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I am a twelfth year pianist, and I have done a fair amount of composition. However, I have no idea why the major five chord sounds so much different when played over the major seventh in the bass. Example: the second chord in Pacebel's Canon in D is an Amaj/C# chord. If you were to play a regular Amaj chord, it is different enough to be almost unrecognizable as the same chord.
Any theory explanation?
First things first: The Amaj/C# is the V chord in first inversion. Try to think of C# as the third of the A chord, not as the 7th of the D chord.
Inversions generally change the sound of the chord and composers use them for this exact reason. It would be boring to play just the A chord in a whole composition, so they spice it up a bit by taking the notes in that chord and mixing them up. Using the third as the bass of the chord gives a different sound, using the fifth as the bass gives yet another sound and you can even use the seventh(if your chord has one) as the bass.
The quality of the chord doesn't change. This means that whether you play A or A/C#, the quality of the chord will be the same. You can try try inversions out for yourself and see what you like and then you can use them yourself in your songs.
From a technical point of view, inversions sound different from each other because of the relations of the upper notes in the chord to the overtones (harmonics) of the bass of the chord. The harmonics for C can be seen in the following picture (from Wikipedia):
Looking at the above picture, the first 6 harmonics of a note are:
I0, I1, V1, I2, III2, V2
where Roman numbers are the degrees of the scale and Latin are the octaves.
For A, C# and E the first 6 are:
In an A chord, the notes from lowest to highest would be A, C#, E. We can see that the upper notes match the first 6 harmonics of the base. This gives a very "consonantic" sound. Indeed, the (uninverted) major chord is the most "consonantic" of all chords.
In an inverted chord with C# (first inversion - 6/3) as the bass, the G# is a consonance with C# and E, but E# is a consonance with C# and not with E. Since this clash happens only in the 5th harmonic, it is not as noticeable.
In an inverted chord with E (second inversion - 6/4) as the bass, the B is already a dissonance with C# though not with E and the G# we covered above. Here the clash happens already in the 3rd harmonic, it is a bit more noticeable. The second inversion can be considered a dissonance in some cases.
Although we disregarded harmonics of the higher notes and not really defined how much of a dissonance each note is with another, we do have a qualitative assessment and an understanding of the different sounds they give.
To add on to what user1803551 posted, two pianos playing the same pitch of C4 will sound the same harmonically. If you add an octave below it sounds a little bit different, if choose to add the octave above instead it's going to sound different even from the previous octave played.
So yes even though all the pitches in the chord are the same and serve a similar harmonic function they sound very different because of the intervals. Also, you'll probably run into a music theory class that will further explain that a chord such as an inverted V 4/2 will sound different from a regular V chord. A regular V chord sounds stronger when it resolves to a I tonic that it was establishing than any other cadence. Most music that wants to emphasize an ending uses a perfect V - I cadence because it sounds stronger.
