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Dec122013

Ben Negley: Beat Mapping in Orchestral Music: An Empirical Exposition

 

 

Introduction

            Increasingly sophisticated recording technology allows for not only the propagation and individualization of recorded music, but also the opportunity to study the styles of conductors, orchestras and performers with empirical performance evidence as well as the primary documents, reviews, and scores that have traditionally been the foundations of musical historiography. Conductors and performers can no longer rely only on these latter documents for prescriptions of performing style, and musicologists must recognize the changing narrative of the musical work via performance and recording. In sampling and analyzing a large amount of data from recordings and using only empirical data–as opposed to journalistic surveys of the styles and tempi of conductors–this study analyzes a small section of Mahler’s Second Symphony in search of answers not available in the score.

            Studies of tempo and duration have exploded over the last twenty years. This explosion is perhaps not only the result of better recording technology and the higher number of recordings on the market, but also the exponential improvements in computing power. Computers allow for vast amounts of data to be collected, stored, represented and analyzed cheaply and efficiently, and most empirical studies of recordings rely on computers for data storage and analysis. Nonetheless, earlier studies in duration are still of interest.

            T.C. York’s book from 1929, How Long Does it Play offers timings for the most popular symphonies, concertos, overtures, and other orchestral works performed during the early 20th century.[1] Certainly not intended as any sort of scholarly study, but rather as a practical guide for conductors and concertgoers, York’s timings are rounded to the nearest minute and taken from the performances of a variety of premier British conductors. A similar guide, if released today, would most likely include all of Mahler’s symphonies, but York’s guide only includes timings for the First and Fourth Symphonies, two of Mahler’s shortest and most frequently performed works. In contrast, Solomon Aronowsky’s gigantic Performing Times of Orchestral Works, published in 1959, includes all of Mahler’s Symphonies as well as many individual movements that can be programmed as stand-alone works. But, like York, Aronowsky gives little indication as to the sources of his timings and alludes only to timing many concerts, and striking a “happy average” in each printed duration.[2] Concerning Mahler’s Second Symphony, Aronowsky’s published duration is 85 minutes­–a slightly longer than average timing–but the reader has no way of knowing if the usual silences between movements are included or not.[3] Thus, while Aronowsky’s timing does indicate to the listener a ballpark figure, it ignores the striking variety in a work like Mahler’s Second, and misrepresents the almost thirty minute difference between the longest and shortest recording of the work.[4]

British conductor and composer Sir George Smart, who was a personal acquaintance of Beethoven’s, timed himself conducting a variety of works between 1819 and 1843. One is immediately tempted to hold up Smart’s timings as evidence of a by-gone glory era (he knew Beethoven!), but his timings pose more questions than answers. Smart leaves no indications of repeats, spaces between movements, and in some cases he fails to even mention the particular work being timed. Nicholas Temperley describes these problems in his 1966 article “Tempo and Repeats in the Early Nineteenth Century.”[5] In what must have been one of the first articles of its kind, Temperley compares Smart’s timings with the timings of recordings. In speculating on the types of repeats Smart took in his timed works, Temperley gauges Smart’s timings with timings of recordings with varying repeat usage. Comparing Smart’s timings to timings recorded in the 1960s, Temperley is able to speculate on what types of repeats Smart took. Smart’s durations vary from the recordings studied by Tempereley, but elicit no discernible regression towards longer or shorter durations. 

A variety of more recent studies have carefully examined durations and tempi. The work of José Antonio Bowen is central to this study and the basis on which its methodology is constructed. In his 1996 article “Tempo, Duration, and Flexibility: Techniques in the Analysis of Performance” Bowen introduces a variety of techniques in the analysis of recorded music.[6] Building from Ingarden’s distinction between performances, scores, and musical works, Bowen seeks to examine recordings as entities separate from their associated scores. Using various modes of graphical representation, Bowen demonstrates how the analysis of recorded performances can be used as a means to a variety of ends. Several of Bowen’s conclusions are particularly poignant and are reproduced below:[7]

 

1. While detailed listening to individual performances is crucial, historical investigations of performance tradition must use data sets as large as possible.

 

3. Tempo data should be measured in the most accurate way possible and on the smallest level.

 

            Some of the most interesting recent work in empirical studies of recordings has been done by CHARM in London, a research group that was directed by Nicholas Cook and appears to have gone defunct in 2009.[8] Using a variety of software applications, CHARM focused on the tempo, duration, dynamics and style in recordings, and helped develop Sonic Visualizer Software, which allows for many different types of recording analysis and was used extensively in this project.

 

Methodology

My methodology builds on the work of Bowen, and focuses on a single orchestral work with a huge variety of recordings. Quantitatively describing the placement of individual beats, or ‘beat–mapping’, is achieved somewhat easily with Sonic Visualiser software.[9] Though several VAMP plug-ins intended to automatically map beat onsets are available for Sonic Visualiser, they work very poorly for orchestral music, and the beat–mapping must be achieved manually for maximum accuracy. Once an audio track is imported to Sonic Visualizer, mapping is achieved by depressing a key on the keyboard as the beats are encountered. Once annotations are placed, the annotation layer can be exported and copied into spreadsheet or statistical software.

To test various applications of this mode of beat mapping, I collected data from two sections of the first movement of Mahler’s Second Symphony and applied the data for two separate tests. The first compares the rallentando in the climactic measures in both instances, while the second examines two recordings by Pierre Boulez, and correlations between beat placement within a measure, and beat durations.

            In the first test, I mapped the beats for two very similar instances in the first movement of Mahler’s Second Symphony. I consider the first instance to be a part of the exposition and the second to be a part of the recapitulation. Both instances culminate with climaxes that are typically characterized by large-scale rallentando. In the first instance, the rallentando is followed by a dotted funeral-march theme:

 

In the second, the climax is defused by a quick decrescendo in lieu of the dotted march theme:

 

 

The entire movement is in common time, and in mapping the beats of both of these sections, I hoped to be able to compare two nearly identical sections of music with very sharply contrasting formal significance. Eight recordings were sampled, including two by Pierre Boulez, two by Otto Klemperer, two by Leonard Bernstein, one by Hermann Scherchen and one by Simone Young. These were somewhat arbitrarily chosen, based on the recordings available at my disposal, but I chose multiple recordings by single conductors to explore how conductors change not only from exposition to recapitulation, but years.       

            The second test involved a larger set of data, but only the two recordings of Boulez. These two recordings are particularly interesting because the first was recorded in 1973 and the second as part of a cycle in 2005. Thus, this test considers Boulez’s style over a 32–year period, using beat-length data from 28 measures in each the exposition and recapitulation of the same movement of Mahler’s Seconds Symphony. Instances 1 and 2 are measure 23, in the exposition and recapitulation of these test 2 samples, respectively.

 

Results

 

Test 1

            The beat durations for the five beats tested in Test 1 are displayed below:

 


1(1)

2(2)

3(3)

4(4)

1(5)

boulez bbc(1)

0.891065759

1.024580499

1.166802721

1.767619048

0.833015873

boulez bbc(2)

0.873514739

1.056258503

1.046349207

1.663854875

0.873469388

boulez vpo(1)

0.832040816

0.807687075

1.26430839

1.631496599

0.816462585

boulez vpo(2)

0.897800453

0.963628118

0.89829932

1.904036281

0.634217687

scherchen(1)

0.915011338

0.892743764

1.005759637

0.864943311

0.806893424

scherchen(2)

1.023492064

1.10478458

1.044739229

1.123265306

0.777868481

klempvso(1)

0.836734694

0.787755102

0.938775511

0.679614512

0.815396825

Klempvso(2)

0.761587301

0.750861678

0.920997733

0.581587301

0.551473923

young(1)

0.70367347

0.751836734

1.048163266

0.895873016

0.722721088

Young(2)

0.639886622

0.703968254

0.806031746

0.7061678

0.663809524

bernstein 63(1)

1.071655329

1.048049887

1.232108843

1.184013606

0.95569161

bernstein 63(2)

1.000090703

1.119773242

1.463854876

1.584285714

0.751995465

klempphil(1)

0.751950113

0.774058957

0.722312925

0.722585034

0.749092971

Klempphil(2)

0.845578231

0.762743764

0.722970522

0.916530612

0.792176871

bernstein 87(1)

1.098276644

1.211292517

1.340680272

1.059319728

1.044399092

bernstein 87(2)

0.952517007

0.902993197

0.867188209

1.03707483

0.96569161

 

            In this table, the printed durations correspond to the difference between the beat listed at the header of the column and the beat listed at the header of the next column. Thus, the length of Young’s beat 1 in Instance 1 is about .7 seconds. Or, the difference between Young’s 1st and 2nd beat in this Instance is .7 seconds.

One would expect beat 4, being the climactic rallentando beat, to typically be the longest, with beats 1 through 3 serving as a gradual rallentando. But this is not always the case. Boulez’s two recordings–recorded more than 30 years apart–both represent dramatic elongation of beat 4 in all instances. But most of the other sampled recordings elongate beat 3 in relation to beat 4 in at least one of two instances. Klemperer’s Vienna Symphony recording is dramatically different than Boulez’s recordings because in both instances beat 3 is elongated at the expense of beat 4. This is not the case in Klemperer’s later Philharmonia Orchestra recording, though, where neither beat is longer than the other in the 1st instance, but beat 4 is longer than its predecessor in the 2nd.

The chart below characterizes the elongation of beat 4 in relation to the elongation of beat 3:



boulez bbc(1)

0.600816327

boulez bbc(2)

0.617505668

boulez vpo(1)

0.367188209

boulez vpo(2)

1.005736961

scherchen(1)

-0.140816326

scherchen(2)

0.078526077

klempvso(1)

-0.259160999

Klempvso(2)

-0.339410432

young(1)

-0.15229025

Young(2)

-0.099863946

bernstein 63(1)

-0.048095237

bernstein 63(2)

0.120430838

klempphil(1)

0.000272109

Klempphil(2)

0.19356009

bernstein 87(1)

-0.281360544

bernstein 87(2)

0.169886621

 

Interestingly, in every example except Klemperer’s Vienna Symphony recording, the elongation of beat 4, relative to beat 3, increased from the 1st instance to the 2nd. This increase suggests a relative increase in elongation in the 2nd incident compared to the 1st, or a relatively more emphasized climax. This relative increase is contextualized by the fact that in terms of differences between beats 4 in both incidents are only positive in half of the recordings:

 

boulez bbc(1)

-0.103764173

boulez bbc(2)


boulez vpo(1)

0.272539682

boulez vpo(2)


scherchen(1)

0.258321995

scherchen(2)


klempvso(1)

-0.098027211

Klempvso(2)


young(1)

-0.189705216

Young(2)


bernstein 63(1)

0.400272108

bernstein 63(2)


klempphil(1)

0.193945578

Klempphil(2)

 

bernstein 87(1)

-0.022244898

bernstein 87(2)

 

 

            Thus, although the elongation of beat 4 relative to beat 3 increased from the first instance to the second in 7 of the 8 recordings, the actually length of beat 4–the climactic upbeat–only increased in half of the recordings.

 

Test 2

            In looking for correlations between beat position in the measure (1,2,3,4) and beat length, the second test examines the expressive style of Pierre Boulez in two recordings spanning 32 years. Correlations between beat position and beat duration, by measure, are reproduced below, with the positive correlations highlighted in gray:

 

measure

bbc(1)

bbc(2)

vpo(1)

vpo(2)

1

0.63

-0.67

-0.61

0.39

2

-0.89

0.22

-0.86

0.77

3

-0.26

0.67

0.58

0.75

4

0.08

-0.98

-0.23

-0.19

5

-0.45

-0.08

0.98

-0.50

6

-0.56

0.62

0.80

-0.26

7

-0.37

0.31

0.65

0.65

8

-0.07

-0.41

0.11

-0.90

9

-0.55

-0.59

-0.63

-0.14

10

0.64

0.64

-0.18

-0.98

11

-0.24

-0.41

-0.82

0.01

12

-0.69

-0.17

-0.12

0.87

13

0.33

-0.63

-0.44

0.73

14

-0.82

-0.74

-0.06

-0.23

15

0.37

-0.83

-0.36

-0.35

16

-0.25

-0.69

-0.23

0.71

17

-0.36

-0.79

-0.94

0.54

18

0.71

-0.09

-0.99

-0.60

19

0.25

-0.28

-0.85

-0.38

20

0.51

-0.56

0.04

0.22

21

-0.54

0.92

-0.50

-0.08

22

0.32

0.64

-0.06

0.83

23

0.93

0.88

0.94

0.77

24

-0.62

-0.80

-0.82

-0.69

25

-0.93

0.45

0.11

0.45

26

0.15

0.45

-0.36

0.54

27

0.05

0.05

0.62

0.42

28

-0.85

0.87

0.85

0.99

 

            As expected, the only measure with strong positive correlations in both instances in both recordings is measure 23, which is the climactic measure highlighted in Test 1. Thus, these correlations do not appear to suggest a pattern in Boulez’s style, at least in this short, 28-measure passage.

            The averages and standard deviations for the beat lengths are presented below:

 


1

2

3

4

boulezbbc(1)avg

0.75

0.76

0.76

0.77

boulezbbc(1)stdev

0.05

0.07

0.10

0.20






boulezbbc(2)avg

0.70

0.68

0.70

0.71

boulezbbc(2)stdev

0.06

0.08

0.10

0.20






boulezvpo(1)avg

0.72

0.70

0.72

0.74

boulezvpo(1)stdev

0.06

0.05

0.13

0.18






boulzevpo(2)avg

0.68

0.68

0.67

0.74

boulezvpo(2)stdev

0.05

0.06

0.06

0.24

 

            In every case, beat 4 has a higher average and standard deviation, but these facts are probably at least partly explained by the dramatic elongation of beat 4 in measure 23.

 

General Discussion

 

            The two experiments conducted above did not necessarily yield important conclusions on the nature of tempo rubato, or beat emphasis in recordings by Boulez, but I believe that similar analytical techniques applied to larger sample sizes or different musical excerpts could produce interesting results as to not only the nature of expressive interpretation, but also the importance of the conductor and her gestures. What if, through empirical studies of recordings, we could compare the styles of conductors beyond the journalistic opining that makes up the majority of the literature on conductors and conducting? And, what if quantitative comparisons of several recordings by a single conductor, as in my second test, yielded no discernable empirical similarities? What if we could quantitatively show which conductors maintained salient expressive characteristics over multiple recordings and which ones did not? I believe that empirical studies of tempo and duration in recordings could be one of the first steps in de-mystifying conducting and an integral part of a well-needed critical ethnography of the conductor.

 

Bibliography/Discography

 

Aronowsky, Solomon. Performing Times of Orchestral Works. London: Ernest Benn Limited, 1959.

 

Bernstein, Leonard. New York Philharmonic Orchestra. Deutsche Grammophon, 423 3952, 1988, compact disc. Recorded in 1987.

 

_______________. New York Philharmonic Orchestra. Sony, SM2K 89499, 2001, compact disc. Recorded in 1963.

 

Boulez, Pierre. Vienna Philharmonic Orchestra. Deutsche Grammophon, DG 477 6004, 2006, compact disc. Recorded in 2005.

 

___________. BBC Symphony Orchestra. Originals, 855, 1995, compact disc. Recorded in 1973.

 

Bowen, José Antonio. “Tempo, Duration, and Flexibility: Techniques in the Analysis of Performance.” The Journal of Musicological Research 16 (1996): 111-156.

 

Cannam, Chris, Christian Landone, and Mark Sandler. “Sonic Visualiser: An Open Source Application for Viewing, Analysing, and Annotation Music Audio Files.” http://www.sonicvisualiser.org/.

 

Klemperer, Otto. The Philharmonia Orchestra. EMI, EMI 724356725553, 1963, compact disc. Recorded in 1961-2.

 

_____________. Vienna Symphony Orchestra. Testament, JSBT 2 8456, 2010, compact disc. Recorded in 1951.

 

Scherchen, Hermann. Vienna State Opera Orchestra. Theorema, MCAD2-9833, 1993, compact disc. Recorded 1958.

 

Temperley, Nicholas. “Tempo and Repeats in the Early Nineteenth Century.” Music and Letters 47, No. 4 (Oct., 1966): 323-336.

 

York, T.C. How Long Does it Play: A Guide for Conductors. London: Oxford University Press, 1929.

 

Young, Simone. Hamburg Philharmonic Orchestra. OEHMS, OC412, 2010, compact disc. Recorded in 2010.

 

 


[1] T. C. York, How Long Does it Play: A Guide for Conductors (London: Oxford University Press, 1929).

[2] Solomon Aronowsky, Performing Times of Orchestral Works (London: Ernest Benn Limited, 1959), ix.

[3] Aronowsky, Performing Times of Orchestral Works, 452.

[4] Of the 52 recordings analyzed in my master’s thesis (Ben Negley, Variability in Mahler’s Second Symphony: An Empirical Approach, Unpublished, 2012), Otto Klemperer’s 1950 account with the Sydney Symphony Orchestra was the shortest at 66 minutes and 40 seconds and Hermann Scherchen’s 1958 Vienna State Opera Orchestra recording was the longest at 93 minutes, 07 seconds.

[5] Nicholas Tempereley, “Tempo and Repeats in the Early Nineteenth Century,” Music and Letters 47, No. 4 (October, 1966): 323-336.

[6] José Antonio Bowen, “Tempo, Duration, and Flexibility: Techniques in the Analysis of Performance,” The Journal of Musicological Research 16 (1996): 111-156.

[7] Bowen, “Tempo, Duration, and Flexibility: Techniques in the Analysis of Performance,” The Journal of Musicological Research, 145, 146.

[8] See http://www.charm.kcl.ac.uk/index.html

[9] Sonic Visualizer software is available for free download at http://www.sonicvisualiser.org/.

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