# perfect 4th in third(3rd) inversion and more

I know that a perfect 4th is dissonant at above the bass, but some explanation says that: "If the note closest to the bass is not a 4, (like a 42 chord of 3rd inversion) that is not dissonant.(not sure write, more exactly "3rd inversion 4th is not to be resolve unlike 2nd inversion") But why? I don't understand the reason.

And if that is possible, is a perfect 4th in a 43 chord (second inversion of a 7 chord) not dissonant?

Why is this possible? I can't find any explanation.

• What type of seventh chord are you asking about? For example, a dominant seventh chord in third inversion contains an augmented fourth, not a perfect fourth. Commented May 5, 2022 at 3:25
• GBCE <-- in c major c is perfect 4 Commented May 5, 2022 at 3:30
• but main question is why 'If the note closest to the bass is not a 4, that is not dissonant'? Commented May 5, 2022 at 3:31
• ah, you ask third inversion . BCEG in c major or g major .. Commented May 5, 2022 at 3:40
• You say "some explanation". Whose explanation? Is that Palestrina or your cousin Joe? Commented May 5, 2022 at 14:39

...but some explanation said...

I think the exact source would help to make sense of the writer's intention.

There are three ways I think of defining "dissonance." The first two are very standard concepts.

• Contrapuntal practice: perfect unisons, octaves, and fifths; and major and minor thirds and sixths are consonant all other intervals are dissonant.
• Acoustic: simple interval ratios are more consonant that complex ratios, so the unison 1:1 is most consonant, the octave 2:1 is next consonant, and so on. 3:2 is a perfect fifth, 4:3 is a perfect fourth, and 5:4 is a major third.

The third idea is sort of my own mixed with an old idea called klang, or "chord of nature", and a bit of acoustics for the harmonic series.

• A root position major triad is the principle consonant harmony. Changes to that chord - the minor form, altering the fifth, extending it with sevenths, ninths, etc. and inverting it so thirds become sixth, fifth become fourths, etc. make the chord less consonant, less stable.

By the acoustic measure, the perfect fourth is not dissonant. It would be consider more consonant than a major third!

By contrapuntal practice, which carried over to centuries of harmonic practice, the fourth is a dissonance that normally will be resolved to a third. In this practice the only thing that matters is the relationship of the tone which forms a perfect fourth in relation to the bass. In cases like parallel 6/3 chords the perfect fourth formed by the top two voices does not constitute a dissonance concern. The dissonance of a perfect fourth between the bass and any upper voice is not mitigated by any other additional voices.

By the "chord of nature" concept, the perfect fourth is an inversion of a consonance, which makes it a dissonance and unstable. (Again, that is my personal take on the topics involved.)

...If the note closest to the bass is not a 4, (like 42chord of 3rd inversion) that is not dissonant...i can't find any explanation

Based on the music theory sources I know, you will not find an explanation, because that statement is contrary to how things are taught.

Possibly the author meant something like when a chord is just harmonic filler between a proper bass and melody that chord doesn't need to be treated with traditional contrapuntal/voice leading rules. There are plenty of examples of that in various styles. But if that is the intention, the particular way you phrased the "rule" isn't clear.

I think you would need to go back to the original source to get a better explanation.

EDIT:

Original source, an online discussion...

(him) :The reason that the 4th note of 46 (triad chord 2nd) has a particularly different tendency to descend is that the closest note from the bass is a 4th away (perfect 4th) in the old days, it was a dissonant interval, and it was because of the remnants of the counterpoint that solved this, not the root. The 7th chord 3rd isn't like that, so it's different from the triad chord 2nd –

(me) : Even the 7th chord 3rd inversion is the same 4th away from the base, right? If 'closest note' means that it is the closest note to the chord, do you mean that the 7th chord is different because the closest note to the bass is not the 4th, but the 2?

(him) : yeah, right.

I still think the "closest to the bass" explanation is either plain wrong, or at least unclear, because the explanation does not specifically give the scale degrees nor the resolution of the dissonant fourth.

These details...

(him) : ... 46 (triad chord 2nd) ... the closest note from the bass is a 4th away (perfect 4th) ... (me) : Even the 7th chord 3rd inversion is the same 4th away from the base, right? ... (him) : yeah, right

...are still unclear.

All the diatonic seventh chords in third inversion have a perfect fourth above the bass except the dominant seventh chord. That distinction is not insignificant, because depending on the type of chord `V4/2`, `ii4/2`, etc. the resolution differs. But, I think it can still be explained with a few examples.

I think we need to few guidelines up front.

• When looking at "standard" harmony and voice leading issues, the context is often chord root progression by descending fifth.
• Dissonance handling involves attention to potentially three factors: preparation, dissonance, resolution.

The chord discussed is a second inversion (6/4) triad, and while the discussion didn't specify, I assume the case to me a major or minor triad. The typical place to find a 6/4 triad are with the tonic `I` or dominant `V`.

• The notes in blue indicate the voice with the dissonant perfect fourth.
• prep. in the first case means preparation, which is the first occurrence of a consonant pitch that is next repeat but as a dissonance
• sus. in the first case means suspension which is the particular non-chord tone name for the pitch creating the dissonant fourth above the bass.
• res. is the resolution of the dissonant fourth, which is accomplished by moving the voice above the bass down a step to form a third.
• appog. in the second case means appoggiatura which is the particular unprepared non-chord tone name for the pitch creating the dissonant fourth above the bass.

The second chord discussed is a third inversion (4/2) seventh chord. The discussion seems to be looking at any type of seventh chord, except a dominant seventh chord, but the handling will be the same. We can cut to the case as just show all the diatonic 4/2 chords being resolved via a descending fifths sequence.

• The green notes show the dissonant perfect fourth, but in this case the resolution is different that the triad, both voices move by contrary motion to a sixth.
• each two chord iteration of the sequence follows that same voice leading resolution of a fourth resolving by contrary motion to a sixth.

It doesn't matter how the voices are arranged as long as the chords are still 4/2 chords resolving to 6/3 triads.

Another version of that sequence uses all seventh chords.

• In this case the dissonant fourths, whether perfect of augmented, resolve by the bass voice moving down a step to form consonant perfect fifths.

The conclusion of this is: just because the upper voice of a dissonant fourth does not move in some of the possible resolutions does not mean those fourths are not dissonant.

The thing that is dissonant is the interval.

How the two voices forming the dissonant move to a resolution is the detail of voice leading.

There is a scientific basis for consonance/dissonance. With pure tones, 2 notes are considered consonant if the ratio of their frequencies is a low whole number ratio (eg 2:1, 3:2, etc) or closely approximates such a ratio (Equal tempered intervals are slightly out of tune and can therefore have wildly complex ratios, but we still hear them as the simple ratio, just slightly off.) The lower the numbers, the greater the consonance. With the complex sounds generated by real musical instruments, it's more complicated because each note is made of many pure tones (its partials). But it's basically the same principle. Two notes are considered consonant if one's partials are consonant with the other's. This explains why a 4th is more dissonant than its inversion, a 5th. You can prove this to yourself by writing out the harmonic series for C4, F4, and G4 and comparing them.

We mostly hear the stronger lower partials. In theory, harmonic series are infinite, but in reality they quickly fade to nothing and/or extend beyond human hearing. So realistically we only care about the first several partials. Consequently, dissonant intervals sound less dissonant when the notes are widely spaced because those stronger lower partials are separated registrally so they clash less. This explains why a 4th between the bass and tenor voices (eg C3 and F3) will sound more dissonant than a 4th between the bass and soprano voices (C3 and F5).

Also note that consonance/dissonance is a spectrum, not a binary classification. Intervals can be more or less consonant, and the same interval can sound more or less consonant in different contexts.

Finally, which intervals we consider to be dissonant evolves over time, and some of these "rules" that have been handed down since the classical era or earlier simply don't apply to modern listeners. This is my way of saying that the advice you're quoting is perhaps a useful rule of thumb at best, but I wouldn't take it as gospel. Use your ears and do what sounds right to you.

Dissonance, in music, means: "tends to move" or "unresolved"; it has little to do with acoustics. Consonance means, "tends to remain" or "resolved"; again, little to do with acoustics.

It's a contextual context; intervals or chords are dissonant or consonant according to their use, not necessarily by their construction.

The general assignments of consonance and dissonance in early polyphony are:

Perfect consonance: unison, octave, perfect fifth, perfect fourth (with a caveat). Imperfect consonance: major third, minor third, major sixth, minor sixth. Dissonance: major second, minor second, major seventh, minor seventh, all augmented and diminished intervals, perfect fourth (caveat = dissonant against if lowest interval.) All intervals needing an explicit sharp or flat is also dissonant.

One can discriminate more finely or change things around, but the list serves pretty well. It allows for some short descriptions of procedures. Particularly, the procedure with parallels in counterpoint. "Always approach a perfect consonance by contrary motion" works as a pretty good guideline.

The problem with perfect fourths is that chords like G-C-E have usually been treated quite differently from C-E-G or E-G-C; the latter two are treated as consonant and the G-E-C has been treated as dissonant. In cases like F-D-A followed by G-C-E followed by G-B-D, etc., the G-C-E has been treated as a G with two suspensions C-E moving to B-D. Other cases like G-B-D then G-C-E then B-D-G have been treated as consonant (passing chord) but I think it's really the same as the cadential 64.

After all that, the 6-3 chord E-G-C is treated as consonant because the intervals are measured against the bass. (Parallels seem to be treated against all other voices as these are melodic problems having to do with the independence of voices.) The diminished 63, like D-F-B, gets treated almost like a consonance in older style counterpoint as the D-F is a third and the D-B is a sixth and these are consonant intervals. The main point is that consonant intervals need not be resolved nor prepared in any particular manner, but dissonant intervals do.

As an aside, in blues harmony, the functionality of the harmony is provided by the root movement of chords. One basically has I-IV-I-V-I as a harmonic pattern with each chord decorated by a minor seventy I7-IV7-I7-I7. In this style, the sevenths are not treated as dissonant.

### Summary

Seventh chords all have a root, a third, a fifth, and a seventh. Within the chord, the root, third, and fifth are considered stable tones, but the seventh is required to resolve.

In a second inversion seventh chord, the bass — the chordal fifth — forms a fourth with the root. When these form a perfect fourth (as is always the case except in half- and fully-diminished chords), and since these are both stable tones within the chord, they don't have to resolve.

However, in third inversion, the bass — the chordal seventh — forms a fourth with the third. The seventh is required to resolve, so no matter whether a perfect or diminished fourth is formed, the interval is considered dissonant in the sense that one of the pitches is required to change.

### Examples

Major seventh chords

Consider a chord like C-E-G-B.

• In second inversion we have G-B-C-E, containing a fourth between G and C
• In third inversion we have B-C-E-G, containing a fourth between B and E

The reason the fourths against the bass resolve differently is because different chord tones are involved. The G and C are both stable tones within the chord, so they need not resolve; however, the B, being the chordal seventh, must resolve, which means the B-E fourth resolves.

Minor seventh chords

The situation here is essentially the same. Given C-Eb-G-Bb we have:

• second inversion = G-Bb-C-Eb
• third inversion = Bb-C-Eb-G

Again, the G-C fourth is stable within the chord, but the Bb, being the chordal seventh, must resolve.

Other seventh chords

In dominant, half-diminished, and fully diminished seventh chords, at least one of the fourths is not a perfect fourth. So the 7-3 fourth must either resolve by virtue of involving the chordal seventh or because it both involves the chordal seventh and forms a diminished fourth with the chordal third.