Is there scientific evidence that a timpano can be tuned to achieve a true sense of harmonicity?
A seminal study on timpani harmonicity was conducted in 1973 by Arthur H. Benade of Case Institute of Technology/Case Western Reserve University in Cleveland, Ohio. In Severance Hall, Benade measured the frequency ratios of the first ten components of a timpano belonging to Cloyd Duff, principal timpanist of the Cleveland Orchestra. Duff’s instrument, a Dresdner Apparatebau Anheier/Jähne & Boruvka timpano with a calfskin head, was analyzed, though Benade did not specify which drum from Duff’s set was used.
The chart below shows the frequency data Benade reported for Duff’s timpano, tuned to C3 (130.8 Hz). The labels correspond to vibrational modes: P = (1,1) principal tone, Q = (2,1), R = (0,2), S = (3,1), T = (1,2), U = (4,1), V = (2,2), W = (0,3), X = (5,1), and Y = (6,1). The preferred modes are P, Q, S, U, X, and Y. Modes R, V, and W are more heavily damped and thus are not included in harmonicity analysis.
The missing fundamental effect might then give you the pitch C2 for the instrument under certain conditions and dynamic levels.1
Benade did not analyze amplitude or decay time, but the frequency alignment of the principal tone, fifth, octave, and tenth, Modes (1,1), (2,1), (3,1), and (4,1) was remarkably close to harmonic. The near-perfect harmonicity of Modes (3,1) and (4,1) contributes strongly to the perception of a coherent virtual pitch.
Many timpanists report improved pitch clarity and harmonic alignment when using calfskin heads. Fleischer and Fastl similarly observed more consistent harmonicity in the lower vibrational modes of calf heads compared to synthetic alternatives. This enhanced harmonicity is largely attributed to the greater mechanical compliance of natural skin. Unlike synthetic materials (which are often stiffer and more uniform) calfskin exhibits anisotropic elasticity and natural damping characteristics. Its variable fiber structure allows for more gradual stress distribution across the membrane, leading to better modal coupling and suppression of spurious overtones. As a result, the lower modes align more closely with harmonic ratios, contributing to a clearer and more focused pitch perception. 6
Natural vs. Synthetic: How Material Structure Affects Timpani Sound
The chart below shows a pitch-class equivalent representation of Duff’s timpano after the head had been cleared. The accompanying audio demonstrates only the preferred modes.
Benade goes on to further explain Duff’s clearing process for achieving timpani harmonicity.
It is not sufficient merely to get the overall skin tension correct for the desired pitch of the kettledrum, one must also make small additional changes in the tension produced by the various screws around the periphery of the drum. Cloyd Duff has a particularly apt word to describe this process of subsidiary adjustment which compensates for the inherent irregularity of the skin and for the possible eccentricity of the kettle rim. When everything is in perfect adjustment, the drum is said to have been “cleared.” It is a revelation to listen to an expert such as Duff clearing a good drum, making the tone ring with smoothness and clarity. This clearing in fact is a process of persuading the partials to more closely match the ideal. As a matter of fact, Duff apologized for his drum’s lack of tonal clarity–a season’s hard use had battered the skin to a point where he no longer considered it possible to bring it into proper adjustment. 2
Cloyd Duff was an extraordinary musician who was known for his wonderful tone and impeccable intonation. His legacy continues through the students he taught at the Cleveland Institute of Music; many of which hold positions in the world’s finest orchestras. His term clearing has now become synonyms with fine tuning the instrument.
It’s important to note that Benade documented only a single mode set, a snapshot of Duff’s drum spectrum. Whether this near-perfect harmonicity held consistently across the drum’s circumference is unclear. Given Duff’s own comment about the worn condition of the head, uniform results are unlikely. Nevertheless, the measurement provides a compelling benchmark for what is acoustically possible.
How does this compare to other studies? Good science must be replicable. Notably, the nearly harmonic spectrum Benade measured does not align with the findings of Thomas D. Rossing and colleagues, who, around the same time, reported significantly more inharmonic spectra. This discrepancy raises questions about methodology, equipment, and tuning skill.
When questioned, Benade replied to physicist W.E. Baylis:
The timpani question is more than a little messy. First of all, I stand by the accuracy of my frequency measurements made on the instruments of one (if not the) leading players in the world (Duff). Lesser players can be spotted at once from the “whack” they get instead of a “bong” when the drum is struck. That is, lesser players do not know how to tune out the inharmonicity very well. In this regard then, Rossing’s measurements do not have to be considered in conflict with my own. 3
Benade’s argument is persuasive: multiple variables, tensioning precision, membrane irregularities, kettle shape, and player technique, strongly influence the resulting spectrum. Rossing himself noted the difficulty of tensioning heads accurately in his own experiments. 4 His studies also used Ludwig Professional timpani, which may not match the acoustic quality of the Dresdner Apparatebau instruments used by Duff.
Since Benade’s and Rossing’s early work, numerous studies have analyzed timpani acoustics. Some confirm that timpani pitch is better understood as an interplay of pitch zones, multiple overlapping modes, rather than a single fundamental. 5 6
Given Benade’s high-quality measurement on a well-tuned professional instrument, and Duff’s expert execution of the clearing process, this study will serve as our benchmark, a “gold standard” for what is achievable in timpani harmonic alignment.
Benade’s measurements give us a practical benchmark for what “harmonic alignment” can look like on a real instrument in expert hands, but the value of that benchmark depends on whether we can describe it precisely. Terms like mode, node, preferred partial, degeneracy, lifted degeneracy, and missing fundamental are not academic decoration, they are the labels that let us talk about what Benade actually measured and what Duff actually adjusted. Without a shared vocabulary, “clear tone,” “ring,” and “inharmonicity” stay stuck as musician shorthand: useful in the studio, vague on the page. So before we go further into the Duff Clearing Process and the physics behind why small lug changes reorganize the spectrum, we need to define the key terms we’ll keep using.