The Timpani

The timpani has a round head stretched over a sealed enclosure. The tension may be altered by means of a footpedal which actuates tensioning elements.

The choice of striking point emphasizes the preferred modes of the circular membrane. The sounded frequencies are further influenced by the enclosed air cavity.

Timpani details
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Timpani Details

The round head of a timpani can vibrate in a large number of vibrational modes. The fundamental is not generally used in music; it is highly damped and does not produce as pleasing a sound as some other modes. When the head is struck a few inches from the rim, the timpani's fundamental mode is not excited. The player tries to excite the preferred modes 11, 21, 31, 41, 51, 61 . The head is struck about halfway to three quarters of the way out from the center. This is near the nodal line of several of the modes which minimizes their contribution to the sound. The actual sounded frequencies are further affected in a significant way by air damping to finally produce the sequence of frequencies actually heard from the instrument.

By contrast, the snare drum is struck in the center and only excites the 01, 02, 03, modes (Sundberg, The Science of Sounds p91)

The pedal connects to the lugs which control the tension in the membrane. Early timpani had calfskin heads. Modern timpani heads are usually made of mylar.

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Sounding Frequencies, Timpani

The timpani sound involves the vibrational modes of a circular membrane, but the technique of playing specifically excites the preferred modes of the membrane. These are further affected by air damping, which finally leads one to the set of frequencies which are actually produced by the instrument. An actual set of frequencies is reported by Benade for an instrument which is tuned to C3 (130.8 Hz).
Mode
Theoretical
Ratio
Measured
Ratio
P
1.00
1.00
(130.8 Hz)
Q
1.35
1.504
R
1.67
1.742
S
1.99
2.00
T
2.30
2.245
U
2.61
2.494
V
...
2.800
W
...
2.852
X
...
2.979
Y
...
3.462
From Benade, Ch 9, p143-144. Measured timpani of Cloyd Duff of Cleveland Orchestra
It is remarkable that the tones actually produced include the musical intervals of a fifth and octave above the fundamental (P, Q, S). Also note that with respect to C2 (65.4 Hz) the resonances form a harmonic sequence up to the 7th harmonic (P=2, Q=3, S=4, U=5, X=5.96, Y=6.92). The missing fundamental effect might then give you the pitch C2 for the instrument.
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Percussion instruments

Musical instruments

Reference
Benade
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