Why are there no cadences for the melody scale degree 4 and 6 in tonal harmony?

Question

A simple question yet I cant seem to find an explanation for this in either of my tonal harmony books. They all parrot each other and talk about cadences where the melody note ends on ^1 ^3 and ^5 over the tonic chord or cadences where the melody ends on ^2 ^5 and ^7 over the dominant chord. But what about the other scale degrees ^4 and ^6? Melodic phrases can end on these scale degrees too right and they will need harmonic support yet these are not in any of the cadences discussed.

Answer 1

In common practice style cadences are formulaic endings meant to affirm the importance of the tonic and dominant triads.

The standard formulas:

• V I authentic
• ...V half
• V vi deceptive
• IV I plagal (if you want to include that)

All of those formula involve either the tonic or dominant chord. The conclusiveness of each is determined by whether the final chord is the tonic.

In a deceptive cadence the typical voice leading is the deception part ^5 ^6 in the bass, with the other voices moving to ^1 or ^3, and where ^1 would be the usual tone to double. From the melodic point of view a deceptive cadence still moves to tonic chord degrees ^1 or ^3.

The hierarchy of common practice functional harmony, and especially the structural phrasing purpose of cadences is not egalitarian. The point is not to accommodate cadences to all scale degrees and diatonic chords. The point is to affirm the importance of the tonic and dominant chords.

This is a fundamental concept in tonality. Not all tones are of equal importance. The common practice style emphasized the relationship between a major or minor triad tonic and a major triad dominant. You could choose to emphasize different diatonic chords, like ♭VII I, and then maybe you could melodically cadence on ^4, but the tonality would not be common practice, it would be more like a modal style.

Answer 2

As you're well aware, there are four basic cadences (not including those more specific which seem to be used more in US).

They are:

Perfect and Plagal - ending ^1^3^5.

Imperfect - ending ^2^5^7.

Interrupted - ending ^1^3^6.

Those are using triads - 3 note chords. Add a fourth third, which is the oft-used next chordal note, and we get:

Perfect and Plagal - ^1^3^5^7.

Imperfect - ^2^5^7^4

Interrupted - ^1^3^6^5.

So, it appears there is ^4 coming out to play, and ^6 was there all the time!

I'm using the British labels - US use different names.

Answer 3

Doubtless your books discuss the four popular cadences, Perfect (authentic), Plagal, Imperfect (half) and Interrupted (deceptive). That's V-!, IV-I, something-V and V-vi.

Are we interested in just the final chord of each type? Then we've got ^6 in the Interrupted variety. You're right that none of the basic cadences end on a triad containing ^4.

I have no idea why, in my example below, B, C and D are classed as elementary types of cadence, A is not.

Answer 4

If you want to end a melodic phrase with ^4 or ^6 you cannot use a perfect, plagal, or imperfect cadence. The most common form of the interrupted cadence is V - VI, which would allow you to end on ^6, but not ^4. However an interrupted cadence is not restricted to dominant - submediant (V - VI).

From Wikipedia,

"A cadence is called 'interrupted', 'deceptive' or 'false' where the penultimate, dominant chord is not followed by the expected tonic, but by another one, often the submediant." (my emphasis)

If you play "shave and a haircut - two bits" (which ends on the tonic) with various final chords -

1. I gives you the usual perfect cadence
2. VI gives you the most common interrupted cadence
3. IV gives you a different interrupted cadence

The third cadence would allow you to change the melody to end on ^4 or ^6 instead of ^1, noting that the preceding melody note might also need to be changed to make melodic sense.

If you are using ^4 as your final note you can also use the interrupted cadence V - II.

Answer 5

On the harmonic possibilities for a cadence on melodic 4 or 6

The idea of a cadence, or course, is that it represents a point of (relative) stability in a piece of music, which is often desirable at the end of a phrase or the end of a piece. Harmonically, the tonic chord is the most stable, with the dominant chord also providing stability, though less than the tonic. The submediant chord also provides a sense of stability, since it can serve a tonic function.

When speaking in terms of triads, scale degrees 4 and 6 are harmonically problematic for cadences. 4 could be harmonized by VII, II, or IV, and 6 could be harmonized by II, IV, or VI (the last being covered by the deceptive/interrupted cadence). Here is why, except for 6 against VI, those are rare, at best.

The VII chord

In nutshell, the VII chord is simply too unstable to be a cadence-point in Common-Practice Tonality. There is no sense of rest, between the presence of both the leading tone and diminished fifth. (The V7 chord also contains both the leading tone and diminished fifth, but the presence of 5 stabilizes [in relative terms] the chord. In the V chord, of course, the diminished fifth isn't present, also helping make that chord more stable that VII.)

The II chord

The II chord doesn't have the stability problem of the VII chord, but it doesn't set up well to create a satisfying cadence. Notice that the penultimate chord in the three standard cadences is (usually) either the dominant chord (authentic, deceptive/interrupted) or predominant chord (half, plagal). Since the II chord can function as either a dominant or predominant chord, it's presence at a cadence point would tend to take on the characteristic of the chord preceding it. Thus, it would be perceived either as an extension of a half cadence or as a pre-dominant harmony, usually not stable enough for a cadence.

The exception here might be a phrase that ended I-II; a sort of half cadence with II standing in for V. However, this is certainly uncommon, at best, in the Common Practice.

The IV chord

This has essentially the same problem as the II chord, but without the II's exception of I-II. A I-IV cadence will tend to sound like a modulation, since I is also V/IV.

Answer 6

I've found a category of examples of cadences in the classical period where the melody has ^6 on a strong beat at the cadence. The category is sonata form, secondary theme in the dominant key area and the harmony is a half cadence - like a V/V.

• Example: Maria Hester Park, Piano Sonata in C major, first movement, measure 33, half cadence in G on a D major chord with A in the melody.

Obviously this won't do for ^4 because V/V has a raised fourth scale degree as its third.

I found a cadence with ^4 in the melody in the recapitulation of the same piece.

• Example: Maria Hester Park, Piano Sonata in C major, first movement, measure 101, half cadence in C major on a G7 chord.

I see your comment on Tim's answer about "triads only". I don't understand how or why you would impose that limitation. If you're asking "how to harmonize ^4 at a cadence", the answer is "with a V7 chord as part of a half cadence".

If every line besides the melody is playing ^5, ^7, and ^2 and the melody is playing ^4, then we will hear a V7 chord even though the ^4 is in the melody. That harmony works and is at least somewhat popular.

So your answer is half cadences in both cases.