Saint Jake needs me to break down the Phoenician alphabet.
I have found your mystery alphabet, aka the Phoenician alphabet. Here is a printout of the 22 Unicode Code Points for the Phoenician alphabet (thank you for a useful exercise in Java programming):
𐤀𐤁𐤂𐤃𐤄𐤅𐤆𐤇𐤈𐤉𐤊𐤋𐤌𐤍𐤎𐤏𐤐𐤑𐤒𐤓𐤔𐤕
Should you need more information, please refer to this article on the Phoenician alphabet:
http://en.wikipedia.org/wiki/Phoenician_al...

As in Hebrew, read right to left.