Tube end conditions determine which harmonic partials an instrument produces

Evidence

Half-open straight tubes are missing half their partials, imparting a certain characteristic “hollow” sound to the instrument. The clarinet is a prime example. A double-open tube has a full spectrum of harmonic partials, but keeping the playing end open is a challenge. The flute works well as a double-open tube, but a tube with a reed is necessarily closed at the reed. If a reed is attached to the apex of a conical horn, a saxophone is born. — Eric J. Heller, Why You Hear What You Hear- An…, 1461

In a tube of finite length, the terminations reflect waves back so that standing waves appear, resulting in modes and resonance frequencies. Figure 2.12 depicts the lowest modes in a tube that is left open at both ends and in another tube that is closed at one end. The first case is approximated, for example, in the flute, generating all harmonics, and the second case in the clarinet, where (low order) even harmonics are weak due to lack of resonance. — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 242

Categorization

• SEED: Angle: ‘Why the clarinet sounds hollow but the saxophone doesn’t’ — a musical-instrument-design explainer built purely from boundary conditions at tube ends.
• SHARE: Send to a musician friend — the physical origin of the clarinet’s hollow timbre versus the sax’s full spectrum.
• XREF: Explains why flute and clarinet timbres differ — connects to any instrument acoustics knowledge and to wind instrument sound synthesis. — connects to: Resonator geometry shapes which harmonics appear in an instrument’s sound — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1228
• corroborated: 2 independent passages support this claim — Eric J. Heller, Why You Hear What You Hear- An…, 1461; Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 242