A practical overview
Each chord number corresponds to one of the notes of in any major scale, which can be extended into the second octave. This gives us: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15. We can and do use these numbers for scales. 8va means up or down an octave. 15ma means to go up or down two octaves.
You will also never see 1 in a chord, because 1 is always the root or name of the chord.
You will also never see 8, 10, 12 or 14 in chords. They are octaves of 1, 3, 5 and 7. No chord is marked with 15. However, 2, 4 and 6 are used and are important.
The chord system is useful for instant transposition. All chords are described by degrees in a major scale. If you know your major scales, you can instantly play any chord you know in any other key.
The symbol “b” after a number means lower the note 1/2 step. It does not mean a black note. The symbol “bb” after a number means lower it a whole step.
The symbol “# means to raise the note 1/2 step. That’s the end of it.
The system is very simple, very concise, very practical and very powerful.
There is point that is peculiar to this system that is vital to remember. The 7th note of any major scale is always marked maj7. No exceptions. When that note is lowered 1/2 step, which would be b7, the “b” is always omitted. It is simply understood to be there. So G7 is really G (b7) 5 3 1. That (b)7 is simplified to 7. You will never see a “b” before the 7 in chord, only in my explanations.