Apologies if this stuff is obvious to you, it wasn't to me once upon a time.
When people talk about "theory" they're talking about harmonic theory. Melodic theory exists (most famously in counterpoint) but that's not what theory is generally about. Rhythm theory, Timbre theory and Expression theory are not well documented.
Most of the following statements can easily be shown to be wrong in part but this misses the point - Theory assumes them to be true and then extends to encompass the exceptions.
Scales consist of 7 distinct notes. This is a massive lie (but see above).
Scales are defined by their intervals (the gaps between the notes of the scale). These intervals are measured in tones and semitones (brit) or steps and half steps (yank)
The intervals in music are named...
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0 semitones perfect unison (aka the same bleedin' note)
1 semitone minor second
2 semitones major second
3 semitones minor third
4 semitones major third
5 semitones perfect fourth
6 semitones diminished fifth or (occaisionally) augmented fourth
7 semitones perfect fifth
8 semitones minor sixth
9 semitones major sixth
10 semitones minor seventh
11 semitones major seventh
12 semitones perfect octave (aka the same bleedin' note an octave higher)They are...
The Major Scale
The Natural Minor Scale
The Harmonic Minor Scale
The Melodic Minor Scale
The Major Scale has the intervals Tone-Tone-Semitone-Tone-Tone-Tone-Semitone.
So A Major starts on A (that's why it's called A Major).
The next note is a tone (2 semitones or notes higher) - B
The next note is a tone higher. It's a black note so it could be called C Sharp(#) or D flat(b). In this case we don't have a C and in general you try to stick to only one of each letter per scale (this is why the black notes have two names) so C# is chosen.
The next note is a semitone higher - D
Up a tone - E
Up a tone - F# (same logic as before)
Up a tone - G#
Up a semitone - back to A
That's it - A Major. A, B, C#, D, E, F#, G#, A
Move (transpose) all that lot up a semitone and you get Bb Major - Bb, C, D, Eb, F, G, A, Bb
Note that if you call the first note A# you get A#, C, D, Eb, F, G, A, A#. Two A's (one sharpened) mixed with a flat (Eb). If you call Eb D# then you also have two D's. That's why it's Bb not A# in this case.
Transpose up again and you get B Major etc, etc.
The only other Major scale worth enumerating in detail is C Major...
Start on C
Up a tone D
Up a tone E
Up a semitone F
Up a tone G
Up a tone A
Up a tone B
Up a semitone C
As you can see C Major has no sharps or flats, it's white notes all the way. This is why it gets used so much in teaching theory. And this leads to another point...
All theory works in all 12 keys. The only difference between the keys of A and C is that everything in C happens 3 semitones higher than happens in A.
This is why theory often gets taught in roman numerals, it makes it key independant. Here's how it works...
I - the first note (Tonic) of the Major Scale
bII - out of scale
II - the second note of the Major Scale
bIII - out of scale
III - the third note of the Major Scale
IV - the fourth note of the Major Scale
bV - out of scale
V - the fifth note (Dominant) of the Major Scale
bVI - out of scale
VI - the sixth note of the Major Scale
bVII - out of scale
VII - the seventh note of the Major Scale
It really is that simple. These are called "scale degrees". They all have names like mediant, sub dominant etc. None of these names (except the two I've shown - Tonic and Dominant) get used in real life.
Minor scales
Start on the sixth degree of the major scale and ignore the out of scale degrees and you get the Natural Minor Scale. It's intervals are Tone-Semitone-Tone-Tone-Semitone-Tone-Tone
So
A Natural Minor is A, B, C, D, E, F, G, A
C Natural Minor is C, D, Eb, F, G, Ab, Bb, C
and in roman notation...
I, II, bIII, IV, V, bVI, bVII
Harmonic Minor sharpens the seventh degree to give a so called "leading" tone. It's intervals are tone-semitone-tone-tone-semitone-tone and a half-semitone
A Harmonic Minor is A, B, C, D, E, F, G#, A
C Harmonic Minor is C, D, Eb, F, G, Ab, B, C
and in roman notation...
I, II, bIII, IV, V, bVI, VII
Melodic Minor sharpens the sixth and seventh degrees. It's intervals are tone-semitone-tone-tone-tone-tone-semitone
A Harmonic Minor is A, B, C, D, E, F#, G#, A
C Harmonic Minor is C, D, Eb, F, G, A, B, C
and in roman notation...
I, II, bIII, IV, V, VI, VII
Chords consist of 3 or more notes played simultaneously.
Chords are made by stacking thirds. Another lie, another assumption you have to make to learn theory.
There are two kinds of thirds (see above) which means there are four possible triads (3 note chords)
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Diminished - Minor third + Minor third (3 semitones + 3 semitones)
Minor - Minor third + Major third (3 semitones + 4 semitones)
Major - Major third + Minor third (4 semitones + 3 semitones)
Augmented - Major third + Major third (4 semitones + 4 semitones)Stack on another third and you get the following 4 note chords...
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Diminished 7th - Minor third + Minor third + Minor third(3 semitones + 3 semitones + 3 semitones)
Half Diminished 7th - Minor third + Minor third + Major third(3 semitones + 3 semitones + 4 semitones)
Minor 7th - Minor third + Major third + Minor third(3 semitones + 4 semitones + 3 semitones)
Minor Major 7th - Minor third + Major third + Major third(3 semitones + 4 semitones + 4 semitones)
Dominant (or usually just)7th - Major third + Minor third + Minor third(4 semitones + 3 semitones + 3 semitones)
Major 7th - Major third + Minor + Major third(4 semitones + 3 semitones + 4 semitones)
Augmented Major 7th - Major third + Major third + Minor third(4 semitones + 4 semitones + 3 semitones)If I think of anything else...
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