Brass instrument design transforms odd-only pipe modes into a near-complete harmonic series

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

Categorization

• DEFINE: Explains the acoustic engineering goal of brass instruments: converting odd-only pipe modes into near-harmonic modes.
• corroborated: 2 independent passages support this claim — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1250
• XREF: connects to: The conical horn converts a closed-reed tube into a full harmonic instrument; 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; Loudly driven brass columns self-organize into phase-locked shock waves. (+16 more)

Broader Connections

• Brass instruments differ sharply in how many harmonics their tones carry #qualifies (0.80)
• A closed pipe’s first mode sits an octave below an open pipe’s #expands (0.75)
• Organists shape timbre by selectively reinforcing harmonics of one series #complicates (0.72) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1526