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Preliminary sonification of ENSO using traditional Javanese gamelan scales
Sandy Hardian Susanto Herho, Rusmawan Suwarman, Nurjanna Joko Trilaksono, Iwan Pramesti Anwar, Faiz Rohman Fajary
TL;DR
Sonification’s preservation of dynamical structure is underexplored, especially for culturally situated representations of complex systems. This study maps ENSO data into Javanese gamelan scales and analyzes acoustic phase-space trajectories, finding that composition strategies and scale families yield distinct recurrence, geometric, and coupling regimes.
Problem
Whether sonification preserves the dynamical structure of complex systems, including how musical frameworks shape that preservation, remains underexplored.
Method
The study maps the 1870–2024 Niño 3.4 SST anomaly index into Javanese pelog and slendro audio, then evaluates acoustic trajectories using recurrence and geometric diagnostics.
Results
Alternating modes show the highest recurrence, layered modes explore broader phase space, and pelog exhibits anti-phase brightness–energy coupling while slendro is near-independent.
Takeaways & Limitations
Phase-space trajectory analysis offers a principled toolkit for comparing sonification designs and selecting composition strategies for quasi-periodicity or acoustic-state diversity.
Takeaways & Limitations
The implementation simplifies gamelan practice through equal-temperament tuning and MIDI synthesis and lacks assessment of cultural resonance with Indonesian communities.
Abstract
from arXiv · showhide
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.
1 Introduction
The introduction frames ENSO as a complex dynamical system whose structure is difficult to represent through conventional visualization, motivating culturally situated sonification with Javanese gamelan scales. The study evaluates which dynamical signatures survive this transformation using phase-space trajectories and recurrence-based diagnostics.
- ENSO as a complex dynamical system: ENSO exhibits irregular 2–7 year oscillations, warm–cold amplitude asymmetry, annual phase-locking, and sensitivity to stochastic forcing.These features arise from coupled ocean–atmosphere feedbacks, including the Bjerknes mechanism, delayed oscillator dynamics, and recharge processes.
- Motivation: Sonification complements visualization by using auditory sensitivity to temporal structure, recurrence, and multi-stream processing.The passage characterizes sonification as a complex mapping rather than merely an alternative output format.
- Research gap: Climate sonification has largely relied on Western musical frameworks, leaving alternative tonal systems underexamined as encodings of dynamical structure.The introduction identifies this gap as a missed opportunity for culturally and structurally different mappings.
- Cultural and structural rationale: Javanese gamelan offers cyclic, hierarchical, polyphonic, and non-uniform interval structures that map naturally onto ENSO dynamics.Its geographic and structural relevance is reinforced by Indonesia’s high ENSO sensitivity and Java’s exposure to drought, fires, and flooding.
- Study contribution: The study maps ENSO variability into pelog and slendro audio, represents outputs in phase space, and applies recurrence diagnostics to compare resulting acoustic trajectories.It investigates which dynamical signatures survive transformation and reports quantifiably different phase-space geometries between the two scales.
2 Data
The study uses the Niño 3.4 sea surface temperature anomaly index from HadISST 1.1 as its primary ENSO indicator, spanning monthly observations from January 1870 through December 2024.
- Data: The Niño 3.4 index comprises monthly mean SST anomalies averaged over the equatorial Pacific region from 5°N–5°S and 170°W–120°W.The data come from the HadISST 1.1 dataset.
- Data: The time series contains N = 1,860 observations covering 155 years, from January 1870 to December 2024.The series was obtained from the NOAA Physical Sciences Laboratory.
3 Methods
The methods characterize ENSO dynamics, map anomalies and evolution rates into Javanese gamelan sonifications, and evaluate the resulting audio as trajectories in a two-dimensional brightness–energy space. Eight variants are compared using recurrence, geometric, dispersion, and coupling metrics.
- ENSO characterization: ENSO dynamics were characterized using distribution moments, lag-1 autocorrelation, operational episode thresholds, and first-order anomaly differences.Episodes required at least three consecutive months with anomalies ≥+0.5°C for El Niño or ≤−0.5°C for La Niña.
- Sonification mapping: Parameter mapping converts anomalies θ(t) ∈[−3, 3]°C into quantized pitches across pelog Φpelog = {0, 1, 3, 7, 8} and slendro Φslendro = {0, 2, 3, 7, 9} semitone systems.The monotonic mapping makes warm anomalies produce higher pitches while preserving ordinal structure.
- Sonification mapping: MIDI velocity combines anomaly magnitude and rate of change as v(t) = clip(80 + 20|θ(t)| + 30 |∆θ(t)| , 40, 127).The rate term β2 = 30 exceeds the magnitude term β1 = 20, emphasizing rapid ENSO transitions.
- Trajectory analysis: Each sonification is represented by smoothed, normalized spectral centroid and RMS energy trajectories, whose geometry and coupling are quantified in acoustic phase space.Metrics include convex hull area A, path length L, efficiency η, centroid dispersion, Pearson correlation ρCE, and revisit rate Rϵ.
4 Results
Results show that the ENSO index retains strong persistence, asymmetry, and quasi-periodicity, while sonification variants systematically differ in acoustic statistics and phase-space geometry. Alternating modes maximize recurrence, layered modes expand phase-space coverage, and pelog versus slendro produce distinct brightness–energy coupling regimes.
- ENSO index characteristics: The Niño 3.4 index had mean θ̄ = −0.098°C, standard deviation σ = 0.775°C, range 5.06°C, and lag-1 autocorrelation ρ1 = 0.926.Its positive skewness and excess kurtosis indicate warm-phase amplitude asymmetry and heavier-than-Gaussian tails.
- Acoustic features: Across eight variants, mean spectral centroid ranged from 809 Hz (pelog melodic) to 1,863 Hz (slendro layered), with slendro consistently brighter.The reported difference is attributed to slendro’s more uniform interval spacing distributing pitch content across a wider spectral range.
- Phase-space geometry: Pelog layered occupied the broadest phase-space region, with convex hull area 0.529, whereas slendro melodic had the smallest area, 0.211.Exploration indices were uniformly low (η ∈[0.001, 0.004]), indicating highly meandering trajectories.
- Dynamical signatures: Alternating modes had the highest revisit rates, Rϵ = 0.240 for pelog and 0.230 for slendro, while layered modes had the lowest.The results attribute this recurrence to the period-4 forcing introduced by the round-robin composition strategy.
- Dynamical signatures: Pelog exhibited predominantly negative brightness–energy coupling, ¯ρCE = −0.558, while slendro showed weak mean correlation, ¯ρCE = −0.074.Pelog alternating reached −0.790, whereas slendro layered uniquely showed positive coupling (+0.317).
- Dynamical signatures: Aggregated slendro trajectories were longer and slightly more recurrent than pelog trajectories but covered less area: L = 169, Rϵ = 0.187, and A = 0.337 versus L = 131, Rϵ = 0.176, and A = 0.376.This summarizes slendro’s “wandering but revisiting” behavior versus pelog’s “expansive but less recurrent” behavior.
5 Discussion
The discussion presents phase-space analysis as a general toolkit for characterizing sonification dynamics, while showing partial preservation of ENSO structure and emergent scale-dependent coupling. It also identifies temporal compression, implementation simplifications, absent fidelity measures, and missing perceptual validation as limitations motivating targeted future work.
- Analytical contribution: Phase-space metrics provide a geometric toolkit for characterizing sonification designs beyond gamelan, distinguishing high-recurrence/low-area alternating modes from low-recurrence/high-area layered modes.The framework supports choosing composition strategies according to desired acoustic dynamical properties.
- Data-to-sound mapping: ENSO structure is only partially preserved: source lag-1 autocorrelation ρ1 = 0.926 corresponds to acoustic persistence with ρ1 > 0.958 for all modes.ENSO’s quasi-periodicity also appears as nonzero acoustic phase-space revisit rates, although recurrence structure depends strongly on composition mode.
- Limitations: Increasing brightness and decreasing energy over time are attributed to temporal compression rather than preserved ENSO properties.The 155-year record was compressed to 7.75 minutes, potentially inducing synthesis-engine-related non-stationarity.
- Scale-family effects: Brightness-energy coupling bifurcates by scale family, with strong anti-phase behavior in pelog and near-independence in slendro.This emergent difference arises from interactions between interval structure and the parameter-mapping algorithm.
- Limitations: The implementation simplifies gamelan through 12-tone equal temperament, General MIDI timbres, omission of pathet, and limited engagement with traditional practice.These choices discard microtonal embat, bronze-metallophone timbral characteristics, and pathet’s temporal and affective functions.
- Limitations and future work: The study lacks mapping-fidelity measures and perceptual validation, so acoustic characterization cannot establish listener pattern recognition, event identification, or data comprehension.Future work should add information-theoretic measures, full RQA with systematic embedding selection, perceptual comparisons, and multivariate ENSO mappings.
6 Conclusion
Traditional Javanese gamelan scales provide a viable framework for ENSO data sonification, yielding eight acoustically distinct variants whose phase-space dynamics can be characterized with nonlinear-dynamics tools. Slendro produces higher spectral centroids than pelog, while layered compositions explore broader phase space with lower recurrence.
- 6 Conclusion: Traditional Javanese gamelan scales yield eight acoustically distinct ENSO sonification variants whose phase-space dynamics can be rigorously characterized using nonlinear-dynamics tools.The conclusion presents this as the study’s overall contribution.
- 6 Conclusion: Slendro modes generate consistently higher spectral centroids than pelog modes, reflecting the influence of interval structure on spectral properties.The comparison is attributed to differences in the scales’ interval structures.
- 6 Conclusion: Layered compositions explore broader phase space with lower recurrence.This finding is listed among the conclusion’s key results.