Timbre Analysis of the Hulusi, a Southwestern Chinese Free-Reed Instrument, using Machine Learning

Yang Xia; Rolf Bader

cs.SDSep 14, 2026

Timbre Analysis of the Hulusi, a Southwestern Chinese Free-Reed Instrument, using Machine Learning

Authors: Yang Xia, Rolf Bader

Organizations: College of Art, Zhejiang Normal University, Jinhua 321004, China · Institute of Systematic Musicology, University of Hamburg, Hamburg 20354, Germany

Abstract

The hulusi is a wind instrument that was invented in Yunnan Province, China, and has become tremendously popular in recent years. It consists of a mouthpiece, a gourd, and three bamboo tubes, all with free reeds made of copper. The main bamboo tube in the middle has seven finger holes. In this instrument, the pipe length, not the free reed's eigenfrequency, determines the instrument's pitch, unlike, for example, with the Western accordion or the blues harp. In this study, a machine learning model implemented in the COMSAR framework (https://github.com/ifsm) was used to investigate the timbre characteristics of the hulusi to cluster different instruments and pitches. The measured hulusi pitches C, B, A, G, and F were analyzed according to seven psychoacoustic features, among which only the spectral centroid, sharpness, and fractal correlation dimension are shown to form pitch clusters. These timbre features were used to train Kohonen self-organizing maps (SOMs) for clustering. Brightness and sharpness analysis revealed that the highest pitches were less bright and less sharp than mid- and low-range pitches were. Furthermore, the fractal correlation dimension, which mainly determines the chaoticity of the initial transients, was the best-clustering timbre feature for the hulusi, with the highest pitches showing the least chaoticity. This result is supported by defining a cluster quality index for the SOMs.

Figures & tables

Figure 1: Hulusi structure: front (left) and back (right) of the hulusi . A player blows into the mouthpiece and the attached gourd. In the gourd, three tubes are placed with free reeds within the gourd. The middle tube has seven finger holes. The left and right tubes are drone tubes without finger holes and can be turned on or off using plugs at the tube ends.

Figure 2: Hulusi fingering for producing the lowest note: front (left) and back (right) of the hulusi .

Instrument	Fingering
	1 (usol)	2 (ula)	3 (usi)	4 (do)	5 (re)	6 (mi)	7 (fa)	8 (sol)	9 (la)
F1	C4 265 $\pm$ 1	D4 293 $\pm$ 1	E4 328 $\pm$ 1	F4 348 $\pm$ 1	G4 389 $\pm$ 1	A4 439 $\pm$ 1	B $\flat$ 4 468 $\pm$ 2	C5 521 $\pm$ 0	D5 584 $\pm$ 1
cents	$-471.7$	$-297.8$	$-102.5$	$\mathbf{0.0}$	$192.8$	$402.2$	$512.9$	$698.6$	$896.3$
F2	C4 265 $\pm$ 1	D4 294 $\pm$ 1	E4 328 $\pm$ 1	F4 347 $\pm$ 1	G4 389 $\pm$ 1	A4 437 $\pm$ 1	B $\flat$ 4 474 $\pm$ 1	C5 520 $\pm$ 2	D5 584 $\pm$ 1
cents	$-466.7$	$-286.9$	$-97.5$	$\mathbf{0.0}$	$197.8$	$399.2$	$539.9$	$700.3$	$901.2$
G	D4 296 $\pm$ 1	E4 332 $\pm$ 1	F $\sharp$ 4 371 $\pm$ 1	G4 394 $\pm$ 1	A4 442 $\pm$ 1	B4 497 $\pm$ 1	C5 530 $\pm$ 2	D5 593 $\pm$ 2	E5 666 $\pm$ 2

Table 1: Nine hulusis in keys F1 to C3, showing note names, solmization, and measured fundamental frequencies of the notes played on the instruments. Values following the note names are the mean fundamental frequencies

\pm

standard deviations in Hz obtained from ten measurements. For each instrument, the second row gives the interval in cents relative to fingering 4 ( do ), which is defined as 0 cents.

Figure 3: The results of training a self-organizing map of the hulusi’s timbre features using an 18 $\times$ 18 u-matrix. The notes used to train the SOM are represented by colored dots, with different colors representing the instrument’s pitches: the blue dots in the lower left corner represent the treble region, the orange dots represent the midrange region, and the pink dots represent the bass region.

Figure 4: SOM of the spectral centroid. Left: U-matrix, the background color represents the similarity of neighboring neurons, darker regions represent lower values. Right: component plane; the background color represents the spectral centroid feature. The dot colors represent the recorded pitches. The pitches are arranged from high to low. Treble tones: blue, where la, sol, and fa transition from light blue to dark blue. Midrange tones: yellow, where mi, re, and do transition from light yellow to yellow. Bass tones: red, where usi, ula, and usol transition from orange to dark red.

Panel of Figure 5 — Figure 5: SOMs and component maps of the sharpness (a, b), fractal correlation dimension (c, d), and spectral flux (e, f) features. The background color corresponding to neighboring neuron similarity is shown on the left, and the background color corresponding to the feature strength is shown on the right. The sharpness and fractal dimension plots show clusters for high-pitched tones but not for midrange and low-range registers. The flux results do not display any clustering, and the feature strength does not align with the pitches.

Panel of Figure 6 — Figure 6: Multi-feature SOM maps with neighbouring neuron similarity as background color. The large left panel shows the SOM and feature maps obtained using spectral centroid, sharpness, and correlation dimension. The two smaller panels on the right show the SOM and feature maps obtained using spectral centroid, spectral flux, and sharpness, and using spectral centroid, sharpness, spectral flux, and correlation dimension, respectively.

Figure 7: Distances of hulusi pitches, indicating the ability to form clusters for the single features and feature combinations. Pitches are arranged from low to high; purple indicates close distances and good clustering, whereas green indicates far distances and poor clustering. The last three rows of the vertical axis are the features discussed in Section. 3.2.

Figure 8: Timbre features corresponding to the minimum distances for all pitches from Fig. 7. The fractal correlation dimension is the best feature for clustering hulusi tones.

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A Lightweight Slot-Attention Framework for Multi-Instrument Multi-Pitch Estimation

Michael Taenzer

Electronic Media Technology Group Ilmenau University of Technology Ilmenau, Germany

Slot Attention Music Information Retrieval Permutation-Invariant Learning

Open paper AskPDF arXiv

Multi-pitch estimation (MPE) typically predicts which pitches are active in a mixture, but not which instrument or source produced them. This paper investigates a lightweight slot-attention framework for multi-instrument MPE (MI-MPE), where a mixture CQT is mapped to an unordered set of source-like pitch maps. The model uses permutation-invariant Hungarian matching to avoid fixed output semantics and treats the number of slots as an upper bound on the number of active sources. We further study two modular extensions: a self-supervised timbre encoder that provides training-time targets for slot-level timbre embeddings, and a polyphony branch that regularizes the pitch density of mixture- and slot-level predictions. Experiments show that Hungarian matching substantially improves instrument family decomposition on URMP. Stem-level prediction remains more challenging: timbre and polyphony supervision improve selected configurations, but do not consistently resolve source assignment. The results suggest that slot-based architectures are a promising direction for source-aware MPE, while highlighting the need to couple auxiliary musical cues to slot identity more carefully.

Abstract

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