The air column is the "invisible string" of a wind instrument. Its shape—the —determines the harmonic recipe of the sound. Cylindrical vs. Conical Bores
Apply undercutting and modify chimney heights to align the fundamental pitches with their corresponding upper octaves.
Produces all harmonics (fundamental, octave, 12th, double octave, etc.). The frequencies follow the integer pattern: Acoustic Formula: The fundamental wavelength ( ) is twice the length ( ) of the tube: λ=2Llambda equals 2 cap L Cylindrical Bores (Closed at One End) The air column is the "invisible string" of
: The clarinet acts as a closed pipe, supporting only odd harmonics ( ), which gives it a distinct "hollow" sound.
The arrangement of toneholes along the bore forms a , which behaves as an acoustic filter with a characteristic cutoff frequency . Below the cutoff frequency, the lattice acts as a stop-band: low-frequency waves are reflected by the first open hole, which provides an acoustic "short circuit" to the outside air, fixing the pressure at atmospheric and creating a pressure node. Conical Bores Apply undercutting and modify chimney heights
Raise the pitch and offer a freer blowing experience. 4. Tuning, Intonation, and Venting
An instrument tuned in equal temperament is a series of compromises. Each tonehole must be sized and positioned so that: The arrangement of toneholes along the bore forms
Whether you are a musician wondering why your clarinet squeaks, a physicist curious about acoustics, or a luthier attempting to build the next great saxophone, Hopkin’s work provides the vocabulary to understand the "why" and "how" of wind instruments. It is a testament to the elegance of physics—that the sublime beauty
The layman’s mistake is assuming a tonehole acts as a hard cutoff—that the wave simply stops at the hole. Hopkin explains the concept of . A tonehole does not act exactly where it is drilled; the acoustic "end" of the tube extends slightly past the hole. This phenomenon is known as the End Correction .
, this 42-page manual is specifically designed for makers—particularly of flutes and reed instruments—who want a "nuts-and-bolts" understanding of how bore shape and tonehole placement dictate sound. Bart Hopkin Key Concepts Covered
