Is i-V a stronger progression than I-V?

I'm just starting to learn a little music theory (in connection with learning to play the ukelele), and I repeatedly see I-V as basically the strongest chord progression (in whatever sense "strongest" is being used in a given article). I haven't seen any explanations of why, and I assume it has a lot to do with centuries of trained musicians saying "that sounds great!". I started looking at the intervals present in this progression to see if that was the reason, and indeed it has a tone of "good" intervals:

               V
R    3    5
R | P5 | M7 | M2 |
I  3 | m3 | P5 | m7 |
5 | P1 | M3 | P5 |


The table above shows the notes of the V across the top, and the notes of the I down the left hand side, and at the intersection of each note, shows the interval going from I to V. After looking at this, I'm assuming that all those Major and Perfect intervals is a big part of why the I-V progression sounds good

But noticing the minors in the third row, these can easily be turned into majors by changing I (Major tonic) to i (minor tonic):

               V
R    3    5
R | P5 | M7 | M2 |
i  3 | M3 | A5 | M7 |
5 | P1 | M3 | P5 |


And the only trade off is that one of the Perfect fifths turned into an Augmented fifth.

So questions is: do these interval tables have much at all to do with why a progression sounds good and if so wouldn't the i-V progression (which I guess would come from a harmonic minor scale) be stronger than I-V?

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I would suggest that the interval between the third of the V and the root of the I is a minor second, rather than a major seventh. Also, if you use a V7 chord, its seventh will generally move to the third of the I via another minor second. V7 to I is a very strong resolution because the diminished fifth between the V chord's third and seventh can resolve to a major third. – supercat Jul 10 '14 at 16:50
@supercat: I wrote all the intervals as going from a note in the tonic to a note in the dominant, not the other way around. I see that M7 and m2 are inverse of one another, so from from the third of the V to the root of the I would be a m2, but is there significance to describing it one way or the other? – sh1ftst0rm Jul 10 '14 at 16:55
Chord progressions are to a large extent compelling (or not) because of the movement of the notes within the chord. A major seventh will only be perceived as a movement if no other notes are nearby. While your question may have been for tonic-dominant, I think looking at what makes V7-I is compelling (and trying it with different voicings) will help you understand other chord changes. Try doing chord progressions with three notes in different octaves (for G7 use G-B-F) and you'll notice that arrangements where all three pitches in one chord are near those in the other are more compelling. – supercat Jul 10 '14 at 17:18
Thanks, that's really helpful! – sh1ftst0rm Jul 10 '14 at 17:23
You ask if i-V or I-V is stronger. V-i and V-I are usually regarded as the strongest.And if you look at 4 note chords instead of 3, there's even more strength. I based my deleted answer on the latter premise, which is why it's now gone. – Tim Jul 10 '14 at 17:28

You are looking at the chords in an interesting way, but you are over complicating the subject a lot and have a few slight misconceptions. I to V or i to V is a very normal chord movement and it is quite strong, but the the opposite is much stronger i.e. V to I or V to i. The movement is so strong at the end of a phrase the movement is known as an authentic cadence.

The reason V to I and V to i progressions are so strong is because V leads to I(i). In C major a G (with the notes G B D) would go to a C (with the notes C E G). As you can see the G is common in both chords and the B in the G (also known as the leading tone) goes to a C by going up a half step (m2) and the D goes up a whole step(M2) to the E.

In C minor a G (with the notes G B D) would go to a Cm (with the notes C Eb G). As you can see the G is common in both chords and the B in the G (also known as the leading tone) goes to a C by going up a half step (m2) and the D goes up a half step(m2) to the Eb.

The only difference between the two is that instead of going up to the 3rd by whole step in the V-I you go to the 3rd by half step in V-i which is considered a stronger movement because there is a smaller distance between the notes.

When trying to figure out how strong chord movement is, look at the smallest intervals between notes.

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Thanks, Dom, super helpful! (And thanks for fixing up the formatting on my question!) – sh1ftst0rm Jul 10 '14 at 12:59
It may be worth noting that in a V7-I progression (e.g. G7-C), the third and seventh of the V chord (B and F) form a diminished fifth that produces tension; moving to the I chord changes the B to a C and the F to an E--both minor-second moves. In a G7-Cm resolution, because the F in a G7 creates much more tension than the D, the F-Eb movement will be more noticeable than the D-Eb, even though the latter interval is smaller. Because F-Eb is a major second, it's not as compelling a move as the F-E in a V-I. – supercat Jul 10 '14 at 16:56