Love that one Colin, made me think for a moment.
FED C DEFG It does of course depend on which way one is counting and the C is common when talking Diatonic.
One of the things that really messed me up in the beginning is that when talking Chromatic one counts intervals not notes and Diatonic one talks actual notes.
As for the word mathematics, please forget it. That simply puts people off. Music is a natural element and owes nothing to mathematics although like any tool simple arithmetic can assist. If a person can arrive at a lesson on the correct day (7 in a week and a Diatonic set) at the correct time (12 on a standard clock and a chromatic set) and pay the correct money for the bus fare (100 cents in the dollar/pound and 100 cents in a semitone 12 Tone Equal Temperament) they know all the arithmetic they will ever need in music.
Yes I am familiar with the mathematical wonders of Iannis Xenakis see
http://www.sabinepyrker.at/multimedia_en.php
but he depends on music, music does not depend on him.
Sorry BigMartin I could not disagree more about the use of zero. As a computer analyst/programmer/accountant all my life I have been frustrated by the fact that people like Codd did not understand the concept of zero. Yes his infamous 12 rules of database are actually 13, counting from zero is a nonsense. Euclid had it correct when he defined a point as having position but neither breadth nor width nor length. That is it is where two objects meet. Zero is a point on the number line, above it one has a dollar below it one owes a dollar.
Now of course if somebody can answer my question about the perceived advantage of going clockwise for Flats as opposed to going clockwise for Sharps as in the classical way I would be delighted.
Apologies for the rant but it does bug me that people are put off music theory because the mention of maths brings back bad school memories. As one lady said to me only last week "As long as my bottom points to the ground A is not a number". She thinks I am weird because I like reading books about why E=MCsquared. (Oops can't remember how to do a superscript outside of Word.