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CONFIRMATION OF THE DATING OF THE KARR-KOUSSEVITZKY DOUBLE BASS

INTRODUCTION

To our knowledge, the recently published article by Henri Grissino-Mayer et al. (1), is the first work appeared in the

literature, which relies on the segmentation program COFECHA of R. Holmes (2) to confirm the crossdating of a

musical instrument, whose ring series, before being subjected to this analysis, had to be initially subjected by the

authors to a partial standardization ( which according to the criteria of the American School of Dendroclimatology,

clears the medium frequency variations - such as those due to aging of the tree -, but not the low-frequency ones,

whose knowledge is essential for Dendroclimatology) and then to the transformation of its elements in "residuals",

which will result in a white noise series, cleaned from the effects of autocorrelation, as we have amply discussed in

Notebok2.

Our method of standardization, instead, follows the criteria proposed by M.G.L. Baillie in his book Tree-Ring Dating

and Archaeology (3) and by M.G.L. Baillies and J.R.Pilcher (4) in their article A Simple Crossdating Program for Tree-

Ring Researh, who obtains this function with an autoregressive model based on a moving average 5 in 3, giving a %5

filter.

This method already described in our Manual (2005) and applied in earlier versions of Synchro Search, in the last

version 2.2.1 has become much more flexible because the filters can be easily varied from %3 to %9 and beyond, to

obtain in one step only the white noise series in which the autocorrelation can be eliminated (Manual 2 and 3).

Furthermore, in the version 2.2.1, a new sub–routine has been implemented which allows the analysis by segments of

the matching, simpler than COFECHA and extremely user-friendly, so that the Segmentation becomes an operation to

be currently used in real time, which has been fully described in Notebooks 2 and 3.

In view of this it seemed interesting, in order to validate our methodology and our Guidelines, to replicate with our

procedure the published dating of the Kousseviztky Karr double-bass obtained by the American Dendroclimatologists.

MATERIALS AND METHODS

We downloaded from the website of the Tree-Ring Society, the article cited, where Grissino-Mayer et al., published

in the appendix the numerical values of the ring widths measured on both the lower parts of the double-bass, letting

so to repeat their experiment, in which the year 1761 was replicated as the terminus post quem for the bass-side and the year 1741 for the treble-side, but without telling us with which method they had initially obtained those dates,

that, according to the methodology described in the COFECHA tutorial (5), we can guess that it could be a visual

method such as skeleton plot.

Concerning the reference chronology to be adopted, due to the lengths of the two series (298 rings for Karr06 and

297 rings for Karr, 03, for a total of 316 years) we had a limited choice among the masters PCAB Giertz Obergurgl

1274-1974, the equivalent PCAB Siebenlist-Kerner Oetztal 1274-1974 and our "46th parallel" master of 3 different

species of wood grown in 36 sites inthe Alps in that parallel (see Notebook 1)

The crossdating has been performed according to the procedure 1 as specified in an exercise of Notebook 4, entitled

“How to perform a crossdating with a reasoned approach”

2

Karr03

A matching in the raw format of the Karr03 ring-series against the master PCAB Giertz Obergurgl shown in Fig.1,

gave the maximum Gleichläufigkeit (64%) value for the period 1445 - 1741.

Fig.1

1445 1741

In the graph of Fig.1 we can also see that isotropy of the two curves in raw format, highlighted by green light,

confirms, according to the theory of Baillie and Pilcher, that the analysis of the correlation could be properly

performed.

Then, according to those authors, on the sample and master series that were fully detrended by standardization with

our autoregressive model consisting of indexing with moving averages properly chosen to nullify the autocorrelation, a

crossdating was performed.

We also carried out in parallel in the same standard format a crossdating after transforming the series values from

arithmetic to logarithmic in order to normalize their Gaussian distribution, as we described in the notebook 3.

Finally, the Segmentation analysis was performed with segments of 100 rings, with the "Segmentation window"

completely open (see Notebooks 2 and 3).

Karr06

From a comparison in the raw format of Karr06 series against the master PCAB Giertz Obergurgl shown in Fig.2, the

maximum Gleichläufigkeit (63%) was observed for the matching 1464 to 1761. For the matching of the graph of Figure

2, the same comments of the graph of Fig.1 are valid.

Fig.2

1464 1761

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RESULTS

After crossdating in the indexed format the ring widths of the bass side (Karr 06) and those of the treble side (Karr

03) of the doble-bass always against the reference chronology PCAB Giertz Obergurgl 1274-1974, the two most likely

dates, namely 1761 for Karr 06 (bass) and 1741 for Karr 03 (treble) were found, which were further confirmed by the

Segmentation procedure, in real time at the segment frequency level corresponding to 100 rings for three statistical

parameters: Pearson’s r, Gleichläufigkeit and Pearson's r + Gleichläufigkeit. (See Notebooks 2 and 3).

The results for Karr 06 are shown in Figures 4, 5, 6 and 7.

The results for Karr 03 are shown in Figures 8, 9, 10 and 11.

In all plots the division into segments shown in the graphs of the Match screening routine is reporting for each

segment its calendar limits and the intercorrelation values for the pair r + Gleichläufigkeit.

Fig.3

Figure 3 shows the System Settings of the program adopted for crossdating the measures of the ring widths of the

two part Karr06 (bass) and Karr03 (treble) of the instrument including the analysis by segments, which are as follows.

- The index r has been calculated according to Pearson's correlation using the canonical equation.

- The Segmentation window of 9999 years that we have chosen, indicates that the spread of the length of each

segment of the master against which each segment of the series of the sample will be compared, will be + / - 9999

years. This means that each segment of the sample (of any length may be) has been actually crossdated against the

whole extension of the master PCAB Giertz Obergurgl ranging from 1276 to 1974.

- The standardization has been performed by indexing with a moving average 7 in 4 (filter% 7) that will give us a withe

noise series from which all the variations of ring widths have been removed, including those due to autocorrelation,

preserving only those exclusively produced by climatic variations.

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Fig.4

In Figure 4 the crossdating of Karr 06 in the range 1467 – 1758, which actually has been considered the best on the

basis of statistical results,is shown. Segmentation has been performed with 100 ring segments..

The values of the Person’s r of the second, third, fourth and fifth segment are higher than the benchmark limits for

segments of 100 rings (0.2324), not only, but are the most probable for their unicity, confirmed by the value of H= 0

which means that there are no other hints in the whole range of the master (1276-1974), since the Segmentation

window has been enlarged to + / - 9999 (see Papers 2 and 3).

Adding to the year 1758 the years that were lost at both ends of the moving average of 7 to 4, that gives the

filter value% 7 (which has completely eliminated the autocorrelation), we reach the year 1761 which is

consistent with the terminus post quem proposed by H. Grissino-Mayer.

Fig. 5

5

Fig.5 reproduces the subroutine “Other inf” showing the table of the “Advanced statistic” relating to the crossdating

shown in Figure 4.

Fig.6

In Fig.6 is shown the same crossdating of Karr 06 of Fig.4 conducted on the values of ring widths of the series

expressed in semi-log form in order to implement the normalization of the Gaussian distribution.

Fig.7

The Fig.7 reproduces the subroutine “Other inf” relating to the matching of Fig.. 6, showing the table of the

“Advanced statistic” relating to that matching. Note as the indexing filter %7 has completely eliminated the

autocorrelation and note also as the expression of the data in semi-log format did not affect the terms of the

crossdating but only caused an insignificant variations of the r values of the segments.

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Fig.8

Fig.8 shows the Match screening graph of the crossdating of the ring widths series of the treble side Karr03 against

the master PCAB Giertz Obergurgl 1274-1974, which has given as the most probable dating the range 1448 – 1738,

confirmed by the results of the Segmentation carried out with 100 rings segments, which show that the r values of all

the five segments are above the limits of the benchmark (0.2324), not only, but that their unicity is confirmed by the

value of H= 0, which means that there are no other hints in the whole range of the master (1276-1974) having been

brought the Segmentation window value to + / - 9999 years.

Fig.9

Fig.9 reproduces the table of the sub-routine Other inf with the Advanced Statistic relating to the matching shown in

Figure 8. Note the complete elimination of autocorrelation obtained by indexing with the filter %7.

Adding to the year 1738 the years that were lost at both ends of the moving average 4 in 7, we come to

1741 which is consistent with the terminus post quem proposed by H. Grissino-Mayer.

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Fig.10

In Fig.10 is shown the same matching of Karr 06 of Fig.4 conducted on the series values expressed in semi-log form in

order to implement the normalization of the Gaussian distribution.

Fig.11

Fig.11 reproduces the sub-routine Other inf with the Advanced Statistics relating to the matching shown in Figure 10.

Note the complete elimination of autocorrelation and how the semilogarithmic expression of data did not affect the

terms of the crossdating, while slightly improved the intercorrelatio r values of the 100 ring segments.

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CONCLUSIONS

We have demonstrated that with our dendrodating procedure, employing the program Synchro Search, applied to

measurements made by H. Grissino-Mayer et al., the terminus post quem of 298 rings in the bass side of the Karr-Koussevitzky double bass Karr06 is 1761 while that of the 297 rings of the treble side is 1741.

These values agree exactly with those obtained by the authors who performed the Segmentation analysis with

COFECHA program, certainly not so easy to use as ours which returns in real-time the segmentation results, which

are not only based on the analysis of the correlation, but also of the Gleichläufigkeit and, always in real time, not only

allows to vary the length of the sample segments, but also to vary the segmentation window, i.e. the spread of the

related segments in the master, for a greater efficacy of assessing the likelihood of the dating.

It is also to be remembered that with the change in real time of the indexing filter the total cancellation of the

autocorrelation, becomes possible.

We also note that the use of the ring widths values of instrument and master in the semilogarithmic format rather

than arithmetic in order to "normalize" them in a Gaussian distribution (see Manual 3), has not introduced any

variation of the dates, while the other statistical parameters differed quite negligibly. The same applies to the values

of the statistical analysis of each segment.

It has to be outlined that indexing the series by applying the filter %3, as can be seen in the graph of Figure 12, the

dating year 1741 for the karr03 series is confirmed, even if the autocorrelation value went down only to 0.63 from the

value 0.81 of the series in raw format (see guideline IV). The action of filter% 3 in fact creates a white-noise series

in which actually it is only deleted the trend due to aging of the tree. From this we may deduce that it is not

necessary to totally eliminate the autocorrelation for dendrodating investigation, so much so that Baillie for this

purpose has always used the filter %5 (see the Table of Guideline IV).

Fig.12

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It is therefore naturally recall the quote from Munro that we cited at the end of guideline III :

.. It is important to bear in mind that filters constructed for other purposes (such as dendroclimatology) will not

necessarily be the best ones to use for crossdating problem.

REFERENCES

1 H. Grissino-Mayer and collaborators, “Tree-ring dating of the Karr-Koussevitzky double bass: a case study in dendromusicology “ ,Tree-Ring Society Bulletin (Tree-Ring Research 61 (2): 77-86).

2 R.Holmes, “ Computer-assisted quality control in tree-ring dating and measurement “Tree-Ring Bulletin, 43,1983

3 M.G.L Baillie, Tree-Ring and Archaeology, University of Chicago Press, 1982

4 M.G.L. Baillie and J.R. Pilcher, A Simple Crossdating Program for Tree-Ring Research, Tree-Ring Bulletin, Vol 33,

1973.

5 H. Grissino-Mayer, “COFECHA program tutorial ”, Tree-Ring Society Bulletin (Tree-Ring Research 57:205-221).

6 M.A.R. Munro, “An improved algorithm for crossdating tree-ring series. Tree-Ring Bulletin 44, 17-27.