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<div> Thought this interesting and in depth. Pianos are not violins but spruce wood is a resonant material and they both use it in different forms and species. The discussion over time on the list has been heading in the direction of wood quality doesn't matter that much and may be that's true, except for weight and density issues.. It got me thinking that becasue mass, and stiffness are critical, both quality of wood and density seem linked.<br>
Del proposed the idea that density/ weight have yet to be explored very clearly. This is at least a scientific study looking at weight and density and the comparative density between early and late wood of modern and ancient instruments. The densities are proving to be very interesting and very different between the two version (new vs. old) The density of the early and late woods is far more similar in the older instruments than in the newer. Typically late/winter wood is heavier than spring wood.<br>
I heard a Guarneri myself, close up an personal last fall in a dead hotel like dining room, similar to the recent exhibit hall. It was a fantastic sound, full bodied and projecting in a very un-acoustic space with acoustic ceiling tiles acting as a sound sponge. It was played by the former first chair of the Modesto Symphony, Mark Jordan<br>
It was an impressive sound<br>
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<h1 rel="dc:type" href="http://purl.org/dc/dcmitype/Text">A Comparison of Wood Density between Classical Cremonese and Modern Violins</h1>
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<div>Classical
violins created by Cremonese masters, such as Antonio Stradivari and
Giuseppe Guarneri Del Gesu, have become the benchmark to which the sound
of all violins are compared in terms of their abilities of
expressiveness and projection. By general consensus, no luthier since
that time has been able to replicate the sound quality of these
classical instruments. The vibration and sound radiation characteristics
of a violin are determined by an instrument's geometry and the material
properties of the wood. New test methods allow the non-destructive
examination of one of the key material properties, the wood density, at
the growth ring level of detail. The densities of five classical and
eight modern violins were compared, using computed tomography and
specially developed image-processing software. No significant
differences were found between the median densities of the modern and
the antique violins, however the density difference between wood grains
of early and late growth was significantly smaller in the classical
Cremonese violins compared with modern violins, in both the top (Spruce)
and back (Maple) plates (p = 0.028 and 0.008, respectively). The mean
density differential (SE) of the top plates of the modern and classical
violins was 274 (26.6) and 183 (11.7) gram/liter. For the back plates,
the values were 128 (2.6) and 115 (2.0) gram/liter. These differences in
density differentials may reflect similar changes in stiffness
distributions, which could directly impact vibrational efficacy or
indirectly modify sound radiation via altered damping characteristics.
Either of these mechanisms may help explain the acoustical differences
between the classical and modern violins.</div>
</div>
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<div class="authors"><span rel="dc:creator"><span>Berend C. Stoel</span></span><sup><a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#aff1">1</a></sup><sup><a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#cor1" class="fnoteref">*</a></sup>, <span rel="dc:creator"><span>Terry M. Borman</span></span><sup><a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#aff2">2</a></sup></div>
<div class="affiliations"><a name="aff1" id="aff1"></a><strong>1</strong> Department of Radiology, Division of Image Processing, Leiden University Medical Center, Leiden, The Netherlands, <a name="aff2" id="aff2"></a><strong>2</strong> Borman Violins, Fayetteville, Arkansas, United States of America</div>
<div class="abstract"><a id="abstract0" name="abstract0" title="Abstract"></a><h2>Abstract <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#top">Top</a></h2>
<div>Classical
violins created by Cremonese masters, such as Antonio Stradivari and
Giuseppe Guarneri Del Gesu, have become the benchmark to which the sound
of all violins are compared in terms of their abilities of
expressiveness and projection. By general consensus, no luthier since
that time has been able to replicate the sound quality of these
classical instruments. The vibration and sound radiation characteristics
of a violin are determined by an instrument's geometry and the material
properties of the wood. New test methods allow the non-destructive
examination of one of the key material properties, the wood density, at
the growth ring level of detail. The densities of five classical and
eight modern violins were compared, using computed tomography and
specially developed image-processing software. No significant
differences were found between the median densities of the modern and
the antique violins, however the density difference between wood grains
of early and late growth was significantly smaller in the classical
Cremonese violins compared with modern violins, in both the top (Spruce)
and back (Maple) plates (p = 0.028 and 0.008, respectively). The mean
density differential (SE) of the top plates of the modern and classical
violins was 274 (26.6) and 183 (11.7) gram/liter. For the back plates,
the values were 128 (2.6) and 115 (2.0) gram/liter. These differences in
density differentials may reflect similar changes in stiffness
distributions, which could directly impact vibrational efficacy or
indirectly modify sound radiation via altered damping characteristics.
Either of these mechanisms may help explain the acoustical differences
between the classical and modern violins.</div>
</div>
<div class="articleinfo">
<div><strong>Citation: </strong>Stoel BC, Borman TM (2008) A Comparison of Wood Density between Classical Cremonese and Modern Violins. PLoS ONE 3(7):
e2554.
doi:10.1371/journal.pone.0002554</div>
<div><strong>Editor: </strong>Ananth Grama, Purdue University, United States of America</div>
<div><strong>Received:</strong> March 18, 2008; <strong>Accepted:</strong> May 30, 2008; <strong>Published:</strong> July 2, 2008</div>
<div><strong>Copyright:</strong>
© 2008 Stoel, Borman. This is an open-access article distributed under
the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided
the original author and source are credited.</div>
<div><strong>Funding:</strong> The authors have no support or funding to report.</div>
<div><strong>Competing interests:</strong> The authors have declared that no competing interests exist.</div>
<div><a name="cor1"></a>* E-mail: <a href="mailto:B.C.Stoel@lumc.nl">B.C.Stoel@lumc.nl</a></div>
</div>
<div id="section1"><a id="s1" name="s1" title="Introduction"></a><h3>Introduction <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#top">Top</a></h3>
<div>For the past 300 years, the violins of <span class="note public minrcrctn" title="User Annotation"><a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#" class="bug public" id="annAnchor1" title="Click to preview this note"><span>1</span></a>Antonio Stradivari (1634–1737)</span>
and Giuseppe Guarneri del Gesu (1698–1744) have excelled in molding a
many-nuanced sound that seems to better express the intent of composers
and musicians. These classical Cremonese violins have become the
benchmark to which all violins are compared. Presently, many believe
that violin craftsmanship is at its most advanced point since the days
of the Cremonese luthiers, and yet instruments produced today do not
match the classical instruments in their abilities of expressiveness and
projection. It remains unclear what has kept them, for such a long time
and through such changing musical needs, as the most sought after.</div>
<div>Research into the
production of high quality sound has focused on a wide range of
variables, such as the arching design and contours <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone.0002554-Sacconi1">[1]</a>, plate thickness <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone.0002554-Loen1">[2]</a>, the impact of varnish layers <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone.0002554-Schelling1">[3]</a>, <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone.0002554-Schleske1">[4]</a>,
as well as the various elements of set-up, such as the angle of the
neck, the impact of the fingerboard and the angle of the strings passing
over the bridge. Extensive work has been done searching for the ideal
wood properties <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone.0002554-Wegst1">[5]</a>–<a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone.0002554-Bucur1">[9]</a>,
although none corresponding exactly to known Cremonese wood properties
as most tested samples have been of significantly higher median density
than those found to be the case in this study.</div>
<div>Tracheid clusters,
produced during annual growth cycles of the tree, create the prominent
light/dark grain lines in wood. Early growth wood, created during
spring, is primarily responsible for water transport and thus is more
porous and less dense than late growth wood, which plays more of a
structural support role <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone.0002554-Butterfield1">[10]</a>,
of much more closely packed tracheids. Wood is an orthotropic material,
having differing mechanical properties in three directions: along the
grain, across the grain, and slabwise (circumferentially) <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone.0002554-ZinkSharp1">[11]</a>.
The differences in density between early and late growth wood may
impact the detailed vibrational behavior, either directly or through
altered stiffness or damping characteristics due to these variations.
The complex three-dimensional shape of the violin body means that
vibration within the audio range involves extensional, bending and shear
deformations of the wooden plates involving all three directions.
Researchers have commented on wood selection preferences based on these
differentials <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone.0002554-Bucur1">[9]</a>,
although detailed data are lacking on fine instruments. Wood density is
difficult and invasive to measure directly, as an isolated part of the
instrument, wrapped in a waterproof container, must be immersed in water
to estimate its volume, and the density is calculated by dividing its
weight by this volume <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone.0002554-Schleske2">[12]</a>.
Furthermore, this technique does not provide data on density
differentials. Computed Tomography (CT) has been used by other
researchers <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone.0002554-Gattoni1">[13]</a>–<a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone.0002554-Skolnick1">[15]</a> primarily for visual analysis, without fully employing its ability to quantify density or density differentials.</div>
<div>Here we examine the
wood density of five classical Cremonese violins; three by Giuseppe
Guarneri del Gesu and two by Antonio Stradivari, using quantitative CT
densitometry, a rapid and non-invasive technique usually applied in a
medical setting <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone.0002554-Stoel1">[16]</a>.
The results from these classical violins were compared to those of
eight contemporary violins, made by T. Borman, A.T. King and G. Rabut (<a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone-0002554-t001">Table 1</a>),
in order to determine whether objective measurements of material
properties can explain the historical consensus on the differences in
quality of sound between classical Cremonese and modern violins. At the
end of this article we will outline in detail our methodology.</div>
<div class="figure"><a name="pone-0002554-t001" id="pone-0002554-t001" title="Click for larger image " target="_blank" href="http://www.plosone.org/article/slideshow.action?uri=info:doi/10.1371/journal.pone.0002554&imageURI=info:doi/10.1371/journal.pone.0002554.t001"><img src="http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0002554.t001&representation=PNG_S" alt="thumbnail" class="thumbnail" align="left" border="1"></a>
<div><strong><a target="_blank" href="http://www.plosone.org/article/slideshow.action?uri=info:doi/10.1371/journal.pone.0002554&imageURI=info:doi/10.1371/journal.pone.0002554.t001"><span>Table 1. </span></a> <span>Table of instruments studied.</span></strong></div>
<span>doi:10.1371/journal.pone.0002554.t001</span></div>
</div>
<div id="section2"><a id="s2" name="s2" title="Results and Discussion"></a><h3>Results and Discussion <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#top">Top</a></h3>
<div>The
violins were scanned at Mount Sinai Hospital in New York City, USA,
using a multi-detector row CT scanner (Sensation Cardiac 64, Siemens,
Germany). These scans produced 3-dimensional data sets of approximately
1200×512×512 voxels for each violin.</div>
<div>A dedicated computer
program was developed to automatically detect the superior and inferior
surface of the top and back plates. From these surfaces, the local plate
thickness, median wood density and density differential were
calculated, as discussed below. Additionally, the volume of the sound
box (luminal volume) was calculated (<a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone-0002554-t001">Table 1</a>).</div>
<h4>Plate thickness</h4>
<div>From the
vertical distance between the superior and inferior surface, a thickness
map (0–5 mm) was constructed, which represents the plate thickness at
each location. <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone-0002554-g001">Figures 1A and 1B</a>
show the thickness maps of the top and back plates, respectively, with
the classical violins displayed on the bottom and the modern violins on
the top row of the figures. We have adopted the medical model of
anonymity. These thickness maps clearly show differences between the
violins as well as various repairs. The bass bar could be discerned as a
slight thickening in the top plate, since the computer program could
not perfectly separate the two wood pieces. The antique plates, with the
exception of #3, had very little repair, while resolution was such that
even the paper labels with the makers' name could be discriminated (see
the rectangular thickening in the back plates, near the left c-bout in <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone-0002554-g001">Figure 1B</a>).
Note that the high X-ray absorption by the metal in the fine tuner on
the e-string causes image reconstruction artifacts. The Moiré-like
pattern is caused by the somewhat limited resolution of the scanner.
Loen <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone.0002554-Loen2">[17]</a>
has done extensive thickness mapping of violins although a comparative
analysis of findings is beyond the purview of this article and our maps
are included solely on the basis of the intrinsic link between density
and thickness.</div>
<div class="figure"><a name="pone-0002554-g001" id="pone-0002554-g001" title="Click for larger image " target="_blank" href="http://www.plosone.org/article/slideshow.action?uri=info:doi/10.1371/journal.pone.0002554&imageURI=info:doi/10.1371/journal.pone.0002554.g001"><img src="http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0002554.g001&representation=PNG_S" alt="thumbnail" class="thumbnail" align="left" border="1"></a>
<div><strong><a target="_blank" href="http://www.plosone.org/article/slideshow.action?uri=info:doi/10.1371/journal.pone.0002554&imageURI=info:doi/10.1371/journal.pone.0002554.g001"><span>Figure 1. </span></a> <span>Thickness maps of the top (A) and back plates (B).</span></strong></div>
<div>The
contemporary violins are presented on the top row, and the antique on
the bottom row. The violins have been anonymised. Scales are given in
mm. The fourth instrument on the upper row is a viola, which typically
is thicker than a violin (image size has been reduced to match that of
the violins).</div>
<span>doi:10.1371/journal.pone.0002554.g001</span></div>
<h4>Median density</h4>
<div>The computer
program defined an intermediate layer of the violin plates, which was
centered exactly between the superior and inferior surfaces. From this
intermediate layer, a density map was created, in which the physical
density was calculated at each location within the plates. <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone-0002554-g002">Figures 2A and 2B</a>
show the detailed density maps of the top and back plates,
respectively. The top and back plates differ in density, as top plates
are made from spruce (<em>Picea abies</em>) and the rest of the instrument, including the back plate, is made from maple (<em>Acer Platanoides</em>).
Repair work was clearly visible in the top plates, as indicated by the
regions of increased density. Hide glue, used exclusively for violin
repair, has a higher density than wood and saturates into the adjacent,
undamaged material, thus increasing localized density readings. From
this density map, the median density was calculated at five standardized
regions of interest (ROI); on the left and right side of the upper and
lower bout, and one at the centre (see <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone-0002554-g003">Figure 3</a>);
care was taken to avoid regions of repair work. No significant
differences were found between the median densities of the modern and
the antique violins (two-tailed Mann-Whitney U test: p = 0.884 and
0.143, for the top and back plate, respectively).</div>
<div class="figure"><a name="pone-0002554-g002" id="pone-0002554-g002" title="Click for larger image " target="_blank" href="http://www.plosone.org/article/slideshow.action?uri=info:doi/10.1371/journal.pone.0002554&imageURI=info:doi/10.1371/journal.pone.0002554.g002"><img src="http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0002554.g002&representation=PNG_S" alt="thumbnail" class="thumbnail" align="left" border="1"></a>
<div><strong><a target="_blank" href="http://www.plosone.org/article/slideshow.action?uri=info:doi/10.1371/journal.pone.0002554&imageURI=info:doi/10.1371/journal.pone.0002554.g002"><span>Figure 2. </span></a> <span>Density maps of the top (A) and back plates (B).</span></strong></div>
<div>The
contemporary violins are presented on the top row, and the classical
Cremonese on the bottom row. The violins have been anonymised. Scales
are given in kg/m3. The central violin in the lower row has had more
repair work than the other antique violins as evinced by reduced
thickness (<a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone-0002554-g001">Figure 1</a>.)
and increased densities. The dark areas at the centre of the lower
third of all violin tops are metal artifacts from the string ends. The
dependency of the measured density on plate thickness was eliminated in
the quantitative analysis.</div>
<span>doi:10.1371/journal.pone.0002554.g002</span></div>
<div class="figure"><a name="pone-0002554-g003" id="pone-0002554-g003" title="Click for larger image " target="_blank" href="http://www.plosone.org/article/slideshow.action?uri=info:doi/10.1371/journal.pone.0002554&imageURI=info:doi/10.1371/journal.pone.0002554.g003"><img src="http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0002554.g003&representation=PNG_S" alt="thumbnail" class="thumbnail" align="left" border="1"></a>
<div><strong><a target="_blank" href="http://www.plosone.org/article/slideshow.action?uri=info:doi/10.1371/journal.pone.0002554&imageURI=info:doi/10.1371/journal.pone.0002554.g003"><span>Figure 3. </span></a> <span>Regions of interest (ROI's) on violin plates.</span></strong></div>
<div>Five
different ROI's of 100×100 pixels were defined, carefully avoiding
repair work. The same areas were taken from the top and back plates.</div>
<span>doi:10.1371/journal.pone.0002554.g003</span></div>
<div>Apart
from genetic factors, the overall density of wood is influenced most
significantly by the microclimate at the tree's location. A tree growing
in a cool area with limited direct solar exposure and little access to
water supplies or quality soil will grow slowly and have relatively high
overall densities. On the other hand, a tree of the same genetic makeup
would grow faster with lower overall densities, if it were located in a
more hospitable microclimate, i.e. with adequate solar access, a
nutrient laden soil, sufficient quantities of water, a relatively flat
local, and without traumatic events causing formation of very dense
wood. The former conditions have historically been thought to create
high quality tone wood although our findings indicate that the latter
conditions will more closely mimic the densities found in this study. As
we did not find significant differences in median density between these
particular classical and modern violins, these large-scale factors
would not be relevant to the sound quality difference between the
classical Cremonese and the modern violins.</div>
<div>A violin
produces sound by transforming the energy provided by the musician into
perturbations of the air. At lower frequencies, below ~800 Hz, the
majority of these waves are produced by the violin acting as a whole.
Above this frequency range, specific areas of the instrument vibrate to
produce sound. At the current state of understanding, most of these
areas are located on the top plate. For this reason, our discussion is
primarily focused on spruce wood.</div>
<div>Even after a
violin is built, its wood density could vary, since wood is a
hygroscopic material and changing relative humidity (due to temperature
as well as water vapor levels) would change the measured density. In
this context, however, this is not germane, since the studied violins
are never exposed to extreme humidity variations due to the conditioned
air environments of modern musical settings.</div>
<div>As there was
little to no difference in the median wood densities between the modern
and the classical Cremonese violins, it may be assumed that modern wood
selection practices are similar to those employed in the 1700s.</div>
<h4>Density differentials</h4>
<div>In order to
determine the amount of late and early growth grains in the wood of each
violin plate, we calculated the histogram of densities from each ROI (<a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone-0002554-g003">Figure 3</a>).
Wood density may vary each 0.1 mm, which is beyond the resolution of
CT. Therefore, a density value of the early and late growth grains could
not be determined definitively. A surrogate grain density measure was
defined instead by the spread of the bimodal density distribution. The
90<sup>th</sup> and the 10<sup>th</sup> percentile points were
considered representative of the density of the early and late growth
grains, respectively, and the difference between these percentile points
was denoted as the ‘density differential’.</div>
<div>In <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone-0002554-g004">Figure 4</a>,
the density differential is plotted against the median density,
averaged over all ROIs, which were compared using the two-tailed
Mann-Whitney U test. The density differential was significantly lower in
the classical Cremonese violins as compared to the modern violins both
in the top and back plate (p = 0.028 and 0.008, respectively), meaning
that the densities of early and late growth wood were closer together,
in the classical violins. The mean density differential (SE) of the top
plates of the modern and classical violins were 274 (26.6) and 183
(11.7) gram/liter, respectively. For the back plates, the values were
128 (2.6) and 115 (2.0) gram/liter, respectively. <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone-0002554-g004">Figure 4</a>
shows four clear “clusters” whereby the wood of the instruments is
delineated into two groups: the old and new top plates and the old and
new back plates.</div>
<div class="figure"><a name="pone-0002554-g004" id="pone-0002554-g004" title="Click for larger image " target="_blank" href="http://www.plosone.org/article/slideshow.action?uri=info:doi/10.1371/journal.pone.0002554&imageURI=info:doi/10.1371/journal.pone.0002554.g004"><img src="http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0002554.g004&representation=PNG_S" alt="thumbnail" class="thumbnail" align="left" border="1"></a>
<div><strong><a target="_blank" href="http://www.plosone.org/article/slideshow.action?uri=info:doi/10.1371/journal.pone.0002554&imageURI=info:doi/10.1371/journal.pone.0002554.g004"><span>Figure 4. </span></a> <span>Density differential versus median density of all top and back plates.</span></strong></div>
<span>doi:10.1371/journal.pone.0002554.g004</span></div>
<div>Due
to the increased repair work on one of the classical instruments, it
was necessary to choose the ROI's carefully so as to reflect the true
wood density, not that of the repair. In order to realistically compare
wood densities, the inclusion criteria for a modern instrument was that
the woods were of known European provenance and that they were in a
“natural state”, i.e. not treated in any way to alter its material
properties. When we noticed the one modern top and back plate of
extremely low differential, we contacted the maker who reviewed his
records and found that he had acquired these pieces of wood from a
supplier who occasionally treated his wood prior to sale. When
questioned, the supplier could not be certain if these particular pieces
were treated or not. If these plates of unknown origin were removed
from the analysis, the differences of the density differential of the
top plates between the old and new would be even more striking. In our
test pool of spruce tone wood samples we found a similar pattern i.e.
new wood having median densities in the same general range and density
differentials much higher than that of the Cremonese violins tested.</div>
<div>Spruce density
may vary within a tree by as much at 5–8% due to its vertical location
within the trunk. Within same tree specimens density is typically lowest
between 3 and 6 meters of height. Below 3 meters to ground level there
is a slight increase and above 6 meters of tree height density increases
in a fairly linear continuum to the apical bud <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone.0002554-Saranp1">[18]</a>.
Since the classical median densities are at the very low end of those
found in spruce, this region would provide the closest approximation
within individual samples. Additionally, the distance from the pith
(centre of the tree) to the perimeter is a well-identified source of
density variations within the same tree specimens and in most species,
including <em>Picea abies</em>, density typically decreases with
distance outwards from the pith. This decrease in density has been found
to be due to a reduction in early wood density as well as a reduction
in late wood proportion and may amount to 15–20% density variations from
pith to perimeter <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone.0002554-Koubaa1">[19]</a>.
Taken together the north/south (sample height) and east/west (pith to
perimeter) localized impacts can amount to an almost 25% density
variation within the same tree.</div>
<div>Widths of the
individual growth rings are yet another factor influencing wood density
that has been well documented to date, although disagreement exists on
the quality of this relationship. Growth Ring Width (GRW) in Norway
spruce has been shown to have a negative correlation with average
density <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone.0002554-Wilhelmsson1">[20]</a>
and therefore a non-linear relationship with greater reductions in
basic density when the ring widths decrease to 2–3 mm and lesser overall
reductions with increasingly wider ring widths. Giordano <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone.0002554-Giordano1">[21]</a>
on the other hand, found a relatively linear relationship for these
same parameters. Another study, specifically targeted at violin tone
wood <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone.0002554-DiBella1">[22]</a>,
did not find a linear relationship and their experimental data pool of
300 samples showed no apparent pattern in density distributions vs. GRW.
Their sample ring spacing was however relatively limited, varying only
from 0.5 mm to 2 mm, whereas Giordano extended this range to 4 mm (the
maximum ring spacing usually found in violins is 2.5 mm to 3 mm; in
violas 3 mm to possibly 4 mm and in cellos this can reach 5 mm).
Saranpää and Giordano concur that GRW can account for min/max density
variability of ~40%, although arriving at their respective results in
different manners <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone.0002554-Saranp1">[18]</a>, <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone.0002554-Giordano1">[21]</a>. The current state of wood biology delves very little into density differential with the exception of Koubaa <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone.0002554-Koubaa1">[19]</a> using x-ray densitometry to redefine Mork's index (the transition from early wood to late wood).</div>
<h4>Conclusions</h4>
<div>The density
differentials found in this study may contribute to the generally
recognized superior sound production of classical Cremonese violins.
Within the violin making tradition there have been many reported
‘secrets’ of the Cremonese makers although usually with little or no
supporting documentation. Sporadically, reference is made to the wood
treatment referred to as ‘ponding’, whereby wood submerged in stream
water (to facilitate transportation or to alter the properties of the
wood intentionally) is responsible for the classical Cremonese sound. It
has been documented <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone.0002554-Eriksson1">[23]</a>
that ponding does alter wood properties significantly, by causing
decomposition of various wood elements depending on the particular
bacteria or fungus introduced into the wood. Although data on density
alteration are not currently available, it is reasonable to assume that
this degradation would result in lowered densities; how this impacts
density differential would be dependant on the specific treatment. It
has been shown that the wood of the classical Cremonese instruments was
likely not ponded <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone.0002554-Barlow1">[24]</a>.
However, this does not rule out bacterial or fungal attack as a means
of altering new wood to more closely match the material properties of
the Cremonese wood. As mentioned earlier, one back and one top plate of
the new instruments may have been treated and if this were indeed the
case, the treatment used by the supplier would have been ponding.
Another technique, referred to as “stewing” wood has been mentioned
whereby wood is boiled in different solutions to achieve alterations of
density although there is no published data on what this process is
actually doing to the wood. Bucur has shown that time plays a role in
altering wood properties by decomposition and loss of hemicellulose,
thereby resulting in lower density <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone.0002554-Bucur1">[9]</a>
and a priori an alteration of differential, which may also explain our
results. Fuming with nitric acid or ammonia are treatments that have
been used throughout the years by instrument makers and it is a
reasonable assumption that the destructive properties of these agents
would lower the density and change the differential depending on which
grains, early or late, are most affected. Many other possibilities have
been proposed over time, but these are the only ones directly related to
density that we are aware of.</div>
<div>In summary,
our results clearly document basic material property differences between
the woods used by the classical Cremonese and contemporary makers.
Although at this point we can do no more than speculate as to the cause,
these findings may facilitate replicating the tonal qualities of these
ancient instruments.</div>
</div>
<div id="section3"><a id="s3" name="s3" title="Materials and Methods"></a><h3>Materials and Methods <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#top">Top</a></h3>
<div>As
CT densitometry depends on a wide range of variables, settings were
optimized for the highest sensitivity in distinguishing different wood
densities. We analyzed the histograms from four test plates (two top
plates and two back plates) and selected the settings, which produced
bimodal histograms with the highest separation. The final image
acquisition protocol was defined for a multi-detector row CT scanner: 80
kVp, effective mAs of 53, collimation 32×0.6 mm, 1 sec. rotation time,
512×512 matrix, 0.6 mm slice thickness, 0.3 mm increment with a
reconstruction filter B50s.</div>
<div>Volumetric analysis
was performed with PulmoCMS (Medis Specials BV, Leiden, the Netherlands)
and a separate computer program was developed for wood densitometry on a
Matlab platform (Matlab, version R2007a, The Mathworks, USA), with its
image processing toolbox. The superior and inferior contours were
detected in each axial slice by a minimal costs algorithm, using a Sobel
edge detector. By stacking all contours, a curved multi-planar
reformatted (MPR) image was constructed. No user interaction was needed
in the analyses of the violins.</div>
<h4>Validation</h4>
<div>Constancy of
the CT scanner was monitored using nine test pieces of maple and spruce.
The standard deviation of the differences was 7.5 kg/m<sup>3</sup> (1.8%) and 10.9 kg/m<sup>3</sup> (4.8%) for the median density and density differential, respectively.</div>
<div>Due to edge
enhancement during CT image reconstruction, density values were found to
be dependent on plate thickness (as illustrated by comparing <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone-0002554-g001">Figure 1</a> and <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone-0002554-g002">2</a>
in the main text). Therefore, the presented density values were
corrected for thickness, based on measurements from a different sample
set of 10 wood samples with thicknesses, ranging from 2 to 6 mm. The
measurements were corrected based on a mathematical model, in which the
dependency of the median density on plate thickness was estimated (see <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone-0002554-g005">Figure 5A</a>).
The correction was effective, since subsequently no correlation was
found between the final density values and the thickness of the plates
from all regions of interest (<a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#pone-0002554-g005">Figure 5B and 5C</a>).
As there was no significant difference in plate thickness between the
classical and modern violins (Mann-Whitney U test: p = 0.770 an 0.188,
for the top and back plate, respectively), plate thickness was not a
confounding factor in studying the differences in wood density.</div>
<div class="figure"><a name="pone-0002554-g005" id="pone-0002554-g005" title="Click for larger image " target="_blank" href="http://www.plosone.org/article/slideshow.action?uri=info:doi/10.1371/journal.pone.0002554&imageURI=info:doi/10.1371/journal.pone.0002554.g005"><img src="http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0002554.g005&representation=PNG_S" alt="thumbnail" class="thumbnail" align="left" border="1"></a>
<div><strong><a target="_blank" href="http://www.plosone.org/article/slideshow.action?uri=info:doi/10.1371/journal.pone.0002554&imageURI=info:doi/10.1371/journal.pone.0002554.g005"><span>Figure 5. </span></a> <span>Relation between thickness of the plate and median density.</span></strong></div>
<div>(A)
The relation was obtained from the central layer within five spruce and
five maple test plates. The curved lines show the mathematical models
fitted to this data. (B) The thickness-density relation from the
individual ROIs in the violins. (C) The thickness-density relation after
correction.</div>
<span>doi:10.1371/journal.pone.0002554.g005</span></div>
<div>To
test the accuracy of the thickness measurements of the plates, the same
wood samples were used as in the correction for the thickness
dependency. The measured values from CT were compared to the actual
thickness measurements using a micrometer on the actual pieces. A small
systematic difference was observed of 0.1 mm, which is a fraction of the
dimension of one pixel (0.4×0.6×0.6 mm), meaning that plate thicknesses
were slightly over-estimated with a constant magnitude, independent of
plate thickness.</div>
</div>
<div><a id="ack" name="ack" title="Acknowledgments"></a><h3>Acknowledgments <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#top">Top</a></h3>
<div>We thank the owners
of the classical and modern violins for making their instruments
available for this study, Mount Sinai Hospital in New York City, Maynard
High Ph.D and Jeffrey Doy for their radiological support, Aracelis
Perez, CT technician at Mount Sinai Hospital, for her patience and
dedication, Jeff Loen and Nora Cooper for their editorial assistance,
and Prof. J.H.C. Reiber, Prof I. Watt, Evan Davis Ph.D and Prof Jim
Woodhouse for their critical discussions and reviewing of the
manuscript.</div>
</div>
<div class="contributions"><a id="authcontrib" name="authcontrib" title="Author Contributions"></a><h3>Author Contributions <a target="_blank" href="http://www.plosone.org/article/fetchArticle.action?articleURI=info:doi/10.1371/journal.pone.0002554#top">Top</a></h3>
<div><span class="capture-id">Conceived
and designed the experiments: BS TB. Performed the experiments: BS TB.
Analyzed the data: BS TB. Contributed reagents/materials/analysis tools:
BS TB. Wrote the paper: BS TB.</span></div>
</div>
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