Woodwind instruments must play across multiple octaves using the same set of toneholes. However, a tonehole configuration that is perfectly in tune for the first register is often out of tune for the second register.
Cylindrical pipes are mathematically simple, but most instruments (oboes, bassoons, saxophones) are conical—their bore expands linearly from mouthpiece to bell. A complete cone behaves like an open pipe of equivalent length, producing all harmonics. However, a truncated cone (like a saxophone) creates a unique impedance spectrum. Conical bores provide a richer, more blended set of partials and facilitate easier overblowing into the upper registers than a purely cylindrical closed pipe. Woodwind instruments must play across multiple octaves using
| Instrument Type | End Condition | Harmonic Series | Example | |----------------|---------------|----------------|---------| | Open-Open | Both ends open | All harmonics (f, 2f, 3f…) | Flute | | Open-Closed | One closed end | Odd harmonics only (f, 3f, 5f…) | Clarinet | A complete cone behaves like an open pipe
: Generally produce a complete harmonic series (all integer multiples of the fundamental) if open at both ends, or only odd harmonics if closed at one end. | Instrument Type | End Condition | Harmonic
The mass of the air column trapped inside the chimney of the hole.
The shape of the tube profoundly determines the harmonic series the instrument produces. can be considered in two configurations: