It is said and felt that (in major keys) scale degree 4 has a downward tendency, a tendency to release its tension at scale degree 3. It is said and felt that (in major keys) scale degree 7 has an upward tendency, a tendency to release its tension at the tonic. But why should this tension arise in the 1st place, and why should the resolutions point so strongly to the tonic and the mediant of what is now known as the major scale?

Tendency is a very important quality inherent to each note, and not uniquely those of the major scale (the tendencies of the notes F and B will also apply to the A minor scale). As a matter of fact, tendency has nothing to do with scales. It might even be the other way around, tendency actually being an important element in "creating" scales by determining the specific disposition of tones and semi-tones.
     For each note, there are two levels of tendency -
          (a) Global tendency is Chrominicism itself - the sharper a note is with respect to its Window, the more it has a tendency to ascend, and the flatter is it, the more it has a tendency to descend.
          (b) Local tendency depends on the Voice-leading of the Orbit of this note, whether it ascends or descends, especially if it is a secondary note.
     These two tendencies will, at times, coincide, providing the chord with maximum strength, and, at other times, conflict, depriving the chord of its strength. If the two tendencies coincide, that note will have a strong resolution. If they conflict, that note will have a weak resolution. The strength of resolution of the complete chord will depend on the sum of its parts.
EXAMPLES -
     G7 is strong because the tendencies of the two secondary notes coincide but Am7 is weak because the descending G is only slightly flat but mostly because the ascending C is quite flat.
     The same note, in the same Window, may have a completely different local tendency on another chord - the Voice-leading of the note B is ascending on the chord of G7 but descending on the chord of Cmaj7. Since the note B is the sharpest in the natural Window, it will have a strong resolution on G7 but a weak one on C maj7.
Many thanks for bringing this up - a very, very good question.

Your news of December 2003 led me to your new version of tendency in the CQ where the question concerns the notes F and B in the Key of C. However, also in C, when one speaks of the leading tone, one only speaks of the note B . Knowing how you like to invert things, I thought it might be possible that the F could be the "inverted" leading tone in the key of A minor ?

Yes it is, but we will need new definitions to elaborate this topic (here again, with no scales involved) -
     The TONIC chord of C has 2 Leading Tones placed at a semi-tone distance from its FRAME
          a diatonic Leading Tone B placed below the FRAME, the MEDIAN of the DOMINANT G7, and
          a chromatic Leading Tone Ab placed above the FRAME, the MEDIAN of the DOMINANT Fm6.
     The TONIC chord of Am has 2 Leading Tones placed at a semi-tone distance from its FRAME
          a diatonic Leading Tone F placed above the FRAME, the MEDIAN of the DOMINANT Dm6, and
          a chromatic Leading Tone G# placed below the FRAME, the MEDIAN of the DOMINANT E7.
               The G# as Leading Tone of A minor should come as a surprise to no one.
All the FRAMEs in the Window have their 2 Leading Tones (mostly chromatic) -
     The FRAME F-C has both the E (from C7) and the Db (from Bbm6).
     The FRAME G-D has both the F# (from D7) and the Eb (from Cm6).
     The FRAME D-A has both the C# (from A7) and the Bb (from Gm6).
     The FRAME E-B has both the D# (from B7) and the C (from Am6).
A chord may very well possess both Leading Tones of the following chord -
     The chord of G7 with a flat 9 (for which we prefer the Chord Symbol G7s-2) has both
          the First Leading Tone B, the MEDIAN, and
          the Second Leading Tone Ab, flat 9, the Superior Chromatic Non-chordal Tone of the COMMON TONE.
     The chord of Fm6 with a sharp 4 (for which we prefer the Chord Symbol Fm6p+4) has both
          the First Leading Tone Ab, the MEDIAN, and
          the Second Leading Tone B, sharp 4, the Inferior Chromatic Non-chordal Tone of the COMMON TONE.
               The functions of the notes B and Ab are exactly reversed (for either C major or C minor).
     The same would apply to the chords of Dm6 and E7 in A minor (or major).
The reputed jazz guitarist Joe Pass (an Italian by the name of Giuseppe Passalaqua) once proposed that -
          a dominant seventh chord (like G7) can posses either a major ninth A or a minor ninth Ab, but that
          a minor seventh chord (like Dm7) can only posses a major ninth E and not a minor ninth Eb.
     Why ? Because one must have the first Leading Tone before applying the second -
          G7 has a MEDIAN B and therefore can support either the A or the Ab, but
          Dm7 does not have an MEDIAN F# and can only support the E and not the Eb.
Many thanks for your question, it was a beauty !

It seems to me that root motion sounds generally major when it moves up a 4th, 2nd, or 6th, and it sounds minor in the opposite direction. I think this can be explained through your explanations of tenant chords and chord shadowing (I don't remember the difference). Does this sound right to you guys?...

We are not quite sure what you mean by a root motion sounding "major" or "minor." The terms major and minor are usually used to describe the mode or quality of a single chord, i.e., whether it has a major or minor median (third), or as descriptive of a tonality or key center, i.e., whether its Tonic Chord is major or minor. It occurred to us that by major sounding root motion you may mean root motion that descends by 5th in a flattening direction, which would be the predominant direction within the fundamental major mode (as well as the chromatic minor mode - see Four Strong Modes on the website). If this is this case, then your observations seem correct, as an ascending 4th is a descending 5th, an ascending second is really a Metamorphosis 4 followed by a descending 5th progression, and an ascending 6th could be a descending 5th progression in which the second chord (1) has undergone Metamorphoses 1 and 4, or, (2) more simply, is an incomplete or "deceptive" triad. Is this what you meant by "major" root motion - that which descends by fifth?

If so, then it appears that your statement is accurate, although the choice of the term "major" to describe this is probably not the best. By the way, Tenant chords are neighboring chords that are used to embellish the main chord by taking part of the rhythmic value of the main chord. So tenant chords are a very RHYTHMIC operation. Chord Shadowing occurs between two tetrads, one in the major half, one in the minor half, of the diatonic window, that share the same four notes.

...For example, when C goes to Em either the C shadows to Am then to Em, or the C goes to Em which shadows G. either way the progession is sharpening (up a 5th).

This is correct, however, in your second example it would be more clear to say "C goes to G which shadows Em" instead of "C goes to Em which shadows G." Also, don't forget that C to Em might not involve a progression at all! The C and the Em might very well both be incomplete versions of a Cmaj7 tetrad. The first being a "real" triad, the second being a "deceptive" triad. See Harmony/Transformations/Incompleteness on the site.