Drum membranes always have one clamped-edge circular node

Evidence

The boundary around which the membrane is stretched is the analog of the two points between which a string is stretched. With a few notable exceptions (the tabla for example manages a more harmonic relation of its modes by membrane density variations), almost all instruments use a membrane uniformly stretched in all directions and uniform in thickness (mass density). The equations and the solutions governing the motion and modes of such a membrane are well-known. — Eric J. Heller, Why You Hear What You Hear- An…, 1358 (#expands, via linked claim)

Categorization

• XREF: connects to: Striking a membrane at a nodal line silences that mode entirely; The tabla achieves near-harmonic modes through membrane density variation — Eric J. Heller, Why You Hear What You Hear- An…, 1358; Instrument stiffness versus tension determines how widely its modes are spaced (+1 more)

Related

• The tabla achieves near-harmonic modes through membrane density variation (similarity 0.90)
• Drum membrane modes are not harmonically related (similarity 0.86)
• Drum-kit drums are deliberately tuned non-pitched so they fit any musical key (similarity 0.84)
• A free-edged cymbal plate produces inharmonic, mixed modes (similarity 0.83)
• Membranes of any shape lack harmonic spectra, unlike strings (similarity 0.82)
• Percussion instruments divide into bar, membrane, and plate classes (similarity 0.82)
• A clamped drum edge always forms one circular displacement node. (similarity 0.81)
• Higher drum modes self-compensate and leave kettle volume unchanged (similarity 0.80)
• Nonharmonic natural modes give struck percussion instruments their clangy identity (similarity 0.80)
• Stiffness-based instruments space their modes wider apart than tension-based ones. (similarity 0.80)

Broader Connections

• Striking a membrane at a nodal line silences that mode entirely #responds-to (0.82)
• Percussion instruments divide into bar, membrane, and plate classes #exemplifies (0.80)
• The tabla achieves near-harmonic modes through membrane density variation #expands (0.75) — Eric J. Heller, Why You Hear What You Hear- An…, 1358
• Instrument stiffness versus tension determines how widely its modes are spaced #qualifies (0.72)