Mixed-end tubes resonate only at odd multiples of the fundamental frequency
Evidence
In a complete brass instrument, it is possible through the use of an appropriately shaped bell, mouthpiece and mouthpipe to construct an instrument whose modes are frequency shifted from the odd-only modes of a stopped cylindrical pipe to being very close to a complete harmonic series. In practice, the result is a harmonic series in which all modes are within a few percent of being integer multiples of a common lower-frequency value except for the first mode itself, which is well below that lower-frequency value common to the higher modes, and therefore it is not harmonically related to them. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1250 (
#qualifies, via linked claim)
Categorization
- XREF: connects to: Sounding boards do not amplify every frequency via resonance; A closed narrow-end cone acts like a double-open cylinder giving all harmonics — Eric J. Heller, Why You Hear What You Hear- An…, 1472; A closed pipe end reflects a pulse with no energy loss without moving (+11 more)
Related
- Brass instrument design transforms odd-only pipe modes into a near-complete harmonic series (similarity 0.87)
- Cylindrical stopped-pipe bores support only odd-numbered modes, forcing extra finger holes (similarity 0.85)
- The conical horn converts a closed-reed tube into a full harmonic instrument (similarity 0.84)
- An open-open pipe’s modes form a complete harmonic series at integer multiples (similarity 0.83)
- A stopped cylindrical pipe supports only odd-numbered modes (similarity 0.83)
- A closed narrow-end cone acts like a double-open cylinder giving all harmonics (similarity 0.82)
- The source excites all harmonics even when a resonator only supports odd ones. (similarity 0.82)
- Cylindrical stopped pipes support only odd-numbered modes, making instruments sound an octave lower (similarity 0.82)
- Reed excitation injects all harmonics even when resonator rejects even modes (similarity 0.81)
- Tube end conditions determine which harmonic partials an instrument produces (similarity 0.80)
- Even harmonics appear in clarinet sound despite its closed cylindrical resonator (similarity 0.79)
- Of four brass instruments, only the trumpet shows prominent high harmonics (similarity 0.79)
- Sounding boards do not amplify every frequency via resonance (similarity 0.79)
- Brass instruments are lip-driven pressure valves that behave acoustically like stopped pipes. (similarity 0.79)
- Pipe length sets pitch while diameter and material shape harmonic strength (similarity 0.79)
Broader Connections
- A closed cylindrical resonator filters sound to odd harmonics
#corroborates(0.98) - Even harmonics appear in clarinet sound despite its closed cylindrical resonator
#qualifies(0.95) - Brass instrument design transforms odd-only pipe modes into a near-complete harmonic series
#qualifies(0.92) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1250