There is a specific formula for finding the proper notes for these variations.
To begin, we will do the C Major chord. The formula is 4 + 3 chromatic. That is, place your thumb on the C key, and go up 4 chromatic notes, then an additional 3.
With the thumb on the C note, advance 4 by going upwards: C#, D, D# and the 4th is an E. So now we have the thumb on C and the forefinger on the E. To get the 3rd note, advanced upwards again: F, F# and then G. Placing your pinkie on the G note, you have the C Major chord C - E - G
For minor chords, the formula is 3 + 4 chromatic. The first note is C, the second note advances 3 to the Eb, and then 4 more to the G. So the C Minor chord (triad) is C - Eb- G
For the C Augmented chord, the formula is 4 + 4. The first note is C,
advance 4 chromatic notes to get the E and again 4 chromatic notes to get the G#
In other words, the C
augmented chord is created by taking the notes of a C major chord (C, E, G) and
raising the fifth (G) by a half-step to G♯.
C - E - G#
To play the C Diminished chord, the formaula is 3 + 3. The first note would be C, then advance 3 notes to the D# (Eb), then 3 notes to the F# (Gb). So the C Aug chord is C - Eb and Gb
Chromatic means count every note in order, without counting the first note, C.
The chromatic scale is C, C#/Db, D, D#/Eb, E, F, F#/Gb, G, G#/Ab, A, A#/Bb, and B
Using this formula, you can figure out the various chords for each note in the scale.
Hope this helps!