The Stradivari code
FIG. 1: Stradivarius violin mold with the G spot and circle arches.
One point, two arcs. Looking at Stradivarius molds, we observe this geometric construction: a point and two arcs (fig. 1). Why draw the same diagram on each mold? What would be the key to this still unsolved enigma? At first glance, these marks seem to be templates used to define the height of the ribs, as suggested by Simone Fernando Sacconi. This height is indeed correct, but then why was it drawn on each mold? A simple template could be placed anywhere, but this is not the case. The two arcs are drawn from the same precise center, but its location differs slightly for each mold (fig. 2).
FIG. 2: Average of GB and GC on 8 Stradivarius molds
Our research began several years ago by questioning this point 2.
To find the center of gravity of a mold, simply suspend it by one of the holes next to the corners and let a plumb line hang from it (fig. 3). The intersection of the plumb line with the median line indicates its center of gravity; we have called it point "G," and it is precisely at this point that the point drawn by Stradivarius is located.
No direct source proves that Stradivari used this method, but the hypothesis is consistent with the marks observed on his molds.
FIG. 3: Diagram of the mold suspended by one of the holes to locate point G
At the center: the G-spot. Around it: harmony.
To understand the symbolic significance of this point, let's take a detour through architecture and humanist thought.
It is commonly accepted that the architecture of the violin is similar to that of an ancient temple.
In the Middle Ages, cathedrals were built, their keystones distributing the thrust across the entire structure. We will see later the analogy between this keystone and the point we are studying.
Let's move further back in time to the Renaissance and allow ourselves to be guided by Leonardo da Vinci and the Vitruvian Man. We arrive at the era of the birth of the violin.
FIG. 4: Superimposition of Leonardo da Vinci’s “Vitruvian Man” and the diagram of the violin mold.
If we insert Leonardo da Vinci's Vitruvian Man into the diagram of a violin mold (fig. 4), it is positioned so that:
The arms and legs touch the limits of the circle, echoing the Vitruvian principle: the human body inscribed in a circle.
The navel coincides with a central point, which corresponds to our point G. In our study, point G corresponds to the intersection of the four corner ends of the violin.
In Renaissance thought, the navel is the natural center of the human body. Stradivarius, heir to this humanist tradition, could have applied a similar principle:
Replace the human body with the “body” of the violin.
Use a center (point G) as an absolute reference.
Dividing space by circles or musical ratios (third, fifth, octave), in the same way that Vitruvian Man inscribes anatomy in a proportional framework.
These associations should not be understood as exact acoustic equivalences, but as proportional analogies consistent with the mathematical and symbolic thinking of the time.
On the other hand, there is a small cone embedded in the instruments of the Amati family, which is located at the center of gravity (fig.5).
This point is also present on instruments in the Guarnerius family. (see study of point G2)
FIG. 5: Violin under construction, balanced on its center of gravity
Curiously, this cone is not present in Stradivarius violins, even though they were made in the Amati workshop. This leads us to the following question: Could there be a link between the small Amati cone and the dot marked on the Stradivarius molds?
And yes, this point on the Stradivarius molds is indeed located at the center of gravity of the mold.
This point could be considered the keystone of the violin.
It is well known that the artisans of Amati's time did not work with the metric system, but used standard measurements that varied from city to city. In Cremona, the unit of measurement was the braccio, equivalent to 483.5 mm³.
When we take the measurements of the violin, we find that the distance from the top nut to the bottom nut is equivalent to one braccio (fig. 6).
FIG. 6: 1 braccio, from nut to nut, of which 2/3 is for the vibrating string.
The GB and GC radii measure 30.2 mm and 32.2 mm respectively.
The following reports can be considered:
- The large radius 32.2, equivalent to 1/15 of the braccio 483.5 mm
It is also in a major third relation with the vibrating string (322/10) by the ratio (5/4=10/8)
and in octave relation with it (322/10) by the ratio (2/1=10/5)
(This same principle is observable in the positioning of the violin’s ankles).
- The small radius 30.2, equivalent to 1/16 of the braccio 483.5 mm, is in octave relation (2/1=16/8) with it
These rays reported on the vaults from the center of gravity allow to locate the modal zones of thirds and octaves.
Since each model is slightly different, the center of gravity must be recalculated for each mold. This may be an explanation of Stradivarius' need to mark one point and two arcs of a circle on each of his molds.
The practical method for the violin maker would be to postpone these circles on the vaults to define modal zones of thirds and octaves from and around the G-point, and to guide the thickening of backs and tables.
One could consider the braccio as a geometric unit as well as a vibrant entity on which all the violin is built.
Thus, the fractions 1/16 (GB) and 1/15 (GC) are not "the third" or "the fifth" properly speaking, but proportional subdivisions of the braccio that agree with an ancient thought. In this perspective, Stradivarius could have used these arcs of a circle as concrete geometric-acoustic landmarks, while inscribing his work in a culture of proportions linking forms, numbers and sound.
In our study The well-harmonized mussel,7 we found that the vibrating string was equal to 2/3 of the braccio, or a fifth of the braccio (fig. 6).
The tracing of the G-point and the arcs of a circle could be compared with the Pythagorean theory of the monochord. Taking as the fundamental length the braccio ( 483.5 mm, assimilated to the length of the upper saddle – lower saddle), then its fifth, the vibrating length of the strings 322.5 mm the ratio 3/2 then becomes a possible starting point for tracing circles from the center of gravity of the background. The radii 32.2 mm and 30.2 mm then express elementary acoustic ratios in geometry (octave, fifth, third).
Note that 32.2 and 30.2 can also be obtained by the Pythagorean sequence of fifths, which reinforces the hypothesis of a geometric-musical coherence.
Thus, the lengths are neither arbitrary nor pure intervals, but marks linking the geometry of the instrument to sound consonances.
Any reading only acoustic or geometric would be reductive: the richness of the «stradivari code» resides in this articulation.
This approach links the work of Stradivarius to a tradition where the art of form is at the service of a science of resonance. The back and the table are not simple supports but vibratory co-actors integrated into the overall sound architecture of the instrument.
Workshop reflections.
In the same logic of proportional relationships, let’s bring the violin closer to another sound domain: campanology (or study of bells).
There is no absolute historical certainty to affirm that the luthiers of Cremona, including Stradivarius, deliberately adopted the principles of the art of the bell in the design of their instruments. However, many concrete clues suggest a deep acoustic relationship between these two areas of expertise.
Bells and violins, although belonging to different instrumental families, share fundamental characteristics: the organization of partials, or partial notes, the central role of vibratory modes (modal circles), or even the search for coherence between form, thickness, material and frequency. In both cases, the sound results from a finely controlled balance between geometry, mass and internal tension of materials.
At the end of the 17th century, knowledge related to the making of bells was well established and passed on between founders, artisans and musicians. These acoustic principles were part of a shared culture through the instrumental making workshops, including in Cremona.
We know that exchanges existed between sound professions, and it is plausible that analogies have nourished certain empirical approaches, without ever being codified.
Thus, when we observe the modal distributions on the tables and backgrounds of old violins, or even certain ratios of dimensions close to those used in the bells (thirds, fifths, octaves), the hypothesis of a campanary imprint in the acoustic architecture of the
violins becomes reasonable, if not demonstrable. It does not take away anything from the singularity of the violin, but illuminates differently the refinement both architectural and acoustic of the Italian master luthiers.
By way of conclusion.
The hypothesis that we present, based on the acoustico-geometric reading of the arcs of a circle traced on the moulds of Stradivarius, does not claim to provide a single or definitive explanation. It nevertheless proposes a coherent reading grid: that of an artisan who would have been able to organize the geometry of his instruments according to simple proportions in resonance with harmonic relationships (third, fifth, octave).
This approach sheds light on one of the possible reasons why Stradivarius' violins exhibit such remarkable sound richness and coherence. It does not close the research, but it opens a new track that connects geometry, music and acoustics in the art of lutherie.
Study carried out in collaboration with Jean Plétinckx
Brussels on October 12, 2025
André Theunis
Legal deposit Nr 2025/01300
Notarial study JADOUL, KMÉTABOLISME, GENICOT & DIERCKX
Notes:
The original molds are located at the Museo del Violino in Cremona.
Cf: Stewart POLLENS, , 1992.
François DENIS, Treatise on Lutherie, published by ALADFI, 2006.
Simone Fernando SACCONI, “Segreti” di Stradivari, Cremona, 1972.
2. André THEUNIS, The violin's "G" spot, 2008.
3. Official table of weights and measures published by royal decree of May 20, 1877.
4. This logic is similar to that already observed in the pegbox of Cremonese violins, and copied by later luthiers: the respective positions of the pegs are also in musical harmony, presenting thirds, fifths, and octaves.
(André THEUNIS and Gunnar GIDION, The fine-tuned universe, in The Strad, June 2019, p.67. https://www.wolf-tuner.com/peg-box-study?lang=en ).
Fig. 7: Stradivarius “Messiah”
5. Dividing a string into equal intervals produces pure chords :
- by 2: this is the higher octave compared to the entire string (ratio 2/1);
- by 3: this is the perfect fifth (ratio 3/2), meaning that we multiply the frequency of the fundamental by
3/2 to obtain that of the fifth.
- by 5: this is the major third (ratio 5/4).
These simple divisions follow the same tradition of simple integer ratios
(octave 2/1, fifth 3/2, third 5/4) used to link architecture and harmony.
6. Geometric-acoustic reading:
At Stradivarius, the same measurement (e.g., 30.2 or 32.2 mm) can be read as:
• as a geometric fraction of the braccio (483.5 mm),
• or as an acoustic ratio close to a musical interval.
7. André THEUNIS and Alexandre WAJNBERG, The well harmonized mold,
in The Strad, February 2022, pp. 48-53.
https://www.wolf-tuner.com/le-moule-bien-harmonis%C3%A9?lang=en