A local bore constriction can tune individual pipe modes separately

Evidence

The upper part of Figure 4.23 (taken from Figure 4.18) indicates the pressure and velocity node and antinode positions for the first three standing wave modes. The lower part of the figure exhibits plus and minus signs to indicate where that particular mode’s frequency would be raised or lowered respectively by a local constriction or enlargement at that position in the pipe. The size of the signs indicates the sensitivity of the frequency variation based on how close the constriction is to the mode’s pressure/velocity nodes and antinodes shown in the upper part of the figure. For example, a constriction close to the closed end of a cylindrical pipe will raise the frequencies of all modes since there is a pressure antinode at a closed end, whereas an enlargement at that position would lower the frequencies of all modes. However, if a constriction or enlargement were made one third of the way along a stopped cylindrical pipe from the closed end, the frequencies of the first and third modes would be raised somewhat, but that of the second would be lowered maximally. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1225

Categorization

• XREF: Connects to how organ builders and flute makers voice instruments by bore geometry; also resonates with the practical ear-tuning knowledge in Murray Campbell’s acoustics work. — connects to: Only bores keeping fixed mode ratios as holes open are musically useful — David Howard, Jamie Angus, coustics and Psychoacoustics, 1240; Pipe bore constriction shifts mode frequencies depending on standing-wave node position — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1222; Instrument makers tune pipes by flaring ends or adjusting bore shape — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1219 (+1 more)
• SHARE: For a woodwind maker or organ builder friend — the trick of a constriction one-third along a stopped pipe affecting the second mode differently from the first/third.