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Sorry for the very basic question, but my only experience comes from using DAW software.
The rule I use to create a triad is playing three notes at {0,4,7} semitones for a major chord and {0,3,7} semitones for a minor chord. I apply the same rules for other degree of the scale, ie starting from E instead of C. This is quite easy to do in a piano roll. The question is, does this rule apply on any degree and on any scale?
0, 4, 7 in Integer form is equivalent to P1, M3, P5 in interval form. If you start on a note with MAJOR chord quality in your scale, it will be a primary triad. If you don't it's considered secondary (or auxillary).
C Major Scale (UPPER = MAJOR / lower = minor)
C d e F G a b C
Has primary triads of C - e - G, F - a - C and G - b - d and secondary triads of d - F - a, e - G - b and a - C - e based on the chord quality of the scale degree.
As long as you stay with the intervallic pattern for the triad, you should be good to go..doesn't really matter if it's Major, minor, augmented, diminished, sus2 or sus4.
MAJOR (0 – 4 – 7) minor (0 – 3 – 7) AUGMENTED (0 – 4 – 8) diminished (0 – 3 – 6) sus2 (0, 2, 7) sus4 (0, 5, 7)
Using your system, with 0 as the Root of the scale, the major chord starting from that root will always be {0,4,7} and the minor will always be {0,3,7} :)
I'm not sure what you mean by the grade of the scale? If you mean the degree, (eg starting on the 2nd note of the major scale) then usually Your chord would be minor(taking the 2, 4 and 6), but because you're working in semitones you can just move up and up the notes and will always have the same triad type as you started with.
The short answer: No.
Long answer: Your method is valid for major and minor chords, but there are other chords. For example the 7th degree of the major scale, using your notation, is {0,3,6} (diminished 5th). The 3rd degree of the minor melodic scale is {0, 4, 8} (augmented 5th) and the 6th and 7th degrees of that same scale are also diminished 5th so {0,3,6}.
