4-bar analysis

Attention, there are 5 chords and not 4 measures.

So, between the first and the second there are no problems, I mean regarding how the voices are arranged, because E and G remain unchanged while C descends to B and the C in the bass rises to E; a contrary motion occurs between the bass and tenor, an octave-fifth between C-C and B-E, but between inner parts (to give you an example, not between "extreme" parts, as could be between the bass and soprano). The problem arises between the third and the fourth chord, at least if you intend to work strictly within the tonal framework; this succession of chords produces two consecutive fifths in direct motion in an ascending direction:

the "first" between the bass and alto (F-C / G-D), the second directly within the chord played by the right hand (A-E / B-F), so you find yourself with a double error in voice leading, an error which you can remedy by keeping the F in the bass steady instead of rising to G and arranging the third chord not with B-D-F, but for example with B-D-G; you would thus have a dominant seventh chord (the dominant in this case is G, the fifth degree of C major) with the seventh (F) tied. When possible, it is always advisable to keep common notes tied between the preceding and following chords, but even if it wouldn't be necessary to prepare the dominant seventh (by holding it tied from the previous chord) because it is of the first species, built on the fifth degree of the major scale, in this case you would be dealing with a dominant seventh in third inversion, meaning it is not built starting directly from G in the bass (I mean G in the bass, because harmonically you start in this case, in C major, from G to build the seventh, but the arrangement of the notes is not "regular"; in practice, instead of starting from the bass with G-B-D-F, you have F-B-D-G, and G is the root of this chord), so the preparation would be perfect since the seventh would not derive from leaps.

At the beginning of the second measure, descend with the F to E and resolve the seventh, while in the upper staff you can have C-E-G, with the G remaining tied from the previous chord and B-D moving in contrary motion, one rising, the other descending to C, thus doubling the root of the chord, namely C.

The succession in this case is: 2_4 / 6_3 or 6 (even if the G of the dominant seventh chord is actually at a real distance of a major 9th; the "descriptive" distance between F and G is logically a major 2nd; that 4 instead specifies the distance between F and B, the third of the G chord you are in, B which is also the leading tone of this scale and must rise to C.

It should also be noted that by using "tight" chords (like the first, third, fourth, and fifth), i.e., those that remain within a range below an octave, you have more difficulty moving the individual voices; it is better to use medium-wide and wide chords, respectively at the limit of the octave and above the octave in terms of the range between the notes that constitute them. For example, at the beginning, instead of starting with the classic C-E-G, you could start with E-G-C; that perfect 4th distance between the alto and soprano could help you better manage the subsequent harmonic development.

You must obviously follow what is your own musical taste, but if you want to respect the rules of tonal harmony at the same time, you must take into account many aspects related to the movement of individual voices and the whole as it is being formed.

This is just one example, but there could be multiple solutions.

Since I haven't studied for years, I hope I have remembered correctly and haven't written anything inaccurate.

I, with that C bass (mi fa sol do), would have harmonized it as follows:

I I6 II56 V7 I

This relationship between bass and tenor is already a bit complicated, it's something new for me..
What does I I6 II56 V7 I mean? I stands for first degree, II second etc., but what about the numbers?

After millennia, I am returning to this subject.
First of all, a distinction must be made between the bass line that you see written (real bass) and the bass that functions as the root in the chord you are analyzing.

This bass line can be summarized as follows, first defining the real bass (or melodic bass, the one you see written) and the harmonic bass (the one that, as I wrote a moment ago, constitutes the root of the chord):

Real bass:
I_I6_II56_V7_I (actually written: I_III_II_V_I)

Harmonic bass:
I_I_VII_V_I

The I6 would be a first inversion on the third degree (E, so the chord is, from bottom to top: C_E_G with the E written in the bass).
The third, II56, is a first inversion on the II with the seventh (B_D_F_A).
The V7 is a dominant seventh (G, the dominant of C major in this case); the seventh is built on the G: G_B_D_F.
In the "simplest" cases, the seventh resolves by descending to the lower degree; for example, the F of the V7 descends to E (E which constitutes the 3rd degree of the C major chord).

Another important thing to know to properly define what is being analyzed, always regarding the bass.
It concerns the definition of the bass at a melodic and harmonic level in a given context:

Root (Fondamentale)
Tonic (Tonica)

The root is the note played by the bass, regardless of the line that the latter follows.

The tonic is more specific; that is, the "tonic" is that note which, played by the bass or by another voice, is the first degree of the key (even a temporary one) in which we find ourselves.
This is an important distinction, if only at the level of definition.

I hope I have written correctly; it has been quite a long time since I last applied my mind to harmony, and moreover, I used to use a different numbering system.

"The fundamental is the note played by the bass, regardless of the line that the latter follows."

It is better if I clarify this point well: so, what I mean to say is that every single chord presents a note that, by necessity (unless it is omitted due to a specific choice by the composer, but that is another story), is the base upon which the chord is built (as we know from the bottom up); if, as in the case of the I6, you have E in the bass, one must be careful between definition and practice: the definition establishes E as the melodic bass and the third of this chord in first inversion, but the "true" bass of the chord in question is C, the fundamental and (precisely because we are in this key) the tonic of C major.

Instead, in the case of the II56, you have D in the melodic bass (the one written), but the fundamental in this instance is B, the seventh of the key of C major, therefore not the tonic (even though it is the note upon which the seventh chord on the II degree in first inversion is built) but still the fundamental.

Yannick wrote:

This relationship between bass and tenor is already a bit complicated, it's something new for me..

What does I I6 II56 V7 I mean? I stands for first degree, II second etc., but what about the numbers?

It means that the bass line will be: Do Mi Fa Sol DO and from low to high the chords will be formed by the following notes (in parentheses the interval distances from the bass):

Do mi sol (35)

Mi sol do (36)

Fa la do re (56)

Sol si re fa (357)

DO mi sol (35)

The numbers 35 are omitted, so

Do mi sol ()

Mi sol do (36 but also just 6)

Fa la do re (56)

Sol si re fa (357)

DO mi sol ()

so

I

I 6

II 56

V7

I

I made a mistake defining the II56 as the first inversion on the second degree.

The consequences of being away from study

So that VII (which seemed strange to me while I was writing) is a IV.

Something like this? (even here, tons of rust…)

I would say so, the only "rust" is the missing king in the 3rd beat.

ehehe, I had thought IV...

Don't worry, I'm the only one who should be ashamed since I don't lay a hand (or my head) on the harmony manuals (which, besides instrumentation guides and other educational texts, are practically jewels, let alone gold, diamonds, etc.).