Differentiable Karplus-Strong

Pablo Tablas de Paula, David Marttila, Joshua D. Reiss
Centre For Digital Music (C4DM), Queen Mary University Of London
Digital Music Research Network One-day Workshop 2025

Abstract

We present a differentiable, time-domain implementation of an extended Karplus-Strong Algorithm (KSA) that can be optimised end-to-end as a Differentiable DSP (DDSP) paradigm. We show its ability for instrument modelling by reconstructing an acoustic guitar dataset, where our proposed Gradient Descent (GD) baseline outperforms a Genetic Algorithm (GA).

Differentiable Karplus-Strong architecture

Figure 1: Proposed architecture, where coloured blocks are optimised by gradient descent. Lagrange is short for Lagrange interpolation, while g stands for gain stages.

Gradient Descent vs. Genetic Algorithm

Table 1: Baselines Comparison. Lower values, in bold, are better.
Baseline \(\mathcal{L}_{\mathrm{MSS}}\) MFCC Encodec MS-CLAP
Gradient Descent 0.79 ± 0.11 2.32 ± 1.50 19.89 111.30
Genetic Algorithm 1.43 ± 0.31 4.10 ± 1.75 216.93 346.93
Ground Truth Gradient Descent Genetic Algorithm

Model Expressivity Test per Octave and Dynamics

Table 2: \(\mathcal{L}_{\mathrm{MSS}}\) mean difference to overall mean (0.62) across MIDI velocities and octaves for our GD baseline. Negative values are better.
\(\downarrow\) Oct. Vel. \(\rightarrow\) 25 50 75 100 127 mean
E2–E3 +0.27 +0.23 +0.33 +0.30 +0.36 +0.30
E3–E4 -0.02 +0.07 -0.02 +0.07 +0.01 +0.02
E4–E5 -0.18 -0.10 -0.05 -0.13 -0.08 -0.11
E5–E6 -0.19 -0.26 -0.27 -0.18 -0.11 -0.20
mean -0.03 -0.01 +0.00 +0.02 +0.05 +0.00

Click any cell in the table above to explore audio examples for that specific combination of pitch and dynamics.

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Ground Truth Gradient Descent

BibTeX

If you use this work, please cite:

Tablas de Paula, P., Marttila, D. and Reiss, J.D., 2025 December. Differentiable Karplus-Strong. In Digital music research network one-day workshop (DMRN+20).

@inproceedings{tablas2025diffks,
  title     = {Differentiable Karplus-Strong},
  author    = {Tablas de Paula, Pablo and Marttila, David and Reiss, Joshua D.},
  booktitle = {Digital Music Research Network One-day Workshop (DMRN+20)},
  year      = {2025},
  month     = dec
}