Dendrochronological Dating and Provenancing of String Instruments

Summary

The dendrochronological analysis of a stringed instrument requires inspecting the top plate, measuring the tree ring widths, establishing the chronology of the instrument, and dating through determining the end date-the year of the formation of the most recent tree ring.

Abstract

Dendrochronology, the science of dating tree rings in the wood, defines in which calendar year a particular tree ring was formed. The method can be used to determine the age and authentication of wooden musical instruments. We present a protocol describing how to perform a dendrochronological analysis on stringed instruments and how to interpret the dating. The protocol describes the basic steps in the analysis of top plates, which are usually made of Norway spruce (Picea abies) or, more rarely, silver fir (Abies alba). First, the top plate is carefully inspected, and then the tree ring widths are measured directly on the instrument using high-resolution images. After completing the measurements, a tree ring sequence of the instrument is created, and, in the next step, dating is performed with a number of reference chronologies of the tree species from different geographical areas and instruments. The specialists who date the instruments also invest work in creating reference chronologies. The dendrochronological report provides the dating of an instrument as a calendar year (end date), indicating the year in which the last (most recent) tree ring on the top plate was formed when the tree was still alive. The end date represents the terminus post quem, the year after which the instrument was made or before which it could not have been made. To estimate the year of manufacture, one must consider the time required for wood drying and storing and the number of tree rings removed during wood processing. This protocol is intended to help those commissioning such an analysis to better understand how the analysis is performed and how to interpret the dendrochronological reports in terms of the age, origin, maker, and authenticity of the instrument.

Introduction

The goal of this study is to present a protocol for the dendrochronological analysis of tree rings on the top plate of a wooden musical stringed instrument. Dendrochronology is used as a method to determine the age of the wood of the instrument by determining the year in which the youngest tree ring on the plate was formed and after which the instrument was made (or before which the instrument could not have been made).

Dating a musical instrument (such as a violin) is an important step in its authentication^1,2,3,4,5,6. It is a complex process that involves the year in which the instrument was made, as well as the maker or instrument-making school or geographical area. To do this, dendrochronology is often combined with other techniques, which include the study of the label on the instrument (which is often not reliable) and the inspection of the instrument and its parts such as the outlines, scroll, wood figure and aging, varnish, f-holes, and purfling (Figure 1). The authentication can only be done by experts^5,6,7.

Figure 1: The top of the violin and its parts. The wood of the top plate (also called the front plate, belly, or soundboard) made of Norway spruce (Picea abies) can be dated by dendrochronology. The characteristics and dimensions of other parts such as the scroll, f-holes, and purfling are studied by organologists and help to authenticate the instrument. Scale = 20 cm. Please click here to view a larger version of this figure.

Dendrochronology is the science of dating tree rings in the wood, also called annual rings, growth rings, or growth layers, which are formed every year in the trees of temperate zones. Dendrochronology clarifies in which calendar year a particular tree ring was formed. By dating the outermost and most recently formed tree ring just below the bark, the last year of a tree's life before it was cut down can be determined.

Dendrochronology is based on the principle that annual variations in tree ring width (and other characteristics) are largely influenced by the environment, especially the climate, in which the trees grow. When conditions are similar over an area, trees of the same species show similar tree ring variations from year to year⁸. This means that the tree ring series (i.e., the temporal sequence of tree ring widths over time) is similar for trees of the same species in the same area.

The dating of wooden instruments follows the principles used for dating historical objects. In most cases, it is based on measuring tree ring width, creating tree ring series of the same object, cross-dating (to determine their matching position), and averaging them into a floating chronology of an object showing the tree ring series in relative time^3,4,6.

Absolute dating (determining the calendar year of tree ring formation) is accomplished by cross-dating with one or more reference chronologies established for a particular tree species and geographic area^4,6. The reference chronologies must be based on the tree ring widths of a sufficient number of trees (replication) and should be long enough to cover the period of interest.

Dendrochronology is regularly applied to determine the age of stringed instruments such as violins, violas, and cellos^{1,9,10,11,12,13}. For stringed instruments, the wood of the top plates (also the front plate, belly, or soundboard) can be dated. They are usually made of Norway spruce (Picea abies) or silver fir (Abies alba)^4,6,13. The measurements must be made in a non-invasive way directly on the instrument or by using images. The measurements are usually made at different locations on the top plate to establish a sequence for the instrument that can be dated with reference chronologies.

Dating is the most critical step because a reference chronology must be available for the species, geographic area, and time period of the instrument being studied. Many chronologies are available at the International Tree Ring Data Bank (ITRDB)¹⁴, but only a few are of Norway spruce or silver fir from the region covering the period of interest⁶; therefore, dendrochronology laboratories put a lot of effort into constructing reference chronologies. The likelihood of dating increases if a network of chronologies is available, including those from exactly defined forest sites, dated instruments, and instrument collections from various manufacturers like the Stradivari, Guarneri, and Amati families from Italy^5,6,15,16, Jacob Stainer from Austria, as well as Joachim Tielke and members of the Hoffmann family from Germany^17,18,19. The fine historical instruments made by the manufacturers in the 16th century to 18th century are most prized by musicians and collectors, although the importance of many less-known makers is also growing^3,4,6,12.

Dendrochronology provides the end date, which must be considered the terminus post quem – the year after which the instrument was made. Dendrochronology is also used for dendroprovenancing, which helps to determine the geographic origin of the wood and to assign instruments to specific violin makers or violin-making schools^3,4,6.

The dendrochronological end date almost never coincides exactly with the year the instrument was made, and the latter must, thus, be estimated, which requires a lot of supporting information and cooperation between experts of different fields.

Protocol

1. Inspection and description of a stringed musical instrument - violin

NOTE: Violins are the most frequently investigated stringed instruments. Therefore, we describe the procedure on a violin.

1. Examine the instrument and all its parts. Take detailed photos of the front (top), back, side, scroll, and label along with the measuring scale for the final report and the archive (Figure 1).
2. Examine the top plate of the instrument to determine how it is constructed. If possible, remove the strings from the instrument to facilitate the analysis.
3. Check whether the top plate is made of one, two, or more parts and how they are joined together. Here, the procedure is described for a top plate made of two parts, which is the most common case.
4. On the radial board of the top plate (Figure 2A,C), examine the structure and orientation of the tree rings. They are seen as bands of annual growth layers, consisting of light-colored earlywood and darker latewood and delimited by the tree ring boundaries (Figure 2D).
5. Based on the location and transition of earlywood to latewood, determine which side is the bark and which side is the pith (Figure 2C,G). In most cases, the most recently formed tree rings are located at the joint in the center of the top plate (when it consists of two parts; Figure 2C,D,F). These are the rings that were the nearest to the bark when the tree was still growing (Figure 2D,G).
   NOTE: Since we need to look at the radial structure, the tree rings appear as bands and not rings. Nevertheless, the terms tree rings and tree ring width (TRW) are used in this protocol.

2. Selection of the locations for measurements on the musical instrument

1. Inspect the widest parts on each piece of the top plate.
2. Check for any damage, repairs, retouching, or dirt, and where the varnish is transparent enough to see the tree rings. If the instrument is opened (in the case of ongoing repairs or during restoration), measure the tree rings on the underside of the top plate, where no varnish is applied.
3. Select the area with the greatest number of tree rings and check if the boundaries between the rings can be recognized (Figure 2C,D). The measurements can only be correct if the wood structure is clearly visible.
4. Try to clearly see the tree rings that were near the bark as the tree was growing for an accurate identification of the end date (Figure 2D). Use a magnifying lens or stereo microscope for the observations.
5. Mark the measuring line in the direction from the bark to the pith. Equip it with a measuring scale (Figure 2C). Place the scale (for instance, a commercially available paper measuring tape) on the board for this purpose.

3. Capturing digital images

1. Capture images to measure the tree ring width with an image analysis system. Place the violin top plate side on the scanner and scan the parts selected for the tree ring measurement (Figure 2B). Select a resolution of 1,200 dpi or higher. Use a scanner that allows a high depth of field.
   NOTE: Scanning is not the only way to capture images. A camera or other equipment can be used as well. If several images have to be captured, they must be stitched together properly. It is also possible to measure the tree ring width directly on the violin with the aid of a microscope and a special measuring device (e.g., a measuring table). This is especially useful in cases of poor visibility of the structure and if observation under a stereo microscope lens is needed. In this case, the images are valuable for further control of the measurements and for the archive.
2. For editing the images, use a graphics editing program to check the quality of the image and adjust the color, brightness, and contrast to best see the annual growth rings and the boundaries between them. This step is useful when measuring tree rings with an image analysis system.
3. To store the images, save the images in an adequate format (.tiff, .jpg).

4. Measurement of tree ring width

1. Start an image analysis system, preferably one designed for the automatic and manual detection of tree rings and the measurement of TRW.
2. Open the image and check or set the calibration manually by measuring the distance of a known length on the measurement scale that is part of the image (Figure 2C,D).
3. Start the measurement by clicking on the tree ring boundaries so that the distance between them, representing the TRW, is recorded (Figure 2D). Note whether the first tree ring measured is closer to the bark or closer to the pith. For violins, click the tree ring boundaries manually, because the automatic detection of TRW is usually not possible or requires too many corrections.
4. Measure all the TRWs along the measurement line. Save the data as the tree ring series (Figure 2E), with each TRW recorded for a specific relative year. Save the data in one of the widely used data formats. Perform more than one measurement on the same board for later verification.
   NOTE: There are also other options (not described here) for the TRW measurements. Option 1: Use a general image analysis system, open and calibrate the image, measure the TRW, and note the measurements. Option 2: Using a 10x magnification lens with a built-in metric scale, measure the TRW directly on the violin and record the measurements. Option 3: Use a classic setup of dendrochronological equipment consisting of a movable measuring table, a stereo microscope, and a special program to record the measurement^4,15. Place the violin on the table and observe it under a stereo microscope. Start the program for tree ring measurement and measure the TRW by clicking the tree ring boundaries.

5. Data processing, cross-dating, and building the chronology of the instrument

NOTE: For cross-dating, a specialized program and suitable reference chronologies are needed.

1. For data processing, open the data file. We describe here how to use the raw TRW series (i.e., TRWs (in mm) against years; Figure 2E).
   NOTE: It is also possible to work with indexed data.
2. For cross-dating a tree ring series of the same instrument, open the tree ring series to be cross-dated and another tree ring series of the same instrument to serve as a reference and run the cross-dating, which moves them into the synchronous (cross-dated) position.
3. Check the tree ring patterns and the cross-dating parameters. If the measurement is correct, the tree ring patterns, especially those of the same board, are very similar (Figure 2E), and the cross-dating parameters are high.
   1. Check for the following main cross-dating parameters used in studies of violins: the concordance coefficient Gleichläufigkeit (Glk%), the Baillie and Pilcher t-value (TVBP), and the Hollstein t-value (TVH)^20,21,22.
   2. Consider the parameters statistically significant if Glk ≥65%, TVBP ≥4.0, TVH ≥4.0. In the case of dating musical instruments, keep the criteria stricter and parameter values higher (e.g., TVBP ≥7.0).
   3. Consider the overlap (OVL), which indicates the overlapping period of two tree ring series, in years as well.
4. When the two tree ring series are on the same relative time scale, save the position of the series. Repeat this step until all the tree ring series of each board and instrument are cross-dated.
   NOTE: The cross-dating is based on the comparison of (two) tree ring series by calculating the statistical similarity parameters and graphical comparison (matching) of the graphs. A good agreement between the tree ring series (of the same instrument) confirms the correctness of the measurement, which is compromised if the tree rings are very narrow or indistinct or if they are missing (i.e., did not form in a tree).
5. For creating the chronology of the violin, when all the TRW series of the same board and instrument are cross-dated, look at their graphs. Then, select those that have no measurement errors and average them to form a chronology of the instrument. At this stage, the chronology is not yet dated.
   1. For this purpose, produce at least two measurements from each part of the top plate. If the agreement between the series within the instrument is statistically significant, average all the tree ring series into one chronology of the instrument.

6. Dating of the instrument

1. Cross-date the chronology of the violin with the reference chronologies. Use several reference chronologies in this step. Perform the cross-dating, check the parameters of the agreement, and visually assess the proposed dating position.
   1. For successful dating, ensure that the same end date is confirmed by multiple chronologies with statistically significant parameters, as well as by optical comparison of the sequences. Use additional techniques such as the formation of average chronologies from matching curves or the segmentation of longer series for additional confirmation of the dating.
      NOTE: This is a very critical step because one needs proper reference chronologies for dating. Some reference data are available on the ITRDB¹⁴.
2. Report the end date, which is the final result of the dendrochronological analysis²³. Estimate the number of years, which should be added to the end date to propose the potential date of manufacture of the instrument. For this purpose, use the information on the label (if original) and other sources about the potential age, geographic area, manufacturer, and organological characteristics of the instrument assessed by other experts.
3. Try to confirm the assumptions about the age, maker, and area of origin as this helps to decide if the violin is authentic or not.
   NOTE: The end date does not indicate the year in which the violin was made, and this must be estimated.
4. Write a report that includes the dendrochronological end date and sufficient information about the investigation supported by information that may help in the interpretation of the dating.
   NOTE: The most important steps of the protocol are illustrated in Figure 2.

Figure 2: Detailed representation of the steps of the protocol. (A) A violin with the top plate made of two resonance boards (bass and treble); (B) scanning of the top plate; (C) part selected for the tree ring width (TRW) measurement (precision 0.01 mm) and measurement direction from the bark to the pith (which were outside the board); (D) tree rings as bands on the radial board and the TRW measurement direction from the darker latewood to the light colored earlywood; asterisks indicate where the two boards with end dates of 2003 and 1995 are glued together; +1, +2, +3… denote the locations of the tree ring boundaries (+) and the tree ring numbers (1, 2, 3); scale bar = 1 cm; (E) tree-ring series of the treble and bass side of a violin in cross-dated position and end dates 2003 and 1995 indicated; (F) different end dates of the two boards due to different numbers of tree rings being removed during the manufacturing of the instrument; (G) orientation of the resonance board in the tree and the tree rings corresponding to the end date and the last tree ring below the bark formed before the tree was cut. Please click here to view a larger version of this figure.

Representative Results

A typical case in which a dendrochronological study was requested is a violin allegedly made by Andrea Guarneri of Cremona belonging to the family/school that produced numerous valuable instruments^16,24. The violin in question contained two labels. One stated that the instrument was made by Andrea Guarneri of Cremona in 1747, while the other stated only 1867. However, the organological examination of the violin (Figure 3) suggested that it was probably of German origin and about 300 years old.

Figure 3: The historical violin, dated by dendrochronology. (A) The top, (B) the back, and (C) the scroll of the violin, which contained two labels with the inscriptions (1) Andrea Guarneri of Cremona in 1747 and (2) 1867. The top plate was made of two resonance boards (bass and treble), and the end date of the youngest tree ring (arrow) on the plate was dendrochronologically determined to be 1640. The instrument was probably made a few years after 1640, as the Δt-interval (the number of years between the end date and the date of manufacture) averaged 14 years for many instruments of Jakob Stainer who probably made the instrument. Please click here to view a larger version of this figure.

The top plate of the violin was made of two radial boards of Norway spruce (Figure 3A). The tree rings were very narrow, averaging 0.69 mm (ranging from 0.28 mm to 1.25 mm) and locally poorly visible due to the surface treatment (dark varnish). Therefore, the measurements were repeated several times at several locations on the instrument. Dendrochronological cross-dating of the series of the two resonance boards revealed that both originated from the same tree, so that they could be averaged to a 141 year chronology of the instrument (Figure 4).

The dating was performed by experienced dendrochronologists using reference chronologies from the laboratories of the University of Hamburg, the University of Ljubljana, the BOKU University of Vienna, the Laboratory for Dendrochronological Analysis of Musical Instruments and Objects of Art²⁵, as well as chronologies published in the ITRDB¹⁴. Over 110 reference chronologies of spruce from different forest sites, historic buildings, individual instruments, and instrument collections of known violin makers were used, covering the period from 1137 to 2009. In more than 70 cases, the same end date of 1640 was defined²⁵, which must be considered the terminus post quem, meaning that the tree for the board was felled after 1640 (Figure 4).

Figure 4: Tree ring series of the historical violin dated with a reference chronology. Tree ring series of the violin (red line) with the end date 1640 terminus post quem, and a published reference chronology of a high elevation Alpine stand in Austria²⁶ (black). The statistical parameters of agreement are: OVL = 141, GLK = 63**, TVBP = 5.0, and TVH = 5.6. Please click here to view a larger version of this figure.

The statistical parameters of dating showed the best agreement with the chronology of instruments made by the violin maker Jakob Stainer (1618/1619-1683) from Austria (OVL = 141, GLK = 66*** [99.9% confidence]^4,20, TVBP = 7.4, and TVH = 8.7)²⁵. The same date and good agreement were also found when dating with various chronologies from Austria and southern Germany, as well as instruments made by Austrian and German violin makers. Jakob Stainer was a famous violin maker in Austria, known for his outstanding instruments, which he built in Innsbruck, Vienna, and for various orchestras throughout Europe¹⁷.

In this way, the most probable violin maker (the workshop) and the geographical area of the wood source were suggested. On the other hand, dendrochronology could not give a more precise date (year) for when or how many years after 1640 the instrument was built. This depends on how many tree rings (from the outside of the tree) were removed by the craftsman during the woodworking and making the instrument and for how many years the wood was dried and stored.

However, it is estimated that the instrument was made a few years after 1640. This assumption is based on information that the Δt-interval (i.e., the number of years between the end date and the date of manufacture of the instrument)^27,28 averaged 14 years for Stainer's instruments¹⁷ with original labels examined by various experts.

Is the instrument then original or fake? The instrument presented here was most probably not made by Andrea Guarneri, as one of the labels claims, although it was made during his lifetime (1626-1698). The dendroprovenance suggests that the wood came from Austria or Germany and that the instrument was probably made by the Austrian luthier Jakob Stainer (1618/1619-1683), a contemporary of Andrea Guarneri. The instrument was built after 1640 and is thus much older than the inscriptions on the labels (1747 and 1867).

Discussion

The presented protocol describes the procedure of the dendrochronological dating of a violin. The procedure includes several critical steps. The first one is to identify the tree rings in order to properly measure their width. This is critical because the tree rings are often very narrow or have unclear boundaries due to the small amount of latewood (step 1.3). The detection of tree rings can be complicated by aging of the wood, dark and opaque varnishes²⁸, or damage, repairs, retouching, or dirt (step 2.2).

However, it is possible to modify and improve tree ring detection (and measurement) by using high-resolution cameras^4,15 and advanced microscopy techniques to acquire high-quality images (e.g., confocal laser scanning microscopy [CLSM])²⁸ supported by advanced software that allows the stitching of multiple images^29,30. A very promising and increasingly widespread technique is X-ray computed tomography (CT), which allows virtual cutting of the instrument and observation of the tree ring structure in different views^31,32,33.

Once a reliable tree-ring series is established (step 4.4), dendrochronological dating follows. This is another critical step because it requires the use of appropriate reference chronologies for dating, as described in step 6.1.

As mentioned earlier, dendrochronological dating also has its limitations. First, we may not have an adequate reference chronology, or there may be no chronology for a particular area or time period, and, therefore, dating may not be possible. Another limitation is that dendrochronology only gives the end date (i.e., the year in which the last tree ring measured on the instrument was formed). Therefore, the year of manufacture must be estimated (step 6.2). According to the literature, the number of years between the end date and the date of manufacture of the instrument ranges from a few years to a few decades^13,23,27.

In any case, dendrochronology is a significant scientific dating method based on the comparison of tree-ring patterns, which depend on the climate and the physiology of the tree species, supported by statistics^6,27. In contrast, other commonly used methods depend on other sources of information, such as the label on the instrument, which is often not reliable, and the inspection of the instrument and its parts. Furthermore, dendrochronology can be used for dendroprovenancing, the determination of the geographic origin, as well as the luthiers or schools that made the instrument.

Given its strengths and the expected future improvements in imaging techniques, networks of reference chronologies, and the dendroprovenancing method³⁴, dendrochronology, in combination with other techniques, is expected to remain an important tool for dating and authenticating stringed instruments of valued and lesser-known makers. For optimal use, it is important to know the procedure, although it is recommended that an expert performs the analysis and interpretation of the results.

Materials

Name	Company	Catalog Number	Comments
CDendro	Cybis Elektronik & Data AB	https://www.cybis.se	program CoDendro for dendro data management and crossdating
CooRecorder	Cybis Elektronik & Data AB	https://www.cybis.se	program CooRecorder to measure tree ring widths on images
TSAP-Win	RINNTECH	https://rinntech.info/products/tsap-win/	Time series analysis software