In order to harmonize a scale you need to know a couple of new things:
1) How to harmonize an ascending progression of VII-I scale degrees (in C major - notes B-C).
2) How to harmonize a descending progression of I-VII scale degrees (in C major - C-B).
The first ascending progression is best harmonized by the 1st inversion diminished chord D-F-B (ovii6) and tonic. The rule is to double the bass (D) and move it stepwise to the tonic note (C). The upper three voices move to the closest notes of the tonic chord upwards (contrary motion). In order to avoid the forbidden augmented interval in minor between VI and VII scale degrees, use major subdominant with a raised VI scale degree (just like in melodic minor).
The second progression is best harmonized by the tonic and the root position third scale degree chord, in C major - E-G-B (iii). Again, double the bass part here. In minor, this chord will be major (III). Since these two chords are positioned a third apart, they have two common notes (in C major - E and G).
So the rule to connect them is very simple - move the bass from the root of one chord to the root of another chord by the interval of the third. Keep the common notes constant and move the free voice downward in a stepwise manner.
Since we know how to conncect ovii6-T and T-iii already, let's play a major scale:
I (T) - II (D) - III (T) - IV (S) - V (T) - VI (S) - VII (ovii6) - I (T).
I (T) - VII (iii) - VI (S) - V (T) - IV (S) - III (T) - II (D) I (T).
I (t) - II (D) - III (t) - IV (s) - V (t) - VI+ (S) - VII+ (ovii6) - I (t).
I (t) - VII (III) - VI (s) - V (t) - IV (s) - III (t) - II (D) - I (T).
Practice these exercises in various major and minor keys (first writing on paper and later harmonizing on the instrument). Make sure you take a very slow but steady tempo. If you want to master these scale harmonizations, aim for at least 3 correct repetitions in a row.
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