The basic layout of 12 consecutive semitones is what defines an octave (i.e. the eight - octa - white keys on the keyboard going from C to C); and it is from these 12 semitone increments that scales are defined.
Scales are basically strings of notes (played consecutively) that begin on a specific note (C for example) and finish on that same note one octave up or down. There are many such scales in music, each has a specific name that supposedly reflects its sound and/or structure.
The simplest of these is the chromatic scale: this scale consists of all the white and black notes between two notes of the same name. In order to play it, simply play all the notes between two Cs, or two Es, or two F#s, etc. Looking at it from a different angle, a scale is defined by the increments in which the notes ascend, so you can play the chromatic scale corresponding to any note just by playing all the keys between two notes that are an octave apart.
For example, if you start on A and go up (or down) in semitones until you reach the next A (i.e. play all the keys between them), then you have just played the chromatic scale in A. If you start on the Bb and do the same you will play the chromatic scale in Bb. It is the same for all the notes: as long as the string of increments within an octave is the same, then you can play the same scale for any note you want. In the case of the chromatic scale the increments are all semitones.
Chromatic Scale in C C C# D D# E F F# G G# A A# B C Chromatic Scale in C#/Db C# D D# E F F# G G# A A# B C C# Chromatic Scale in D D D# E F F# G G# A A# B C C# D Generic Chromatic Scale st st st st st st st st st st st st
st = semitone
Looking at the scales written above, and the keyboard picture again, we can see that it is the difference between the notes (i.e. the increments) that define the scale. Once that is known, we can play that particular scale starting on any note.
This is how all other scales are defined; some of which you have probably heard of:
The major scale is defined as:
Generic Major Scale t t st t t t st
So starting on C the scale would go: C, D, E, F, G, A, B, C. If you play it on a keyboard you will see that the scale sounds “happy” or “agreeable”, and this is why the piano keyboard is designed as it is: in order to make it easier to play the C major scale. Please note that black keys do not occur between two keys that are only a semitone apart, i.e. B and C, E and F, since there are no more notes to be played within a semitone increment. The black keys are called accidentals (the white keys are called naturals), and are refered to as #s (sharps) or bs (flats). As you have probably already guessed, a sharp is a semitone higher than the white key is named after (e.g. F# is a semitone higher than F) and a flat is a semitone lower than the white key it is named after (e.g. Gb is a semitone lower than G).
Since a black key is surrounded by two white keys, it always has two names: the more observent of you will have noticed that F# and Gb refer to the same note. Any notes with the same pitch but different names are referred to as enharmonic. It is also possible to refer to white keys as sharps or flats (e.g. B can be called Cb, and C can be called B#) since the terms only refer to the difference in pitch; however, this is rare in piano-playing, and I have never heard it used in harmonica-playing.
Now see if you can work out how to play the major scale in F#. Just follow the rules, starting on F# and going up: tone, tone, semitone, tone, tone, tone, semitone. You will see that this scale also sounds happy or agreeable. Just remember that a tone is the same as going up two keys at once.
Major Scale in F#/Gb F# G# A# B C# D# F F# Generic Major Scale t t st t t t st
Generic Minor Scale t st t t st t t
If you look carefully you will see that this is equivalent to taking the last two increments of the major scale and moving them to the front. So if you play: A, B, C, D, E, F, G, A, then you have just played the minor scale in A.
So, what have we looked at so far? Well, you now know the origins of modern music theory, the history of musical development, and you can now play 36 different Scales (12 each of chromatic, major and minor).
Not bad for half an hour.