x-Music Lab
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x-Music Lab

[x-Music Lab 21秋] How can time be expressed through use of sounds? Implementation and suggestion through use of Helmholtz Resonance.

Keio University Environment and Information Studies Miku Fujimoto

The aim of this exploration is to find how time can be expressed through use of sounds.Time is a measurable period and it exists when the events occur. Time has been investigated in many fields such as quantum gravity physics, cognitive science and art.Time in the quantum gravity field is founded after the 21st century. It shows the new facts of time. Understanding quantum gravity can be very important as it proves some conditions for improving our daily life.Before investigating how to create a clock by sounds, factors in time are discussed.

What is time? No one can define “time”. It is because it is related in many fields like physics, philosophy, cognition, even in art…Time is very complex. Even though time is difficult to define, a lot of people used time as a calculation figure and used time in differential equations.The units of time can be a day, a calendar, the sun day, sidereal day, the rotation of the earth, and a year. Time tells us where we are at. On the other hand, in the 20th century, it became apparent that the law of gravity causes time velocity to change.

History of Time

History of a clock begins and ends with the key word, oscillation. The first clock was a sundial. Next, there is a water/sand clock. These are the correct clocks that have been on the earth for a long time. The mechanism is also simple. You fill a bowl with water or sand, make a hole at the bottom, and the water or sand falls from there to calculate the time. After a sand/water clock, there is a pendulum clock. A pendulum clock is way more constant than before. To make the pendulum more constant, escapements came into use. After that movement, mechanical clocks were introduced in the 14th century. These oscillations become more and more accurate. To measure the time without error, sounds are used. In 1866, Niaoude invented the tuning fork clock. The tuning fork clock is a clock that the tuning fork is used for . When an electric current is applied to the tuning fork, it oscillates precisely. After mechanical clocks, tuning forks came into use because of their high oscillation accuracy.

And, it is called a fork tune clock. This clock applied an electric current to the fork-tune and measured its oscillation, which was usually 60 Hz. As oscillation is the key word, the next one to be used was a crystal. The frequency was 2.5Mhz. However, the quality of the crystal can affect the quality of the time measurement. After this movement, the field of quantum mechanics came into play.

In order to make a measurement, the atoms are made to resonate and vibrate. And the vibrations became more “minute”. For example, an atom resonates at 1420405752 Hz. An atom of rubidium resonates at 6834682608 Hz. An atom of cesium resonates at 9192631770 Hz. The smaller the vibrations, the more accurate the realization that time will be.A metronome oscillates at a constant speed, and musicians adjust its speed to measure the tempo of a piece of music. In this way, periodic objects are useful for measuring time.

To conclude the history of the clock, we can say that clocks count cycles and hence count time. People have also created clocks using the terms oscillation and resonance. In the near future, clocks will become more and more accurate with the development of quantum physics.

The past and the future are completely different. Time is sometimes symbolized as an arrow. The end of an arrow can be the past and the tip can be the future. There are two major theories that explain gravity and time. One is the loop quantum theory. In the loop quantum field, it is not possible to distinguish between the future and the past. This is because the law of entropy cannot be applied. People see the world brulee. People do not see the world clearly because it is too detailed. Also, in quantum gravity theory, there is a smallest unit, which is called Planck time. Time does not flow, it moves from unit to unit. Nor can we find a point in time. This is because time exists in a quantum superposition.

Figure 1. Factors of time in the quantum physics field

Musical Time

First, musical time is very different from physical time. This is because music time is dependent on human cognition. Therefore, each person has his or her own sense of time. In addition, as music is said to be the art of music, sound is on a time axis. In the field of music, time is perceived as a one-dimensional thing, but in the field of music, it can be more than two-dimensional.

Furthermore, designing time is different from other fields. The reason is that time, unlike products, has no form. Time is a continuous thing, just like space. However, people cut out a certain continuous time in order to give meaning to that continuous time. Music is in that designed time. It usually has an opening, middle, and end. For example, the rondo form is composed of episodes.

Karlheinz Stockhausen (1928–2007) and his pupil John Cage described time in the music field. John Cage said Stockhausen thought time is very important. Musical time should not be defined by time. Music creates musical time itself. Music makes audiences have new experiences. By listening to music,” there is an experience of forgetting oneself.” -Stockhausen. Re-listening to music is to know how long it takes. “reading music scores is to see as a program because they see music with a separation” -Bayle. These quotes show the different perception of the musical time.

Some artworks are themed time which is mostly in the physics field. Goto Akinori created an artwork called toki-ballet #1/1. This is a time sculpture in which 3D printed materials are used. It is very important because the artwork represents the time flow that we recognise in real life. Also, it is important to be known because it is expressing the 2nd factor “Time flows discreetly” .

Electric Delay Time Automatic Calsulator by Tomoya Matsura is expressing the 3rd factor “There is a minimum unit for time” (Figure 1.). In this work, there is no minimum unit. Also, the length of minimum unit changes.

Telly Riley created a music called Poppy Nogood. Daniel Charles created graphical music and it changed the relationship between performers and music without changing time


This project started in April 2021 as graduation project-1. The theme of the project is decided by time because I read Carlo’s book . After I read that book, I got schock. It was a life changing experience that time is not flowing. Therefore, I decided to tell everyone that time’s actual features to surprise them.

OneSeconds was exhibited. For this exhibition, a wide range of members of the Shinya Fujii Research Group x-Music, from first-year undergraduates to researchers, participated from 16th to 17th. The students in charge of all the projects had weekly individual critique sessions with their mentor teachers (Yuta Uozumi and Kenta Tanaka) to continue to brush up their concepts and quality. The event will be held in the spacious Osanbashi Hall, which has a capacity of approximately 2,000 m2 and can accommodate up to 1,200 people. In accordance with the theme of this year’s exhibition, “Synthesize,” we will exhibit works synthesized from a perspective slightly different from conventional music and sound art.

One seconds is the artwork which shows the time differences in the space. Carlo Rovelli wrote L’ordine del tempo and it gave people new facts of time. There are few genres about time such as musical time, time scene and time in quantum physics. However, it is focused on the theory of loop quantum gravity. It is because the book gave me a life changing experience, thus, I wanted to give people a new experience. In the book, there are four important factors. 1. we cognise time in the relation between time and phenomenon. 2. time moves descretive. 3. time has a minimum unit which is called plank time. 4. Time occurs when gravity exists (Figure 1.). In these factors, the 4th factor is considered to be the most important, hence, it is expressed in “one seconds”. The speed of time varies depending on the gravitational field, but it is the same on Earth and in space. It is not well known that time varies with gravity. Also, people cannot feel the difference in speed. Therefore, the difference of one second is expressed by a clock.

Helmholtz resonances are used to make OneSeconds because all the previous clocks were using oscillations and resonances. I reckon Helmholtz resonances are suitable to make it happen (and it’s a new idea).

OneSeconds is differ to the tuning fork clock because electric current is used directly to oscillate a tuning fork. Tuning fork is using sounds to measure the timing. However, OneSeconds is using sounds to move the thingsSimilarity is periodic sounds(oscillation) is used to express time. OneSeconds have a way of simple constructionOneSecond’s disadvantage is the speed of rotation depends on the bottles.

Through making OneSeconds, there are some trials and errors. Firstly, Dr Denjiro’s website is referred to. It explains the mechanisms of helmholtz resonance and how the things can be moved by sounds. After the article was read, Investigation was held using a Ping-pong ball. However, it did not work. Therefore, plastic bottles are decided to be used. After plastic bottles were tested, it worked well. It rotated well and fast enough. Next, speed of rotation is investigated. Materials used for this investigation were two 1.5 liter coke plastic bottles, plastic strings and a branch. Sound pressure, frequencies and weight of materials directly affect on the speed of rotation. If the sound pressure is high, it rotates well because sounds resonate with the bottles. Also, after measuring the frequency of the bottles, those frequencies will be able to control the spin of the bottles. If the frequency of the frequency rotates most, it makes bottles move slower. Also, weight for materials affects the speed of rotation. Of course, if the material’s weight is low, it rotates well. However, bearings between a prop and stick are needed because it does not limit rotation. If the stick is suspended by plastic strings, it rotates. In conclusion, controlling sound pressure, material weights, and frequencies make speed of rotation changeable.

In the exhibition, I gave some explanations about the work to the audiences. The explanations were “This artwork is called OneSeconds and It is a clock which explains the possible time that exists in space. Time exists because of gravity. Therefore, I convert gravity to sounds because there are all oscillations. In this clock, there are no motors. Only principals of helmholtz make clock move”.After it was explained, audiences were curious how the clocks move. Some audiences asked me how it moved. Also, audiences may look at the fluctuations of sounds.

OneSeconds can be defined as visual art, sound sculpture, sound installation or kinetic art. It can be a visual art because it is converting sounds into lights. Also, it can be sound sculpture because it combines visual art and sounds. The reason it can be kinetic art is because it rotates. In the exhibition, a lot of audiences thought it was a kinetic artwork according to numbers one to three. It is because a lot of people have not seen moving objects by sounds in their life.

This artwork is differ to the 2.4.1 Artworks of Time. They are expressing time through music. However, this artwork is expressing the time and sound at the same time. As it is explained in the overview, gravity is converted into sounds (oscillations). In addition, previous artworks are scaled only in time. They are not expressing the time in the universe. On the other hand, OneSeconds is expressing the time in the scale of the Universe.

The significance of this paper was to explore the possibility of representing time with sound. By the history of time and clocks, music seems suitable to represent time. It is because oscillation was a keyword of its history and sound is composed by oscillations. Also, music will be able to express four factors of time. The first one was time born through events. In other words, time creates events. Furthermore, music creates events. Listening to music is one of the events that music makes people do. And one of the answers is to propose a method of representing time using Helmholtz resonance.

It was hard to connect the props together. It is because there needs to be permanent rotation when there are sounds. In addition, 3D printed materials were fragile. Even though it is farm enough, it is needed to treat carefully, it might break by oscillations.


The artwork OneSeconds was the one example of expressing the time by use of sounds. Helmholtz resonance made the way of the expression. It is made into visual art, sound sculpture, sound installation and kinetic art. In the exhibition, it was successful in introducing the factor of time. It could be shown by the surprising face that audiences gave. Also, all the music predecessors tried to control time in music, OneSeconds could be said as it controlled time indirectly.

OneSeconds as a clock, it is not accurate enough to produce. However, it is easy to construct compared to the previous clocks.By expressing that the time speed changes by gravity, it also represents that the time is continuous. For the future work, all the four factors will be contained into one piece of artwork. Also, in masters, I would like to challenge myself to create bottles. For OneSeconds, it was impossible to create the original bottles in this short period of time. If original bottles are made, the artwork will look more sophisticated.


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