Anyone not familiar with what a is or how they are named should read Notes: Naming Them first.
There are only 12 different notes in Western Art and popular music. Scales are a succession of notes. When played or written one after the other the interval, or distance, between notes is either a tone (T), also called a whole step, or a semitone (ST), also called a half step. As implied, there are 2 semitones in a whole tone.
One type of scale, the chromatic, uses all 12 notes. A chromatic scale is simply a succession of semitones, starting from any of the 12 notes. For example, a C chromatic scale is C-C#-D-D#-E-F-F#-G-G#-A-A#-B-C. (Not thirteen notes; scales begin and end with the same note an higher.)
C chromatic scale:
(Notice there are no sharp (#) notes between the notes E-F and B-C, the 5th and 6th and the 12th and 13th notes, respectively. And no flat (b) notes between them when descending. Those notes, E-F and B-C, are the only ones separated by a semitone rather than a tone. Look at a piano keyboard and notice there are alternating groups of two and three black keys. Between these groups are two white keys with no black key between them. To the left of the two black keys are the notes B-C. To the right are E-F. Why are these the only notes separated by just a semitone? It has to do with the physics of a vibrating string and the resulting overtones. Google it if you like.)
Major and Minor Scales
Chromatic scales are not commonly used. Two scale types it is essential to understand are major and minor. These scales begin and end with the same note, an octave apart. Octave equals eight, meaning both that there are eight notes in a major or minor scale and that any note an octave in distance (eight notes apart) from itself is the same note. It is an octave higher or lower.
Major and minor scales have distinctive sound qualities, due to the intervals between successive notes and the harmonies built on top of each note. More on that when I write the Harmony page (Done, here). Recall there are two intervals: tone (T) or whole step, and semitone (ST) or half step. Each scale type has a specific tone-semitone order.
Major scales are ordered T-T-ST-T-T-T-ST. Always. That pattern is what makes a major scale a major scale
An ascending C major scale:
You will notice each note has three labels, excluding the T and STs: the letter name, the scale degree (a Roman Numeral), and a functional or relationship one. I’ll say a bit about the leading tone shortly, and much more about the function/relationship between notes and harmonies when I write the harmony page. (Done, here).
Here is an A major scale. Note the T-ST order is the same as the C major example – as it is for every major scale. The scales sound both the same and different. The same because the T-STs are the same; different because the starting note’s pitch is different.
An ascending A major scale:
Minor scales are more complicated. There are three flavours: the natural minor scale, the harmonic minor scale, and the melodic minor scale. The T-ST order in the natural minor scale is T-ST-T-T-ST-T-T.
A natural minor:
The harmonic minor scale raises the 7th note, the leading tone, a semitone. The T-ST order is T-ST-T-T-ST-T+ST-T. Notice the raised leading tone creates a tone plus a semitone distance between the 6th and 7th notes. The leading tone is raised to create a sense of leading into, or needing to resolve to the tonic, the first and last note in the scale. As does the leading tone in the major scale.
A harmonic minor:
The melodic minor scale has a different T-ST pattern when ascending than it does when descending. Ascending melodic minor scales raise both the 6th and 7th notes by a semitone. When descending both notes are played as they would be in the natural minor scale, without the raised semitones. The 6th note is raised to smooth out the irregular T+ST interval that occurs between the 6th and 7th notes in the harmonic minor scale. The ascending melodic minor T-ST order is T-ST-T-T-T-T-ST. As with the harmonic minor scale, the leading tone is raised to create a sense of leading into, or needing to resolve to the tonic. When descending there is no need for a “leading” quality, so the 7th note is played according to the natural scale. And since there is no T+ST gap to smooth, so is the 6th note. The melodic minor descending T-ST order is the same as the natural minor scale, T-T-ST-T-T-ST-T. (There’s no need for the harmonic minor scale to keep the raised leading tone when descending either, but it does. I have no explanation why, other than it just sounds nice!)
A melodic minor:
Keys and Key Signatures
Music is written in specific keys. Meaning the scale is specific to the music, at that particular point in time. If the scale is A major the key is A Major; D minor D Minor. Scales can start on any of the 12 chromatic tones. The important thing to remember is the interval pattern between the notes in any major scale is always the same. So is the T-ST order in each of the three minor scale types. That is why there are key signatures. Rather than write out sharps or flats whenever the appropriate notes appear, the sharps or flats are placed at the start of each line of the music. For example, an A major scale has the notes F-C-G raised a semitone so as to observe the T-ST order of a major scale. Rather than write a sharp every time those notes appear the three sharps become the key signature, meaning when those notes are played they are to be played sharpened, raised a semitone. Same concept applies to keys with flats, except of course the notes are lowered a semitone.
Key signatures either have sharps or flats. They are never mixed (in all but experimental music). That’s what happens when following the strict scale T-ST order. Increasing the number of sharps or flats in the key signature is additive. If there are three sharps, as there are in the A major example above, they must be F-C-G sharp; four F-C-G-D sharp, etc. The maximum number of sharps or flats in a key signature is seven – because there are only seven different notes in major and minor scales. The order for sharps is: F-C-G-D-A-E-B. For flats: B-E-A-D-G-C-F. Once again, these “rules” occur because of the T-ST basis of the scales. It just works out that way. The Circle of Fifths explains it further. It is a way to map the keys and show how the sharps and flats are additive. Wikipedia has an excellent article on the Circle of Fifths, here. The Circle of Fifths is an after the fact, secondary explanation. The T-ST pattern in the scales permits the creation of the map, not the other way around.
There is a relationship between major and minor keys. It has to do with the key signature. Specifically, the key signature in one major scale uses exactly the same sharps or flats, or none at all, as the key signature for one minor scale, in each of its three flavours. The relationship is called “relative”. In the C major scale example above there are no sharps or flats in the key signature. Same for all A minor examples. A minor is the relative minor of C major and C major is the relative major of A minor.
A note is a sound or tone having two aspects:
1) The primary, auditory one, is pitch. Each note has a unique pitch, with a sound wave frequency measurable in hertz. In many parts of the world instruments are tuned to A at 440Hz.
2) The secondary, temporal one, is duration, called "time value" or "note value". When written or played each note has a specific duration, how long it lasts relative to the beat.
When pitch and duration are combined we get melodic shape and rhythm. Pitch creates melody and gives it direction, the melodic shape; duration provides the melodic rhythm.
The word octave describes two things: most importantly, an octave is the same note 8 notes above or below a given note; "octave" may also be used to measure the range in a group or series of notes, as in "the melody's range is an octave"; meaning the distance between the lowest and highest notes is an octave, 8 notes apart.
Because octaves are the same note they have the same letter name. They are the same note in a different register and should be heard as "higher" or "lower", but not "different".
C in four octaves.
More information and the science behind why we hear octaves as the same note is here.