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Part 22c

A Delay Line Is a String

Speed up an echo until the echoes merge into a note. A very short delay with feedback is a vibrating string. That is all physical modeling is.

From Echo to Pitch

Hit the excite button. You will hear a click followed by echoes. Now drag the delay time shorter. The echoes get faster.

Keep going. At some point the echoes are so fast they fuse into a musical tone. That tone's pitch is set by the delay time: a 2.27ms delay repeats 440 times per second, so you hear an A4.

This is a Karplus-Strong string. The delay line IS the string. The noise burst is the pluck. The feedback is the string vibrating. The damping filter is the string losing energy -- high frequencies die out first, just like a real string.

Try it -- press Play, then hit Excite to pluck the string. Start with the "Slow Echoes" preset to hear individual repeats, then switch to "Nylon Guitar" to hear them fuse into a pitch. Use the piano keyboard to play melodies.

Preset
50.0 ms / 20.0 Hz
String
Auto-Excite
Waveform
Spectrum

Why This Works

A vibrating string is a wave bouncing back and forth between two fixed endpoints. A delay line with feedback is exactly the same thing: a signal bouncing through a buffer over and over. The round-trip time sets the pitch. The feedback amount controls how long the note rings. The lowpass filter in the feedback path mimics the way real strings lose high frequencies faster than low ones.

Kevin Karplus and Alex Strong published this algorithm in 1983. It was one of the first practical physical modeling synthesis techniques, and it remains one of the most efficient. You get a convincing plucked string from just a delay line, a filter, and a burst of noise.

What the Controls Do

Delay Time sets the pitch. Shorter delay means higher pitch. The display shows both the delay in milliseconds and the resulting frequency and note name.

Feedback controls how long the string rings. Higher feedback means longer sustain. It is capped at 98% to prevent runaway oscillation.

Damping is a lowpass filter in the feedback path. Lower values make the string sound warmer and duller, like a nylon guitar. Higher values keep the brightness, like a steel string or harpsichord.

References