Notation. A plus ("+") character means play the notes at the same time. A hyphen ("-") character means play the notes and/or chords in sequence. C4 means middle C.
Some scale formula degrees and intervals convey a lot of suspense. Some have a little. And some have no suspense and are completely restful. Let's take a closer look.
7 is an unstable degree and it wants to resolve up a min2 to 1' (pronounced "one prime"). 1' is the tonic an octave above 1. You can think of it as 8 if you prefer. The tendency to move 7-1' is very strong, and it explains 7's technical name: the leading-tone. The leading-tone functions to lead the ear home to the tonic, and the ear gets there—at least in terms of anticipation—before the tune does. Here's a scale in the key of C. That penultimate 7 (the B4 note) keeps you hanging for a moment in anticipation of the eventual resolution to 1' (the C5).
Now consider the dominant triad, whose symbol is V. Like all major triads, V's formula is root+3+5. And in terms of I, V is the degrees 5+7+9. We can use that 7 (the 3 of V) to show another example of the 7-1' effect. We only need two notes from each triad, so we'll play just the root+3 of IV, then V, and then we'll resolve to I (5+root only). In the key of C, those triads (dyads, really, because we're only using two notes) are F-G-C. Just like in the example above, you'll hear the same B4 leading the way to C5 (and as you can see that's the only note that changes between the second and third chords).
The V-I cadence, or perfect cadence, is everywhere in music. Whenever you play V, and for as long as you sustain it, the leading-tone contained within it generates musical tension. We're conditioned to expect, and to want, that leading tone to resolve to the tonic. Relief comes only when V leads us back home to I (although, as we'll see later, 7 is not the only degree that plays a role in the V-I, or V7-I, resolution). This time, still in the key of C, we play full F-G-C triads with the root in the bass.
Another chord that contains 7 is iii. Like all minor triads, iii is root+b3+5 which, in terms of I, is 3+5+7. We can use the 7 in iii to resolve to 1', although the effect is not quite as strong as it is with V. In this next example, also in the key of C, there's something interesting about the B4 that's held for two beats in the third bar. It's just a 5 in the local tonal center of the Em chord. But when the final restful C provides some comparison by reminding us what the key is, the ear re-evaluates the instability of that B4 and decides that it really was a leading-tone.
So, 7 is the 3 of V (which is 5+7+9). And 7 is the 5 of iii (which is 3+5+7). The other triad that contains 7 is viib5, which is a diminished triad so its chord formula is root+b3+b5. In terms of I, viib5 is 7+9+11. You don't often hear a viib5 being played. But if you splice together a V (5+7+9) and a viib5 (7+9+11), you get a V7 chord (also called a dominant seventh chord) whose formula is 5+7+9+11. And a V7-I resolution is even more compelling than—and nearly as common as—a V-I. We'll talk more about V7-I on the Cadences page.
4 is also unstable, and it wants to resolve down a min2 to 3. For example, in the key of C, F wants to resolve down a min2 to E. Notice that 3/4 and 7/1' are the only two places in the major scale formula where a min2 occurs, and that the 4-3 effect involves a descending min2. Also, 4-3 is a milder effect than the leading-tone's 7-1'. Try playing the following series of notes and see if you hear it: (beginning with the fifth finger of your right hand) C5-B4-A4-G4-F4-(pause, then bring your third finger over your thumb)-E4. Or try playing a C chord (which includes E) instead of that last E4 on its own.
In this next example, we use dyads to highlight the F-E descent. This root+4 to root+3 change is the essence of a sus4 (suspended fourth) resolution.
The effect is clearer when we add 5 to form a triad. Here, the tonic sus4 triad (root+4+5) resolves to the tonic triad (root+3+5). In the key of C, that's Csus4-C.
A 4-3 effect doesn't have to involve the 3/4 of the key, either. It can be the 3/4 of a local tonic. Let's demonstrate with a sus4 that's not the tonic sus4. Here's a piece in the key of C, meaning that the whole piece can be viewed in the context of the global tonal center of C (with a major modality). Nested within that global tonal center, two G chords establish G as a local tonal center (a temporary tonal center). While this local tonal center of G lasts, the G note takes the role of 1, and then B is 3, C is 4, and D is 5. So, looking at the piece from the beginning: the opening C chord establishes itself as I. Then the Gsus4 (Vsus4) sets up a local tension that resolves to G (V). From the perspective of the local tonal center of G, this is actually a Isus4-I resolution. But resolving to that G triad only reveals its true identity as V of the global tonal center. As V, it embodies an even stronger tension than the local sus4 did, and it now wants to resolve back to C (I).
It's significant that the local 4-3 resolution (the notes C5-B4) of the Vsus4-V cadence is the exact reverse motion of the much stronger global 7-1' leading-tone resolution (the notes B4-C5) in the V-I resolution that follows. It's as if resolving the sus4 this way is suddenly revealed to be a blunder, like moving a pawn out of harm's way but by the same move discovering an attack on your Queen. In any case, these same two notes, even when played in opposite motions, still function as resolutions of different kinds relative to different tonics.
In this next example, we experience the tension of sus4 but we resolve it in a different way. Let's listen to an A4 note repeatedly sung over different piano chords in the key of A major. The A4 is 1 in the global tonal center of A. Relative to the local tonal center of the F#m triad (vi), the A4 is b3 and it feels restful. Relative to the D (IV), the A4 is 5 and it feels restful still. Then another F#m. But then, over the E (V), the A4 is 4 and the piano harmony and the vocal melody at this point combine to form an effective Eadd4 chord. And that 4 sounds suspenseful and at odds with the 3—the G#4—a discordant min2 below it. In this example we play an A chord, which resolves both the sus4 effect and the 7 effect in the V chord.
In that example, the E chord and the A4 note are like two story characters in conflict with one another due to some incompatibility or competition. Their conflict generates drama until it is resolved when "somebody bends" to quote a Howard Ashman lyric (which reminds us that suspense and relief lives in romance just as much as it does in antagonism). The E chord gave way in the example above, and became A. If we'd taken the 4-3 resolution option, we'd have kept playing E and dropped the A4 to G#4. But that would still have left the V unresolved. Another option is to raise the A4 to B4, and another is to change the chord back to an F#m or to a D. Try it out yourself on your piano or keyboard, and experiment with resolving the suspense. Either sing the A4 note, or else play it with your right hand.
To my ears, the sung A4 seems to rise slightly in pitch as it coincides with that final concordant A chord, as if the force that the E chord was previously exerting on it, trying to pull it down to G#4, has been released. Does it sound that way to you? I only recorded that sung A once (there are five repetitions of that identical recording in the mp3 above) so any changes we hear in it are an illusion. The parallel in drama would be that even the character who doesn't "bend" seems somehow changed by the change in the other, or else is returning to normal after having been adversely affected by the stress of suspense. Psychologically, a change in a thing's surroundings can affect our subjective perception of it. This applies to colors; and to the perceived sizes of objects in illustrations; even spoken syllables can be perceived differently if, at the same time, we're shown video of a mouth appearing to make a different sound.
Ok, so we know that 4 (which is a per4 above 1) is unstable and wants to resolve down to the more stable 3. But is it the scale formula degree that's unstable, or the interval? The answer is subtle: the scale formula degree is unstable because the per4 occurs between those two particular scale formula degrees. To make this clear, let's talk about the cases in which a per4 gives a sense of suspense and the cases in which it sounds restful.
You'll recall that we refer to the very lowest note heard at any given time as the bass note. If a per4 exists between the bass note and another note then that is considered a suspenseful interval. In the first two examples in the effect of 4 segment above, the per4 is between the bass and another note. And in those examples the per4 sounds suspenseful. Those examples are meant to represent sus4 chords, which is a kind of chord named for the situation where a note is supended (or held over) from a previous chord and forms the 4 of the following chord in place of its 3. The expected resolution for a sus4 is just to lose the 4 and restore the 3.
In a second-inversion triad, the bass note is a per4 below the root note. So that should mean that second-inversion triads are inherently unresolved. If you think of IV in second inversion (formula root+4+6), then the resolution would be to I (root+5+7).
Getting back to the cases where a per4 is suspenseful or not. If the per4 does not include the bass note (it's between higher notes) then suspense depends on whether the two notes forming the per4 are notes of the triad being played (taking the bass note into account). If the notes are notes of the triad then the per4 sounds restful; if they are not notes of the triad then the per4 sounds suspenseful. There are examples of both of these cases in the third example in the effect of 4 segment above. The C chords that begin and end the example are played in first inversion (3+5+root), and that gives us a per4 between the upper two notes. Those notes are G and C (5 up to 1), which are notes of the C triad (C+E+G), so the effect of that per4 is stable. But drop the E note to D, as we do in the Gsus4, and that same per4 between the same notes now functions as a sus4 (1 up to 4). The C is now not part of the G triad (G+B+D) and so the per4 is now unstable. And so the next step of lowering that C5 to B4 stabilizes the sus4 chord into a restful G major (we'll come back to this chord in a moment) and then we complete the sequence with a V-I.
In this next example, after hearing a Csus4 in root position (containing a per4 involving the bass, therefore unstable), the root is moved an octave higher to put the chord in first inversion. The F and the C notes are now a per5 apart but, ignoring octaves, the shortest distance between them around the tone clock is still a per4. And one of those two notes is still in the bass, so the interval is still unstable, as you can hear. In fact, because F is not a note of the triad, the instability would remain even if the bass were not involved in this per4. As expected, it is resolved by dropping the F to E.
You may have noticed that there's another per4 in that third example in the effect of 4 segment above that I haven't yet mentioned. It's the one in the Gsus4 and G chords between the D and the G notes. The D is the bass note, so theory says this per4 is unstable. But between the Gsus4 and the G we only resolved the higher per4. We didn't address the lower per4, which is the result of the G being in second inversion. We sidestepped the issue and just moved straight from V back to I in the global tonal center of C. But we have other options. For example, we said above that we can resolve a second-inversion triad in a IV-I movement. So what if we'd instead treated that G chord as the IV of D major and then resolved to I. Let's see how that looks and sounds.
Another option is to look at that Gsus4 in a different way. Instead of it being a root+4+5 formula (sus4) relative to G, we can choose to interpret the same D+G+C notes as a root+2+5 formula (sus2) relative to C. Once we see it that way, it's a sus2 at the bottom of the chord that we need to resolve, and not a sus4 at the top. And once we've resolved that sus2 (by moving to a C major chord), the lower per4 is gone and there's nothing more to do.
This last example is interesting because it seems to offer an explanation for the perhaps mysterious nature of that suspensefulness. In the case of the per4 between G and C in the Gsus4/Csus2 chord, the suspense feels like it's a result of ambiguity. We're not sure what we're hearing: should we interpret that per4 as being between 1 and the 4 above, or between 5 and the 1' above? They're two sides of the same coin, and the suspense lasts until either the per4 changes to a maj3 by moving the C note (so the per4 was 1 up to 4), or else any doubt about whether or not the C note is a note-of-the-chord is removed by moving the D note (so the per4 was, and still, is 5 up to 1'). Once we choose either of those resolutions, the ambiguity disappears and so does the suspense. It's the same in stories and jokes: suspense (and the relief that eventually follows) is due to uncertainly, ambiguity, and double-meanings.