The word scale is not very descriptive. In French, it's 'échelle', meaning 'ladder', which is much better. You go up and down ladders. Scales are the ladders you use to go up and down the notes. It's the way the rungs are laid out that makes them different. The Major Scale is the Mother of them all, but there are many other scales, and most teachers will insist that you know them all and that can name them all.
'Modes' are scales. Modes are embedded in the major scale: Look at the scale clock graphic, do one lap around starting from any of the 7 notes: that's a mode. There are 7 modes, each with a Greek name. The major scale itself is a mode. I have played for 50 years, 40 of them professionally, without once thinking 'mode'. Draw your own conclusion.
The famous Pentatonic scales are also just part of the scale-clock, as is the 'blues' scale.
I de-emphasize the learning of scales. I think too many twangers get bogged down in endless study of scales when it is actually melody they should be paying attention to. Knowledge of scales, modes and intervals will follow naturally if you begin to hear and learn melody.
I always recommend that you figure out how to play the melody of any tune you're working on. It may be tedious and difficult at first, but the more you learn, the more naturally it will come and the quicker you will be able to invent and play melodies on the spot. The last thing you want is to be stuck playing perfect scales up and down the neck with no melody.
Scales are the raw ingredients — melody is the music.
All western music comes from a mother scale called the Major Scale (It has a couple of other names too: the 'diatonic scale' and the 'Ionian Mode'). It is NOT a sequence of notes, rather it's a sequence of seven intervals spanning an octave.
We already know that there are 12 intervals of one semi-tone in an octave, and that 7 does not go into twelve, so the scale must be uneven. Let's get an idea of how it works with some simple graphics.
The formula for the major scale is Tone Tone Semitone, Tone Tone *Tone* Semitone ... if you remember nothing else, remember this formula. It can start on any of the 12 notes. Notice that there's an extra Tone in the second half, the one that put '*' around. I did this only to show you graphically that this scale is irregular, uneven, asymmetric ... this 'kink' in symmetry of the scale coupled with the 'kink' in the tuning is what makes playing the guitar so frustrating at first. The two discrepancies make it very difficult to see any consist pattern to the fretboard.
Below is that graph again of the chromatic scale showing those intervals. Remember, a tone equals two semitones. I've only shown one octave but the scale keeps repeating in both directions, up and down. The last note of one becomes the first note of the next and vice versa. The notes are often sung as the Do-Re-Mi syllables I've written above the notes, which represent the scale degrees rather than actual notes. 'Scale degree' is simply the number of each note, so "Do-Re-Mi" could just as easily be "One-Two-Three", or "First-Second-Third" ...
To simplify things from now on, I'll use the C scale for all my examples, only because it is made up of all the natural notes (no sharps or flats), and it makes it clearer to see what's going on. But always remember that a major scale is always the same formula no matter which of the 12 you start from. Below is a simple representation of the scale starting at C. Left to right is low to high.
So the Major Scale template consists of 7 intervals, and when applied to the chromatic scale (all notes) selects 8 notes ... BUT, the first and last notes are the same name, so in effect, there are 7 notes in the scale.
I like to think of the scale as fitting around a clock. Just as there are 12 hours on a clock face, there are 12 notes in the chromatic scale. Thinking of the scale starting at noon, the 7 scale notes will be found at 12, 2, 4, 5, 7, 9 and 11 o'clock. Pictured to the left is the C major scale. It will keep running around and around the clock face, from the lowest notes we can hear to the very highest. We humans have a range of around ten octaves, so ten times around the clock. Dogs probably hear the next three or four octaves. Watch the movie at the top of the page to see how it looks and sounds on the spiral staircase graphic.
This uneven scale is the blueprint for all western music. From it comes everything, including all the other scales. It repeats through the octaves also, so you can imagine them tagged end to end. Refined over the centuries, mostly through the physics of vibrating strings, the order of intervals should be committed to memory (even if you don't know why yet): "Tone tone semitone, tone tone tone semitone". Scales are not yet music. They do allow for melody, which certainly is music, but more structure is needed for the kind of music we love to listen to. Chords are the main structures and I've dedicated a whole section to them, but first we'll look at the way the major scale works on a guitar fretboard.