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Singing Bowl, What's The Secret

Singing Bowl, What's The Secret

Introduction

In this article, we will talk about the uniqueness of Himalayan Singing Bowls (also known as Tibetan Singing Bowls and Sound Healing Bowls). We will learn what makes the sound of singing bowls so unique and why listening to these instruments can be healing.

This article presents interesting facts about the imprint of harmony within the timbre. We will also look deeper into the acoustic phenomenon such as dissonance, and brainwave entrainment.

The majority of sound healing schools are attributing mystical properties to singing bowls. The salesman's stories about healing chakras with the seven sacred metals-made Tibetan singing bowls are spread all over the internet. After reading this article, you will have a much better understanding of the nature of the singing bowl’s sound.

It really has nothing to do with how to heal, cleanse, balance or open your chakras with the specific note sounded by a singing bowl. So, do you want to know what's the buzz? Read this article through the end, and please share it with your sound healing practitioners friends.

If you feel called to become a sound wellness arts performer (sound healer), please consider enrolling in my "Sound Healing Teachers Training Course". 

From the author

My name is Guy Yair Beider. For many years I was seeking a practice that would help me become a better version of myself and bring benefits to others. In 2007, while studying the properties of psychedelic plants, I was honored to be invited to take part in an Amazonian sacred plant ceremony. I was told to prepare for the journey by observing a special diet. Also, the person who invited me emphasized that I should come having an intention for the sacred plant ceremony.

Keeping to the diet appeared to be easy, but I found myself having a hard time figuring out what should be my intention. I didn't know what I should be asking for from the experience with a sacred plant, and to be honest, I struggled to connect with the concept of "sacred." I ended up setting as my intention to find what is sacred for me.

Here I am on my first psychedelic journey with Ayahuasca. I am facing my personal Jesus and purging. Facing my demons and purging again. I am mentally and emotionally overwhelmed and getting to the point of no return. The insanity is inevitable… but all of a sudden, I reach the state of emptiness and oneness with the whole of creation.

It's hard to estimate how much time I spent in this ecstasy. All I remember that the next thing that captured my whole essence was sound: It was the sound of liquid gold, the sound of a Himalayan singing bowl.

That moment that I heard the complex simplicity of the singing bowl for the first time, I skipped a breath, my heart stopped beating and after the long pause of the inner silence and death of an ego I caught myself thinking - "this is what I was looking for!” It felt like my perception was hacked and rebooted at once. Something inside of me proclaimed: "sound is sacred!"

When I got back home from the ceremony, I was a completely different person. I discovered that my purpose is now to educate myself on the benefits of sound and to unveil the sonic beauty of Singing Bowls to the people. Since 2011 I've conducted hundreds of sound journeys and have nourished thousands of people with the hypnotic frequencies of Himalayan singing bowls.

What is a Singing Bowl?

A singing bowl is a bell that rests on the horizontal surface with the opening upward. The sound results from striking the bowl with a mallet. Also, singing bowls can be played with a friction mallet, when rubbing the stick around the rim of the bowl.

Antique Himalayan singing bowl

*Antique Himalayan singing bowl

How old are Himalayan singing bowls?

The oldest Himalayan (the more common but misleading name is “Tibetan”) singing bowls known today are about 600-800 years old. I've met experts that assume the first singing bowls appeared 2800-3000 years ago. I tend to believe this is true.

During the years of my research, I've discovered beautiful myths and speculations about the original purpose of singing bowls. Some of these myths are simply naïve and lacking the connection with reality. I have no agenda spreading myths; instead, I'll share the "grounded" vision of why I consider a singing bowl as an extremely unique and healing sounding object.

Where are singing bowls from?

The experts whose opinion I trust, claim that singing bowls originated in Mesopotamia and most likely were used as utilitarian vessels for storing foods. They found their way all over the Himalayas through the well-established Silk Road trading network.

Somewhere later in history, several Buddhist temples adopted these bronze vessels to perform certain rituals and collect offerings. Till today, singing bowls can be found in the Buddhist monasteries in Nepal, India, Tibet, China, Korea, and Japan. I met Buddhist monks in Nepal and Tibet holding a specific type of singing bowl to collect donations.

Whether the bowls were used to store edibles or produce sound, their sonic properties have been acknowledged for centuries. The physical characteristics of bronze of which singing bowls were made of and the geometry of the vessel makes it clear that acoustic properties were of primary importance.

What are singing bowls good for?

Himalayan singing bowls have been known to Westerners since the late '60s. They made their way to Europe, the US, and other countries with spiritual seekers that were exploring India. Right away it became evident that the timbre of singing bowls can help reduce stress, anxiety, physical pain, normalize blood pressure and simply clear the mind if you give it a chance.

Focusing on the complex sound of singing bowls is a great practice to enhance one’s cognitive functions. And, singing bowls are great for meditation. Although not much is known about how singing bowls were used in the past, modern holistic medicine (sound therapy) practitioners are developing new skills and inventing techniques for utilizing singing bowls for balance and harmonization.

There are many skeptical opinions about singing bowls, but if you know how to choose the right one and what to do with the bowl (most importantly, how to properly listen to it) – you'll see that it works!

These days the market is flooded with whatever the sellers are calling “authentic Tibetan singing bowls”. The name “Tibetan” is wrong, to begin with, and in many cases, what you would be offered to purchase are machine-made bowls made in China or India. Even the hand-hammered ones are just replicas with the sonic resemblance to the authentic instruments.

The sound of these easily-available machine-made bowls usually is not as soft, pleasant and complex as of authentic original singing bowls.

*Contemporary machine-made Himalayan singing bowl

The original (authentic) Himalayan singing bowls have very unique sonic properties. So let's dive in and check what these properties are but first, we need to learn the terminology and briefly walk through some interesting facts about sound.

What is sound?

Any physical object in motion creates vibrations. The term “sound” is applied to vibrations that typically propagate as audible waves of pressure, transmitted through a medium, such as gas, liquid or solid. In human physiology and psychology, sound is the perception of such waves conducted by the hearing organs, bones, and skin.

What is frequency?

Any vibration that recurs at regular intervals has its own "frequency" or “pitch.” Frequency indicates how FREQUENT the cycle of motion is happening within a fixed unit of time. Vibration with no periodic activity has no frequency.

The measuring units of frequency are Hertz (Hz). One Hz equals one full cycle per second. The average adult person can hear sounds with frequencies between 20 to 20000Hz.

What are overtones and harmonics?

Now let's talk about a very important property of sound – timbre. What makes your voice unique or what makes the sound of a flute different than the sound of a horn is the character of the sound, aka "timbre." Timbre is a structure of the sound. It is the color of the sound, its roughness, firmness, brightness, and spice.

Like an image on a color television, that can be broken down to the basic colors red, green, and blue, so the natural timbre of any sound (except for pure tone) is a combination of many frequencies. Each of these frequencies, which we call sound partials, has its own unique pitch and volume.

The strongest sound partial of a timbre is called its "fundamental". Fundamental tone is the lowest sound partial of the timbre. Other partials are called overtones.

Overtones always have a higher pitch and typically appear with a specific ratio to the fundamental. Usually, it is nearly impossible to pick them out individually by ear.

When the ratio between the frequency of overtone and the fundamental (f) is equal to a positive integer multiple (fx2; fx3; fx4), we give this overtone the term “harmonic”.

A series of harmonics are present in any voice, any musical instrument, and practically every natural sound. String instruments, as well as a human voice, for example, would show the whole series of multiple integers (from 1xf, 2xf, 3xf to infinity). Closed - open air column instruments (didgeridoo, horns, clarinet), only have odd harmonics 1xf, 3xf, 5xf, 7xf, etc. The timbre of an open - open tube (organ pipes, flutes, whistles) consists of all integer multiples frequencies 1xf, 2xf, 3xf, 4xf, 5xf, etc.

* The screenshots below were taken from a sound analyzer app.

What you see in the first picture is the timbre of my voice. I am vocalizing a fundamental tone of 100Hz. Please take a good look at the several frequency spikes. The lowest one (the fundamental tone) is 100Hz, the next spike is 200Hz, the next ones are 300Hz, 400Hz, etc.

sound analyzer app

* In the next screenshot, you'll see a graphical representation of the timbre of my guitar. I especially tuned one of the strings to the same frequency of 100Hz (please disregard the minor inaccuracies).

As you can see, the ratios of the overtones are similar to the ratios between the sound partials of my voice: 2, 3, 4, 5, etc. (200/100; 300/100; 400/100; 500/100).

sound analyzer app - 2

 

Now let's take a look at the timber of a didgeridoo. Didgeridoo is considered as a close - open pipe wind instrument.

*The fundamental tone is: 118.7Hz.

The first overtones’ value is 355Hz, which is triple the frequency (disregard a minor inaccuracy) of the fundamental tone. Therefore, we can call it a third harmonic.

The second overtone is 592.5Hz, five times higher than the fundamental.

sound analyzer app-3

What are consonance and dissonance?

Now, I'd like to talk about what is happening with our perception of sound when we listen to more than one tone. Why do certain combinations of tones sound pleasant and some not?

Consonance and dissonance are two subjective concepts describing the perception of a certain sequence of tones. Consonance is associated with pleasantness, sweetness, and acceptability. Dissonance is associated with unpleasantness, harshness, and unacceptability.

Some say that the history of finding consonant ratios goes back in time to ancient Greece. This discovery is assigned to mathematician and philosopher, Pythagoras. The story goes like this… Pythagoras plucked a string under tension with a movable bridge between the two fixed ends. He found that dividing the string at the ratio of 2:1 (an octave) sounded good. Another pleasant sound was resulting from dividing the string to the ratio of the lengths 3:2 (perfect fifth).

To learn what makes two tones sound consonant, we will have to take a look at the harmonics of each tone. We may find that some combinations of tones (also called musical intervals) share common frequencies when it comes to their natural harmonics series.

table of 10 common harmonics

This table above, represents five tones. For the simplicity of the demonstration, I did not relate these tones to the actual frequencies of musical notes, but I kept the real musical ratios between them. 

The "Base" note is a reference note from which I'll build either dissonant or consonant musical intervals. The fundamental tone of the Base is 100Hz. 

Knowing the sequence of the natural harmonic series, I gave the value of 200Hz to the second harmonic, 300Hz to the third harmonic, etc. 

The minor second (m2) is known as a dissonant musical interval. Its ratio to the base note is 16/15. To calculate the fundamental tone of the minor second interval, I am multiplying a 100 by 16/15. 

The result is 106.66Hz. 

The second harmonic of the resulting interval is twice as high, 213.33. The third harmonic is triple the frequency of 106.66 and so on…

The next dissonant interval is the Major second (M2). 

Its ratio to the base note is 9/8. 

To calculate the fundamental tone of the Major second, I am multiplying 100 by 9/8. 

The result is 112.5Hz. 

The second harmonic is twice as high, 225Hz. The third harmonic is triple the frequency of 112.5 and so on…

Let's take a look rather: the harmonics of these two dissonant intervals are matching with the harmonics of the base note.

As you can see, they match only at one point the ninth harmonic of the base note and the eighth harmonic of the major second interval.

table of 10 common harmonics - 2

*Please take a look at the presence of common harmonics between the base note and two consonant intervals: the perfect octave (PO) and the perfect fifth (P5)… and notice how many common harmonics these two intervals are sharing with the base note.

table of 10 common harmonics - 3

Both consonant and dissonant intervals are equally used in the music making process. And who would disagree that music can hack the brain?! 

Now I will discuss two very specific cases of dissonance that are not being implemented in music composition, yet are often infused in New Age music. 

These cases of acoustical dissonance have a strong influence on brain activity. They are called monaural beats and binaural beats.

When sound waves of various frequencies enter the inner ear, they cause different areas of the basilar membrane to vibrate accordingly to the frequency of the signal. Two frequencies that are close together cause an overlapping response on the region of the basilar membrane. 

When the interfering frequencies are almost the same, the brain cannot distinguish them as separate tones. Instead, we hear an average frequency. This frequency appears to the listener as a pulsation also called a “beat”. 

Increasing the difference between the two frequencies entering the ear will result in faster beats and eventually will make these two frequencies distinguishable as two separate tones.

When the two frequencies close to each other are being emitted from two sources (the left side of headphones for one frequency and the right for another), the beats that result as synchronization of two signals are called “binaural beats”. 

If two tones with slightly different frequencies are sounding from one source, this produces the phenomenon known as “monaural beats”.

What are brainwaves?

The communication between neurons within our brains is the root of all our thoughts, emotions, and behaviors. “Brainwaves” result from the synchronization of electrical impulses from neurons communicating with each other.

Brainwaves are a continuous spectrum of consciousness. They change according to our physical, mental, and emotional activity, and are divided into bandwidths, assigning to each wave specific characteristics from low mental activity to high. 

Any process that changes your perception, changes your brainwaves.

The measuring unit to define brainwave frequency is (also) Hertz. Brainwaves are commonly divided into bands describing slow, moderate, and fast modulations.

The following description is very broad – in real life, brainwaves occur in different locations of the brain, reflecting various brain activities. 

Also, while our brains show the presence of numerous waves at the same time, you can learn about the activity of the brain by the pattern (wave) that is currently dominant.

Brainwaves are measured with an electroencephalograph (EEG). The EEG shows electrical activity at the brain surface. This activity appears on the screen of the EEG machine as waveforms of varying frequencies and amplitudes.

* Disclaimer: following characteristics of brainwaves were collected from several internet sources and summarized in this article. The author of the article is not advocating the credibility of this information. 

Infra-low (<0.5Hz)

Very little is known about infra-low brainwaves. They are hardly detectable and difficult to measure because of their slow nature. Infra-low brainwaves appear to play a major role in brain timing and network function. 

Infra-Low brainwaves are thought to be the basic cortical rhythms that underlie our higher brain functions. 

Delta waves (0.5 TO 4Hz)

Delta brainwaves are the slowest waves that have significantly high amplitude. Delta brainwaves are generated in dreamless sleep and deepest meditation. 

Regeneration of the organism is stimulated in this state: that is why deep restorative sleep is so important to wellness. 

Theta waves (4 TO 8Hz)

Theta brainwaves are dominant in deep meditation and REM sleep. They are known as a gateway to memory, learning, and the body's knowledge. When Theta waves are dominant, our senses are withdrawn from the external world and focused on signals within.

Theta is a state in which we access our intuition and information beyond our normal conscious awareness. 

Alpha waves (8 TO 12Hz)

Alpha waves predominantly originate from the occipital lobe during wakeful relaxation with closed eyes. Alpha waves are reduced with open eyes, drowsiness, and sleep. 

Historically, they were thought to represent the activity of the visual cortex in an idle state. More recent papers suggest that they inhibit areas of the cortex not in use, or that they play an active role in network coordination and communication. Occipital alpha waves, when eyes are closed, are the strongest EEG brain signals.

Alpha waves dominate during quietly flowing thoughts and in some meditative states. Alpha waves aid overall mental coordination, calmness, alertness, and learning.

Beta waves (12 TO 38Hz)

Beta brainwaves are dominant in the waking state when we are focused on cognitive tasks and the outside world. Beta is a relatively fast activity of the brain that occurs when we are engaged in problem-solving, being alert, making decisions, or focusing on any mental activity.

Beta brainwaves are divided into three bands: low-Beta (12-15Hz) is the state of relatively slow mental engagement; mid-Beta (15-22Hz) is a high engagement or actively figuring something out. Hi-Beta (22-38Hz) occurs during highly complex thinking, high anxiety, excitement, or integrating new experiences.

Gamma waves (38 TO 42Hz)

Gamma brainwaves are the fastest waves. These waves relate to the simultaneous processing of information from different brain areas. When our brain is quiet and transparent, the information is being passed with high frequencies and low amplitude. Gamma waves pass information rapidly and quietly. 

When Gamma brainwaves were discovered, they were first considered as a brain noise until researchers observed that they appeared during highly active states of universal love, altruism, and higher virtues. Also, frequencies of Gamma waves are above those of neuronal firing. It remains a mystery how these waves are generated. One of the speculations is that Gamma patterns modulate perception and that a greater presence of Gamma waves relates to expanded consciousness and spiritual emergence.

Brainwave Entrainment

Brainwave entrainment is a method to stimulate the brain's electrical response to rhythmic sensory stimulation, such as pulsating light, sound, or electromagnetic field. 

The external (entraining) pulses evoke the brain's “frequency following response” to align to the frequency of a given signal. This method is commonly used to induce many brainwave states, such as relaxation, trance, enhanced focus, meditative state, or sleep induction. 

How can the binaural and monaural beats be used for brainwave entrainment? 

Entrainment takes place when conscious listening to purposely adjusted bandwidths of frequencies engages the listener with a specific rate of beats: to slow down the brain activity, choose a slower rate; to raise the activity, increase the arithmetical difference between the contributing frequencies to accelerate the rate of pulsations.

What is known today as brainwave entrainment either with sound or light is not a new invention. Ancient shamans and yogis understood the relationship between the rhythmic entrainment of music and altered states of mind. Drumming, rhythmic movements, and rhythmic breathwork were practiced to heal and to enter the realm of spirits. 

The development of digitally encoded audio beats, strobe lights, or low-energy electromagnetic fields has not stopped since the 1970s. There is a lot of marketing hype around brainwave entrainment. Today you can find a wide variety of different gadgets on the market, including apps and music files that claim to help stabilize brainwaves. In an advertisement for these products, you may see promises of increasing IQ, promoting weight loss, getting rid of addictions, enhancing creativity, improving concentration, and more.

While these claims may not be entirely valid, they may not be altogether false: in practice, such claims may be based on an overly simplistic view of brainwave functions. 

Overtone-emitting Instruments

As we learned before, almost all natural sounds consist of multiple or, in some cases, even infinite, sound partials. Nonetheless, we hear this combination of separate sounds as a superimposed tone and cannot differentiate between the contributing partials.

Humankind has learned to isolate these sound partials and make instruments that produce distinctive overtones. Also, some cultures have learned to isolate overtones with the voice. Throat (overtone) singing and overtone-emitting instruments have a special place in history. 

Meditative, and even mystical properties have been claimed for these overtone-emitting instruments: these instruments have special effects on the listener's attention like no other.

Let's analyze what happens when we listen to the overtone-emitting instrument such as a Himalayan singing bowl.  

First of all, our ear and the stream of consciousness organically flow with the timbre, which has no distinguished separation between sound partials.

Listening to sound partials that are isolated from each other and sound so prominent within one instrument, attracts different zones of our attention. It simply hacks the pattern of anything we used to listen to. I would even say that it splits the consciousness of the observer, but please, don’t take my words here as scientific fact! 

When the Himalayan singing bowl is vibrating, you can hear more than one tone at the same time (polyphony). If you listen carefully, you may catch three, four, or even more sonic serpents. Each of these serpents has a different color, length, and shape of a wriggling body. Each of them is rushing to disappear into the void with different velocities, and the way it hides behind the curtain of silence is unique for each serpent.

Very often, when I analyze a bowl 6"-12" in diameter, I find the presence of the 3rd, 6th, 10th, and 14th harmonics. (The same thing would apply to smaller singing bowls, with the rare exception of the 2nd harmonic presence.) Some Himalayan singing bowls will show the presence of the 2nd, 3rd, 4th, 5th, 6th, 9th,10th, 12th, and 14th harmonics but generally speaking, the ratios between the sound partials in a timbre of singing bowls are unpredictable.

Before we move on, I want to mention that in many cases the sound partials that Himalayan singing bowls emit are not harmonious at all. We may see that the ratios between the overtones are not multiple integers of the fundamental tone.

A lack of the constant pattern that characterizes the timbre is not the only aspect that makes Himalayan singing bowls so different from other instruments. There is another very unique sonic property. Each sound partial is determined not by one, but two and in some cases three frequencies. The interference of these frequencies creates the phenomenon of monaural beats. 

Take a close look at the next screenshot. This photo was taken while I was analyzing a singing bowl from my collection, whose fundamental tone is the closest to 100Hz. The reason I chose this bowl was to keep my demonstration close to the fundamental tone of 100Hz, to make the calculations of harmonics easy for everyone. 

timbre of the singing bowl

*As we can see, the fundamental tone is defined by two frequencies 102.1Hz and 104.3Hz. As a result, the bowl is emitting 2.2 monaural beats per second (which corresponds with the Delta brainwaves).

The first overtone (second harmonic fx2) is 209.8Hz and 204.3Hz. The pulse of this sound partial is slightly faster than the pulse of the fundamental. Its rate is 5.5 beats per second (corresponds with the Theta brainwaves).

The second overtone (third harmonic fx3) is 311.9Hz and 306.9Hz. The monaural beats rate is 5 (corresponds with the Theta brainwaves).

The third overtone (fourth harmonic fx4) is 414.1Hz and 409.9Hz. The monaural beats rate is 4.2 (corresponds with the Theta brainwaves).

picture shows the presence of the 6th, 9th, 12th, and 14th harmonics

* The screenshot above is the timbre of the same bowl scrolled to the register of higher frequencies. This picture shows the presence of the 6th, 9th, 12th, and 14th harmonics. 

The singing bowl we just analyzed is really pleasant to listen to. The sound partials are sounding harmonious and the rate of pulsations of each prominent tone is pretty slow. 

However, this is not the case with all singing bowls. 

Please take a look at the next picture and bear with me to analyze this weird instrument…

timbre of the singing bowl

* The screenshot above represents the timbre of the singing bowl that is just hard to listen to for a long period. The sound of this specific bowl is somewhat irritating. I demonstrated this bowl to hundreds of people and they all, with no exception, found it as a strong focus magnetizer and alarming instrument. 

Look at how different are the timbers of two bowls:

The first bowl showed the presence of the fundamental tone, 2nd, 3rd, 4th, 6th, 9th, 12th, and 14th harmonics.

The timbre of the second bowl consists of the fundamental, 2nd, 3rd, and 6th harmonics only.

Note that the fundamental tone of the second bowl is defined by two frequencies that are 9.8Hz apart from each other (246.2Hz and 236.4Hz). Such a fast pulsation does not sound very relaxing. Instead, it draws the focus of the listener and, after a short time, listening to this bowl can create some tension. Please pay attention to the first overtone: its frequencies are 492.4Hz and 472.8Hz. The monaural beats in this case are even faster than the pulsations created by the frequencies of fundamental partial. 

Striking a singing bowl creates dynamic deformations of the vessel. The walls of the bowl expand and contract relative to its center. The bowl will repetitively deform creating complex geometrical forms and eventually reverts to its original circular shape before embarking upon another expansion or contraction. As its energy dissipates throughout repetitions, the bowl will come to rest… in its original shape.

dynamic deformation of the vessel

With each expansion, the bowl creates a sound. With each contraction, a slightly different sound is emitted. The overlapping of these two sounds, which have a small difference in frequency and amplitude, results in the "pulsating" or "fluctuating" effect that itself is an easily identifiable signature of singing bowls. This overlapping of slightly different frequencies is a dissonance that manifests through monaural beats.

The same phenomenon simultaneously takes place with all sonic partials of each bowl!  

As the fundamental tone pulsates with a slow rhythm, the overtones may beat faster or vice versa. The greater the difference between two frequencies of the same partial, the faster is the pulse! The speed of these modulations is a function of the bowl's geometry and physical properties. 

Several pulsating layers of a different pitch inhabit the acoustic space as soon as the bowl is being struck. 

Each sound partial is beating in an individual rhythm and the relationship between these partials is often aligned with the natural harmonic series.

The recognition of harmony is imprinted in us. We react to harmonic tones with a sense of high esthetics and emotional admiration. Finding a singing bowl with harmonically aligned sound partials is pretty easy, but the paradox of a singing bowl appears in the coexistence of harmony and dissonance. 

Harmony lays in the consonant intervals between the sound partials (harmonics) while the dissonant interference manifests through the monaural beats.  

Remember the analogy between the sound partials and an image being broken down to the basic colors Red, Green and Blue? Now imagine that you are looking at a flight of a colorful hummingbird, whose body offsets to separate images of different colors. I am choosing this visual analogy to emphasize that each sound partial in the timbre of a singing bowl is individually distinguished. It looks like a blue image of a hummingbird separately flies next to the green and red images. A psychedelic hummingbird, ha? 

More than that… each of these monochromatic images is swinging the wings at a different speed, like each sound partial of a singing bowl is pulsating with its beat. 

Conclusion 

The unique sound of Himalayan singing bowls involves the listener on multiple levels. In my long practice of working with singing bowls, I have witnessed so many breakthroughs and miracles happen to the audience. Conscious listening to the sound of these unique instruments is a great practice of meditation and self-development. The sound of Himalayan singing bowls is the sound that makes me silent, it is the sound that helps me to become open to listening. Sometimes it is not so easy to focus on such a complex game of tones but it's always rewarding with the calmness and clarity of mind after the conscious listening. 

Comments on this post (1)

  • Jun 02, 2023

    hi, i practice singing bowl too , and recently i am interesting in explaining the sound of inging bowl in the field of execution function .

    do you have information to share ?thanks

    — feifei

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