You might have heard about the concept "playing diatonically" and wondered what that is. Well, diatonically means to play along the diatonic scale in any key. It applies to modal music as well (changing the key and playing in two more keys than one at the same time).
When I say scale I mean a given interval sequence. An interval is a distance between two notes. Therefore, given a start note (i.e. key) the intervals in the scale tells us how to traverse it to the end of the scale. Mostly they are octave repeating (i.e. they end an octave above the start).
But what is the diatonic scale then? Well, the word is greek (διατονικός = "diatonikos") and means "progressing through tones" [1]. More specifically, it means it is an heptatonic scale (7-note scale) that is octave repeating and where the tones are as equally spaced as possible. This means that we try to take 7 notes out of the 12 available from the chromatic scale (i.e. a scale with all notes) but we chose them so that the scale is as "smooth" as possible. This gives us 5 whole steps and 2 half steps. These two half steps (semi tone or minor second intervals) must therefore be separated by two and three whole steps.
This is disturbingly similar to how the white keys are layed out on a piano, and in fact, it is. Therefore the diatonic scale is often called the white note scale. So there are actually 7 modes of the diatonic scale since there are 7 notes. A mode is simply a displacement of the scale. It means you start the scale somewhere else. Two scale modes sound very differently to our ears. In fact, the first mode has a major character and the second mode has a minor character. Here are the diatonic modes (examples in C-major (i.e C-ionian)):
Name Formula Example
Ionian: W-W-H-W-W-W-H C-D-E-F-G-A-B-C
Dorian: W-H-W-W-W-H-W D-E-F-G-A-B-C-D
Phrygian: H-W-W-W-H-W-W E-F-G-A-B-C-D-E
Lydian: W-W-W-H-W-W-H F-G-A-B-C-D-E-F
Mixolydian: W-W-H-W-W-H-W G-A-B-C-D-E-F-G
Aeolian: W-H-W-W-H-W-W A-B-C-D-E-F-G-A
Locrian: H-W-W-H-W-W-W B-C-D-E-F-G-A-B
Where W means whole step and H means half step.
For instance, the C ionian mode comprises of the tonal sequence C-D-E-F-G-A-B-(C) and the A aeolian mode comprises of the tonal sequence A-B-C-D-E-F-G-(A). Try to play these notes on your instrument and you will here the difference. The former will sound major and the latter will sound minor. The A aeolian simply is the C ionian where you instead start with the A-note. In fact, these particular modes constitutes the so called tonic parallels. The main meaning of this, I think, is that if you look at a given key signature, it could be either a major key or a minor key. For instance; a key signature without any sharps/flats would be either C-major or A-minor. If the key signature has one flat, then it must be a song that goes in either F-major or D-minor and so on. Just listen to the characteristics of the music and you can easily tell which is the one.
So what about the black notes? Well, they have a name too of course. Not only the black note scale but it is more famously known as the pentatonic scale. This is simply because it has 5 notes, just like the diatonic scale has 7 notes. The two scales are disjunct, meaning they have no tones in common. You either play on the black piano keys, or you play on the white ones. If you play on all of them, then it is the chromatic scale. You can think of it like 7+5=12, or diatonic + pentatonic = chromatic.
You can easily hear pentatonicism in blues-based muisc. Diatonicism however, is more predominant in classical music. I will of course go into more detail with all of these scales. This is just a primer.
References:
1. http://en.wikipedia.org/wiki/Diatonic_scale
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