I have had several people ask me what is the 11th harmonic of one of their crystal singing bowls. They have heard about the research of Dr. Holland, who found that in a laboratory setting, under a microscope, he was able to shatter cancer cells with two different frequencies with one being the 11th harmonic above the lower tone. This is very fascinating research but sadly it does not occur with the frequencies that we hear or that any of our musical instruments can produce.
The point to note in Dr. Holland's research this is that he was working with frequencies in the 100,000 to 300,000 hertz level. Singing bowls are in the 130 hertz to 630 hertz level. Singing bowls are far too low to create his results.
Another way to put this into context, the highest note in a piano is around 3,520 hertz.
This comes from the research by Dr. Holland made popular with his 2013 TED Talk. Holland explained his approach in the TEDx talk as targeting the cells with energy at two different frequencies to achieve an “11th harmonic” that produced a change in the cells’ shape and behaviour visible under a microscope.
Holland found that the cancer cell types he tested were said to be “vulnerable” to this energy delivered “between the frequencies of 100,000 and 300,000 hertz,”.
The company Holland created to pursue the work never reported further tests to explain the significance of the cell-shape changes observed, or any animal or human test results.
Now, let's say you still want to know the 11th harmonic of your bowl.
I did the calculations of the 11th harmonic of an 18" crystal singing bowl singing E3 at 164 hertz. The 11th harmonic would be A6+43 at 1,084 hertz The highest note we have with crystal singing bowls is D#5 at 622 hertz.
This page tells you the hertz of each note.
This page has a calculator for finding the harmonic of a note.
This page tells you what note each frequency sings.