In Search of the Missing Fundamental: by Richard K. Jones
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How “The Weather” Affects Timpani Pitch – Environmental Considerations

The consistency of harmonic timpani pitch requires stable environmental conditions. A crucial component to the production of harmonic timpani pitch is how the vibrating head interacts with the air above and below it (air loading). Equalizing the density of the volume of air inside the drum (i.e. air pressure, temperature and moisture content) to that of the density of the air above the head is integral. The interaction between the masses of air inside and outside of the drum contributes significantly to the actual pitch and perceived harmonicity of timpani. Ideally, these masses of air should have the same density as when the heads were last tempered in a stabilized environment. Since ideal conditions are not always feasible, tempering is sometimes necessary when environmental conditions change. Caveat: Temper only when the drums will remain in consistent environment for a substantial amount of time. Temper only after the drums have acclimated to the new environmental conditions.

Both the vibrating head and the volume of air inside of the bowl have specific modes of vibration; the air masses inside and outside of the bowl interact with the head. This interaction has a direct influence on how the head will vibrate based on the external air density and the volume and density of air contained within the bowl.

Preferred ModesPreferred Modes (1,1)  (2,1) (3,1) (4,1) (5,1) of the vibrating head.40

Air-Modes-Kettle

Vibrational modes of the air enclosed within the bowl 41

The frequencies of the vibrational modes of the volume of internal air enclosed within the bowl are higher than the frequencies of the membrane modes to which they couple,41 but since the motion of these air modes is dependent on the viscothermal (viscosity and thermal conduction) characteristics of the enclosed air, changes in air density can cause these modes to interact differently with upper partials of the vibrating membrane, which have similar frequencies. Consequently, certain notes will tend to sing more on some days than others or the overtones will tend to be sound more in-tune depending on changes in environmental conditions.

With the head being the primary vibrating system, the air mass outside of the drum reacts against the volume, mass and stiffness of the air modes enclosed inside of the bowl adjusting the vibrating modes of the head, in particular, a small group of partials called the preferred modes. When aligned just right via the proper tensioning of the head, these preferred modes of the air-loaded head will vibrate as a harmonic system giving the drum its sense of pitch, harmonicity, and projection.

Because the head is clamped at the bearing the edge (lip), the bowl becomes a sealed enclosure acting as a baffle (not as a resonator). This baffle separates the internal and external air masses and prevents them from interacting with each other, much like that of an enclosed speaker system.

The vibrating system (significant tension on the head is assumed) is influenced by three factors:

1) the volume and viscothermal characteristics of the air modes inside of the bowl
2) the density of the air pressure outside of the bowl
3) the motion of the vibrating head

The three parts are of equal importance in determining the frequencies and overall vibrational shapes (preferred modes) that define the pitch and harmonicity of the instrument. When the conditions of the internal and external air masses differ significantly, the  preferred modes of the vibrating head do not respond as they did when the head was originally tempered and the sense of harmonicity and projection is affected.

Head-BowlGraphic courtesy of Gordon Reid

Three Part System Defining
the “Harmonicity” of Timpani Pitch

1) internal air modes
2) external air pressure
3) vibrating membrane

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