Sound Creation Based on Nonlinear Cell Circuits
Naruno Fujii and Hiroshi Yamamoto

Yoshifumi Nishio

Faculty of Science and Technology, Sophia University
7–1, Kioi-cho, Chiyoda-ku, Tokyo 102–8554, Japan
Email: nanno0917@sophia.ac.jp

Faculty of Electrical and Electronic Engineering, Tokushima University
2–1, Minami-Josanjima, Tokushima 770–8506, Japan
Email: nishio@ee.tokushima-u.ac.jp

Masaki Bandai and Mamoru Tanaka
Faculty of Science and Technology, Sophia University
7–1, Kioi-cho, Chiyoda-ku, Tokyo 102–8554, Japan
Email: mamoru.tanaka@gmail.com

I. A BSTRACT

we showed to be able to generate the musical tone from the stateequation.

The sound has three elements. They are ”Sound volume”, ”Musicalpitch”, and ”Tone color”. First, ”Sound volume” changes by theamplitude of the waveform. When the amplitude is large, the soundwill be also large. And the other hand, when the amplitude will besmall, the sound will be also small. Next, about ”Musical pitch”, Itchanges depend on its frequency. The sounds with high frequencies
become high-pitched sounds, and the sounds with low frequencies
become low-pitched sounds. The last, ”Tone color” can be decided by
its waveforms.Sound is classified into three kinds by the waveform.
They are ”Pure tone”, ”Musical tone”, and ”Unpitched sound”. ”Puretone” is a sound that has only one sine wave. And, ”Musical tone”
is the lasting sounds that have regular vibrations except for thepure tone. Then, ”Unpitched sound” is a sound that has almost noregular vibrations. In this research, we focused on the musical tone
waveform. Now, the signal processing is mainly used in order togenerate the musical tone waveform. Then, we propose the method
for generating the musical tone waveform from the state equation asa new method. We calculate the state equation from the nonlinear
circuit that is modified Nishio circuit. In this method, the frequency
and the musical tone waveform can be changed easily by changing
the value of capacitance of the nonlinear circuit.

4
%
dIk


L=v−RIj

1k
dt

j=1


di

L2 dtk = vk
C dvdtk = −Ik − ik − f (vk )



k −1|
f (vk ) = −α |vk +1|−|v2α = 0.012(1)

The information of music is usually written in its score. In thisresearch, MIDI information plays the role of score. MIDI informationshows the property of each music such as length and pitch ofeach note. In this MIDI information, quarter note are defined as
one second. Actually to play the musics by using this method, it
is necessary to combine such data into this system. To keep the”Sustain” of each notes which is decided by MIDI information, andto realize the smooth ”Release” , changing the volume of resistance
α is needed. It can be expected that resistance α works as like ainclination when sound is releasing. Then it leads smoothly shift tothe next note.
III. C ONCLUSION

II. S IMULATION R ESULTS

I1

L1

I2

v1 C i1 v2C
L2f(v1)

I3

I4

L1

i2 v3 Ci3 v4 Ci4

L2f(v2 )L2f(v3 )L2f(v4 )L1

L1RFig. 1.
Circuit model. L1 = 100.7[mH], L2 = 10.31[mH], C =12.69[µF],and R = 26.72[Ω].

The nonlinear circuit which used this research is shown in Figure
1. The state equation obtained from this circuit is shown in (1). In thisresearch, we calculated the voltage waveform of the capacitor fromeach node electrical potential. We considered as the waveform to
be a musical tone waveform, and generated the musical tone. Thus,

In this paper, we showed that the musical tone can be generated
by using the state equation that had been obtained from the nonlinear
circuit that the Nishio circuit had been modified. And to realize
not only generate the musical tone but also generate the comfortable musical tone from state equations, what we focused on was”Enverope”. ”Enverope” are consisted of four elements as follows,”Attack”, ”Decay”, ”Sustain” and ”Release”. In order to improve
the quality of sound, ”Release” can be the very important elementin particular. Smooth ”Release” makes the sounds more artistic andnatural. Resistance α works as like a inclination of ”Release”. Then,it can be expected that resistance α is the key point of ”Release”.
R EFERENCES[1] Y.Nishio and A.Ushida, ”Chaotic Wandering and its Analysis in Simple Coupled Chaotic Circuits ”, IEICE Transactions on Fundamentals,
vol.E85-A,no.1,pp.248-255,Jan.2002.