Simpleware Case Study: Demystifying the Sound of the Japanese Koto

Overview

Applying computer-aided techniques to musicology is a relatively new field, but one that has great potential for studying instruments. The main challenge for this approach is to characterize instruments that cannot be easily studied physically due to internal parts. CT scanning and modeling an instrument solves this problem and allows for better understanding of the special characteristics of its different components.

In this study, Simpleware software was used to segment a CT scan of a Japanese koto, an ancient hand-crafted instrument, and prepare a high-quality mesh for COMSOL Multiphysics^®. The goal of the project was to understand the distinct tone colors of the koto, taking into account as many real-life measurements as possible. Comparison with experimental data and validation gave insights into the koto’s functions, including its inner chamber, and the properties of its specific wood materials.

Highlights:

CT scanning enables inspection of internal feature of a hand-crafted Japanese koto
Simpleware software was used to segment and overcome meshing challenges for image data
Simulation provides comprehensive insights into unique internal structure of the koto
Results help demystify the sound of the koto from first principles (ab initio) and Japanese sacred geometry associated with the ellipse

Thanks to:

University of Adelaide (Elder Conservatorium of Music): Prof A. Kimi Coaldrake

“I needed to see inside my valuable musical instrument without splitting it open and damaging it. Other methods had been unsuccessful. The Simpleware tools allowed me to take 2300 DICOM images from a CT scan and convert them to a mesh suitable for finite element modeling. It helped me to understand the origins of the unique and complex sounds of the Japanese koto that have rarely been studied.”

References:

A.K. Coaldrake. Construction and validation of a high-resolution finite element model of the Japanese koto, The Journal of the Acoustical Society of America, 144, 1891 (2018)

Modeling the Complex Koto Geometry

The process of creating FE models of the koto relied on developing both simplified conceptual shapes and a high-resolution computer tomography CT scan of the instrument. Scanning Electron Microscopy was also used to capture the highly anisotropic characteristics of the paulownia wood used in the koto to study different grain orientations in COMSOL Multiphysics^®. CT scanning was particularly valuable for understanding the unique internal structure of the hand-crafted koto, including clarification of the lack of holes in the inner chamber dividing wall.

CT scanning the koto at the Radiology Department, Royal Adelaide Hospital.

Segmentation and Meshing in Simpleware Software

Simpleware ScanIP was used to segment the koto into seven components: its top plate, base plate, internal partitions, struts, bridges, feet, and end plates. Despite difficulties associated with separately segmenting several components comprised of the same wood, and local greyscale variation in wooden parts due to the wood’s grain, Simpleware ScanIP’s wide range of tools enabled accurate segmentation. In regions where the image data was distorted due to metal artefacts associated with the bridges, Simpleware ScanIP’s interpolation toolbox was used to ensure these artefacts did not affect the quality of the segmentation.

CT image slice of the koto (left), and a cross-section through the segmented koto (right).

Using the Simpleware FE module, a high-quality volume mesh of the koto was generated quickly and easily. The +FE free meshing algorithm ensured that the model was true to the image geometry while keeping the element count within appropriate limits. The mesh was exported to COMSOL Multiphysics^®, where boundary conditions were applied, and a variety of simulations were performed.

FE mesh of the koto generated with the Simpleware FE module.

Studying Mechanical Vibration of Wood and Physical Sound Waves

The COMSOL model was used to carry out a range of simulations, including the solid mechanics of the koto’s natural vibrations, pressure acoustics (sound production in air), measured at ten locations at 1/48,000 second intervals. Results show insights into the complex acoustics of the koto at 85 Hz and 100 Hz resonances for acoustics for both its external wood shell and internal chambers. Comparison was also made between the COMSOL model being played at 220 Hz and an ‘as played’ Fourier Transform of a recording of Prof Coaldrake on her koto.

Comparison of the COMSOL model playing 220Hz and Prof Coaldrake playing 220Hz.

Conclusions

This study was successful in creating a high-resolution FE model of a hand-crafted Japanese koto, backed by validation against multiple studies, including the literature, acoustic camera data, and vibration analysis. The model resolved two major problems when studying the koto, namely the physical properties of the wood and its complex geometry. Simpleware software enabled the FE mesh to be tailored to a practical simulation workflow without having to sacrifice accuracy, overcoming the obstacle of having a very large mesh. The COMSOL model therefore holds great promise as a quasi-experimental tool, with the workflow applicable to different types of complex and rare instruments.

Any Questions?

Do you have any questions about this case study or how to use Simpleware software for your own workflows?