A singing bowl does not produce a note. It produces several at once, and the relationship between them is what gives the sound its depth and its slightly living quality.
The physics is not difficult and knowing it genuinely improves what you hear.
Fundamental and partials
When any object vibrates it does so in several modes at the same time. The whole thing moves back and forth at one rate, producing the lowest and usually strongest tone, called the fundamental. Simultaneously, sections of it vibrate independently at faster rates, producing higher tones called partials or overtones.
In a violin string or a flute, these higher components fall in a neat mathematical series, whole number multiples of the fundamental, which is why those instruments sound like a single clear note.
In a bowl, a bell or a gong, the partials do not fall into that tidy series. They sit at ratios that are not simple multiples, which is why these instruments sound complex and slightly ambiguous in pitch rather than producing an obvious note.

Why a bowl sounds different from a flute
That is the whole answer. A bowl is a plate bent into a shape, and plates vibrate in complicated patterns, with regions moving up while adjacent regions move down, separated by lines that barely move at all.
Each of those patterns has its own frequency, and the frequencies do not line up neatly. The result is a sound your ear cannot quite resolve into a single note, which is a large part of why it holds attention the way it does.
The wobble, and where it comes from
Listen to a good hand beaten bowl and you will hear the sound pulsing gently, growing and fading a few times a second rather than decaying smoothly. That pulse is the most distinctive quality of a hand made bowl and it has a precise cause.
A perfectly symmetrical circular bowl would produce each vibration mode at a single frequency. A hand hammered bowl is never perfectly symmetrical, so each mode splits into two very slightly different frequencies.
When two tones very close in pitch sound together, they alternately reinforce and cancel one another, producing a rhythmic pulse. The rate of the pulse equals the difference between the two frequencies. Two tones two hertz apart produce two pulses a second.
So the wobble is a direct audible consequence of the bowl having been made by hand. A machine spun bowl, being more symmetrical, has much less of it, which is one reason hand beaten bowls are preferred by most players.

Counting it
A satisfying exercise. Strike a bowl, listen for the pulsing, and count the pulses over a few seconds. That number is the frequency difference in hertz between two very close partials.
Different bowls give noticeably different rates, and the same bowl struck in different places emphasises different modes and can change the rate you hear.
Why two bowls together sound different again
Play two bowls at once and you get the same effect between them. If their fundamentals are close but not identical, you hear a slow pulse; the closer the pitches, the slower the pulse.
This is why players often choose a second bowl close in pitch rather than far from it, since two bowls a whole tone apart simply sound like two notes, while two bowls a few hertz apart produce a shimmer that neither makes alone.
Our chakra set of seven bowls gives a range wide enough to experiment with both.
What binaural actually means, and does not
Worth clearing up, since the word is used loosely in this field.
Binaural beats are a specific phenomenon requiring headphones: a slightly different frequency delivered to each ear separately, with the beat perceived in the brain rather than existing in the air.
What a singing bowl produces is an acoustic beat, which exists physically in the room and is heard by both ears equally. It is a real and audible thing, and it is not the same phenomenon. Claims that bowls produce binaural beats are using the term incorrectly.
Where you strike changes what you hear
Because different vibration modes have different patterns, striking at different heights on the wall excites them in different proportions.
Near the rim tends to bring out the higher partials, giving a brighter sound. Lower on the wall favours the fundamental, giving a deeper one. Rimming emphasises a different mode again, which is why a rimmed bowl often sounds noticeably higher than the same bowl struck.
Try it on your own bowl. Strike at three heights and listen for the difference before assuming a bowl only makes one sound.
Listening exercises
Three that develop the ear quickly. Strike and follow only the pulse, ignoring the pitch. Strike and try to hear the highest component rather than the loudest. And strike, then damp gently with a finger and release, which lets you hear the partials separate as they decay at different rates.
Our guide to choosing a striker covers the practical side of getting a good sound in the first place.
Questions people ask
What is an overtone in a singing bowl?
A higher frequency component produced alongside the main tone. In a bowl these do not fall into the neat mathematical series found in a flute or a string, which is why the sound is complex and ambiguous in pitch.
Why does my singing bowl pulse or wobble?
Because a hand beaten bowl is not perfectly symmetrical, so each vibration mode splits into two very slightly different frequencies. Those alternately reinforce and cancel, producing a pulse whose rate equals the difference between them.
Do singing bowls produce binaural beats?
No. Binaural beats require headphones delivering a different frequency to each ear, with the beat perceived in the brain. A bowl produces an acoustic beat that exists physically in the room and is heard by both ears.
Why does my bowl sound different when I rim it?
Rimming excites a different vibration mode from striking, which is why a rimmed bowl commonly sounds higher than the same bowl struck.
Why do hand beaten bowls sound better?
Largely because their asymmetry produces the pulsing quality that machine spun bowls mostly lack. The irregularity of hand work is what creates the character.