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Harmonic Progression
...is simply progressing from one harmony to another.  In this process there are two basic types of movement, strong and weak.  These are not synonymous with "good" and "bad" or "pleasing" and "displeasing."  In tonal music, strong is generally the norm, but weak is also used in certain instances.

When referring to harmonic progressions, diatonic chord numbers are generally used ( I,  IV,  ii,  V7,  vi,  etc.).  The distance between two chords is measured from the root of one chord to the root of the next chord, regardless of the inversions of the chords.  The note in the bass voice does not determine the distance between the roots of the chords!

For example:

The distance between I and IV is down a 5th (up a 4th).
The distance between I and IV6 is down a 5th (up a 4th).
 
The distance between IV and ii is down a third (up a 6th).
The distance between IV6 and ii is down a third (up a 6th).

 
Strong Root Movement
Many rules and regulations have been formulated over the years to govern what is considered appropriate or strong harmonic movement.  These rules can be summed up, however, in the simple chart below.  (Reminder:  These movements are from the root of one chord to the root of the next, regardless of inversion.)
 


If the movement from the root of one chord to the root of the next chord is down a 5th, it is considered a Strong Progression.
     Examples:
          I --> IV;   ii --> V;   iii --> vi;  etc.

If the movement from the root of one chord to the root of the next chord is down a 3rd, it is considered a Strong Progression.
     Examples:
          I --> vi;   vi --> IV;   IV --> ii;   etc.

If the movement from the root of one chord to the root of the next chord is up a 2nd, it is considered a Strong Progression.
     Examples:
          I --> ii;   iii --> IV;   IV --> V;   etc.

> From a I chord to any other chord is considered a Strong Progression.

> From IV to I is also considered a Strong Progression.
 
Weak Root Movements
Weak root movements are simply the opposite of the strong movements.  Up a 5th, up a 3rd, and down a 2nd are weak root movements.