The tonehole diameter should be roughly 25–35% of the bore diameter for comfortable fingering (recorders), and 40–60% for keyed instruments (flutes, saxophones) to achieve good cutoff frequency.
One of the most compelling sections of the book deals with the imperfection of the natural scale. A tube drilled perfectly mathematically will often sound out of tune to the human ear. Hopkin discusses . The tonehole diameter should be roughly 25–35% of
: Even when closed at the narrow end (like an oboe or saxophone), conical bores produce a complete harmonic series, behaving acoustically like open cylindrical tubes. Hopkin discusses
Today, no wind instrument is designed without acoustic modeling. Software like , Bore 3D , or Acousto allows designers to: Software like , Bore 3D , or Acousto
The book serves as a bridge between the rigid laws of physics and the fluid art of music-making. It peels back the skin of wind instruments to expose the "invisible architecture"—the standing waves, impedance mismatches, and acoustic end corrections that dictate why a saxophone sounds like a saxophone and a clarinet sounds like a clarinet.