I am a mathematician / programmer, and more recently an amateur musician. I definitely agree with your statement about music and programming having similar thought processes. In fact, in my musical studies, i have found that i quicky pick up on a lot of music theorey that a lot of much more experienced musicians do not ever see. Most likely because i am generally looking for the overall patterns and structure of music. That said, i think that the stereotype about programmers all being mathematicians is because math is very much what you describe music being like: patterns, variations on themes, etc. (not really rhythms). But all 3 subjects definitely require very similar thought processes.

Fancy a job in snowy Wisconsin, USA? You can pester me all day abuot regexes, and we have a table soccer in the conference room down the hall. :)