One of the most important criteria in explaining the sound characteristics of a singing bowl is the speed of its pulsations (its modulations, or “beats”).
The key point is that each Himalayan singing bowl produces several “wavy” fluctuating tones at the same time and that each tone within that complex creates — and is affected by — every other modulation!
Let's call these modulations “beats,” or "the pulse of the bowl". Several pulsating layers of a different pitch (fundamental and overtones) inhabit the acoustic space as soon as a bowl is struck. Each pulsating tone interlaced with every other and form magical sonic patterns. Various pulsations from a single bowl may be fast or slow; some hardly noticeable.
In brain entrainment, faster modulations are good for sharpening focus and entering the high Beta state. Slow pulses will ground the listener and induce relaxation (especially if the tone is low).
All you have to do is catch the sonic serpent by its tail and hold it with your attention.
Let's examine now what these pulsating tones are, physically.
By striking the bowl, you cause its dynamic deformation (vibrations). The walls of the bowl expand and contract relative to the center of the bowl. The bowl will repetitively deform to create complex geometrical forms and eventually revert to its (original) circular shape before embarking upon another expansion or contraction. As its energy dissipates over the course of repetitions, the bowl will come to rest… in its original shape.
With each expansion, the bowl creates a sound. With each contraction, a slightly different sound will be emitted. The overlapping of these two sounds, which have a small difference in frequency and amplitude, creates the "pulsating" or "fluctuating" effect that itself is the easily identifiable signature (“characteristic") of singing bowls.
The same phenomenon is happening, simultaneously, with all sonic partials (overtones) of each bowl!
As the fundamental tone pulsates with a slow rhythm, the overtones may beat faster or vice versa. The higher the difference between two tones of the same partial, the more frequent is the pulse! The speed of these modulations (beats) is a function of the bowl's geometry and material.
The (heterodyne) interference of acoustical waves of slightly different frequencies coming out of ONE source is called "monaural beats." The case when TWO sources of sound are emitting the slightly different pitches is called "binaural beats".
If you'd like to understand more about monaural beats, you could experiment with any sound generator that is able to produce two slightly different tones simultaneously; you could also take two devices tuned to produce a slight difference between two tones, to create binaural beats. The introduction of these concepts is the core method used in audio brain entrainment.
A variety of CDs, computer programs and apps producing monaural and/or binaural beats are available for download.
One of the pioneers of "out of body experiences" (astral projection) Robert Monroe, designed a series of audio tutorials based on the binaural beats phenomena. Himalayan singing bowls produce monaural beats NATURALLY!
When describing the sound properties of singing bowls, two frequencies of each partial should be indicated. It is possible to cause either chosen frequency to sound dominant by striking a certain spot on the rim. Some practitioners mark these spots. Also, you can slightly change the pitch of your bowl by pouring a little sand or water in it.
On the image below you can see several tones being captured from a medium-size singing bowl
In this image, you can see the zoomed-in area of the fundamental tone. The analyzer indicates two frequencies:334.1Hz and 335.5Hz
This image captures two frequencies of the first overtone: 932.8Hz and 942.9Hz
Two frequencies of the second overtone: 1742.3Hz and 1747.7Hz
Two frequencies of the third overtone: 2713.2Hz and 2718.5Hz