Analysis of Different Timpani Playing Techniques
Andraž Poljanec
Seminar Thesis University of Music and Performing Arts Vienna, Institute 13/3 November 2012–June 2013
Superviser: Ao. U niv. P rof. D r. M atthias A . B ertsch
Introduction ...................................................................................................................................... 3 Background Aspects of the Instrument and Playing Techniques ................................... 4 Drums history and classification ............................................................................................................. 4 Vibration Modes ..................................................................................................................................... 4 Playing Styles – Grips .............................................................................................................................. 7 Articulation ............................................................................................................................................. 7 Timpani Mallets ...................................................................................................................................... 8 Experiments ...................................................................................................................................... 9 High-‐speed Video Recording of Different Playing Techniques ............................................................... 9 Results and Interpretation of Video Recordings ................................................................................... 13 Sound Recordings ................................................................................................................................. 21 Sound Analyses, Results and Interpretation ......................................................................................... 22 Electromyographical Measurements .................................................................................................... 26 Conclusion ....................................................................................................................................... 26 References ....................................................................................................................................... 27
Introduction The sound of timpani is primarily defined by the type and material of the instrument and through the playing style of the musician. While there is many knowledge and research on the instrument, e.g. the vibration characteristics of timpani heads, there is still a lack of scientific research on the playing technique. The acoustic and physiological aspects of the process striking the timpani are focused in this work. The research idea was to confirm whether a timpanist can perform different sounds on timpani exploring different techniques/playing styles or grips and different strokes to change the degree of articulation. Different mallets were used, also different head tensions and dynamics. Strokes were first filmed in high-‐speed to get slow motion recordings for analysis (Figure 1), then sound recordings of different strokes were made. In addition to sound recordings electromyography measurements (EMG) were made to discover the tension of muscles on timpanist's arm, shoulder and chest while playing (Figure 2). These physiological measurements provided insights to modern analysis techniques. Data acquisition has been stored and analysis can lead to additional research paper.
Figure 1. High-‐speed video analysis.
Figure 2. EMG study.
Background Aspects of the Instrument and Playing Techniques Drums history and classification Drums are known as the oldest musical instruments. They were evolving with human race and always played very important role in every musical culture. We don't know exactly when and where the first membrane drum was made, but some ancient drums are at least 5000 years old (Fletcher and Rossing 1998, 583). Timpani are of Arabian origin. They were originally quite small, introduced to Europe they were called nakers (from the Arabic Naqqareh) (Forsyth 1982, 41). Timpani came to western Europe in 14th–15th century as cavalry instruments; they were played on horseback in pairs. Following eastern custom, they were paired with the trumpet. In the seventeenth century timpani found their way indoors, joining the orchestra along with trumpets, horns and oboes (Beck 1995, 201–202). In general, modern drums can be divided into two groups: those that convey a strong sense of pitch (e.g. timpani) and those that do not (Fletcher and Rossing 1998, 583). As vibrating systems, drums can be divided into three groups: • • •
those consisting of a single membrane coupled to an enclosed air cavity (e.g. timpani), those consisting of a single membrane open to the air on both sides (e.g. tom-‐tom, bongos, conga), those consisting of two membranes coupled by an enclosed air cavity (e.g. snare drum, base drum) (Fletcher and Rossing 1998, 583).
This thesis focuses on the timpani and hence the first group of drums.
Vibration Modes The essential element of every drum is a membrane, which is stretched over a frame. The impact of the striking mallet causes a vibration of the membrane. In contrast to the string which is one-‐dimensional vibrator, the membrane is a two-‐dimensional vibrator (its thickness is negligible) (Campbell and Greated 1987, 411). Non vibrating points on a vibrating string are called nods and their two-‐dimensional equivalents are nodal lines – points on the membrane which remains at rest during the vibration. For a circular membrane of uniform thickness and tension, the nodal lines are either diametral lines (m) passing through the centre of the head, or circles concentric with the frame (n) (Campbell and Greated 1987, 412).
Figure 3 (Ravnikar 1999, 60). Figure 3 shows 25 mode patterns of an ideal membrane with numbers of nodal diameters and nodal circles in brackets. The first mode with no nodal diameters and only one nodal circle (the rim) is (0, 1) mode and so on.
Figure 4. Three-‐dimensional presentation of modes (0, 1), (1, 1), (2, 1), (3, 1) (Bertsch 2001). The mode frequencies of an ideal circular membrane were first calculated already in 19th century (by Lord Rayleigh in 1877). If the properties of the membrane are known, the frequency of particular mode of a circular membrane (m, n) can be calculated by the next formula (Campbell and Greated 1987, 413): 𝑓!" =
1 𝑇 ∙ 𝑗 2𝜋𝑟 𝜌 !" !
!"
where 𝑟 [𝑚] is radius of the membrane, 𝑇 [!] is its tension, 𝜌 [!! ] surface density and 𝑗!" is a value given by Bessel’s function (depending on the number of nodal diameters – m – and circles – n – in the pattern) as seen from the next Table 1:
m
0
1
2
3
4
5
n
1
2,404
3,832
5,135
6,379
7,586
8,780
2
5,520
7,016
8,417
9,760 11,064 12,339
3
8,654 10,173 11,620 13,017 14,373 15,700
4
11,792 13,323 14,796 16,224 17,616 18,982
5
14,931 16,470 17,960 19,410 20,827 22,220 Table 1 (Rayleigh 1945, vol. 1, 330).
As seen from the upper formula the frequency is inversely proportional to the radius, so doubling the radius of a membrane will halve the frequency (the pitch will drop by an octave). Besides the frequency is proportional to the square root of the tension, so in order to raise the pitch by an octave, the tension must be increased fourfold (Campbell and Greated 1987, 413). For an example we can count out the frequency of the first mode (0, 1) for the ideal !"
undamped circular membrane of radius 0,325 𝑚, with surface density 0,26 !! , under a !
tension of 3216,2 !, depending on the value 𝑗!" from Table 1: 𝑓!,! =
2,404 3216,2 𝑘𝑔 𝑚 𝑚! 1 = 131 = 131 𝐻𝑧 2𝜋 ∙ 0,325 𝑚 0,26 𝑘𝑔 𝑚 𝑠 ! 𝑠
This is the frequency of C3. If we continue counting for some more modes (applying values of 𝑗!" from Table 1) we would get this series of pitches, assuming a first mode pitch of C3:
Figure 5 (Campbell and Greated 1987, 412). It is obvious that the normal modes of an ideal circular membrane have frequencies which are strongly inharmonic. Such a sound lacks any definite sense of pitch (Campbell and Greated 1987, 410–411).
So how can timpani produce a definable pitch? It was founded out that the bowl, head stiffness and the surrounding air mass coaxes certain inharmonic frequencies into an ordered set of partials (typically the fifth, sixth, octave, tenth and twelfth), making the timpani a pitched percussion instrument. The mass of air inside and outside of the bowl accentuates the lower partials. On the other hand the tension on the drumhead emphasizes the upper partials (the fifth and above). The bowl separates the upper and lower parts of the head, decreases the decay of the partials and accentuates the principal frequency (Schweizer 2010, 6). Studies were made also about the influence of the air volume in the kettle and the influence on the membrane material. Significant differences were found between synthetic skins, goat skin and calf skin. Another studies were focused on the clarity of pitches on timpani. It was founded that the sound of a calf skin head is clearer than that of synthetic membranes (Bertsch 2001, 3).
Playing Styles – Grips Playing style includes the grip in the first place, very important are also the arm motion, the amount of upper body put into a stroke and standing or sitting position. The French style means the mallet between the first joint of the index finger and the pad of the thumb. Playing with thumbs up and remaining fingers widely cupped around the handle butt allows the timpanist to bounce the stick quickly and to get a bright sound from the head. The French style is usually/historically played in standing position or in higher sitting position. In the German style the handle is gripped between the first joint of the thumb and much higher along the index finger, the other fingers are wrapped lightly around the stick. Playing with palms down creates darker sound. The American style is known as a hybrid between French and German – gripping more in the French manner but with other fingers wrapped around the handle and playing palms down. Mallets are held more firmly, but the strong wrist motion assures great bouncing effect (Schweizer 2010, 14–16). The Austrian grip is a modification of the German one with more thumb pad on the shaft and the index finger slightly more wrapped around. This thesis focuses on French style compared to American style in some cases.
Articulation For the short and bright staccato sound the mallet is usually gripped between the thumb and first two remaining fingers, the wrist helps to achieve quick bouncing effect. We get the legato sound by gripping the mallet much more loosely between the thumb and the index
finger only. The mallet remains on the head slightly longer and produces wider sound (Schweizer 2010, 28–29).
Timpani Mallets Very different mallets are used to bring out a variety of sound and articulation from legato to staccato and from dark to bright. According to material of the handle and the head of the stick the weight changes a lot. Lighter mallets produce a brighter sound with fewer audible lower partials and emphasized upper and nonharmonic partials, heavier wooden mallets with wooden heads bring out the fundamental and lower partials (Schweizer 2010, 9–11).
Experiments High-‐speed Video Recording of Different Playing Techniques
To analyse the contact between the mallet and the timpani head the high-‐speed camera Vision PHANTOM V12.1 was used. Slow motion recordings were filmed in high-‐speed with 2000, 4000 and 8000 images per second. Table 1 shows the relationship between normal movie speed and different slow motions. We get slow motion by filming with more images per second as usual, then we perform the movie with normal speed. normal movie slow motion slow motion slow motion slow motion slow motion
30 images/s 100 images/s 1000 images/s 2000 images/s 4000 images/s 8000 images/s
1 s = 1 s 1 s = 3,34 s 1 s = 33,34 s 1 s = 1 min 6,67 s 1 s = 2 min 13,34 s 1 s = 4 min 26,67 s
Table 2. The relationship between normal movie speed and different slow motions.
Figure 6. 26'' Slingerland timpano.
Slow motion recordings were done with 26'' Slingerland timpano (Figure 6) with Remo Weatherking Renaissance head, applying different playing styles or grips (French and American), different strokes (staccato, legato), dynamics forte and piano, different skin tensions (A2, C3, F3) and different mallets (Figure 7, Table 3).
Figure 7. Timpani mallets used in experiments. working mark
BFS(oft)
BFM(medium)
BFH(ard)
WWF
WW0
handle head cover material core material head diameter [mm] core diameter [mm] mallet weight [g]
Bamboo Felt cork 35,75 (big) 24,05 26
Bamboo Felt cork 27,24 (medium) 19,97 26
Bamboo Felt cork 19,40 (small) 16,02 27
Wood thin Felt wood 18,59 (small) 17,20 51
Wood no cover wood 22,70 22,70 54
Table 3. The composition of five different mallets used in the experiments.
The order of video high-‐speed recordings is presented in Table 4. Each stroke was repeated several times with damping between them. Grip
stroke French legato French legato French legato French stacc. French legato French stacc. French legato French legato American legato French stacc. French legato French stacc. French legato French stacc. French stacc. French stacc. French stacc. French stacc. French stacc.
dynamic tone mallet rec. speed forte roll C3 BFS 2000 forte roll C3 WWF 4000 forte roll C3 BFM 4000 forte C3 BFM 4000 forte C3 BFM 4000 piano C3 BFM 2000 piano C3 BFM 2000 forte C3 BFM 2000 forte C3 BFM 2000 forte F3 BFM 8000 forte F3 BFM 8000 forte F3 BFH 2000 forte F3 BFH 2000 forte F3 WWF 2000 forte F3 WW0 2000 forte A2 BFS 4000 forte A2 BFH 4000 forte F3 BFS 4000 forte F3 BFH 4000
Table 4. The order of recordings (last column presents the recording speed as the number of pictures per second).
Figure 8. The high-‐speed camera Vision PHANTOM V12.1 and technical information.
Results and Interpretation of Video Recordings
Mallet Motion Grip, Articulation, Dynamic, Tone, Contact Time Duration Mallet Duration[ms] (Horiz.-‐Horiz.) [ms]
Wrist Motion Duration [ms]
French, stacc., forte, C3, BFM
24,225
6,000
145,500
French, legato, forte, C3, BFM
30,000
6,450
214,575
French, stacc., piano, C3, BFM
36,000
8,550
141,450
French, legato, piano, C3, BFM
40,500
7,950
147,750
French, legato, forte, C3, BFM
56,100
563,100
American, legato, forte, C3, BFM
50,550
390,450
French, stacc., forte, F3, BFH
28,500
4,950
183,000
French, legato, forte, F3, BFH
30,000
5,550
511,800
French, stacc., forte, F3, WWF
30,600
4,950
161,250
French, stacc., forte, F3, WW0
27,000
5,100
161,850
Table 5 shows following durations needed for the analyses of playing techniques: • • •
the duration of mallet motion between two horizontal positions before and after the stoke, the duration of mallet-‐skin contact, the duration of wrist motion.
Duration of the mallet motion The second column of Table 5 (mallet motion duration) shows how much time (in milliseconds) a mallet needs from the first horizontal position to the next one after the stroke. As seen from Table 5 the mallet playing staccato stroke has obviously higher speed than legato because less time is needed from the first horizontal position to the next one after the stroke. Higher speed of the mallet impacts on the sound, as seen from sound recording analyses in the next chapter. The motion of mallet is presented by the following figures. On Figures 9a–d the mallet BFM (described in Table 3 and seen in Figure 7) is gripped in the French manner and for the staccato forte sound (described on the page 7 – two fingers besides the thumb are holding the mallet).
Figure 9a. Horizontal position before the contact with membrane.
Figure 9b. Beginning of the contact.
Figure 9c. End of the contact.
Figure 9d. Horizontal position after the contact.
On Figures 10a–d the mallet BFM (described in Table 3 and seen in Figure 7) is gripped in the French manner and for the legato forte sound (described on the page 7 – the mallet is held between the thumb and the index finger).
Figure 10a. Horizontal position before the contact with the membrane.
Figure 10b. Beginning of the contact.
Figure 10c. End of the contact.
Figure 10d. Horizontal position after the contact.
Comparison between American and French grip shows higher speed of the mallet using the American grip. The sound recording analyses in the next chapter confirm this. On Figures 11a–c the mallet BFM (described in Table 3 and seen in Figure 7) is gripped in the American manner and for the legato forte sound (described on the page 7 – playing palms down and with fingers wrapped around the handle).
Figure 11a. Horizontal position before the contact with the membrane.
Figure 11b. The contact with the membrane.
Figure 11c. Horizontal position after the contact.
Duration of the mallet-‐skin contact Regarding the contact time duration (the third column of Table 5) the staccato stroke has slightly shorter time compared to legato stroke which is expected. There is an exception in the case of piano dynamic, where the contact time of staccato was 0,6 millisecond longer than legato stroke. At the first glance this is a surprise considering that a timpanist is trying to play staccato with the shortest time contact possible. But we must not forget the staccato stroke speed is higher than legato so the mallet penetrates deeper into membrane which could longer the contact time.
Figure 12. The mallet-‐skin contact is certainly longer with soft mallet.
The wrist motion Regarding the wrist motion (the fourth column of Table 5) it is obviously that the wrist is moving longer playing legato, but the difference is big only in forte dynamic. If we compare French and American grip the wrist is longer in motion using the French one. The wrist motion is presented by the following figures. On Figures 13a–c the mallet BFM (described in Table 3 and seen in Figure 7) is gripped in the French manner and for the staccato forte sound (described on the page 7 – two fingers besides the thumb are holding the mallet).
Figure 13a. Beginning of the wrist motion.
Figure 13b. The lowest point of the wrist motion.
Figure 13c. End of the wrist motion.
On Figures 14a–c the mallet BFM (described in Table 3 and seen in Figure 7) is gripped in the French manner and for the legato forte sound (described on the page 7 – the mallet is held between the thumb and the index finger).
Figure 14a. Beginning of the wrist motion.
Figure 14b. The lowest point of the wrist motion.
Figure 14c. End of the wrist motion.
On Figures 15a–c the mallet BFM (described in Table 3 and seen in Figure 7) is gripped in the American manner and for the legato forte sound (described on the page 7 – playing palms down and with fingers wrapped around the handle).
Figure 15a. Beginning of the wrist motion.
Figure 15b. The lowest point of the wrist motion.
Figure 15c. End of the wrist motion.
The tension of membrane Increasing the tension of membrane from C3 to F3 (as seen from the first and the third column of Table 5) decreases the mallet-‐skin contact time which is expected and also agrees with the study of Wagner on snare drum (Wagner 2006, 35).
Sound Recordings Next part of experimental work was sound recording. Small omnidirectional lavalier microphone AKG C 577 WR was set 15 cm above the timpani head, the recording order was the same as in case with high-‐speed camera. Each stroke was repeated five times with dampening in-‐between.
Figure 16. Microphone was set 15 cm above the membrane.
Sound Analyses, Results and Interpretation For sound analyses spectrograms of the Audacity programme were used. Spectrogram properties were set for the frequency 0–2500 Hz and for loudness 20–75 dB. Spectrogram shows the spectrum of the sound with lines which differ in colour and length. The strongest frequencies of the sound spectrum are coloured white and weaker ones red, violet and blue. Line's length shows how long the partials resist. The biggest difference in sound spectrum is seen between wooden and felt mallets. The sound produced with a hard (wooden) mallet has wider spectrum – that means more higher partials. So hard mallets would produce brighter sound. t [s]
f [kHz] Figure 17. Spectrogram of the timpani sound played with soft felt mallet (F3, stacc., BFS).
t [s]
f [kHz] Figure 18. Spectrogram of the timpani sound played with wooden mallet (F3, stacc., WW0).
Similar difference is seen between staccato and legato articulation. Staccato stroke produces the sound with more higher partials. t [s]
f [kHz] Figure 19. Spectrogram of the timpani sound produced by legato stroke (F3, leg., BFM).
t [s]
f [kHz] Figure 20. Spectrogram of the sound produced by staccato stroke (F3, stacc., BFM).
There is also a difference between the sound produced by French or American stoke. The American one produces larger sound spectrum with higher overtones which decay later. t [s]
f [kHz] Figure 21. Spectrograme of the sound produced by French legato stroke (C3, leg., BFM).
t [s]
f [kHz] Figure 22. Spectrograme of the sound produced by American legato stroke (C3, leg., BFM).
Electromyographical Measurements Together with sound recordings the physiological electromyographical measurements with Schuhfried Biofeedback Xpert 2000 system were made. The EMG setup for all three modules was: sensitivity 0–250 μV, measurement range 100–200 Hz. Electromyography (EMG) is a technique for evaluating and recording the electrical activity produced by skeletal muscles. EMG is performed using an instrument called an electromyograph, to produce a record called an electromyogram. An electromyograph detects the electrical potential generated by muscle cells when these cells are electrically or neurologically activated. The signals can be analysed to discover human movements, in this case the arm motions. Electrodes were fixed on six muscles: Flexor Pollicis Brevis, Wrist extensor group, Biceps, shoulder Deltoid, chest Pectoralis Major and shoulder Upper Trapezius. Data Acquisition has been stored and analysis can lead to additional research paper. Results are not included in this seminar paper.
Conclusion This thesis describes experiments with audio-‐visual recordings of timpani, played with two different grips, two different articulations, using different mallets and varying tensions of membrane. High-‐speed video analysis show different velocities of the mallet depending on which type of stroke and grip are used. Staccato stroke and American grip have higher speed of the mallet compared to legato stroke and French grip. The impact on the sound is seen from the sound recording analyses. Staccato stroke has generally slightly shorter mallet-‐skin contact time. Comparing staccato and legato stroke there is a big difference regarding the wrist motion, which is much longer when playing legato or using French grip. Increasing the tension of membrane decreases the mallet-‐skin contact time. Different spectrograms of recorded sounds prove that the tone colour actually differs, so a timpanist should be aware that not only changing mallets but also applying different techniques (grips, articulation strokes) could differ the tone colour according to the musical context or wishing to blend with the orchestra as much as possible. Sometimes there is no time to change mallets while playing, so different grips serve very well to get a proper tone colour.
References
Beck, J. H. 1995. Encyclopedia of percussion. New York, London: Garland publ. Bertsch, Matthias. 2001. Vibration patterns and sound analysis of the Viennese timpani. ISMA, Perugia. Campbell, Murray, and Clive Greated. 1987. The Musician's Guide to Acoustics. Schrimer Books. Fletcher, Neville H., and Thomas D. Rossing. 1998. The Physics of Musical Instruments. New York: Springer-‐Verlag, 2nd edition. Forsyth, Cecil. 1982. Orchestration. New York: Dover Publications (1st ed. 1914, London: Macmillan) Hall, Donald E. 1991. Musical Acoustics. Belmont, California: Brooks/Cole Publishing Company, 2nd edition. Ravnikar, Bruno. 1999. Osnove glasbene akustike in informatike. Ljubljana: DZS. Rayleigh, John W. S. 1945. The Theory of Sound. New York: Dover Publications, 2nd edition. Schweizer, Steven L. 2010. Timpani Tone and the Interpretation of Baroque and Classical Music. New York: Oxford University Press. Wagner, Andreas. 2006. Analysis of Drumbeats – Interaction between Drummer, Drumstick and Instrument. Master's Thesis. Stockholm: The Royal Institute of Technology. Contact: Andraž Poljanec Slovenia-‐ Ljubljana email: andraz_poljanec1@t-‐2.net
