Intervals
In music what sounds good or bad, major, minor, or just weird, is all about the relationships between the notes. We call these relationships intervals.
Semitones: a semitone is the distance between a note and the note immediately next to it. You might see this called a half step.
Tones: a tone is made up of two semitones. It is also referred to as a whole step.

We work out musical intervals by counting the number of semitones between a pair of notes. Make sure to count ALL the black notes!
Here is a table showing all the intervals within an octave. The best way to learn and understand these, is to play them and hear how they sound.

Augmented means to make the interval bigger, so we add a semitone
Diminished means to make the interval smaller, so we take a semitone away
The Major Scale
The major scale is one of the most commonly used scales in western music. It is made up of 8 notes. You can make a major scale starting on each of the 12 different musical notes (or keys), using this pattern of intervals:
Tone Tone Semitone Tone Tone Tone Semitone
Here is an example starting on C:

Each of the notes in a major scale has a name, based upon its position in the sequence and the interval it makes with the note the scale starts on.

This is how the intervals of the major scale look written out in musical notation:

C - D C - E C- F C - G C - A C - B C - C
Major 2nd Major 3rd perfect 4th perfect 5th Major 6th Major 7th Octave
The Major Arpeggios
Arpeggio means “broken chord.” Using the notes of the scale, we can work out the notes of the arpeggio which belongs with it.
Major arpeggios use the 1st , 3rd, 5th, and 8th note of the major scale.
For C Major, the notes of the arpeggio would be: C E G C
This is how the major arpeggio looks wiritten out in musical notation:

C E G C G E C
The Chords in Major Keys
We can use scales to work out the chords that will work well with a particular key. If you create a tune using the 8 notes of the scale, you can use the chords to make a accompaniment for the tune that will sound right.
Here is an example of how to make the chords using C major:

The chords made from notes 1, 4, and 5 of the major scale are all major chords. They are the most important chords in any major key, think of them as the major key's primary colours.
The chords made from notes 2, 3, and 6 of the major scale are all minor chords. These chords add interest to the accompaniment, you can think of them as the secondary colours of the major key.
The chord made from the 7th note of of the scale is a diminished chord. This isn't used very often due to its strange sound!