A closed narrow-end cone acts like a double-open cylinder giving all harmonics

Evidence

The upshot is that a cutoff cone closed at its narrow end is a lot like a double-open cylinder of the same length. The resonances form a harmonic series, with every frequency represented (no missing partials, unlike the clarinet, which is a half-open cyclinder). The angle between the axis of the cone and its walls can be as little as 1/2 degree in some instruments. An oboe’s bottom note is an octave higher than a clarinet of the same length. — Eric J. Heller, Why You Hear What You Hear- An…, 1472

Categorization

• DEFINE: Explains the acoustic equivalence between a cutoff cone and a double-open cylinder, and why oboes exceed clarinets an octave.
• SHARE: Send to anyone who plays oboe or clarinet — explains concretely why the oboe sits an octave higher than a same-length clarinet.
• corroborated: 2 independent passages support this claim — Eric J. Heller, Why You Hear What You Hear- An…, 1472
• XREF: connects to: The conical horn converts a closed-reed tube into a full harmonic instrument; A closed cylindrical resonator filters sound to odd harmonics; Even harmonics appear in clarinet sound despite its closed cylindrical resonator (+5 more)

Broader Connections

• A closed cylindrical resonator filters sound to odd harmonics #contradicts (0.90)
• Mixed-end tubes resonate only at odd multiples of the fundamental frequency #contradicts (0.85)
• One closed and one open pipe end supports only odd quarter-wavelength standing waves #contradicts (0.85)
• Open-open tubes support standing waves with the same half-wavelength rule #expands (0.80)
• Even harmonics appear in clarinet sound despite its closed cylindrical resonator #exemplifies (0.75)
• Brass instrument design transforms odd-only pipe modes into a near-complete harmonic series #exemplifies (0.75) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1250