PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Study of Ivory Alternatives for Koto Bridges: Correlation between
Sensory Evaluation and Amplitude Modulation of Fundamental
SpectrumShuichi SAKAMOTO1; Shunsuke WATANABE; Taku WATANABE; Yuki SATO; Shuma ITO; Ryota
KOMINAMI; and Yuki AKIBA
1-7

Niigata University, JapanABSTRACT
The bridges of a koto, a Japanese musical instrument, have traditionally been made of ivory for its superiorsound quality and appearance. On the contrary, in the conference of CITES CoP17, 2016, a resolution for theclosedown of the domestic market of the ivory was adopted. Therefore, the demand for substitute materials
for the ivory is expected to increase in future. Despite this, from the viewpoint of sound quality, the currently
available substitute materials used to manufacture koto bridges remain inferior in comparison with ivory.
This study investigates the performance of substitute materials by investigating the properties of koto bridges
made of metal, resin, and wood. A sensory evaluation of a single tone played by professional and expert kotoplayers was performed for all substitute materials. Additionally, a wavelet analysis of the recorded tone wasconducted. The amplitude modulation of the fundamental spectrum level varied in time with respect to eachof the chosen materials. The study also includes an investigation of the correlation between sensory
evaluation and the recorded amplitude modulation of fundamental spectrum.
Keywords: Wavelet transform, Fast Fourier transform, Sensory evaluation, Harmonic, Fundamental mode,
Pearson productmoment correlation coefficient

1. INTRODUCTION
Koto bridge supports strings, thereby transmitting vibrations to the torso (1). In this regard, violin
has been extensively studied because it is a typical stringed instrument with a bridge (2–12). However,Koto bridges have been rarely studied because Japanese Koto is an instrument used only in Japan
mainly. Koto bridges made of ivory have excellent appearance and timbre (when played); thus, they
are in great demand. The Washington Convention was adopted in 1975, and by 1989, the internation al
trade in ivory had virtually ended. A resolution to ban the domestic trade of ivory was adopted at the2016 Conference of the Parties. However, resin-based materials that are currently used as substitutes
for ivory have poor sound quality. Therefore, alternative materials for ivory must be identified.
Physical properties of materials for Koto bridges made of ivory and various other materials were
determined using dynamic viscoelasticity measurements and ultrasonic waves. These studies indicatedthat the physical and mechanical properties of the bridge were closely related to the sound fluctuations.
Analysis of single tones revealed that characteristic fluctuations appeared during reverberation andthese fluctuations differed depending on the bridge material (13–15). From the above, we deduced
that physical and mechanical properties of materials used in Koto bridges affect the sound quality.
Therefore, we built bridges using various materials and performed a trial and a sensory evaluation ofsound using Koto performers. We also examined the correlation between the analysis results ofrecorded data and sensory evaluation.

2. QUANTIFICATION OF THE FLUCTUATION COMPONENT OF
REVERBERATION
2.1
1

RMS Value of the AC Component in the Time Waveform of a Spectrum Level in thesakamoto@eng.niigata-u.ac.jp7557Standard Harmonic Overtone
We recorded the sound played on the Koto and performed wavelet transform. Further, we
determined the time variation of the spectral level for each harmonic to analyze the sound differences
produced due to different Koto bridge materials. The fluctuation in spectrum level affects the sensory
evaluation. Detailed analysis of this fluctuation involved the following steps: 1) conducting a fast
Fourier transform of the time waveform of the spectrum level of the standard harmonic overtone,
determining the frequency and magnitude of the fluctuation component. 2) by focusing on the point
at which the behavior of the time variation of the spectrum level changes with time, applying a filter
to the time waveform of the spectrum level for each frequency band and time, a nd 3) obtaining theeffective value of the AC component for each condition.

Frequency [Hz]Spectral level [dB]

2.2 Procedure for Obtaining RMS Values
We recorded the sound in a studio using a Sony ICD-SX 2000 audio recorder. A recording device
was installed near the hole at the bottom of the Koto. The standard harmonic overtone frequency
unified at ~390 Hz.
The recorded sound was 4.5-s long after the first sound level peak. After 4.5 s, the recorded soundwas almost inaudible and had attenuated by more than 60 dB from the peak value.
The recorded sound was subjected to time–frequency analysis by wavelet transform using an Ono
Sokki Oscope 2 acoustic analysis tool. The Gabor function was used for characterizing the motherwavelet. Figure 1 shows an example of a color map obtained from the analysis. In this figure, thevertical axis represents frequency, the horizontal axis represents time, and the spectral levels are color
coded.

1st harmonic

Time [s]Figure 1– Example of a color map for time–frequency spectral levels

Figure 2 – Time waveform of the spectrum level of the standard harmonic overtone andapproximation line

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Figure 2 shows an extraction of the temporal change in the spectrum level of the standard harmonic
overtone in Fig. 1. For this time waveform, the approximate line obtained using the least squares
method at 4.5 s after the peak is also shown. By removing the slope of this approximate line, only thetime waveform of the fluctuation component of the spectrum level of the standard harmonic overtone
is obtained, as shown in Fig. 3.
Fig. 4 shows the frequency characteristics of the fluctuation components obtained by performinga Fourier transform on the time waveform of Fig. 3. The Fourier-transformed calculation data of Fig.
4 were filtered offline and divided into six frequency bands: 2–6, 6–10, 10–14, 14–18, 18–22, and 22–
26 Hz. By performing inverse Fourier transforms on the data for these six frequency bands, the time
waveform of the spectrum level (Fig. 5) was determined for each band.

Figure 3 – Time waveform of only the fluctuation component in the time waveform of thespectrum level of the standard harmonic overtone

Figure 4 – Frequency characteristic of the fluctuation component in the time waveform of thespectrum level of the standard harmonic overtone

Figure 5 – Time waveform of the spectrum level in a certain frequency band7559

The time waveforms shown in Fig. 5 were divided into three time zones of 0–1.5, 1.5–3.0, and
3.0–4.5 s. Next, by plotting the RMS values of these time waveforms, as shown in Fig. 6, the RMS
values of AC components “for each time zone in each frequency band” were calculated.
The time waveform of the spectrum level at the frequency of the standard harmonic overtone wasdivided into six frequency bands and three time zones. The RMS values of the AC components forthese 18 conditions were then obtained.

Åeffective value

Figure 6 – RMS value of the AC components for each time zone in a certain frequency band
Table 1 – RMS values of the AC components obtained for ivory
0-1.5 s1.5-3 s3-4.5 s2-6 Hz0.0968

0.294

0.385

6-10 Hz0.002380.00168

0.00216

10-14 Hz0.0283

0.105

0.214

14-18 Hz0.01450.05910.173

18-22 Hz0.002380.00168

0.00216

22-26 Hz0.01060.04020.141

Table 1 shows an example of the RMS values obtained for ivory. Observation of the soundcharacteristics of a Koto bridge made of ivory using the RMS values of the AC components revealed
the following. The RMS values of the AC components in the time zone indicate that the latter halftends to be larger. The RMS values of the AC components in the frequency band indicates that thelow-frequency side tends to be larger.

3. CORRELATION BETWEEN SENSORY EVALUATION AND THE RMS VALUESOF THE AC COMPONENTS
We show the correlation coefficient of the RMS values of the AC components and the scores of thesensory evaluation for a total of 73 types of bridges comprising 70 prototype bridges and threecommercially available bridges (including ivory).
First, the “RMS values of the AC components” under the 18 conditions identified in the previous
chapter were obtained for Koto bridges made of 73 materials.
A sensory evaluation of the sound of a Koto being played was also performed for those bridges.
The criteria used in the sensory evaluation are shown in Table 2. The evaluators were five professionalor skilled performers.

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Table 2 – Evaluation criteria for sensory evaluation
Evaluation

PointA

4A-

3.7

B+

3.3

B

3B-

2.7

C+

2.3

C2C-

1.7

㸫

1IndexEquivalent to ivory

Superior to distribution products

Equivalent to distribution products

Inferior to distribution products

As an example of high correlation, the condition of a frequency in the 2 –6 Hz band and a time of
3.0–4.5 s, the RMS values of the AC component, and the scores of the sensory evaluation for eachmaterial were plotted in Fig. 7. Herein, the straight line shows the correlation. The plot with a scoreof 4.0 is for ivory.

Figure 7 – Plots of the RMS values of the AC components and scores of the sensory evaluationfor 73 types of Koto bridges (an example with high correlation).
(Frequency range: 2–6 Hz , Time: 3–4.5 s )7561

Table 3 shows the coefficients of correlation and P-values for 18 conditions by processes like thatin Fig. 7. These coefficients of correlation increase with the passage of time in all frequency bands
except 6–10 Hz. In addition, as the P-values decrease with time, the reliability of the correlation isimproved. Based on these facts, if the RMS value of the AC component in the second half of the soundis large, it tends to be a “good sound evaluation.”
Focusing on the coefficient of correlation in the frequency band in the 3.0–4.5-s zone (Table 3),
we can see the coefficient is high at 14–18 Hz and 22–26 Hz. In addition, because the coefficients ofcorrelation exceed 0.4 in any frequency band, there is considerable correlation.
Here, in the example for ivory shown in Table 1, the RMS value of the AC component becomeshigh as the frequency band becomes low. This tendency is the same in the other materials. Here, we
speculate that the score (hearing sense) is affected by audible sound. Therefore, the score may beaffected by the frequency band in the 3.0–4.5-s time zone in Table 3 with a high RMS value of the ACcomponent.
Table 3 – Coefficients of correlation between the sensory evaluation and the RMS values of theAC components and P-values
Time [s]Frequency

0 - 1.5

1.5 - 3.0

3.0 - 4.5

Correlation - coefficient

0.299

0.358

0.417

P - value

0.008760.001480.000179

Correlation - coefficient

0.362

0.286

0.409

P - value

0.001310.01220.000243

Correlation - coefficient

0.161

0.326

0.420

P - value

0.166

0.00408

0.000159

Correlation - coefficient

0.205

0.3770.470

P - value

0.07500.000789

1.85E-05

Correlation - coefficient

0.362

0.286

0.409

P - value

0.001310.01220.000243

Correlation - coefficient

0.234

0.351

0.467

P - value

0.04180.00187

2.16E-05

range [Hz]2-6

6 - 10
10 - 14

14 - 18

18 - 22

22 - 26

4. RELATION BETWEEN THE RMS VALUES OF THE AC COMPONENTS,
SENSORY EVALUATION, AND FREQUENCY BAND
Figure 8 shows a three-dimensional graph of the “RMS values of the AC components,” “scores ofsensory evaluation,” and “frequency band” for the 18 conditions obtained by the procedure shown inSection 2-2. The vertical axis is the RMS value of the AC component, the horizontal axis is thefrequency band, and the score is in the depth direction. In addition, the magnitude of the effective
value of the AC component is color coded.
From Fig. 8, the higher the score, the higher is the effective value of the AC component. In thelow-frequency band, when the RMS value of the AC component is high, the score also tends to behigh. In the example of ivory shown in Table 1, the RMS value of the AC component is higher in thelow-frequency band. Thus, if a material has a high RMS value of the AC component in the lowfrequency band, then the sensory evaluation score may be high. We believe that this is a useful finding
in the development of and search for alternative materials to ivory.

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0.5
0.4
0.3
0.2
0.1

0.1-0.2

0.2-0.3

2.46
2.52
2.58
2.65
2.68
2.72
2.75
2.75
2.80
2.92
2.93
3.00
3.08
3.20
4.00

2.42

2.40

2.28

2.08

18-22

22-26

10-14

0-0.1

14-18

2-6

Frequency [Hz]

6-10

0

Effective value [V]0.6

Evaluation

0.3-0.4

0.4-0.5

0.5-0.6

Figure 8 – The RMS value of the AC component, the score, and the frequency band
(Frequency range: 4 Hz step from 2 Hz, Time: 3.0 – 4.5 s)

5. CONCLUSIONS
We extracted the RMS values of the AC components in a time change of the spectrum level of thestandard harmonic overtone by analyzing single tones using Koto bridges made of ivory and various
other materials. As a result of examining the correlation between those values and the scores of thesensory evaluation, the following conclusions were obtained.
The correlation between the RMS values of the AC components and the scores of the sensory
evaluation increased with time. The material for a Koto bridge with a large RMS value of the ACcomponent during the 3–4.5 s time period might have a high sensory evaluation score.

ACKNOWLEDGEMENTS
We would like to thank Noriko Sanada of Cera Creations and the performers who participated in
the sensory evaluation, Inoue Kogyo Co., Ltd., Nittax Corporation, Risho Kogyo Co., Ltd., TorayIndustries, Inc., Asahi Kasei Co., Ltd., and Sekisui Chemical Co., Ltd. for providing the materials.

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