Preliminary sonification of ENSO using traditional Javanese gamelan scales

Sandy Hardian Susanto Herho; Rusmawan Suwarman; Nurjanna Joko Trilaksono; Iwan Pramesti Anwar; Faiz Rohman Fajary

physics.soc-phFeb 16, 2026

Preliminary sonification of ENSO using traditional Javanese gamelan scales

Authors: Sandy Hardian Susanto Herho, Rusmawan Suwarman, Nurjanna Joko Trilaksono, Iwan Pramesti Anwar, Faiz Rohman Fajary

Organizations: Department of Earth and Planetary Sciences, University of California, Riverside, CA 92521, USA · School of Systems Science and Industrial Engineering, State University of New York (SUNY), Binghamton, NY 13902, USA · Ronin Institute for Independent Scholarship 2.0, Sacramento, CA 95816, USA · Center for Agrarian Studies, Bandung Institute of Technology (ITB), Bandung, West Java 40132, Indonesia ·

Abstract

Sonification -- the mapping of data to non-speech audio -- offers an underexplored channel for representing complex dynamical systems. We treat El Niño-Southern Oscillation (ENSO), a canonical example of low-dimensional climate chaos, as a test case for culturally-situated sonification evaluated through complex systems diagnostics. Using parameter-mapping sonification of the Niño 3.4 sea surface temperature anomaly index (1870--2024), we encode ENSO variability into two traditional Javanese gamelan pentatonic systems (pelog and slendro) across four composition strategies, then analyze the resulting audio as trajectories in a two-dimensional acoustic phase space. Recurrence-based diagnostics, convex hull geometry, and coupling analysis reveal that the sonification pipeline preserves key dynamical signatures: alternating modes produce the highest trajectory recurrence rates, echoing ENSO's quasi-periodicity; layered polyphonic modes explore the broadest phase space regions; and the two scale families induce qualitatively distinct coupling regimes between spectral brightness and energy -- predominantly anti-phase in pelog but near-independent in slendro. Phase space trajectory analysis provides a rigorous geometric framework for comparing sonification designs within a complex systems context. Perceptual validation remains necessary; we contribute the dynamical systems methodology for evaluating such mappings.

Figures & tables

Figure 1: Niño 3.4 SST anomaly index, January 1870 to December 2024 ( $N=1{,}860$ ). Red/blue shading: El Niño/La Niña conditions ( $\pm 0.5$ °C thresholds). Red circles: extreme events ( $|\theta|\geq 2.0$ °C). The time series exhibits the irregular quasi-periodicity, amplitude asymmetry, and multi-decadal modulation characteristic of low-dimensional climate chaos.

Mode	Brightness [Hz]	Intensity	DynRng	Percuss	Flux
Pelog Layered	1,238	0.021	2.26	0.065	664
Pelog Alternating	1,064	0.013	2.94	0.055	489
Pelog Melodic	809	0.018	2.18	0.041	568
Pelog Spectral	1,270	0.012	2.96	0.053	988
Slendro Layered	1,863	0.022	2.08	0.134	985
Slendro Alternating	1,233	0.011	3.48	0.074	757

Table 1: Acoustic feature statistics for eight sonification variants. Brightness: mean spectral centroid (Hz); Intensity: mean RMS energy; DynRng: dynamic range ratio; Percuss: mean zero-crossing rate; Flux: mean spectral flux.

Figure 2: Spectral centroid trajectories for pelog modes: (a) layered, (b) alternating, (c) melodic, (d) spectral. Terminal descents near $t\approx 470$ s are fade-out artifacts.

Figure 3: Spectral centroid trajectories for slendro modes. Slendro layered (a) achieves the highest mean brightness (1,863 Hz) of all variants.

Figure 4: RMS energy trajectories for pelog modes. All modes show significant negative trends ( $p<0.001$ ).

Figure 5: RMS energy trajectories for slendro modes. Slendro layered (a) achieves the highest mean energy (0.022) across all variants.

Variable	Mode	$\bar{x}$	$\sigma_{x}$	$\gamma_{x}$	$\beta$	$R^{2}$	$\rho_{1}$
Brightness [Hz]	Pelog Layered	1,238	311	0.251	0.031	0.091	0.993
	Pelog Spectral	1,270	157	0.123	0.004	0.005	0.958
	Slendro Layered	1,863	208	0.112	0.002	0.001	0.980
	Slendro Spectral	1,274	162	0.127	0.004	0.006	0.959
Energy [-]	Pelog Layered	0.021	0.005	0.258	$-6.1\times 10^{-7}$	0.118	0.998
	Pelog Spectral	0.012	0.003	0.284	$-1.1\times 10^{-7}$	0.008	0.996

Table 2: Time series statistics for spectral centroid and RMS energy (representative subset).

\bar{x}

: mean;

\sigma_{x}

: standard deviation;

\gamma_{x}

: coefficient of variation;

\beta

: trend slope per frame;

R^{2}

: determination coefficient;

\rho_{1}

: lag-1 autocorrelation.

Figure 6: Phase space trajectories for pelog variants. Each point represents $\bm{\Gamma}(m)=[\tilde{\mathcal{C}}_{\text{norm}}(m),\tilde{\mathcal{E}}_{\text{norm}}(m)]$ . Colors: red (layered), orange (alternating), green (melodic), navy (spectral).

Figure 7: Phase space trajectories for slendro variants. Note the clear spatial separation of layered mode (a) from other modes—a stronger inter-mode differentiation than observed in the pelog family.

Mode	$\mathcal{A}$	$\mathcal{L}$	$\eta$	$\bar{\mathcal{C}}_{n}$	$\bar{\mathcal{E}}_{n}$	$\rho_{\mathcal{CE}}$	$\mathcal{R}_{\epsilon}$
Pelog Layered	0.529	147	0.004	0.302	0.621	$-$ 0.568	0.119
Pelog Alternating	0.285	99.8	0.003	0.236	0.387	$-$ 0.790	0.240
Pelog Melodic	0.356	111	0.003	0.140	0.537	$-$ 0.513	0.183
Pelog Spectral	0.333	166	0.002	0.314	0.354	$-$ 0.362	0.163
Slendro Layered	0.488	183	0.003	0.537	0.665	$+$ 0.317	0.123
Slendro Alternating	0.301	140	0.002	0.300	0.338	$-$ 0.118	0.230

Table 3: Phase space trajectory metrics.

\mathcal{A}

: convex hull area;

\mathcal{L}

: path length;

\eta

: exploration index (

\mathcal{A}/\mathcal{L}

);

\bar{\mathcal{C}}_{n},\bar{\mathcal{E}}_{n}

: centroid coordinates;

\rho_{\mathcal{CE}}

: brightness-energy correlation;

\mathcal{R}_{\epsilon}

: revisit rate (

\epsilon=0.05

). All correlations significant at

p<0.001

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Open paper AskPDF arXiv

The project described in this paper explores the informative sonification of data received in real time from a supercomputer. These data capture the current activities in all the nodes of the computer, therefore, their sonification functions as a form of continuous monitoring of the nodes' behavior and, by extension, of the system as a whole. Because such monitoring is theoretically unending, the resulting sonification must be musically capable of conveying information through sound in a way that remains both intelligible and engaging over long durations. Rather than imposing a predefined musical style onto the data, we sought to identify one which the data themselves could plausibly support. From a small set of candidates, we selected EDM because it is a family of genres whose structural and temporal characteristics align well with continuous, data-driven processes and long-term listening. Through this style-based approach, this research builds on the long tradition of computer data sonification while uniquely combining three elements rarely addressed together: monitoring (rather than debugging) as the primary goal, real-time (rather than post-mortem) data interpretation, and generation of virtually infinite and stylistically coherent (rather than incongruous) music.

Abstract

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