I V covers 5 of 7 tones in major keys:
^1 ^3 ^5 ^7 ^2. To get the missing
^4 ^6 use either
ii. To play that in basic minor key harmony just make the subdominant minor or the supertonic diminished as
But, harmony in minor is a bit more complicated that than, because
^6 ^7 can be in either "lowered" or "raised" forms. The simplest is to only deal with lowered/raised
^7. One common progression to get both forms is:
i v6 iv6 V where the
v6 is a minor dominant chord. If you don't want to play inverted chord you can do it as
i bVII bVI V.
Playing root by descending fifths (circle of fifths) is obvious too
I IV viio iii vi ii V I or in minor
i iv bVII bIII bVI iio V i. I think it is nice to dress up those progression at the end with some cadence other that just
V I. Something like
I6/4 V or
ii6 V6/V V for half cadences.
You asked specifically about major/minor scales, but a chromatic approach is good too. One thing to do is use secondary dominants for each diatonic chord except the diminished chords. You can precede or follow each with a secondary dominant:
I6 IV V6/V V V6/vi vi or
I V6 ii V6/ii iii V6/iii. Those progressions seem to work best when the diatonic roots are separated by whole steps, but you can try hitting all diatonic roots
^1 ^2 ^3 ^4 ^5 ^6 or maybe
^1 b^7 b^6 ^5 ^4 b^3 in minor. Again, avoid the diminished chords. Technically you're tonicizing each diatonic chord, and you can't treat a diminished chord as a tonic.
You may have already noticed how much of these progressions is just roots by descending/ascending fifth. You can generalize that in voice leading terms as two voices moving by step either ascending or descending.
V6 I and
IV6/4 I and their reserve
I V6 and
I IV6/4. Basically there isn't another way to do that voice leading other than to change the major/minor chord qualities.
You can put that voice leading into a chromatic context sequencing the chord changes by ascending or descending whole or half steps. You mix up lots of combinations of chord qualities, voice leading, and interval of sequencing. (Jazz chord symbols will make it easier to read.)
C G/B, Bb F/A, Ab Eb/G... or
Fm/C C, Em/B B, Ebm/Bb Bb... or
Cm Gm/Bb, Bbm Fm/Ab, Abm Ebm/Gb..., etc. etc.
Apply the voice leading to the circle of fifths progression too. You can freely mix and match inversions (root position, first inversion, and second inversion.) Just start with one type and on the next chord pick one of the other two types then sequence the two chord pattern.
I IV6/4 vii iii6/4... or
I6/3 IV vii6/3 iii..., etc.
As far as chord "shape" is concerned, be aware there are only six shapes each for major and minor triads. For major chords the roots are
B ascending chromatically, and for minor
Eb descending chromatically to
Bb. Both encompass a perfect fourth. Both include one of the "all black" triads
#F major and
Eb minor. Just ascend from
F# for the major chords and descend from
Eb for the minor chords. The triads on all the other roots are duplicates in terms of "shape."