We’ve had “Music for Dummies”, but there’s a group (sub-species?) that needs to start off at an (ahem) slightly more elementary level. These individuals, whilst excelling in some simple areas of human endeavor such as computers, stereos, midi and Global Warming, need help in translating music into simple terms that that they can understand.
Yes, I'm talking about Nerds.

Being a nerd myself, blessed by marriage to a talented musician, whom I’ve tried very, very hard to understand, I’ll try to bridge the gap with this article. Musicians, too, may find it interesting to peer into an alien mind.

Part I: what the heck are notes?

The “octave”
The sounds we hear can be broken down into about 7-9 “octaves”, where each octave is double the frequency of the previous one, starting at say 27.5 cycles/second, up to 14,080 or so. An octave in turn is split up into 12 notes, which are spaced out evenly into 12 proportional intervals. It is called an octave and not a dou-dectave as it obviously should be, because musicians can’t count (in school they were "numerically challenged").

Some notes are more equal than others
To non-musicians, most notes seem pretty much the same, except for sounding and bit higher or lower and perhaps needing expensive speakers to accurately reproduce the sweet clear sound of booms, crashes, gunshots and thuds on their simple digital home theaters.

To musicians there is a vast difference, depending on the “root note” or tonic, the special key note (the key for short) an arranger happens to favor to build a song around.

Some fundamental facts

1. Musicians, unlike nerds, are easily bored. This goes triple for directors, who’ve heard it all, and triple more so for arrangers, who’ve studied it all.  Arranger-directors can deduce an entire piece from the first dozen notes.
   
   
2. Starting from the root, another note played with it sounds good (consonant), if it is roughly 1/4, 1/3, 1/2, 2/3 or 2/1 higher, these notes resonate. Per musicians’ numeracy problems, these are called a third, fourth, fifth, sixth and octave intervals respectively. These are the main part of the major scale. The big gap between the third and the root is filled in with a second halfway between. Likewise the sixth and the octave are filled in with an seventh, almost as an afterthought.
   
   
3. Neighboring notes (semi-tone intervals) sound lousy (dissonant) because they make a funny wobble in the sound.
   
   
4. Notes tuned to exactly the square root of 2 above or below the root (a shade below a fifth interval) kind of cancel out the root note and sound weird. This is the dreaded tritone, despair of music directors everywhere, as it happens easily when jumping up and down fifths.
   Tritones are also the despair of singers everywhere, as an arranger may, on whim (see #1 above), sprinkle in a few cleverly hidden tritones for some added spice. (Hint: beware the diminished chord.) Tritones are hard to sing because (1) they are anti-resonant – there’s nothing to latch onto or match, and (2) if you spend 99.9 percent of the time avoiding something it's hard to hit it when a director decides "April Fool".
   
   
5. Notes spaced away from the root note by any interval approximating the 1/3 and 2/3 power of 2 (a shade below the sixth and third) partially cancel the root and sound interesting, but nothing you’d want a steady earful of. These and the notes just below the seventh and second are the minor intervals.
   
   
6. Minor intervals and the tritone were added later. Music terminology still reeks with distain for them; they don’t have their own names and are called accidentals. Arrangers love these guys (see #1 again) and mellow them by blending in other notes into chords.

So how does this relate to the musical staff and why is it so confusing?
Microsoft vs Apple;   Qwerty vs Dvorak;   Pianists vs everyone else
In the distant musical past – there was a rip-snorting battle for market share between piano and other musical arrangers. The pianists won. Pianos then were tuned around C, the fourth note of the octave, and only had white keys. The musical staff we use is basically an early piano keyboard turned sideways.
Lines and spaces on the staff correspond to the white keys of a piano tuned to the C major scale, and musical notation pivots around this weird fixation. Below is listed the notes, with the black keys/accidentals in bold print.

Note   Name    Interval from Root note    Also known as …    Singers name    Ratio   
+12    C           Octave                         Octave                     Doh                   2/1   
+11    B           Seventh                        Major Seventh           Ti                    +7/8   
+10           (blue) Minor Seventh                                                                  +3/4                     
 +9     A           Sixth     Major Sixth                                      La                   +2/3    
 +8                  Minor Sixth           
 +7     G          Fifth                              Perfect Fifth              So                  +1/2   
 +6                  Tritone                          arrgh                        Heck
 +5     F           Fourth                          Perfect Fourth            fa                    +1/3   
 +4     E          Third                             Major Third                mi                   +1/4   
 +3                  Minor Third                                                                        ~+1/5   
 +2     D           Second                        Major Second            Rae                 +1/8   
 +1                  Minor Second           
   0     C           Root    Unison                                              doh                   +0    Boring as Hell

Strange, isn’t it? They call it an “Octave”, but it only has seven “key” notes and it skips that cool minor seventh interval in favor of the dissonant “major” 7th. Go figure! Its hard to believe even early musicians were quite that numerically challenged.

If you go up the scale on the white keys (major & perfect notes), you are following the “Major Scale in the Key of C”. If you follow all 12 notes (semi-tones), that’s the “Chromatic scale”.

Anyway, the important thing is the pattern is simple: go up from the root note in intervals of 2 semi-tones (whole-tones), except for a semi-tone jog from the third to the perfect fourth and a correcting semi-tone jog from the seventh back to the octave. If any sane person (and even some musicians) were to design the staff notation today, it would look a lot better.

You would just put in a symbol marking where the root is, and always assume whole steps, except where some little little brackets would indicate that the whole series of 4 notes is dropped down (flatted) by a semitone and the root note indicated by a little carrot (naturally, Doc). This way, musicians would only need to learn to read two staffs, instead of 24 variations. (The same goes for the piano itself; if they had alternating white keys/black keys, people would only have to learn 2 fingerings, instead of 12! Further, one could … get a lot of blank stares from musicians, who are quite used to being notationally challenged.)
Don’t be too hard on them – do you use a Mac computer and a Dvorak keyboard?

Figuring out the tonic
Its nice to know where on that staff those little jogs are hiding – otherwise you can trip over them and be a semitone out – not a gentlemanly / ladylike thing to do; kind of like farting in public.

The normal musical staff notation assumes the notes correspond to the C-major scale, to get to the other scales, musicians shift the C major notes by the minimum number of semi-tone adjustments sharp or flat, (they don’t like mixtures), to get the major scale needed. In nerd terms, that little jog in the whole-tone spacing of notes is shifted up or down.  

For example, if one pastes on an F-sharp on the staff, that shifts that third-to-fourth jog up and gives us the right jog pattern for a G-major scale; the F-sharp becomes the seventh below the tonic. You can repeat this again, going up a perfect fifth each time.  Music theorists make a big deal of this, calling it the circle of fifths, but it’s just the way the math works. If you see sharps, just sharp the last one.

For flats, the trick works going by down in fifths. The important thing to remember here is that the second to last flat is the tonic, and when you see one flat, the tonic is F. (It’s simpler than counting up a fifth from the last flat.)

Caveats
I have hugely simplified a vast subject, thus violating the maxium:
  'Tis better to keep quiet and be thought a fool than to open one’s mouth and remove all doubt. -Anon.
Please be kind.