Larger holes shift the note sharper when open, but they also radiate more sound power. Designers must balance playability (finger reach, hole spacing) with acoustic output.
Smaller holes restrict air movement, forcing the wave to penetrate further down the main bore. This increases end correction and lowers the pitch. Large holes truncate the wave more cleanly.
Toneholes fundamentally serve to alter the acoustic length of the air column without changing the physical length of the instrument. Shortening the Column Larger holes shift the note sharper when open,
The book includes several technical appendices designed for direct application: Frequency and Wavelength Charts : Standardized data for calculating necessary tube lengths. Mathematical Formulas
Toneholes are not mere holes. They are that effectively lengthen or shorten the air column. When closed, the hole is invisible to the wave. When open, it creates a new effective end of the tube—but not exactly where the hole is drilled. This increases end correction and lowers the pitch
Every Boehm-system flute and modern oboe has its toneholes individually undercut by hand or CNC to achieve a "perfectly" tempered scale.
Points along the air column where air displacement is zero and pressure variation is at its maximum. Shortening the Column The book includes several technical
They restrict airflow, resulting in a softer, darker sound. They must be placed higher up the body to match the same pitch as a larger hole. Chimney Height and Undercutting
This is the practice of flaring or angling the inside edges of the tonehole where it meets the main bore. Undercutting reduces the sharp acoustic resistance of the hole. Designers use it to fine-tune intonation, improve responsiveness, and brighten the tone without changing the outside size of the hole. 5. Modern Design Frameworks and Computational Modeling
Boehm didn’t just tweak an existing design; he rethought the air column as an acoustic filter, then built a mechanical interface to match.
: Found in instruments like the flute or clarinet .