Design Intent
The xiao (洞箫, dòngxiāo) is one of the oldest and most technically demanding of Chinese winds — an end-blown, notch-embouchure flute whose breathy tone has been inseparable from literati and court music since the Tang dynasty. This packet engineers a CNC-turned wooden prototype of the Nan Xiao (南箫), the most widely played southern variant, targeting the G key (root D4).
The primary engineering challenges are: (1) drilling a 22.5 in straight bore through square stock without wander, using the headstock-driven technique; (2) accurate first-order tone-hole placement from the open-pipe model with trim allowance; and (3) characterizing the embouchure end correction empirically on the prototype.
Material note: Traditional xiao are made from madake bamboo. This prototype uses black walnut. The acoustics are governed by bore geometry, not material, but bore finish (BLO/shellac) will affect the effective bore diameter and must be characterized. Internal lacquer shifts pitch; apply before final voicing.
Three Bore Variants
| Variant | Bore type | Bore ID (G key) | Mouthpiece | Character |
|---|---|---|---|---|
| Bei Xiao 北箫 | Capped U-notch | 0.866 in (22 mm) | 2.0 in section | Northern; projecting, fuller tone |
| Nan Xiao 南箫 ← prototype | Open (bamboo-root end) | 0.866 in (22 mm) | 2.5 in section | Southern; warm, breathy; most common |
| Qin Xiao 琴箫 | Capped U-notch (narrow) | 0.551 in (14 mm) | 3.0 in section | Refined; guqin companion |
Acoustic Model
Open-open cylindrical pipe
L_eff = c / (2 · f)
δ_end = 0.6 · r (each open end)
L_bore = L_eff − 2 · δ_end
Speed of sound at 68°F: c = 13,504 in/s
NAF K2 corrections do not apply here. Those corrections are specific to Tony's NAF bore range and embouchure geometry. All xiao predictions are first-order until measured.
G Nan Xiao Prototype Parameters
| Parameter | Value | Status |
|---|---|---|
| Root note | D4 (293.66 Hz) | formula |
| Xiao key (hole 4) | G4 | convention |
| L_eff (acoustic length) | 22.99 in (584 mm) | first-order |
| End correction δ (each end) | 0.260 in — embouchure assumed open | assumption |
| L_bore (physical) | 22.47 in (571 mm) | first-order |
| Bore ID | 0.866 in (22.0 mm) | design table |
| OD | 1.338 in (34.0 mm) | derived |
| Wall thickness | 0.236 in (6.0 mm) | design table |
| Total blank length | ~25.5 in (648 mm) | nominal + trim |
Tone Hole Positions (first-order)
| Hole | Finger | Note | Freq (Hz) | From foot (in) | From foot (mm) |
|---|---|---|---|---|---|
| H1 | RH pinky | E4 | 329.63 | 20.48 ⚠ | 520 ⚠ |
| H2 | RH ring | F4 | 349.23 | 19.33 ⚠ | 491 ⚠ |
| H3 | RH middle | Gb4 | 369.99 | 18.25 ⚠ | 464 ⚠ |
| H4 ★KEY | RH index | G4 | 392.00 | 17.22 ⚠ | 437 ⚠ |
| H5 | LH ring | A4 | 440.00 | 15.34 ⚠ | 390 ⚠ |
| H6 | LH middle | B4 | 493.88 | 13.67 ⚠ | 347 ⚠ |
| H7 | LH index | C5 | 523.25 | 12.90 ⚠ | 328 ⚠ |
| H8 | LH thumb (rear) | Db5 | 554.37 | 12.18 ⚠ | 309 ⚠ |
⚠ All positions first-order. Drill 1–2 mm toward foot for tuning margin. Final positions by undercutting.
Drawings
Bill of Materials
| Part | Description | Qty | Est. Cost | Source |
|---|---|---|---|---|
| XIAO-BLK-001 | Black walnut blank 1.5×1.5×26 in | 1 | $8–15 | Local hardwood |
| XIAO-SCRAP | Scrap pine/poplar blank (bore validation) | 1 | $3–5 | Hardware store |
| XIAO-DRILL-001 | 1/4 in pilot bit, 18 in+ | 1 | $8 | McMaster-Carr |
| XIAO-DRILL-002 | 55/64 in finish bit, 18 in+ | 1 | $25–45 | McMaster-Carr / Toolmex |
| XIAO-REAM-001 | 7/8 in adjustable reamer | 1 | $35 | McMaster-Carr |
| XIAO-FIN-001/002 | BLO + Danish oil finish | 1 set | $9 | Hardware store |
| XIAO-JIG-001 | Tailstock square-stock carrier (shop-made) | 1 | $15 | Shop-made |
| Total (est.) | ~$109 | |||
Build Workflow
Stock Prep
Mill walnut to 1.5 × 1.5 × 26 in. Verify grain, MC ≤ 8%, no knots in bore zone. Cut scrap blank to same dimensions.
Bore Scrap Blank (MANDATORY)
Headstock-driven deep-bore method. Pilot → step → 55/64 in → ream to 0.866 in. Measure bore wander: must be < 0.030 in. Do not touch tonewood until this passes.
Bore Tonewood
Same setup as Step 2. Measure bore at 3 stations: entry, mid, exit. Target 0.866 in ± 0.005 in.
Turn OD from Bore Axis
Mount blank between centers using bore-plug at tailstock. Turn OD to 1.338 in. The bore is the datum — not the original blank centers.
Cut Embouchure Notch
Router or drill press: U-notch ~11 mm wide, ~5 mm deep. Refine inner bevel by hand at ~45°. Test by blowing — stable edge tone = success.
Drill Tone Holes
Lay out 8 holes from foot datum using V-block + length stop. Drill pilot then finish. Sequence foot → head. H8 (thumb) drilled from rear face.
Voice and Tune
Undercut each hole with round file / chisel while measuring with strobe tuner at 68°F. Target ±10 cents per hole.
Finish and Validate
Apply BLO bore finish (cloth strip, 24 hr cure). Re-measure fundamental. Apply exterior finish. Fit adjustable foot plug. Record all results in validation.csv.
Top Build Risks
Model assumes δ_emb = 0.260 in. Measure fundamental on blank before drilling holes. Update L_bore if error > ±15 cents.
22.5 in bore through 1.5 in square stock. Wander > 0.030 in = thin wall = crack risk. Scrap validation mandatory.
U-notch creates stress concentration at wall. Radius corners, seal grain with thin CA immediately after cutting.
Apply BLO before final voicing. Measure fundamental before and after — expect 1–5 cents sharp.
H4→H5 gap ≈ 48 mm. May be difficult for small hands. Document ergonomic minimum; smaller key available from design table.