An open-open pipe’s modes form a complete harmonic series at integer multiples

Evidence

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)

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 (#corroborates, via linked claim)

Complex tones containing frequencies that are related to each other by integer multiples are called harmonic sounds or harmonic tones. The lowest frequency of a complex tone is the fundamental frequency (f0), and the harmonics occur at integer multiples of the fundamental frequency. There are numerous examples of harmonic sounds in our daily lives, such as vowels and sounds typically generated by stringed, woodwind, and brass musical instruments. — Jennifer Lentz, Psychoacoustics- Perception of Normal…, 1180 (#exemplifies, via linked claim)

Categorization

• XREF: connects to: Open-open and open-closed tubes produce different harmonic series; Open-open tubes support standing waves with the same half-wavelength rule; Brass instrument design transforms odd-only pipe modes into a near-complete harmonic series — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1250 (+8 more)

Related

• Cylindrical stopped-pipe bores support only odd-numbered modes, forcing extra finger holes (similarity 0.88)
• Pipe length sets pitch while diameter and material shape harmonic strength (similarity 0.87)
• Brass instrument design transforms odd-only pipe modes into a near-complete harmonic series (similarity 0.86)
• An open pipe’s fundamental period equals twice its length divided by wave speed (similarity 0.84)
• Mixed-end tubes resonate only at odd multiples of the fundamental frequency (similarity 0.83)
• Overblowing a pipe jumps its pitch to the next resonator-supported harmonic (similarity 0.82)
• Brass instruments are lip-driven pressure valves that behave acoustically like stopped pipes. (similarity 0.82)
• The conical horn converts a closed-reed tube into a full harmonic instrument (similarity 0.82)
• Harmonic tones are integer multiples of a fundamental frequency (similarity 0.82)
• Open and stopped organ pipes audibly start on different overblown harmonics (similarity 0.82)
• Chiff-voiced open pipes briefly sound an octave high at onset (similarity 0.81)
• A stopped cylindrical pipe supports only odd-numbered modes (similarity 0.81)
• The harmonic overtone series of strings is a lucky gift, not a fixable property (similarity 0.80)
• Open pipe ends invert pulse polarity while closed ends preserve it (similarity 0.80)
• Open and stopped organ pipes correspond to open-open and open-closed acoustic tubes. (similarity 0.79)

Broader Connections

• Brass instrument design transforms odd-only pipe modes into a near-complete harmonic series #corroborates (0.85) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1250
• Overblowing a pipe jumps its pitch to the next resonator-supported harmonic #expands (0.85) — David Howard, Jamie Angus, coustics and Psychoacoustics, 1211
• Harmonic tones are integer multiples of a fundamental frequency #exemplifies (0.80) — Jennifer Lentz, Psychoacoustics- Perception of Normal…, 1180
• Stopped pipes save space but sacrifice even-numbered harmonics #qualifies (0.75)
• Acoustic standing waves are termed modes with numbered order by frequency #expands (0.70)