--- family: membranophone subfamily: single-headed cylindrical drum stack scale: pentatonic target_pitches: drum-1: A2 # 110.00 Hz drum-2: C3 # 130.81 Hz drum-3: E3 # 164.81 Hz drum-4: G3 # 196.00 Hz drum-5: A3 # 220.00 Hz geometry: drum-1: { od_mm: 300, height_mm: 180, head_diam_mm: 300 } drum-2: { od_mm: 250, height_mm: 160, head_diam_mm: 250 } drum-3: { od_mm: 200, height_mm: 140, head_diam_mm: 200 } drum-4: { od_mm: 150, height_mm: 120, head_diam_mm: 150 } drum-5: { od_mm: 100, height_mm: 100, head_diam_mm: 100 } materials: shell: cold-rolled steel shell_thickness_mm: 1.2 head: synthetic mylar (Remo or Evans coated, 7-10 mil) pole: 25 mm OD stainless tube, 1.5 mm wall base: 380 mm steel plate, 6 mm tuning_mechanism: snare-style external lug ring with 6 tension rods per drum acoustic_intent: pentatonic ascending tom array with metal-shell snap and short sustain --- # Modular Pedestal Drum Stack — Parametric Design ## 1. Family and acoustic target The instrument sits in the **single-headed cylindrical membranophone** family — closest kin are octobans, marching tenors, Roto-toms, and tabla-baya. Distinctive choices: - **Single head**, top-batter only — open-bottom shell radiates downward like a conga or octoban, giving a focussed fundamental rather than a tom's tom-tom blur. - **Sheet-metal shell**, 1.2 mm rolled steel — adds high-frequency cut over wood, shorter sustain than brass or copper, and lets the shells form structural columns on the pedestal. - **Pentatonic five-pitch array** rather than chromatic — favours fast melodic phrases over single-stroke melodies. A2, C3, E3, G3, A3 spans 7 semitones less than an octave, keeping all five within comfortable reach of a single player. ## 2. Membrane acoustics — first-principles The fundamental frequency of an ideal circular membrane of radius `a`, areal density `σ` (kg/m²), under tension `T` (N/m) is: ``` f_01 = (z_01 / (2π a)) · sqrt(T / σ) ``` where `z_01 ≈ 2.4048` is the first zero of the Bessel function J₀. Solving for the tension required to hit each target pitch with a fixed head density: - mylar head, 10 mil (0.254 mm), ρ = 1390 kg/m³ → σ = 0.353 kg/m² - drum-1 (a = 0.150 m, target 110 Hz): T ≈ 425 N/m - drum-2 (a = 0.125 m, target 130.81 Hz): T ≈ 419 N/m - drum-3 (a = 0.100 m, target 164.81 Hz): T ≈ 426 N/m - drum-4 (a = 0.075 m, target 196.00 Hz): T ≈ 343 N/m - drum-5 (a = 0.050 m, target 220.00 Hz): T ≈ 215 N/m Targets cluster in the 200–425 N/m range — well within a standard 6-rod snare-style lug ring's working envelope (a typical 14" snare is tensioned to ~600 N/m for a tight crack). The smallest drum (drum-5) needs the **loosest** tension, which inverts the intuitive "tighter = smaller" assumption for fixed-pitch arrays. See `modular-pedestal-drum-stack-starter.wl` for the full sweep, sensitivity to head thickness, and harmonic predictions. ## 3. Shell role — coupling and damping Unlike a frame drum where the rim is purely structural, a 1.2 mm steel shell of these diameters has its own ring modes in the 800–4000 Hz range, which couple to the head's upper partials. The design intent: - Shell ring mode of drum-1 (300 mm) ≈ 1620 Hz — sits a sixth above the head's third partial (2 z_11/z_01 · 110 ≈ 350 Hz). Mostly decoupled. - Shell ring modes scale roughly inversely with diameter, so drum-5 (100 mm) ≈ 4900 Hz — well above any head partial of interest. Decoupled. - Bearing edge chamfered 45° inward to shorten head-shell contact and reduce ring-mode excitation. See `tuning-notes.md`. ## 4. Pedestal column - **Pole:** 25 mm OD × 1.5 mm wall stainless tube, 1350 mm long (centre-to-base). - **Mounts:** Each drum has a welded internal bracket with two rubber-isolated set screws against the pole. Bracket is a 50 mm long folded U-channel of 1.2 mm steel, TIG-tacked to the shell interior at three points 120° apart. - **Base:** 380 mm diameter × 6 mm steel plate, with a centre-welded socket for the pole and four levelling feet on the rim. - **Spacing:** Drums are 50 mm apart edge-to-edge, with a rubber puck between each shell's lug-ring top and the next drum's bottom rim to damp inter-drum coupling. ## 5. Tuning mechanism Standard snare-style external lug ring with 6 tension rods per drum, anchored to a counter-hoop and pulling against an inverted-U claw that grabs the head's flesh hoop. Bought stock from Pearl or Yamaha hardware lines (see `bom.csv`). Each drum is tuned **independently** with a drum dial; pentatonic tuning is set by the fabricator at final assembly. ## 6. Sheet-metal classification per part | Part | Classification | Forming method | |---|---|---| | Drum shell (×5) | Cylinder | Slip-roll, butt-weld TIG seam | | Bearing edge | Inward-roll on top edge | Bead roller or mill turn | | Internal pole bracket | Folded U-channel | Press brake or finger brake | | Base plate | Flat panel + welded socket | Plasma cut + lathe-turned socket | | Counter hoop (×5) | Rolled ring | Slip-roll + butt-weld + dress | ## 7. Validation gates (see `validation.csv`) - **Acoustic:** Each drum's fundamental within ±15 cents of target after tuning. - **Mechanical:** Pedestal pole bends < 5 mm under 50 N lateral load at top drum. - **Ergonomic:** Top drum head height ≥ 1350 mm for standing play. - **Manufacturability:** Slip-roll minimum radius achievable on 1.2 mm cold-rolled steel (≈ 38 mm — well under the 50 mm minimum radius of drum-5). - **Safety:** All bearing edges deburred and chamfered; no exposed lug-rod tips at player-facing height. ## 8. Open questions / punt to next round - Are the predicted membrane frequencies stable under temperature swings of a rehearsal-room environment? (Mylar has ~3 cents/°C drift.) - Would a **double-headed** variant of drum-1 give a deeper bass? Probably yes — consider as a v0.2 fork. - Is a foot-pedal "select" mechanism (kick the pedestal to rotate the top drum into reach) feasible? Out of scope for blueprint.