In Search of the Missing Fundamental: by Richard K. Jones
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Timpani “Harmonicity”

For synthetic skins, inharmonicity is usually due to an inferior tucking process of the Mylar into the metal hoop ( i.e. the flesh-hoop) in which case the head should not be used. Synthetic heads have no physical backbone as do skins from an animal however, some players believe the backbone or the grain lies in the direction that the Mylar is stretched during production. If this is truly the case then a Mylar head would have infinite backbones, not just one. The manufacturer REMO currently markets three synthetic timpani heads (clear, hazy and custom clear) with an artificial backbone marking. They do not however place the backbone marking on their higher end Renaissance products. The desire for the prominence of (mode 1,1) is perhaps why REMO fabricated their Mylar backbone products.

Some players will mount and place initial tension on a new Mylar head in order to find the best playing spot. Once the spot has been determined, they remove the tension and rotate the head into playing position. Having to find this sweet spot on new Mylar heads is something one should never have to do. Theoretically, if the thickness of the head is uniform, the tucking is consistent, and the fleshoop is flush, it should not matter where you place the logo; one spot should be as good as another. However in practice, this is not always the case as many players prefer to rotate the head to find the best playing spot instead of replacing it. Unfortunately, it is in the tucking process where the companies usually fail. The head should have the same relative tension, pitch and resonance around its circumference in the striking area. This can usually be determined before the head is mounted by visual and aural inspection. If you suspect the head to be inferior, replace it with a new one and return the old one to the manufacturer for a refund.

It is curious that before synthetics heads were introduced, dealing with backbone issues was always a concern for the player. On a natural skin, the backbone zone is the least likely to be chosen as a beating spot because of its lack of elasticity however, the acoustic benefit to the backbone is that because of its lack of elasticity, when placed correctly it acts as a natural physical nodal point for (mode 1,1) which is the principal tone of the timpano’s spectrum. This natural nodal point defining (mode 1,1) is one of the reasons natural skin heads have more of an immediate sense of pitch than do synthetic heads. Many players also comment on the ease of clearing natural skins compared to synthetic heads because the principal tone is so much easier to perceive. With modern synthetic heads, this lack of a backbone is perhaps a likely culprit for why tempering timpani heads presents a challenge for so many people; they simply lack that natural nodal point which helps define the instrument’s pitch.

Timpani pitch is comprised of a congress of similarly matched partials at each tuning lug organized into localized pitch zones. For a timpano to generate a sustained harmonicity of sound, it is imperative that the same frequency for the principal tone be maintained at each lug point as much as possible. However, the actual spectrum at each lug will contain upper partials of the preferred modes with slightly different frequencies. The frequencies of the upper partials will also change slightly for the various notes throughout the range of the drum due to their interaction with the various modes of air contained within the drum as well as slight changes in air density, which may occur during an extended playing period. This is why certain notes will sound better on a drum than others; why some days the drums really sing and other days they sound dead. Why some days the drums wake up quickly and some days they just don’t seem to respond well at all. Slight spectral differences from note to note on a drum is something that is inherent in timpani tone and virtually impossible to control or correct (see Donald Sullivan’s article). A consistent principal tone around the circumference of the drum is the objective, but it is difficult to maintain as a constant.

The harmonicity of a timpano’s spectrum is generated by an amalgamation of pitch zones all vibrating together to create a single perceived pitch structure. A congress of pitch zones, as it were. See Fig. 5a below. The more consistent these pitch zones are, the more the harmonicity will be perceived. Two basic channels and multiple zones within each of these channels define the amalgamated pitch structure. The number of zones in each channel is roughly dependent on the number of lugs the drum has. The two basic channels are the primary striking channel(s) and the secondary sustain channel(s). The primary striking channel(s) are defined by where the oscillation of the head is initiated. Since many players separate their hands 6”-8,” they hit the drum in more than one spot, consequently the primary channel tends to contain more zones. In order to have a varied tonal palette, many players will also strike different parts of the head so it is important that the pitch of every beating spot or zone in the primary channel(s) is consistent. The secondary sustain channel(s) will reinforce the primary strike channel(s) only if and when they are tempered the same as that of the primary channel(s). When the secondary sustain channel(s) are not consistent with the primary channel(s), a pitch shift occurs.

A circular membrane vibrates in two dimensions so the motion of the various modes interact with each other and can cancel or reinforce the motion of other modes depending on where and how the membrane is set into motion. Case in point, the normal striking point for a timpano is such that it reinforces the diametric modes of vibration and limits the vibrations of the concentric modes, especially mode 0,1 which is the fundamental frequency of the membrane.

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