Science & The Schalltrichter
Early in seventeenth century Germany as the pairing of timpani and trumpets began being utilized more regularly in indoor concert music, there was a growing desire to acquire more pitch, resonance and musical sensitivity from the instruments. Most portraiture of the period and iconographic evidence (open to speculation) suggests that for outdoor playing, the drums were generally struck dead or slightly off-center. This method of producing pitch (striking the drum dead/off center) is in fact how noted musicologists Edmund Bowles 53 and John Michael Cooper 29 believe timpani produced pitch until the very end of the 18th century. This purportedly yielded a sound with a very percussive attack with a quick decay, yet the sound still had some discernible pitch.
Portrait of Prince Heinrich von Schwarzburg-Sondershausen
on Canvas circa 1700. Schlossmuseum Sondershausen (Inv.-Nr. Kb 161)
Fine for voluminous and percussive outdoor playing where only a relative sense of pitch was needed, but was this sound the norm for indoor concerted performances as well? It seems highly unlikely that the discerning composers of that period would have willing accepted such a sound for their music. It would also seem logical that choosing a different playing spot (i.e. near the edge as done today) might have solved the problem. However, that was not the method, nor the characteristic sound of the “outdoor” instruments at that time. In fact, striking near the drum near the edge would have produced a very weak, discordant sound. Why?
For the outdoor instruments, in general, poor mechanical tolerances of the bowl and tensioning system along with inferior (half-tanned, not vellum) heads of inconsistent membrane thicknesses made it impossible to adjust the instrument in a manner where the drum was able to produce a strong, clear and sustained sense of pitch. Today, by striking the drum near the edge, the modern timpanist excites what are referred to as the preferred diametric modes, which when aligned correctly, can produce a sustained sense of pitch This occurs because the modern membrane is thin and homogeneous enough to sustain vibrations. The mechanical tolerances of modern instruments are also far superior to those of their early predecessors.
With early timpani, because the membrane did not vibrate evenly (non homogenous, thick head), when struck near the edge, the sound produced would be extremely weak and discordant; the principal tone (the sound we hear as the pitch of the drum) and upper partials were not able to be uniformly adjusted. The accepted technique at the time was to strike closer to the center or slightly off center. This would still excite mode 1,1 to some extent (again, what we hear as the pitch of the drum), but not the upper preferred modes, which provide “harmonic” support, sustain and resonance to the sound. Interestingly enough however, when striking near the center of the drum the early timpanist would have excited something called mode 1,2 (the sixth resonant mode), which on an air loaded membrane has a frequency that is about an octave above mode 1,1. (the principal tone) This mode 1,2 is only some what efficient at radiating its energy so its sound lingers briefly. The result was a sound with a slight sense of pitch, but little or no sustain or resonance.
One solution devised to improve the sustain of the sound was to insert a sound-bell inside of the drum that would vibrate or oscillate as the head was struck. It was believed that this addition would add resonance, as well as collect and focus the vibrations of the head, which purportedly added more sustain to the sound. The appendage to the inside of the bowl first appeared in the German-speaking regions of Europe in the early seventeenth century and was called Schalltrichter, literally sound-bell. The funnel-shaped bell was intended to increase the resonance of the drums. It was clearly established as an essential part of the instrument by the mid-eighteenth century because J.P. Eisel’s Musicus autodidactos (1738), states that when the drum is hit, the Schalltrichter vibrates back and forth, helping to create a “resonant reverberance” (saussenden Nachklang).
It apparently was a continued success because as chronicled by Ben Harms, “They were a common feature in timpani fabricated in Germany for close to 300 years, ca. 1600-1880.”28 Harms further traces the use of Schalltricther in his article Three centuries of “Schalltricther” in German timpani published in Perkussionsinstrumente in der Kunstmusik vom 16. bis zur Mitte des 19. Jahrhunderts : XXXV. Wissenschaftliche Arbeitstagung und 28. Musikinstrumentenbau-Symposium Michaelstein, 4. bis 7. Oktober 2007. The article provides no scientific evidence (other than it was considered to be “an acoustical enhancement”) as to how Schalltricther actually function, only translations of published German writings that mention Schalltricther and documentation of different sizes and styles of Schalltricther that remain extant in preserved historical instruments.58
Schalltrichter Removed from Timpani
courtesy of The National Music Museum
Schalltrichter Inside of Timpani
courtesy of The National Music Museum
The Science
From a physics of vibrating circular membranes perspective, when you strike modern timpani near or in the center, you excite a different set of modal vibrations from when you strike timpani in the modern traditional method. When striking the drum near the center, you excite what are called the concentric modes. Using the concentric modes (or composites) to help produce pitch is not unwarranted, as this is how the heavily loaded head of Tabla (daya) produces a sense of pitch57, but will that work for timpani? It can if the head is heavily loaded, which in this case would mean if the head were thick enough. Interestingly enough, Rosssing et al.,25 Fleischer and Fastl,54 Tronchin,55 and others have documented that the sixth mode of vibration (mode 1,2 ) is very close to a 2:1 ratio, i.e. the octave above mode 1,1 the principal tone. This sixth mode of vibration, mode 1,2 (which is a composite mode) is also very close in frequency to preferred mode 3,1 which is also the octave above the principal tone mode 1,1 as well. From an aural perspective, when the vibrations are initiated by targeting mode 2,1, combining the sound of the three modes (mode 1,1 – mode 1,2 and mode 3,1), your brain interpolates a short lived pitched sound, with a near harmonic octave overtone, provided the head is properly loaded.
Mode 1,2 is unique in that it is a combination of both, a single diametric, and two concentric modes. Mode 1,2 does not radiate energy very efficiently; it has somewhat of a quadrupole type behavior. Thus, the mode 1,2 takes a relatively long time to decay compared to mode 0,1, the actual fundamental, which would also be excited when struck slightly off-center. It is in fact mode 1,2 that helps create the “Octave Harmonic” effect used by mid 20th century composers, including Elliot Carter.
Question:
Is the lack of efficient radiation of mode 1,2 strong enough to produce a viable pitched sound, or just a thud as is does on modern timpani?
Mode 1,2
Figure 2e.1
The sixth mode of vibration mode 1,2, which vibrates with two
concentric modes of vibration and one diametric mode of vibration:
the nodal lines will encompass the entire circumference and diameter of the head
Mode 1,2 in motion
Animation courtesy of Dr. Dan Russell, Grad. Prog. Acoustics, Penn State
For early timpani equipped with thick non-homogeneous heads, if the head was struck slightly off-center, the acoustic effect would be a pitch comprised of a weak principal tone, an octave and possibly a tenth, if the head was loaded properly (i.e., mass/thickness). Because of the presence of the bowl, the concentric modes radiate their energy efficiently, which means that they decay very quickly and are audibly weak; a sound which is considered unmusical by today’s standards. However, since mode 1,2 takes a relatively long time to decay (compared to other concentric modes), provided that mode 1,2 was the principal mode to be excited, as the head was struck slightly off-center, a period drum with a schalltrichter placed close enough to the head would be able to produce a sound that would affect this mode to some extent. If the diameter of the bell were large enough compared to the diameter of the bowl, and placed close enough to the head, the schalltrichter would also influence the actual frequencies of the other audible modes as well.
The acoustic energy of these modes could also be directed through the horn and out the bottom of the drum, as well as to the bowl and the horn itself adding a very small amount of extra resonance to the sound. If the sound were strong enough, the spectrum of a quasi-harmonic octave would certainly be musical enough, it just wouldn’t be very resonant or have much sustain. As mentioned earlier, this method of producing pitch (striking the drum dead/off center) is in fact how noted musicologists Edmund Bowles 53 and John Michael Cooper 29 believe timpani produced pitch until the very end of the 18th century. The addition of the Schalltrichter may have improved the sound enough to where the player would not have to play the drum at high dynamic levels in order to acquire more musical sensitivity from the instrument. Again, it seems highly improbable that later composers like Haydn, Mozart and Beethoven would have accepted such a sound. It is important to note that the addition of the Schalltrichter appeared on drums of the Germanic speaking cultures of Central Europe, and does not appear to be an important addition to the drums built in England, France or Italy. 28 58
Schalltrichter or not, this method of striking and playing the drum (slightly off-center) is in fact still used today by some traditional Cuban Timbaleros. Below is a short video showing the traditional approach to tuning Cuban Timbales, and playing the Cuban “danzón” on Timbales Cubanos. Notice where the timbalero is striking the timbales for the primary notes; near dead center on *do* and just slightly off center for *sol* yet there is still strong sense of the key of F. When he strikes the timbales in the more traditional location, the instruments produce a weak, thin sound. It is not know whether these timpani employ Schalltrichter.
| Tutorial on how to tune Cuban Timbales, and play Cuban Danzón with Canelo Vasquez, drummer and director of the Super Lamas Group of Actopan. |
The heads used on these drums (white opaque) are not half-tanned skins as would have been used on early outdoor cavalry drums, yet they are thick enough to not yield a sustaining pitch when struck near the edge, so the player excites the sound by striking slightly off-center. The voice of these drums (when struck dead/off-center) produces a very short envelope, which is probably very similar to the sound of early 17th and 18th century timpani. Perhaps even more resonant due to the modern heads. If the sound of these drums is even somewhat similar to the sound of early 17th and 18th century timpani, it is easy to surmise that a sustained roll would be executed with a buzz or double stroke, not with a single stroke technique.
Below are other examples of traditional Cuban Timbaleros playing a danzon on traditional timbales in a orquestas típicas style. Again, the players are striking the drums near dead-center, or slightly off-center producing a sound with a relatively short envelope, yet with a distinct pitch (Polo excerpt), or a relative pitch (Veracruz excerpt). This is due to the prominence of mode 1,2 in the spectrum. A clear dominant/tonic relationship (sol-do, C-F) can be heard in the “Polo” excerpt. Again, it is not know whether these timpani employ Schalltrichter.
DANZON EN EL ZOCALO DE VERACRUZ
The great Master Polo, playing a Cuban Danzón
NB The head (membrane) is in fact, the only viable source for the production of a pitched sound that can be varied or shifted to any significant degree. The other parts of the instrument, i.e. the bowl size and volume of internal air simply serve as system modifiers.
Answer:
When struck off-center, a properly loaded head (i.e. thick enough) limits the vibrations of the upper diametric modes (preferred modes) and promotes the vibrations of the lower concentric mode 1,2 to the extent that what is heard radiating from the timpano is a quasi pitched sound with a relatively short sustain.
Animation by Clayton Shonkwiler
The addition of Schalltrichter (as documented by Harms,58) could in fact be “an acoustical enhancement” to early timpani sound, but did it really evolve timpani that much? At this point in the evolution of timpani, we are still in the “Ars Antiqua” period of timpani development. The question of why and when did timpanists begin using thinner heads and shift to a different playing spot still remains.