How does pipe length affect the pitch of an organ pipe?

In a pipe organ, the pitch of a note is directly determined by the length of its pipe. The relationship is inverse: longer pipes produce deeper, lower-pitched notes, while shorter pipes produce higher-pitched notes.12

Specifically, the pipe length dictates the fundamental frequency of the vibrating air column within the instrument. For example, if two comparable pipes are designed to sound an octave apart, the higher-pitched pipe will have an effective length exactly half that of the lower-pitched pipe.231

The construction of the pipe also influences this relationship:
* Open pipes: The pitch is determined by the speaking length of the pipe.4
* Stopped pipes: Because one end is closed, these pipes produce a node at the closed end, causing them to sound an octave lower than an open pipe of the same speaking length.43

Organ builders and voicers tune these pipes by adjusting their effective speaking length—often using cylindrical slides for flue pipes or tuning wires for reed pipes—to ensure precise pitch accuracy.45