How the Virtual Xylophone, Marimba & Free-Bar Overtone Synthesizer Work
Unlike vibrating strings or cylindrical air columns—whose natural overtones occur at integer multiples ($1f, 2f, 3f, 4f$)—a solid rectangular wooden or metallic bar suspended at its two nodal points ($22.4\%$ from each end) vibrates according to the **Euler-Bernoulli fourth-order beam equation**. In an uncarved uniform bar, the first three transverse bending modes vibrate at ratios of $1.000 : 2.756 : 5.404$. Instrument makers carve a graceful parabolic arch into the underside of rosewood marimba and xylophone bars to tune that second partial into musical alignment with the fundamental pitch.
Virtual Xylophone & Marimba Studio models these exact physical overtone ratios in real time using the browser's Web Audio API, paired with a photorealistic HTML5 Canvas stage showing all 15 natural bars (`C4` to `C6`), 10 raised chromatic accidental bars (`C#` / `Db` through `A#` / `Bb`), graduated brass resonator tubes, and animated yarn mallets.
How to Play Glissandos, Chords & Learn Melodies
- Tap or Swipe Across the Bars (Glissando): Click or tap any bar to strike it with the animated left or right mallet. Hold down your finger or mouse button and drag horizontally across the lower row of natural bars to perform a cascading **xylophone glissando** without lifting your hand.
- Computer Keyboard Layout (2-Octave Chromatic Map):
- Lower Octave Natural Bars (C4 – C5): Bottom letter row
Z X C V B N M , - Lower Octave Sharp/Flat Bars: Home letter row
S D G H J - Upper Octave Natural Bars (C5 – C6): Top letter row
Q W E R T Y U I - Upper Octave Sharp/Flat Bars: Number row
2 3 5 6 7
- Lower Octave Natural Bars (C4 – C5): Bottom letter row
- Follow-the-Glow Song Academy: Choose one of the 5 songs in the bottom dock (*Ode to Joy*, *Twinkle Little Star*, *Celestial Magic Box*, *Mystery Forest Arpeggio*, or *Sakura Pentatonic Chime*). A pulsing golden target halo appears on the exact bar you need to strike next, advancing step-by-step as you play.
- Two-Mallet Tremolo Roll: Click Tremolo Roll: On in the floating dock to flutter both mallets rapidly (`14 strikes/sec`) for sustained concert marimba swells.
Euler-Bernoulli Free-Bar Bending & Tubular Resonator Equations
Both the graduated bar lengths on screen and the synthesized harmonic partials follow acoustic physics:
f_n = (π · h / (4 · sqrt(3) · L²)) × sqrt(E / ρ) × (2n + 1)² ⇒ Bar Length Scales as L ∝ 1 / sqrt(f)
2. Quarter-Wavelength Closed Brass Resonator Tube Length Under Each Bar:
L_tube(f) = Speed_of_Sound (34,300 cm/s) ÷ (4 · f) - 0.61 · Radius_end_correction
3. Undercut Arch Partial Ratios:
Marimba Harmonics = { 1.00 · f_0, 4.00 · f_0 (Double Octave), 9.20 · f_0 }
Xylophone Harmonics = { 1.00 · f_0, 3.00 · f_0 (Twelfth / Octave+Fifth), 6.10 · f_0 }
Glockenspiel / Vibraphone = { 1.00 · f_0, 2.756 · f_0, 5.404 · f_0 }
6 Mallet Percussion Instruments & Acoustic Comparison Chart
| Instrument Voice | Bar Material | Tuned Overtone Ratio | Resonator Decay ($\tau$) | Signature Timbre |
|---|---|---|---|---|
| 1. Rosewood Xylophone | Honduran Rosewood | $1 : 3.00 : 6.10$ (Twelfth) | 0.45 s – 0.90 s | Crisp, woody orchestral projection |
| 2. Deep Padauk Marimba | African Padauk / Rosewood | $1 : 4.00 : 9.20$ (2-Octave) | 1.20 s – 2.40 s | Rich, hollow bass-bar warmth |
| 3. Silver Glockenspiel | High-Carbon Tempered Steel | $1 : 2.756 : 5.404$ | 2.80 s – 4.20 s | Brilliant crystalline bell chime |
| 4. Jazz Vibraphone | Anodized Aluminum Alloy | $1 : 4.00$ + Motor Tremolo | 3.20 s + 6 Hz Pulser | Velvety smoky jazz club sustain |
| 5. Crystal Glass Harp | Spun Quartz Silica | $1 : 2.00 : 3.00$ Pure Sine | 2.90 s Soft Bloom | Ethereal singing glass bowls |
| 6. Balinese Bamboo | Seasoned Wulung Bamboo | $1 : 2.92$ + Air Tube Pop | 0.65 s Hollow Pluck | Earthy tropical gamelan resonance |