, onlyvery few sources survived. The earliest and only plans for con-structing a lute and harpsichord, are the drawings of Arnould deZwolle [3] showing the outline and internal bracing of the bellyof a lute. Unfortunately, no other plans have survived, but a lot oftemplates and forms from the workshop of Stradivari do. Theseimplements have at least preserved some traces of the measure-

ment techniques used, like compass marks and give an insightinto the techniques employed at that time. It can be said, that theuse of a compass for design and measuring was very important;one of the earliest portraits of a luthier, Kaspar Tieffenbrucker,

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S.R. Zopf / Journal of Cultur

epicts the master surrounded by various instruments, holding compass in his hand. Calculations or other divisions made by compass are seen on several sketches of Leonardo da Vinci,oo, and the use of a compass during the construction of build-ngs, furniture, book paintings and doors is very well documented4].

Besides the utilization of the compass for designing instru-ents, the knowledge of the applied unit is also crucial. Firstly,

o understand the construction, because the simple comparisonf measurements does not reveal in all cases its design. Secondly,o have a possibility to attribute instruments to certain regions ornstrument makers.

Studies on the proportions of historical instruments are an inte-ral part of the education at the luthiers school in Hallstatt, Austria.tudents learn to measure and draw historical instruments ando understand the geometrical background of the renaissance andaroque. Many different instruments such as lutes, viola da gambas,ihuelas, among others, were successfully analyzed, but a clear andractical method for the violins was missing. With the students ofhe third year, a research project was initiated for the constructionf the f-hole, based on the information Sacconi [5] provided andhe original sketches of Stradivari.

Najmon had investigated two brass rulers of the Stradivariorkshop and proposed a possible measuring unit of 18.66 mm,

ut he also mentioned the Roman oncia, being very close to thisalue (18.58 to 18.75 mm). Pabst [6] tried all relevant units linked toremona, including the unit Najmon had discovered and was look-

ng for whole number values in the measurements of violins – in 13f 22 cases the value of 18.66 mm was fitting. Therefore, this unitas chosen for further investigations. Later, a method to construct

he violin, based on the Roman oncia, was developed and com-ared with the measurements of original Cremonese and Brescian

nstruments.

. Historic origin and use of the Roman oncia

The situation of the Italian metrology is quite complex, many dif-erent local units for different materials were existing and variousubdivisions in palmo (hand), piede (foot) and braccio (arm) wereommon. For Rome, or more specifically, the Vatican City State, 3o 4 different sizes were existing. Namely, palmo romano architet-onico, was used for all normal measurements of objects, buildingsnd woodwork [7].

Thus: Canna architettonico = 2.2319 m, divided in 10 palmorchitettonico, then each divided in 12 oncia, then divided in 120ecimo.

The Roman oncia in the 18th century is thus a unit correspondingo 18.62 mm′′.

The palmo romano is documented in many drawings and plansf architecture, for instance, in the construction of St. Peters Cathe-ral in Rome, and it varies between 223–225 mm [8]. Another

nteresting detail in these plans has come to light: Vignola, therchitect of the Palazzo Farnese in Picenza, was still using his Romanncia, but trying to simplify these measurements for the Piacenzaraccio as well [9].

Also, the use for instrument making is documented in the writ-ngs of Galeazzi [10]. He talks about the best properties of a violinow and states, that the length of an ideal bow should have 25ollici Parigini or 37 once del palmo architecttonico.

Due to the historical variations of this unit (18.58–18.75 mm),or this study, a value of 18.66 mm for the Roman oncia was chosen,

ased on the studies of Najmon. He indicates that this value was theost probable size for a unit, due to the brass rulers of A. Stradivari

e had investigated. The Roman oncia will be abbreviated with theign [′′].

itage 27S (2017) S26–S33 S27

4. Materials and methods

4.1. Corpus under study

4.1.1. PhotographsThirthy-eight photographs of violins, violas and violoncellos of

high quality [11–18] were scaled and calibrated to the exact mea-surements. Furthermore, the pictures were adjusted to take intoaccount the geometrical distortion of the camera’s objective. Thiswas necessary in order to discover a possible geometrical design.Only measurements taken with a caliper were used because violinsare often measured over the arch and these values cannot be usedfor our purposes. Most instruments were chosen from Cremona, afew from Brescia and also instruments from Jakob Stainer, becauseof his possible education by Cremonese instrument makers (seeTable 1).

4.1.2. Drawings, templates and sketchesStradivari’s templates published by Sacconi and Pollens [19]

were calibrated to their true size and measured with the Romanoncia and compared with the construction.

4.1.3. ParchmentA parchment of Cozio di Salbue, now owned by the National

Museum of Music, showing concentric rings was investigated(Fig. 1).

4.1.4. Rulers of A. StradivariNajmon had investigated two brass rulers attributed to the

workshop of Stradivari. The rulers are named parziale and perime-trale, from the parziale certain values could be identified and wereindicating the use of a unit of 18.66 mm. Unfortunately, the ownerof these rulers is nowadays unknown, so only the pictures could bestudied (Fig. 2).

4.2. Method of geometrical analysis

4.2.1. Ancient sources and previous constructionsGeometrical analysis of the shape of an instrument is based on

the idea that luthiers have made conscious use of numerical propor-tion. Whilst this approach is well studied in architecture, because ofa considerable body of historical documents written by architectsthemselves [4], such sources are missing in lutherie. But it can beassumed that an object serving to make music could be designedusing the omnipresent ideas of Pythagoras and using musical inter-vals as proportions. The only historical source for instruments is amanuscript from Arnould de Zwolle in 1452, showing how to drawa lute, a clavichord and a little organ, using numerical proportionsand a compass. No other writing or plan of this time is yet to bediscovered, but lots of templates and sketches from the Stradivariworkshop have survived, showing the use of compass and the con-struction of the f-holes, but hardly any numbers or instructionsremain.

Just a few decades after the decline of the Cremonese school, aninterest had risen in the construction of the violin, and led to a pub-lication in 1782 by Bagatella, [20] dividing the length of the body in72 sections, but showing only a very, roughly defined shape with-out corners. From this point, numerous attempts to understand thedesign of the violin were published, some of them oversimplifyingthe topic, others, complicating it.

An example of the latter, is the construction by Simone Sac-coni, a system, well known and often tried. He used the Cremonese

Braccio (9 units) for the length, but the construction itself is verycomplicated and includes several mistakes.

The important work by Heyde [21] gives an overview for allkinds of instruments and of certain possible methods of proportions

S28

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eritage 27S

(2017) S26–S33

Table 1Measurements of investigated instruments in mm and roman oncia.

Instrument Source

Length Max. width r upperbout

r lowerbout

Distancelb r

Distanceub r

Center of lowerf-holes

Distancecenter-bridge

Violins r.o. mm r.o. mm r.o. r.o. r.o. r.o. r.o. r.o. r.o.

Nicolo Amati 1628 National Music Museum (USA) 19.0 353 11.0 205Nicolo Amati 1635 Four Centuries Of Violin Making 18.9 352 11.0 203.7 3.5 4 1.5 2.90 42.0 2.26 1.15Nicolo Amati 1640 Four Centuries Of Violin Making 19.0 354 11.2 208.2 3.5 4 2.0 3.00 40.0 2.15 1.00Nicolo Amati 1665 Four Centuries Of Violin Making 19.1 355 11.0 205.1 3.5 and 4 4 and 4,5 2.0 3.00 42.0 2.26 1.00Nicolo Amati 1680 Four Centuries Of Violin Making 18.9 352 10.8 201.8 3.5 4 1.6 2.75 44.0a 2.37 1.20Nicolo Amati 1683 Four Centuries Of Violin Making 19.0 354 11.3 210.8 2.1 3.24 42.0 2.26 1.05Nicolo Amati Alard Art Of Violin Making 18.8 350 11.1 205.8 3.5 4 2.0 3.00 44.3 2.38 1.23Nicolo Amati 1628 Luthiers Library 19.0 353 11.0 205 3.5 4 1.8 3.00 38.8 2.09 1.00Nicolo Amati 1670 Luthiers Library 18.8 350 10.7 199 1.7 2.75 43.6 2.34 1.15Nicolo Amati 1670 luthierslibrary.com (USA) 18.8 350 10.7 199A & G Amati 1625 Four Centuries Of Violin Making 18.9 351 10.7 199.7 3.5 4 and 8 1.7 42.5 2.28 1.00A & G Amati 1595 National Music Museum (USA) 19.4 360 11.1 207A & G Amati 1596 Four Centuries Of Violin Making 19.0 353 11.0 204 3.5 4 1.8 3.00 42.0 2.26 1.00Andrea Amati ca. 1577 National Music Museum (USA) 19.0 353 10.8 201.5 3.5 4 1.7 2.75 42.0 2.26 0.80Andrea Amati Charles IX Capolavori 18.9 351 10.8 200 3.5 4 2.0 2.90 42.0 2.26 1.00

Stainer 1659 18.9 351 10.8 200 3.5 4 34.0a 1.83a 1.00Stainer 1650 19.0 353 10.7 199 3.5 4 35.0a 1.88a 0.80Stainer 1671 Jakob Stainer kayserlicher

diener und geigenmacher zu19.0 354 10.9 202 3.5 4 33.0a 1.77a 1.00

Stainer 1678 Jakob Stainer kayserlicherdiener und geigenmacher zu

18.9 351 10.6 198 3.5 4 37.0a 1.99a 1.00

Stradivarius A 1713 Charles Beare 19.0 353 11.1 205.5 3.5 4 2.0 3.00 42.0 2.26Stradivarius A 1709 Charles Beare 19.1 356 11.2 207 3.5 4 2.0 3.00 42.0 2.26 0.90Stradivarius A 1707 Charles Beare 19.0 353 11.2 207 3.5 4 2.0 3.00 42.0 2.26 0.90Stradivarius A 1692 Charles Beare 19.5 362a 202 4 4 0.5 2.76 37.0a 2.0 0.80Stradivarius A 1694 The Metropolitain Museum of

Art (New York)19.4 360a 10.8 200 4 4 0.5 2.75 38a 2.05

A. Stradivari Charles Beare 19.1 355 11.1 207 3.5 4 2.0 3.10 42.0 2.26 1.00A. Stradivari Hellier Charles Beare 19.1 356 11.2 209 4 + 3.5 4 2.0 3.20 40.0 2.15 1.00Andrea Guarnieri 1662 Four Centuries 19.0 354 11.0 204 3.5 4 2.0 3.00 43.0 2.15 1.00P. Maggini 18.8 350 10.9 203 3.5 4 2.0 2.80 42.0 2.26 0.50Guarnieri Andrea 1681 Four Centuries 19.0 353 11.0 204 3.5 4 1.8 3.00 43.0 2.31 1.00Guarnieri Andrea 1662 Four Centuries 18.9 352 10.9 203 3.50 4 2.0 3.00 42.0 2.26 1.00Guarnieri Del Gesu Doubleday 19.0 354 11.0 204 3.5 4 2.0 3.00 40.0 2.15 0.90Guarnieri Del Gesu Haddock 18.8 349 10.9 203 3.5 to 80% 4 to 60% 2.0 3.00 42.0 2.26 1.00

mittelwert 19.00 10.95 40.6 2.18 0.98Other sizesAmati Girolamo 1604 National Music Museum (USA) 18.3 341 10.5 195 3.5 3.5 and 4 1.5 3.50 39.0 2.10 1.00Amati Andrea CA. 1574 National Music Museum (USA) 18.4 342 10.5 195.5 3.5 3.5 and 4 1.5 2.33 40.8 2.19 0.83Amati A. & G. Viola 21.5 400 12.9 240 4 4.5 2.0 3.75 49.0 2.63 1.00Andrea Guaneri Viola 1664 Luthiers Library 25.9 481 0.0 5 5.5 3.0 4.00 53.0 2.85 1.00Jakob Stainer Viola 1660 Jakob Stainer kayserlicher

diener und geigenmacher zu21.7 403.5 12.7 236 3.5 4 42.0 2.26 21.00

Roman oncia (r.o.) 18.6

a Values differ most from mean value.

S.R. Zopf / Journal of Cultural Her

Fig. 1. Violin pattern (parchment) attributed to a Cremonese workshop, 17th cen-tury, NMM T-18, National Museum of Music, Vermilion South Dakota, USA. ex colls:Count Cozio di Salabue. G.B. Guadagnini, Antonazzi family, Bisiach, Milan, Witten-Rcp

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awlins Collection, 1984. Handwriting attributed to Cozio di Salabue. The threeoncentric circles have a diameter of 18.5, 37.5, 56.1 mm respectively, to be com-ared with the Roman oncia is 18.66 mm.

sed in violins, but these might be to simplified for the complexhape of Cremonese instruments.

Coates [22] wrote a whole book dedicated to the design oftringed instruments, which has very interesting ideas and excel-ent drawings showing the construction step by step. He attemptso work out the applied unit, and chooses the Brunswick inch23.78 mm). As far as we know, there are no historical evidences

or this unit in Italy.

Chitwood [23] used another approach: he provides an analy-is of morphological evolution in the violin family, sampling the

ig. 2. Two brass rulers attributed to A. Stradivari, named Parziale and Perimetriale.x colls: Count Cozio di Salabue, Fiorini, E. Sprenger, now private Collection, Prague.oth rulers are about 200 mm long, 2.1 mm thick, made by “Lo Pastorino”.ajmon [1].

itage 27S (2017) S26–S33 S29

body shapes of over 9000 instruments over 400 years. Clusteringof averaged violin shapes places luthiers into four major groups,demonstrating a handful of discrete shapes predominate in mostinstruments. This reveals quite unexpected groups: Stradivari, forinstance is in a cluster with Gagliano, but Stainer is in a clusterwith Testore and Guarnieri del Gesu, but their instruments showno obvious familiarity at all, when the shape of the f-holes or thescroll is compared.

The recent work of Nia et al. [24] attempts a different way toanalyze the shape of f-holes: Their study shows an increase of thef-hole length by roughly 30% across two centuries in the renownedworkshops of Amati, Stradivari and Guarneri, favoring instrumentswith higher air resonance power, through a corresponding powerincrease of roughly 60%. In fact, this is only observed in the instru-ments of Maggini and Guarneri del Gesú, most of the other violinsfollowed the pattern of Stainer, which has a much shorter f-hole orlater, or the model of Stradivari.

Several researchers, like Stewart Pollens, are doubting the useof compass in designing the outline of the violin. But the recentwork of Denis [25] shows a way to construct these shapes, mainlyusing proportions, not fixed values, which is quite convincing.The approach presented in this paper is a development of Denis’work. Indeed, several geometrical points are similar between ourapproach and Denis’ approach. However, we suggest that the use ofanother unit, in use in Italy between the 16th to 18th century couldhave led to a more simple geometrical construction of the violindesign.

4.2.2. New approach of geometrical analysisFollowing the ideas of Heyde and Coates for the construction of

stringed instruments, many different types of instruments could besuccessfully analyzed so the same approach was applied to violins:In some cases, the comparison of the general proportions, such asthe length and width of an instrument, already gives a clear pic-ture of the system the design is based on. The violin does not revealsuch an obvious measuring system, therefore, it was necessary tofind the measuring unit, to understand the design. Moreover, a con-structional system should be found which is clear, logical and notto complicated for the application in a luthiers workshop and mustbe supported by historical facts.

Firstly, choosing a unit of 18.66 mm for our research, the max-imum width of the violin was investigated. The Roman onciasuccessfully fitted into the standard width of most of the Cremoneseviolins 11 times (11 × 18.66 = 205.2 mm). The length of the instru-ment can be constructed in two ways, for instance, placing twoequilateral triangles of 11 inches, one above the other. This givesa length of 19.2 inches or 356 mm, or simply choosing 19 units(353 mm). But the relationship between the numbers did not fullyreveal itself, until a completely, new system of construction, usingconcentric circles, was applied. From the geometrical center of theinstrument, circles in distances of exactly one oncia spacing weredrawn (Fig. 3). Consequently, all necessary reference points (suchas maximum width of upper and lower bout, waist, position of thebridge) for the construction and the radii of the contour, can noweasily be deduced (see Table 2).

4.2.3. The violin – dimensions, reference points, basic circles forthe construction

The violin has a shape similar to the figure eight: the maximumwidth lies in the lower bout, the middle part or c-bout is the narrow-est and the width of the upper bout lies in-between. To constructthe outline, several positional points have to be fixed: the maxi-

mum width and length, and the position of the maximum widthor narrowest part for upper, lower, c-bout. Then, the radii for theoutline has to be chosen, and with at least six circles applied, theviolin’s figure of eight shape is almost finished, except the corners.

S30 S.R. Zopf / Journal of Cultural Heritage 27S (2017) S26–S33

Table 2Step by step construction of a violin, based on Andrea Amati, all numbers in Romanoncia.

a) The width and the length are constructed:11′′ × 19′′

b) From the center circles in one and halfoncia distances are drawn (1–7′′ and 5.5′′)

c) Position of the bridge: one oncia from thecenter down

d) Position of the narrowest part and upperend of F-holes, as well as centerline of c-bout

e) Horizontal line crossing through 3′′ anddiagonals = position of lower counter curve

f) Horizontal line through vertex of 5.5′′

circle = widest part

g) Horizontal line through vertex of 6′′

circle = maximum width upper bout

Table 2 (Continued)

i) Radii for upper bout: 3.5′′ , 1′′ distancedfrom center line

j) Radii for lower bout 4′′ , 1.5′′ distanced fromthe center line

k) Radius for c-bout is a 5′′ circle, 8′′

distanced from center line

I) 1′′ Radii for the counter curve, 6 1/4′′

distanced from the center, upper linecrossing the vertex of the 3 3/4′′ radius

j) Radii for c-bout 1′′ and 3/4′′ on a 4 1/4′′

circle

To construct these, 4 smaller radii on each side have to be drawn(see Table 2, l and j). Depending on the outline, the position of thebridge or body stop is fixed and indicated by little nicks in the f-holes. If the radii and their centers are unknown, designing a violinor analyzing it becomes quite challenging, but when the standardunit is recognized, the possible number of these values decreases.As with any craft or technique numbers linked to each other andeasily remembered are more likely to be chosen than others. Tosupport this process, a special ruler, showing Roman oncia andmillimeters was created.

By analyzing the construction of the violin, certain importantnumbers were found to be missing, for example, the value of 63 mm.Most of the instruments showed this width, doubled, at the bridgeposition, and also the distances at the center of the f-holes, likewise,the value of 42 mm, which is the width of the fingerboard and the

width of the bridge, respectively.

These numbers could be found, by making a geometricsequence, multiplying one oncia 18.66 by the factor 3/2, the fifth orquint. We called this procedure quintisation.

S.R. Zopf / Journal of Cultural Heritage 27S (2017) S26–S33 S31

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Fig. 4. Violin scrolls of left the “Alard” Violin 1649, N. Amati, Cremona, WA1948.135.Ashmolean Museum, Oxford and right the “Emiliani”, A. Stradivari, Cremona, 1703,

ig. 3. Geometrical analysis of the “Gibson” violin, A. Stradivari, 1713, Cremona,rivate collection, all measurements in Roman oncia.

Thus: 18.66 × 1.5 = 28 × 1.5 = 42 × 1.5 = 63, etc.Furthermore, the value of 63 mm can also be found in the projec-

ion (side view) of the violin: the standard height of the top, backnd ribs is 16 + 15 + 32 = 63 mm. Adding the height of a standardridge, 32 mm would give the next step in the quintisation, 94.5 mmo 95 mm.

.2.4. The method of analyzing violins and templatesInitially, photographs of violins or violas were calibrated to their

rue size, and were transferred into autoCAD, a software used forechnical drawing. Then, whole or half number Roman oncia radiifor instance 3.5′′, 4′′, 5′′) were applied to the outline. Tolerances of.5 mm were allowed and the deviation was documented in per-entages. The distance of the centers of the radii defining the lowerr upper bout, and the body stop or the distance of the bridgerom the geometrical center, was measured. Finally, the distancef the centerline of the lower f-holes to the center was docu-ented, because this line was visible in all sketches of A. Stradivari,

egarding the construction of f-holes. The used radii were drawnver the picture of the analyzed violin and the values are recordedn Table 2.

Also several scrolls were analyzed and simple numbers orractions (fractions of a 1/2, a 1/3 and a1/4 were taken into con-ideration) of the Roman oncia were applied to their design (seeig. 4).

Templates of A. Stradivari and the parchment of Cozio di Salabueere also calibrated to their true size and visible compass marks

nd measurements were compared to the Roman oncia.

. Results and discussion

The width of the observed violins fits into a whole numberchedule. The mean value of 32 violins is 10.95′′, being very close

private collection, all measurements in Roman oncia.

to 11′′, the difference of 0.05′′ represents 0.93 mm and can beexplained by of the shrinking of wood or is caused by the workingprocess.

The length of the violin is observed to be 19′′. Although there areseveral violins measuring 19.5′′ the average of all violins is exactly19.0′′.

The main reference points of the violin shape could be con-structed in the following manner: the maximum width of the upperbout is constructed by using the vertex of a 6′′ circle, the lower boutis manifested by drawing a horizontal line to the vertex of a 5.5′′

circle, the narrowest point of the violin is 1′′ from the center. Theradii forming the upper and lower bout, are in most cases, 3.5′′ and4′′ or, a combination of both.

Mensur (body stop) could be detected in the first few steps of theconstruction. Different from most other constructions, the positionof the bridge or body stop is found very easily, being in 16 casesexactly one oncia from the center, and in four others cases 0.9′′

from the center. The mean value is 0.9′′. Only the instrument ofMaggini reveals a body stop of 0.5′′ down the center.

A step by step construction for the violin was developed. It couldbe seen that the main values stay relatively the same, only smallvariations in the construction of the corners from different types ofviolins could be seen. More detailed findings will be presented inanother paper.

In 15 of 32 cases the distance of the center of the circles formingthe upper and lower bouts are in a ratio of 2:3. In 10 cases it isexactly 2′′: 3′′. This value corresponds to the tuning of the violin,the fifths, and may have been chosen deliberately.

The difference between the value Najmon had stated(18.66 mm) and the Roman oncia of the 18th century (18.62 mm)can be, in our opinion, omitted. In relation to the maximum widthof a violin, 11′′, the difference is 205.26 − 204.82 = 0.44 mm and lieswithin the boundaries of shrinkage and craftsmanship.

The main sections of scrolls could be explained by using theRoman oncia and its fractions.

The construction of the f-holes could be explained by using thequintization, giving the distance of the line, as seen on the templatesof Stradivari, from the center to the lower f-hole, 42 mm. The f-holes

of Jakob Stainer are very different (only 34 to 37 mm) than those ofCremonese luthiers. Nevertheless, the mean value of all violins is40.6 mm.

S32 S.R. Zopf / Journal of Cultural Her

Fig. 5. Two paper templates from the Stradivari workshop. Neck and scroll pattern ofthe cello “A”, Museo del Violino, MS No. 308, Cremona, all numbers in Roman oncia,left part describes the back part of a cello scroll, (template is enlarged) distancesolP

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f circles measured from center to center, allowance 0.5 mm, red lines = 1′′ , purpleines = 1.33′′ .icture by Stewart Pollens [19].

The application of the Roman oncia could be found directly onarious templates of A. Stradivari (see Fig. 5). The distances of theenters of the circles for the volute template are 1′′ and 1.33′′. Theadii used for the scroll of a violoncello are 2.5′′ and 3.5′′, the marksf the compass in the middle section of the neck template, probablyhe width of the neck, is 4′′. The diameter for the sound hole of auitar is 3′′, just to mention but a few examples.

The parchment attributed to Cozio di Salabue, shows three con-entrical rings at a distance of 18.5, 19.0 and 18.6 mm from eachther, not from the geometrical center, but from the position of theound post and bass bar (see Fig. 1).

The use of the Roman oncia could be observed in several Bresciannstruments. These findings are beyond the scope of this paper and

ill be presented in another publication.

. Conclusion

The possible usage of the Roman oncia could be identified

n most instruments of the Cremonese luthiers, namely Andreamati, Brothers Amati, Nicoló Amati, Antonio Stradivari, Andreauaranieri, Guarnieri del Gesú, and others like Jakob Stainer, fromyrol and Paolo Maggini from Brescia. The preference of whole

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itage 27S (2017) S26–S33

numbers for the total width and length of the violin is evident,since the mean value of 32 violins is 10.95′′ for the width and 19.0′′

for the length.Also the main radii, used for the outline of the violin can be

expressed as a whole number or half number values of the Romanoncia. (4′′ and 3.5′′) Furthermore, the use of this unit is very likelyin the design of scrolls and templates of scrolls of violins.

On several other items such as a parchment from Cozio di Salbueand templates from Stradivari, circles using whole number Romanoncia could be found.

The new approach to construct a violin using the Roman onciaand concentrical circles in whole number distances from its geo-metric center, could be applied on all investigated violins of theCremonese luthiers. The construction itself is simple to remem-ber and only requires the application of a compass and a ruler.The violins of Stainer were included in this research, too, but hisinstruments seemed to be most deviant in the design of the f-holes.The likely usage of the Roman oncia was also noted in the Brescianinstruments, but this topic will need further investigation.

Acknowledgments

I want to thank all my students of the luthiers school in Hall-statt, especially Daniel Bierdümpfl, Hanna Haslinger, Markus Knoll,Mariella Schöngruber, Johannes Mayer, Sebastian Gabler and Bern-hard Fischer for their incredible amount of patience and theirpassionate support and interest.

My college Felix Winkler for supporting our work so self-lessly and Brian Leonard for his enthusiastic proofreading. AndDr. Michael Malkiewitsch for his support regarding ancient mea-surements, and Dr. Alfons Huber for teaching me those fascinatingtechniques.

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S.R. Zopf / Journal of Cultur

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