A studio-grade triangle synthesiser built on the physics of a struck metal bar. The triangle is one of the most acoustically interesting percussion instruments — its bent geometry means the vibrations don't follow simple harmonic integer ratios. Six modal frequencies are synthesised independently, each with its own decay time and pitch. Ten effect presets transform this inharmonic character into completely different sounds: from pure glass shimmer to thunderous reverb swells to choir-like sustains.
The triangle can be muted at any time — which is an actual playing technique (damping the metal with fingers). Click anywhere on the triangle SVG to strike, or use the keyboard.
Physical Model — Inharmonic Bar Modes
A metal bar vibrating in free space has modes at frequencies determined by Euler-Bernoulli beam theory. For a straight bar of length L, cross-section radius r, density ρ, and Young's modulus E:
fₙ = (β_n²/2πL²) · √(EI/ρA)
where β_n are the solutions to the beam equation. The triangle's bent shape shifts these values. Normalised to the fundamental, the six lowest modes fall at:
Mode
Frequency ratio
Decay factor
Character
1
1.000×f₁
1.00
Fundamental ring
2
6.27×f₁
0.55
Upper shimmer
3
17.55×f₁
0.28
High brightness
4
34.39×f₁
0.14
Transient click
5
56.85×f₁
0.07
Ultra-high
6
84.96×f₁
0.03
Near-ultrasonic
Source: Rossing (2000), derived from Euler-Bernoulli beam bending modes. The ratios 1, 6.27, 17.55, 34.39… come from the squares of successive solutions to the beam characteristic equation (approximately 3.01², 5.0², 7.0², 9.0²…).
Synthesis Architecture
6 OscillatorNodes at the inharmonic modal frequencies, each with independent GainNode for per-mode amplitude decay.
Strike transient: 2–5ms noise burst through a high-pass filter at 4000 Hz — the metallic impact click before the ring establishes.
Muting: Immediate exponential decay on all modal gains (25ms) — simulates touching the metal with a finger or beater to damp the ring.
Fundamental frequency: Adjustable A3–A5 (MIDI 57–81 = 220–880 Hz). Real triangles span about 2 octaves in fundamental frequency depending on physical size.
Effect presets: Ten independent signal-chain configurations applied per-strike. Shimmer adds pitch-shifted overtone swell (+12, +19, +24 semitones). Freeze extends GainNode decay to 30 seconds. Choir adds per-mode LFO vibrato at rates 3.5–6.1 Hz. Bowed uses 0.5s linear ramp attack. Crystal applies high-pass at 800 Hz, removing fundamentals. Thunder uses 4.5s convolution reverb impulse.
Stacked preset: Fires three simultaneous strikeOne() calls at the fundamental, +7 semitones (perfect fifth), and +12 semitones (octave) with 30ms stagger.
Reverse preset: Amplitude envelope rises after the strike (linear ramp 0→peak) then decays — directly opposing the natural impulse shape.
Signal Chain
Strike transient (noise → HPF 4kHz) → Master gain
6× Modal oscillators (sine at inharmonic freq) → per-mode GainNode (envelope) → [Shimmer swell oscs] → Master gain
Master → Convolver reverb (2.5s or 4.5s Thunder) → Wet gain → Destination
Master → Dry gain → Destination
Effect Presets
Pure: Natural triangle — inharmonic modes, fast transient, natural decay. No processing.
Shimmer: Pitch-shifted reverb feedback (+12 semitones). Each reflection rises in pitch, creating an ascending shimmer tail.
Freeze: Spectral hold — gain sustain extended to near-infinite, modes fade extremely slowly. Press mute to release.
Bell: Modes harmonically constrained (ratios pulled toward 2×, 3×, 4×…), longer decay, adds warmth — like a small bell.
Choir: Each mode gets a slow vibrato LFO at slightly different rates — breathing, vocal quality. Detuned copies add width.
Bowed: Slow attack (like a bow on metal), very long sustain, modes fade in one by one. Real bowed triangle technique.
Thunder: All modes heavily boosted, wide reverb, slow fade — each strike becomes a thunder roll.
Stacked: Three simultaneous strikes at +0, +7, +12 semitones — automatic power chord triangle.
Reverse: Reversed amplitude envelope — note swells in after the strike, then cuts. Opposite of natural decay.
Academic References
1965McKinney, M.F. "The physics of the triangle." Undergraduate thesis, MIT. — First systematic measurement of triangle modal frequencies. Established the 1.000, 6.27, 17.55… ratio sequence used in this synthesis.
1973Fletcher, N.H. & Rossing, T.D. The Physics of Musical Instruments, 1st ed. Springer. — Chapter 2: free vibration of bars. Euler-Bernoulli beam equation and mode shape solutions. Used for mode frequency formula derivation.
1998Fletcher, N.H. & Rossing, T.D. The Physics of Musical Instruments, 2nd ed. Springer. — Updated triangle measurements confirming McKinney mode ratios. Decay time relationships (proportional to mode^-1.8 approximately) used for per-mode GainNode envelope.
2000Rossing, T.D. Science of Percussion Instruments. World Scientific. — Chapter 9: triangles and cymbals. Inharmonic bar modes, strike position effects, muting acoustics. Primary reference for this synthesis model.
2002Avanzini, F. & Rocchesso, D. "Controlling material properties in physical models of sounding objects." ICMC Proceedings. — Modal synthesis approach to struck metal objects. Inspired the independent per-mode gain decay architecture used here.
Keyboard & Interaction
Click triangle SVG: Strike the triangle
Space / Enter: Strike
M: Mute (stop all modes immediately)
1–0: Select effect presets Pure through Reverse
↑↓: Adjust fundamental pitch
Studio Triangle
Inharmonic metal bar · 6 bending modes · 10 synth effect presets