numbers instead of letters

To understand music you must understand how notes relate to each other. And since it is easier to figure out how many numbers there are between 2 and 5 than it is to figure how many letters there are between D and G I'm going to give a number to each of the notes.

From now on I'm going to call C "1" and D "2", etc., one octave keyboard

C       D       E       F       G       A       B       C       the C scale
do      re      mi      fa      so      la      ti      do      solfeggio
1       2       3       4       5       6       7       1       the number system
C scale C D E F G A B C
solfeggio do re mi fa so la ti do
number system 1 2 3 4 5 6 7 1

You may want to keep this chart handy.

the in-between notes
When I want to talk about the other notes - the notes in between these - I'll refer to them by using "accidentals": a sharp (#) after a number means the next note higher in the complete 12-note scale: a flat (b) means the next note lower.
home note
Notice how the 1 note sounds more relaxed than the other notes, as if the scale were glad to be home. Maybe it's for that reason that the scale is named for the 1 note: The "home" note - the 1 note - in the C scale is C.
All scales revolve around their 1 note. And most melodies end on the 1 note.