Can you find the shapes formed by the red dots among the other black dots? You will begin to see how octaves work in music when you begin to play and listen to scales.
The chromatic scale contains all possible notes.
The 13th note in a chromatic scale is called the 'octave.'
You can build a chromatic scale on any note. That is, you can use any note as your starting point. The scale forms the same melody, no matter what note you start on. The scale can go up (ascending) or down (descending).
Wind Instruments Use Different Lettering
Some wind instruments have their own system of lettering pitches. A 'G' on the guitar can be an 'E' on a saxophone. The 'A' on a guitar is the same as an 'A' on a keyboard. This is called 'concert pitch.'
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Chromatic Scale The chromatic scale in one octave contains 12 note names. It contains all possible note names including sharps and flats. The 13th note begins a new octave. (More later.)
Each Possible Note On the piano, you get a (multi-octave) chromatic scale by playing each black and white key on the keyboard. On the guitar, you get a (multi-octave) chromatic scale by playing a notes at each fret on each string. Every note is part of the chromatic scale. The chromatic scale has a particular sound. It contains a melody that is always the same, and one you should be familiar with.
No Key Signature A chromatic scale doesn't have a key signature. You don't refer to a chromatic scale as being in a certain key. All major and minor keys are subsets of notes from the chromatic scale.
Formula For Chromatic You can get a (one-octave) chromatic scale by playing every note between the 1st and 13th frets on one string. The 13th note becomes the first note of the next octave. The 13th note shares the same note name with the 1st note. The formula is all the notes on one string between fret x and x + 12.
Note Names You probably know that there is a system of assigning letter-names to musical notes. The name of a note doesn't change. An 'A' is always an 'A' and is never a 'B.'
There are 7 letters with spaces between 5 of the letters. There is no space between B and C, and no space between E and F.

[# = sharp (higher) b = flat (lower)]
Sharps and Flats A# is the same note as Bb. C# is the same note as Db, etc. The two note names are interchangable.
Notes with sharps and flats are no different than notes without sharps or flats.
Every note is an equal distance from the next note. Each note represents a set musical distance.
What in the world were they thinking? Seven letters with sharps and flats? Even though all the notes are the same musical distance? Why? The reason is that nearly all early European music was based on the major scale. Pre-renaissance era music rarely used notes outside of the key signature.
Major Scale The major scale (in one octave) is made up of 7 notes from the chromatic scale. In any major scale, 7 notes are used and 5 notes are not.
The Main Scale The major scale became the main scale used in composition of early European music. That's why it's called the 'major' scale. It is the basis of our seven-letter note-name system. The major scale came before the keyboard, and before any methods for writing music.
Keyboards The design of the piano keyboard, with it's recessed black keys, and the system of giving a letter-name to notes are both based on the major scale - on the idea that in the span of one octave, 7 notes are commonly used, and 5 notes are not.
Major Scale Shape The major scale shape is the most important to guitarists, because this single shape contians other important scale shapes: pentatonic, minor and all of the modes.
I'll explain the relationships between these scales in detail on another page.
The Number System A newer, easier system of describing harmony assigns numbers to notes. The tonic note (tonal center) is numbered '1.' Each of the 7 scale notes is given a number. Non-scale tones are referred to as, for instance, 'sharp 5' or 'flat 7.'
The number system does away with the idea of keys.
Harmony in 'C' has 'C' as a tonal center, and the scale note have no sharps of flats. Harmony in 'Eb' has 'Eb' as a tonal center, and has 3 flatted notes in the scale. With the number system, you don't need a one model to explain harmony in C, and another to explain harmony in Eb. Every key is becomes the key of '1.'
I will explain the number system and how it works together with the note-name system on another page.