The kettledrum outputs a missing-harmonic series yet still conveys a clear pitch

Evidence

Table 4.2 shows the frequency ratios for the lowest 10 modes of an ideal supported membrane (these are the modes shown in Figure 4.31) and those for a kettledrum (adapted from Rossing, 2001). The modes that do not contribute significantly to the overall output from a kettledrum {(0,1), (0,2), (1,2), (2,2) and (0,3)} are indicated with an asterisk. It can be seen that the frequency ratios of the remaining modes are very close to being the second, third, fourth, fifth and sixth harmonics— making the kettledrum an orchestral instrument whose output has a “missing fundamental”—but this does not affect our ability to perceive its pitch as being associated with the missing fundamental, as discussed in Section 3.2.1. A kettledrum then will output a strongly pitched note, provided it is struck in a position that tends not to favor those modes marked with an asterisk in Table 4.2. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1306

Categorization

• XREF: Ties to the broader psychoacoustic theme of pitch perception from missing fundamentals — relevant to the reader’s listening interests, particularly the perceived pitch of ambiguous spectra. — connects to: A kettledrum’s tone is perceived with a missing fundamental — David Howard, Jamie Angus, coustics and Psychoacoustics, 1328; Missing-fundamental pitch does not involve hearing an actual sinusoidal partial — Eric J. Heller, Why You Hear What You Hear- An…, 2284; A melody remains recognizable from a single non-octave harmonic alone — David Howard, Jamie Angus, coustics and Psychoacoustics, 3024 (+7 more)
• CANDY: A fun fact: the timpani’s output is essentially the 2nd through 6th harmonics with no fundamental, yet we still hear its pitch clearly.

Broader Connections

• A kettledrum’s tone is perceived with a missing fundamental #corroborates (0.95) — David Howard, Jamie Angus, coustics and Psychoacoustics, 1328
• Listeners perceive missing fundamentals from the harmonics that remain #expands (0.90) — Professor Dr.-Ing. Hugo Fastl, Professor Dr.-Ing. Eberhard, Psychoacoustics- Facts and Models, 3278
• Removing low harmonics from a complex tone leaves its pitch unchanged. #corroborates (0.88) — Jennifer Lentz, Psychoacoustics- Perception of Normal…, 1192
• Listeners perceive the pitch of a bass note even when its fundamental is absent. #corroborates (0.85) — Toole, Floyd E, Sound reproduction- the acoustics and…, 316
• A pitch can be heard even when only its higher harmonics are present #corroborates (0.85) — Eric J. Heller, Why You Hear What You Hear- An…, 2039
• Sounds missing many harmonics still evoke a weak pitch sensation #corroborates (0.82) — Jennifer Lentz, Psychoacoustics- Perception of Normal…, 1295
• Harmonic amplitudes shape timbre and loudness but not pitch. #complicates (0.80) — Jennifer Lentz, Psychoacoustics- Perception of Normal…, 1195
• A melody remains recognizable from a single non-octave harmonic alone #exemplifies (0.78) — David Howard, Jamie Angus, coustics and Psychoacoustics, 3024
• Missing-fundamental pitch does not involve hearing an actual sinusoidal partial #qualifies (0.75) — Eric J. Heller, Why You Hear What You Hear- An…, 2284
• Clear musical pitch arises from regularly repeating acoustic waveforms #qualifies (0.75)