Cylindrical stopped-pipe bores support only odd-numbered modes, forcing extra finger holes

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 (#expands, via linked claim)

If a pipe is overblown, its f0 jumps to the next higher mode that the resonator can support: up one octave to the second harmonic for an open pipe, and up an octave and a fifth to the third harmonic for the stopped pipe. — David Howard, Jamie Angus, coustics and Psychoacoustics, 1211 (#expands, via linked claim)

Categorization

• XREF: connects to: One closed and one open pipe end supports only odd quarter-wavelength standing waves; Brass instrument design transforms odd-only pipe modes into a near-complete harmonic series — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1250; A closed pipe’s first mode sits an octave below an open pipe’s (+5 more)

Related

• A stopped cylindrical pipe supports only odd-numbered modes (similarity 0.89)
• An open-open pipe’s modes form a complete harmonic series at integer multiples (similarity 0.88)
• Brass instrument design transforms odd-only pipe modes into a near-complete harmonic series (similarity 0.87)
• Brass instruments are lip-driven pressure valves that behave acoustically like stopped pipes. (similarity 0.86)
• Pipe length sets pitch while diameter and material shape harmonic strength (similarity 0.86)
• Cylindrical stopped pipes support only odd-numbered modes, making instruments sound an octave lower (similarity 0.85)
• Mixed-end tubes resonate only at odd multiples of the fundamental frequency (similarity 0.85)
• The player’s lips form a variable double reed making brass a stopped-pipe acoustics (similarity 0.84)
• Overblowing a pipe jumps its pitch to the next resonator-supported harmonic (similarity 0.83)
• Open pipe ends invert pulse polarity while closed ends preserve it (similarity 0.82)
• A stopped pipe sounds an octave lower than an open pipe of equal length (similarity 0.81)
• Conical bores suppress the reflection at the narrow end, yielding all harmonic modes (similarity 0.81)
• Stopped organ pipes trade space savings for weaker harmonic spectra (similarity 0.81)
• An open pipe’s fundamental period equals twice its length divided by wave speed (similarity 0.80)
• The conical horn converts a closed-reed tube into a full harmonic instrument (similarity 0.79)

Broader Connections

• Brass instrument design transforms odd-only pipe modes into a near-complete harmonic series #expands (0.85) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1250
• Stopped pipes save space but sacrifice even-numbered harmonics #expands (0.85)
• Overblowing a pipe jumps its pitch to the next resonator-supported harmonic #expands (0.80) — David Howard, Jamie Angus, coustics and Psychoacoustics, 1211
• An open-open pipe’s modes form a complete harmonic series at integer multiples #qualifies (0.75)
• A closed pipe’s first mode sits an octave below an open pipe’s #expands (0.70)
• A stopped pipe sounds an octave lower than an open pipe of equal length #expands (0.70) — David Howard, Jamie Angus, coustics and Psychoacoustics, 1198