(turn your volume down first!)
Below is another small, high-quality Tibetan bowl:
And here is the same bowl, struck again, but in a slightly different place:
Do you notice the difference?
The most striking difference (excuse the pun) is in the 2nd partial.
In both cases, the 1st partial sounds like this:
But in each case, the 2nd partial is different. In the first strike it sounds like this:
Here it has a distinct rhythm, warble, or "beat". In terms of brain-wave rhythms, it's a theta-wave frequency.
On the second strike, however, this same partial sounds like this:
There is some wavering, but that regular theta-wave rhythm has gone. That characteristic of the bowl's sound has changed, just by changing the strike position slightly.
How does this happen?
When singing bowls vibrate, there are different patterns of vibration, each pattern corresponding to an audible partial. The main patterns or modes of vibration, as they are called, are ones in which the rim of the bowl ripples in and out, as waves travel around it.
Below is a computer-generated "map" of the vibrating areas of the bowl in its 1st mode (the lowest pitched partial). The red is where the greatest movement of the rim in and out takes place. The rest of the colors in order (of the rainbow) are zones of decreasing movement, down to blue, where there is least movement.
Now as it happens, these modes usually occur in pairs. So there is another pattern of movement for the first mode, which looks like this:
It is the opposite way around. The zones of most movement are now in-between where they were in the first case.
Because the bowl is not generally perfectly smooth and uniform around its rim, this pair usually differ, at least a little, in their frequencies of vibration. Together, they combine to form a mode of vibration in which energy shifts from one pattern to the other, causing the characteristic beating, or pulsing, that singing bowls often produce in their partials.
The frequency of this thythm (usually coinciding with a brain-wave rhythm frequency) is about equal to the difference in frequencies between the pair.
The kind of vibration patterns that form the modes, divide the rim regularly into fractions of its circumference, the higher the mode, the greater the division. Here are some more modes of this bowl:
The possible modes don't have all equal strength. Most bowls will have perhaps the first three in the possible series, that are clearly audible. But some bowls have many more.
Striking the bowl in any given position on the rim, will tend to excite all mode patterns that have a red zone (as represented here) in that position. Whereas mode patterns that have a blue zone in that position will tend not to be excited.
If you look ar mode 3, for example:
You can see that to strike the middle of a red zone in the first pattern, will be striking the middle of a blue zone, in the second pattern, which won't excite it. If you do this, the beating in this partial pair will be minimised, because for it to beat requires both patterns to be excited. But if you strike in-between these two positions, you'll be delivering some energy to both modes and the beating will be maximised.
There are a several things to remember, here. Firstly, these two frequencies won't necessarily be sufficiently different to cause a beat in the first place. Secondly, as you can see from the pictures, there is a gradual transition between the red zones and the blue zones. Unless you are striking right in the middle of red zone, it will be difficult to eliminate beating in that mode.
Also, you'll notice that in all modes it is the blue zone that extends to, and covers the bottom of the bowl. This is why the bowl can stand on its base, and still sing. The bottom of the bowl is always a zone of no movement, anyway. To get the most sound from the bowl, you need to strike the rim.
There is no way of telling, just by looking at most bowls, where the red and blue zones, or nodes and anti-nodes, as they are called in acoustics, are going to be, for any given mode. You just have to experiment.