...Some degrees are more stable than others (1, 3 and 5; 1 being the most stable) and some degrees are more unstable (2, 4, 6 and 7; 7 being the most unstable).
The unstable tones are called tendency tones.
...How does that [solfege/tendency tones] work if there is an underlying harmony?
I think the way to think about this is: solfege/tendency tones and functional harmony are just "two sides of the same coin." Solfege tones don't happen over a harmonic background, the solfege tones are the harmony! I don't mean to be glib. We don't fit solfege to pre-existing functional harmony. It's the other way around. When tones move according to characteristic patterns of solfege/tendency then functional chord identities emerge.
The easiest way to think about it is to consider the tendency tones
^7. Together they make a
viio6 chord which has a strong resolution to the tonic chord.
The next question that comes up is: "how to consider the dominant tone
^5?" The dominant can be a chord tone in both the tonic
I and the dominant seventh
V7 chord has a strong resolution to the tonic
I. This seems to case
^5 in an ambiguous role of both stable and unstable. Let's try to clarify this.
^1 and dominant
^5 are both stable degrees. The are the pillars of stability in tonal music! When a plain triad is built on
V is a stable chord! This stability can be clearly head in the half cadence. The leading tone
^7 is in the
V chord so it does resolve to
V should be considered stable as the music can cadence on it.
When the seventh is added to
V to make
V7 the chord becomes unstable.
FA has the tendency to move to
MI and that is the source of the unstability. My understanding (mostly from William Caplin's writing) is that the unstable
V7 would not be the goal of a half cadence.
So, the level stability of dominant harmony is the interplay of stability from
^5 and the instability of
^4. Especially important is which tone is the bass! While
V is stable,
V6 is not.
A similar interplay of tone stability happens with the
IV chord and
I. Obviously the
^1 degree in both chords is stable, but the
^4 in the
IV chord are unstable and resolve down to
^3 respectively. It is interesting to examine bass tones and inversions with these chords. With
I the inverted subdominant is obviously the unstable chord. With that specific voice leading we clearly hear
FA resolve down to
MI respectively. But, what if we use difference inversions and voice leading? With
IV the tonic chord is unstable and
IV becomes relatively stable. This movement can be interpreted as a tonicization of
IV in which case the movement of
However, if we don't have a tonicization and instead it's a move to a half cadence with
I6 IV V we get to another important concept: tendency tones do not always move according to tendency! Again, the harmonic context is critical. In this half cadence progression
FA is the stable root of
IV. Compare this to another harmonic context:
FA is in the bass, but as a chord tone it is the dissonant seventh of the dominant chord.
The examples above may be confusing, because the context keeps changing: tonicization changes the tonic, inversion makes stable chords unstable. But that gives us the background information for a generalization: tendency tones exhibit their tendencies when they are used in dominant harmony. In other words
I is where we see tendency tones in action.
LA as the tone with probably the least tendency, or perhaps the most ambiguity.
LA's tendency to move to
SOL is best understood by
I a contrapuntal movement to resolve the unstable
64 chord, or in cases like
V the move
SOL is about doubling the
V root instead of the chord 3rd/leading tone. The falling thirds sequence is a case where
LA doesn't follow the tendency to
I V6 vi iii6 - in this case
LA moves to
FA notice how that non-tendency movement doesn't involve
- tendency tones are most clearly observed in dominant harmony
- tonicization redefines solfege members and effects tendency
- chord inversion and counterpoint effect tendency
- tendency tones do not always move according to the baic definition