Scientific Catalysts for Change
As mentioned earlier, this was also the Age of Enlightenment and Reason. What type of scientific evidence was there to act as a catalyst for change?
The theory of how vibrating membranes function has been of interest to the scientific community for well over two centuries. In the second half of the eighteenth century the noted Swiss mathematician and physicist Leonhard Euler (1707-1783) presented a treatise titled “De motu vibratorio tympanorum” (On the motion of vibrations in drums) to the Berlin Academy on January 22, 1761 and to the Petersburg Academy on May 17, 1762. It was later published in Novi Commentarii academiae scientiarum Petropolitanae in 1766. This is the first known treatise expressly devoted to the science of a vibrating membrane.
Later on in the century, the lesser known Italian scientist Giordano Ricatti (1709-1790) published his treatise “Delle vibrationi del tambour” (vibration of the drum) in the Saggi scientifici e letterari dell’Academia di Padova in 1786. According to Peter Zimmerman in his 1996 paper “Zur Theorie der schwingenden Membran bei Leonhard Euler und Giordano Riccati: Erfindung, Nacherfindung, Fama“, these two treatises paved the way for our mathematical understanding of how a vibrating circular membrane functions.1
Perhaps the most visible contribution to the understanding of vibrating circular membranes came from the German physicist and musician, Ernst Florens Friedrich Chladni (1756–1827). One of Chladni’s best-known achievements was inventing a technique to show the various modes of vibration on a mechanical surface now know as the Chladni patterns. Chladni’s technique was first published in 1787 in his book, “Entdeckungen über die Theorie des Klanges” (Discoveries in the Theory of Sound).2 These patterns are still in use today to illustrate the vibrational modes of a mechanical surface. Chladni was said to have disbanded his own experiments on real timpani because the heads were not homogeneous enough for his scientific/experimental use.
One must take into consideration that for the mathematicians, scientists and physicists (even during that period), an ideal circular membrane was defined as an absolutely round membrane, infinitely thin, perfectly flexible, completely homogeneous, evenly and uniformly tensioned where the outer circular edge of the membrane constitutes a fixed boundary condition in an in vacuo state (in a vacuum). This type of membrane exists in theory only.
Theory
It is conjectured that a meditated shift to a different playing spot (from center to edge) for “indoor” or concert performances was a gradual evolution that began as early as the second quarter of the 18th century, and was fueled by the music the Rococo and early Classical periods. Contributing factors:
1) With more pitch, sensitivity and musicality being requested of the timpanist due to new demands in the music of the symphony orchestra, innovation was necessary.
2) A growing awareness and understanding about how different thicknesses of heads (based on scientific evidence) could make an improvement in the sound of the instrument.
3) With the demise of the Guilds, military/court, timpanists were gradually being replaced by contracted civilian musicians in the orchestra who were not bound by rigid Guild traditions, and were more open for experimentation and change, and consequently, willing to share their innovations. It was the advent of the orchestral timpanist.
These actions and ideas inevitably led to the growing use of thinner and more homogeneous heads that consequently became more accessible to the new generation of orchestral timpanists via processing improvements as a result of the industrial revolution.
NB To reiterate, 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.
Consequently, the conscious choice of the player to experiment with heads that were thinner and more homogeneous, led to the drums producing more upper partials (more of the Preferred Modes), which gave the instruments a better sense of pitch and greater sensitivity for indoor playing.
The new orchestral timpanists quickly discovered that in order to make use of this new-found pitch, they needed to make slight adjustments to the traditional “outdoor” off-center playing spot by moving closer to the edge of the drum. They also no doubt discovered that as the head was vibrating more, they would need to adjust how they struck the head in order to not damp the sound. There were professional timpanists of that time that were probably no different than the timpani professionals today who enjoy tinkering with their instruments, and their technique to improve the sound. Unfortunately, the documented pedagogy for this new learning (Kastner 1840, Pfundt 1849) would not arrive for a number of years yet.