guitar — a physically-modeled strummed six-string #

A single-file C engine (like pop/accordion/c/ and pop/bell/c/) whose sound comes from six waveguide strings on one bridge, played by one hand. The string is an extended Karplus-Strong loop; the hand is a strum pattern with down- and up-strokes that rake the strings at different speeds, catch different strings, and damp each string for a moment before letting it go. The cult track's guitar() had the string and not the hand; this is the hand.

Zero dependencies beyond libm.

pop/guitar/
  c/strum.c     the engine
  c/build.sh    cc -O2 -std=c11 -Wall -Wextra -o strum strum.c -lm
  out/          demo bank (gitignored, like every pop out/)

The model #

String — a fractional-delay Karplus-Strong loop per string:

y  = allpass(line[idx])                 first-order allpass → exact pitch
lp = b·y + (1-b)·lp                     the string forgets its highs
line[idx] = g·lp + c·(bridge - lp) + exc

• g is a per-sample loss from a T60 per string (5.5 s on the low E down to 2.8 s on the high E, ×1.6 for electric), shortened a little per fret, and blended toward a 0.14 s muted T60 by mute — which is what a palm, a lifting fret hand, and a chuck all are.
• b is the loop brightness: wound strings 0.80–0.86, plain 0.90–0.95, every fret shaving 0.6 %.
• exc is a one-period noise burst comb-filtered at the pick position (--pick, default 18 % of the length — a pluck there cannot feed the harmonics with a node there) and lowpassed by force (900 Hz at a feather, ~8 kHz at full), with a 1.5 ms click for the pick leaving the string. It is added into whatever the string was already doing.
• Pick contact: 3 ms before each pluck the loop loss is multiplied by 0.55 — the pick is resting on the string. A re-strum catches the old note; it does not stack a fresh burst on top of a ringing one.

Bridge — every string feeds c·(mean − own) back into its loop through a 2.5 kHz lowpass (c = 0.03). The mixing matrix is g·I + c·(J/n − I): its common mode keeps gain g, every differential mode gets g − c, so the coupling is passive by construction and energy leaks from a plucked string into the others. A strum rings as one body of six, and a single plucked string makes the others whisper.

Body (acoustic) — a dreadnought's three modal peaks plus presence over a 62 % dry path: Helmholtz air 101 Hz (Q 9), top plate 203 Hz (Q 7) and 398 Hz (Q 5.5), a broad 2.3 kHz bump. Left and right carry the modes skewed ±2.5 % so the box has a width; strings are panned low→left, high→right. DC blocker, 9 kHz rolloff.

Amp (electric) — the strings sum at the pickup then the amp drives them: the cult engine's two-stage asymmetric tanh (tanh(v·k + bias) − tanh(bias), then tanh(·1.8)/2) and its dark one-pole (0.16 @ 48 k), into a 2nd-order 4.2 kHz cab with a 2.4 kHz presence peak. Driving the chord rather than each string is the point: the grind between the notes is the amp intermodulating, and six separately-driven strings never produce it.

Hand — a pattern is one bar, one character per step (16 chars = 16ths, 8 = 8ths, 12 = triplet 8ths), repeating:

Rake time is --rake at full force and shortens with force (a hard strum is a fast strum); the wrist accelerates through the strings (t ∝ k^0.85); later strings in a rake are hit slightly lighter; the top string of an up-stroke slightly harder. --human puts a seeded ±4 ms / ±8 % / ±15 % wobble on timing, force and rake.

Fret hand — --chord "Bm|D|G|Em" cycles one chord per bar. 30 ms before the bar line the strings whose fret changes are choked; on the bar line they retune (the ringing delay line is simply read at the new length, which is what a hammer-on is); and if a wound string moved two or more frets, a 70 ms band of noise around 2.2–3.1 kHz squeaks.

The default pattern is the cult track's STRUM table written in 16ths: D..d..u.u.D..u.. (beats 0, 0.75, 1.5, 2.0, 2.5, 3.25).

CLI #

./build.sh
./strum --chord Bm --out bm.wav
./strum --chord "Bm|D|G|Em" --bars 4 --electric --out cycle.wav
./strum --chord 47,54,59,62 --pattern "D.D.uu.D..u." --electric --out cult.wav
./strum --chord Bm --mute palm --pattern "DdDdDdDdDdDdDdDd" --electric --out chug.wav
./strum --chord "Bm9|Gmaj7|Em9|F#7sus4" --bars 4 --pattern "..D...u.d.U..u.." --rake 24 --force 0.55 --out flower.wav

Chord names: 31 open-position shapes are tabled (E Em E7 Em7 A Am A7 Am7 Asus2 Asus4 D Dm D7 Dmaj7 Dsus2 Dsus4 G G7 C Cmaj7 Cadd9 C7 F Fmaj7 Bm B B7 Bm7 F#m F# F#m7); anything else becomes a barre — E-shape for roots E…B, A-shape for C…D# — with suffixes m 7 m7 maj7 sus2 sus4 7sus4 add9 9 m9 5. A midi list is placed top note first, each on the highest free string that reaches it (the lowest fret), so 47,54,59,62 is x A2+2 D3+4 G3+4 B3+3 x and the up-stroke's "top strings" are the right ones. The voicing is printed on stderr.

Deterministic: one seeded xorshift, drawn in a fixed order. Same flags, same bytes. A 16-bar electric render takes ~0.3 s.

Demos (out/) #

for ch in Bm D G Em; do
  ./strum --chord $ch --out ../out/$(echo $ch | tr A-Z a-z)-acoustic.wav
  ./strum --chord $ch --electric --out ../out/$(echo $ch | tr A-Z a-z)-electric.wav
done                                                          # 1 bar @ 120 = 3.00 s each
./strum --chord "Bm|D|G|Em" --bars 4 --out ../out/cycle-acoustic.wav
./strum --chord "Bm|D|G|Em" --bars 4 --electric --out ../out/cycle-electric.wav
./strum --chord 47,54,59,62 --pattern "D.D.uu.D..u." --electric --out ../out/cult-voicing-electric.wav
./strum --chord Bm --mute palm --pattern "DdDdDdDdDdDdDdDd" --electric --out ../out/bm-palm-electric.wav
./strum --chord "Bm9|Gmaj7|Em9|F#7sus4" --bars 4 --pattern "..D...u.d.U..u.." --rake 24 --force 0.55 --out ../out/flower-acoustic.wav

Notes / honest limits #

• The string is a lossy loop with a one-pole, not a stiff-string model: no inharmonicity, so the wound strings lack the slight "piano" stretch of real bronze, and there is no longitudinal / two-polarization coupling — the slow beating of a real open string is absent.
• The body is a fixed modal EQ, not a measured impulse response; swap the body_init table to chase a specific box.
• The pick is a noise burst: it carries position and force but not the pick's own stiffness, so a felt pick and a steel one are the same pick.
• The fret hand changes chords only on bar lines, and the squeak is a band of noise with no relation to which fret it slid from.
• Output is peak-normalized like the accordion, which means a soft render and a hard one land at the same peak — the dynamics live between the strokes, not between files. Score the level at the call site.
• note/WAV conventions follow pop/bell/c/bell.c.