Cajón Family Design v1

A parametric three-member box-drum family — Compact / Standard / Bass — with four manufacturing variants and an optional snare lineage.

[ family group hero — Compact · Standard · Bass · Heifer Zephyr ]

What this is

A complete parametric design packet for a three-member cajón family. Each member is the same governing physics scaled differently: a thin Baltic-birch tapa over a closed walnut box with a back-port sound hole, optionally fitted with a guitar-string snare or snare-drum wires.

The packet ships acoustic physics, parametric geometry, BOM · sourcing · cut-list · validation, dimensioned drawings, an assembly manual covering all four joinery variants, a red-team risks log, a Wolfram starter notebook, and this build-log site.

Member	Outer dims (H × W × D)	Sound hole	Predicted f_H	Voice
Compact (CJ-C)	15 × 11 × 11 in	4.0 in Ø	≈ 107 Hz	bright G♯2/A2
Standard (CJ-S) ⭐	18 × 12 × 12 in	4.5 in Ø	≈ 96 Hz	balanced G2 — first prototype
Bass (CJ-B)	22 × 14 × 14 in	5.0 in Ø	≈ 77 Hz	deep D♯2/E2

The two co-dominant resonators

The cajón's bass voice is not a single mode — it is the coupling between two systems that sit within a few semitones of each other:

Front-plate (1,1) clamped-rectangular bending mode. The 3 mm Baltic-birch tapa, clamped on all four edges by perimeter screws every 3″, vibrates in a single hump (centre highest) when struck in the centre. For Standard the predicted plate fundamental is ~84 Hz.
Helmholtz cavity. The closed walnut box with a 4.5″ back-port hole acts as a Helmholtz resonator with f_H ≈ 96 Hz on Standard.

When struck dead-centre the player hears the coupled mode of plate + cavity — the deep "thump." When struck on the upper corner the slap zone (the unscrewed top 4–5″ of the tapa) bends and excites the high-mode plate spectrum + the snare wires; the player hears the bright "snap." Two zones, one body.

Helmholtz formula (corrected)

f_H = (c / 2π) · √( A / (V · L_eff) )
       L_eff = t_back + 1.7 · (d_hole / 2)

The original cajón workbook used L_eff = t_back — missing the 1.7·r end correction. That under-predicted L by ~5–10× and over-predicted f_H by ~3×. Risk A2 in risks.md tracks the correction.

Manufacturing variants

ID	Joint	Method	Strength	Visual	Notes
V1 ⭐	Finger / box joint	table saw + jig OR CNC parametric	★★★	★★★	First-prototype default
V2	Half-blind dovetail	CNC	★★★	★★★	Showpiece path
V3	Rabbet	table saw or router	★★	★	Quickest commercial baseline
V4	Miter + spline	table saw + spline jig	★★★	★★★	Spline visual ties to inlay

Snare lineage (orthogonal to joinery)

Option	Snare	Voice
A	None (Peruvian)	dry, woody, deep "thump"; tonal pitch reads cleanly
B ⭐	Guitar strings (adjustable)	bright, snappy slap; modern flamenco default
C	Snare-drum wires	thicker buzz, less articulate; studio

First prototype

Build the Standard (CJ-S) in V1 finger-joint with snare option B. Standard is the family's tonal centre; Compact and Bass scale geometrically once Standard's measured tuning lands.

Estimated material cost: ~$205 (one Standard prototype, walnut + birch ply + brass + tung oil + Arm-R-Seal + abrasives + TBN bit + finger bit).
Estimated build time: ~30 hours over 4 days with CNC for inlay + joinery.

What's parametric vs measured

Parametric (formula-driven, edit the workbook)	Measured (TBD on first prototype)
Helmholtz frequency f_H Plate (1,1) mode estimate Internal cavity volume Sound-hole area + L_eff Family table dimensions Joint / bit / feed parameters	Actual f_H of the assembled cavity Actual plate (1,1) of the mounted tapa Slap-zone vs centre-strike spectrum delta Snare-buzz onset velocity (subjective) Sustain T60 of the bass voice

File map

design.md — governing physics, family scaling law, critical dimensions, open assumptions
family-spec.csv — three-member sizing law
cajon-design-table.xlsx — workbook source of truth for all formulas
bom.csv — bill of materials, by variant
sourcing.csv — suppliers, lead times, price-volatility flags
cut-list.csv — operation-by-operation cut data
validation.csv — predicted vs measured tuning + acceptance bands
validation-report.md — current pre-build validation status
assembly-manual.md — phase-by-phase build procedure
jig-decision.md — fixture choices for square glue-up and repeatable drilling
resources.md — provenance, assumptions, supplier verification notes
supplier-rfq.md — Q2 2026 batch sourcing summary
drawing-brief.md — drawing list + conventions
visual-bom-brief.md — Visual BOM photo brief
photo-shotlist.md — in-shop process photo list
risks.md — red-team failure-mode walk (17 risks, 5 categories)
wolfram-starter.wl — Wolfram package: plate, Helmholtz, two-zone synthesis
drawings/ — dimensioned SVG drawings
cad/ — OpenSCAD parametric master
cnc/ — CNC strategy notes
jigs/ — square assembly and drill-template drawings
scripts/ — generators for xlsx, pptx, pdf binaries

Status & next steps

Design v1 is shipped. The first prototype is the Standard (CJ-S) with V1 finger-joint and snare option B. Tuning calibration is pending the first measurement — once recorded, the family scaling law will be re-checked against the data per the empirical-learning loop in the parent instrument-maker skill.

Highest-priority open items:

Build the Standard prototype.
Measure f_H, plate (1,1), and the slap-vs-centre spectral delta. Update validation.csv.
If predicted-vs-measured cents error exceeds ±50 cents, revisit the family scaling law.
Apply the corrected Helmholtz formula to cajon-design-table.xlsx formulas (currently corrected only in design.md).
Replace simplified SVG sheets with CAD-exported dimensions after build review.
Capture build-log photography per photo-shotlist.md.