Pipe length sets pitch while diameter and material shape harmonic strength

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 (#corroborates, 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 (#expands, via linked claim)

Categorization

• XREF: connects to: Doubling all pipe dimensions lowers its fundamental tone by an octave; String pitch depends on mass per unit length, length, and tension; Wide pipes are weak in upper harmonics due to diameter ratios. (+8 more)

Related

• An open-open pipe’s modes form a complete harmonic series at integer multiples (similarity 0.87)
• Cylindrical stopped-pipe bores support only odd-numbered modes, forcing extra finger holes (similarity 0.86)
• Brass instruments are lip-driven pressure valves that behave acoustically like stopped pipes. (similarity 0.85)
• Doubling all pipe dimensions lowers its fundamental tone by an octave (similarity 0.83)
• The player’s lips form a variable double reed making brass a stopped-pipe acoustics (similarity 0.83)
• Brass instrument design transforms odd-only pipe modes into a near-complete harmonic series (similarity 0.83)
• Wide pipes are weak in upper harmonics (similarity 0.82)
• An open pipe’s fundamental period equals twice its length divided by wave speed (similarity 0.82)
• Overblowing a pipe jumps its pitch to the next resonator-supported harmonic (similarity 0.82)
• Wide organ pipes suppress upper harmonics in their output (similarity 0.82)
• Resonator length and end condition alone determine flue pipe pitch (similarity 0.82)
• String pitch depends on mass per unit length, length, and tension (similarity 0.79)
• A stopped pipe sounds an octave lower than an open pipe of equal length (similarity 0.79)
• Mixed-end tubes resonate only at odd multiples of the fundamental frequency (similarity 0.79)
• Body size relative to open-string pitch shapes each string instrument’s distinctive timbre. (similarity 0.79)

Broader Connections

• Overblowing a pipe jumps its pitch to the next resonator-supported harmonic #corroborates (0.85) — David Howard, Jamie Angus, coustics and Psychoacoustics, 1211
• Reed material and support determine its harmonic content #corroborates (0.82)
• Brass instrument design transforms odd-only pipe modes into a near-complete harmonic series #expands (0.80) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1250