When you open a hole, you effectively insert a "T-junction" in the acoustic line. The sound wave sees a choice: go down the main bore or escape the open hole. The proportion of energy that escapes vs. reflects determines the tuning.
Opening a tonehole creates a localized pressure node, venting the standing wave to the outside air. However, the air inside the tonehole itself has mass. This mass acts as an acoustic inertance, delaying the pressure drop.
The size and depth of a tonehole change how efficiently it vents the air column. When you open a hole, you effectively insert
Undercutting reduces the effective height (
The clarinet overblows a 12th (×3 frequency) because the third harmonic is the first overtone present. The flute and saxophone overblow an octave (×2). Any cylindrical bore with a reed (like a hypothetical clarinet with a reed at both ends) would behave like an open-open tube—but that doesn't exist in nature. reflects determines the tuning
The interaction between air columns and toneholes is governed by several key principles:
Placing toneholes is not a simple matter of marking distances for a chromatic scale. The designer must solve a non-linear equation balancing geometric length, acoustic length, and finger ergonomics. This mass acts as an acoustic inertance, delaying
"But we only have ten fingers," Kael noted. "We can’t keep switching between pipes of different lengths."
Tonehole Lattice o o o o o Low Frequencies: ======X---------------------> (Reflected at first open hole) High Frequencies: ============================> (Passes through, escapes at bell)
Undercutting reduces the acoustic mass of the hole. This raises the pitch of the fundamental frequency and its upper harmonics, allowing makers to correct tuning discrepancies without shifting the physical position of the hole. Engineering the Modern Wind Instrument