Panpipes are a row of tubes stopped at the bottom, one per note, and a stopped tube sounds at frequency f = v ÷ 4L, so each note needs a tube about a quarter of its wavelength long. A tube sounding at 523.25 Hz (the C above middle C) must be 159.4 mm long at 20 °C, and each octave down doubles the length. Tune each tube with a wax plug in the bottom, which can be moved either way, rather than by cutting the top, which can only raise the note.
Part of Music & Simple Instrument Making
Calculating tube lengths for a multi-note panpipe, why plugs beat cutting, and how temperature affects the whole set at once.
One Tube Per Note, Stopped At One End
A tube with the bottom closed (by a node of cane, a plug of wax or clay) resonates at a wavelength four times its length. Blowing across the open top excites the lowest mode. The speed of sound is about 343 m/s at 20 °C, so L = v ÷ 4f. The parent article tells you to cut graduated lengths by ear; this lets you choose them by calculation.
End correction. The open end behaves as if the tube were a little longer, by about 0.6 times the bore radius (a recalled textbook value for an unflanged end). A tube with a 15 mm bore has a radius of 7.5 mm, so subtract 0.6 × 7.5 mm = 4.5 mm from the calculated length.
Worked Example: A Major Scale
Equal-tempered notes from C5 (523.25 Hz) at 20 °C, bore 15 mm:
| Note | Frequency (Hz) | L = 343 ÷ (4f) (mm) | Cut length, minus 4.5 mm (mm) |
|---|---|---|---|
| C5 | 523.25 | 163.9 | 159.4 |
| D5 | 587.33 | 146.0 | 141.5 |
| E5 | 659.26 | 130.1 | 125.6 |
| F5 | 698.46 | 122.8 | 118.3 |
| G5 | 783.99 | 109.4 | 104.9 |
| A5 | 880.00 | 97.4 | 92.9 |
| B5 | 987.77 | 86.8 | 82.3 |
| C6 | 1046.50 | 81.9 | 77.4 |
For an octave lower, double the calculated length (C4, 261.63 Hz, needs 343 ÷ (4 × 261.63) = 0.3278 m = 327.8 mm before the end correction). Note that the end correction is a fixed 4.5 mm for all tubes of the same bore, so it matters proportionally more for the short ones.
The parent article’s suggestion of 5-8 tubes fits a scale of five to eight notes; the table above is eight tubes.
What You Need
- Cane or bamboo of uniform bore, cut just below nodes so each tube has a natural closed bottom; see Frame Materials, Wood, Bamboo & Salvage for bamboo
- A saw and a file
- Beeswax or clay for plugs; see Beeswax
- Cord or two cross-battens to bind the tubes in order of length
- A reference pitch
Method: Build And Tune
Step 1: Cut tubes slightly long, about 10 mm over the table length.
Step 2: Close the bottoms. A natural node is fine; otherwise push in a plug of wax or clay.
Step 3: Tune by moving the plug. Pushing the plug up shortens the air column and raises the note; pulling it down lowers it. This is reversible, which cutting the top is not. Cutting the top only ever raises pitch.
Step 4: Bind in order, with the longest tube at the low side, using two bands of cord or flat cross-battens.
Step 5: Play across the top, the lower lip against the rim, angling the breath across the opening. Expect a few minutes before a steady note.
Why Warm Weather Does Not Ruin The Scale
The speed of sound rises with temperature (343 m/s at 20 °C to 349 m/s at 30 °C, from v = √(γRT ÷ M) with γ = 1.4, R = 8.314 J/mol·K, M = 0.02897 kg/mol). Every pipe scales by the same factor, so the whole set rises by the same 1200 × log₂(349.0 ÷ 343.2) = 29 cents. The intervals between notes are unchanged, but the set will be 29 cents sharp against a string tuned at 20 °C.
Overblowing. A stopped tube’s next mode is three times the fundamental, a twelfth above (an octave plus a fifth), not an octave. If a tube squeals at a high note when you blow hard, that is the cause; blow gently.
Common Mistakes
- Cutting every tube to the calculated length without the end correction. Each tube is then 4.5 mm too long and sounds flat: by 1200 × log₂(168.4 ÷ 163.9) = 47 cents on the C5 tube and by 1200 × log₂(86.4 ÷ 81.9) = 93 cents on the C6 tube, nearly a semitone, so the short tubes are worst.
- Mixed bores. Tubes of different diameters have different end corrections.
- Leaky plugs. Air escaping at the bottom flattens the pitch and softens the tone.
Safety
Mouthed instruments and sharp cane
Cut cane has sharp edges and splinters; file the rim smooth. Seal plugs only with beeswax or clean clay, not paints or salvaged compounds that may contain lead. See Material Selection. Wash the rim between players.
What’s Next
- Learn next: Hole Spacing & Tuning — the single-tube alternative
- Combine with: Group Singing Without Instruments — a set of panpipes can hold the starting note