Usage of sharpened subdominant in minor key: what is the diatonic function?

Question

The piece Für Elise uses a D♯ in the key of A minor in the first bar, which is the sharpened subdominant. (I'm focusing on the first part, up to halfway through bar 23 in this score.) D♯ and G♯ are the only notes used in the song that aren't the A natural minor scale. As far as I understand, D♯ functions as a leading tone to the dominant of E, just like several minor-key songs have a leading tone (Für Elise included, using G♯ in bar 4). Is this the diatonic function of the D♯ note in this case?

(I'm beginning to suspect that this part of the song is actually in E Phrygian/minor/harmonic major and that the D♯ is a leading tone and the G♯ is a major third above the tonic, which is used in several minor-esque key songs.)

Answer 1

Pieces from this era are more easily analyzed from the point of view of Common Practice Period music theory. Beethoven was taught from a more contrapuntal and figured bass viewpoint than later composers. However, CPP theory was designed to cover music from about 1600 to 1900 (and works well for popular, country, Latin, jazz, etc.)

The piece is in A-minor (it can be seen from the cadences and from the title). The notes from A-minor are the same as those from C major with the feature that, in a minor key, scale steps 6 and 7 are mutable; these occur as a lower tone and an upper tone (the lower tone raised a half step). In A major, these steps are the notes F and G that often occur as F# and G# in some circumstances. (I have written about this somewhere on this site so I'll not repeat the several paragraphs there.)

In the quoted excerpt, the G# occurs in E major chords (though the raised G has a few other uses). The point (supposedly, according to the theorists and teachers) is to make authentic cadences stand out more. The dominant chord (built on E) very often (not quite "almost always") occurs as a major chord. In some pieces, non-cadential chords build on scale step 5 do not raise scale step 7; this may just be a convention but it works to separate phrases.

The other case (D# sometimes and D at others) occurs in major keys as well. The pattern: note, note step lower, note, is very common (it's called a "mordent" or sometimes an "inverted mordent"; theorists call it a "neighbor note.") The "upper" neighbor is usually taken to be in the prevailing scale; sometimes a whole step upper neighbor will be chromatically lowered (depends on which the composer likes better.) Lower neighbors are almost always chromatically altered (if necessary) to be a half step below the principle note. In the case given, scale step 5 (E) has a lower neighbor (D) that has been raised (D#). The second D in the first (and similar) measures is not altered as it moves downward to C. This isn't really an example of minor key mutable tones (steps 6 and 7); it's just the way ornaments tend to be played.

Answer 2

Let's start with the excerpt...

The key signature is zero sharps/flats, and the beginning harmony is Am & E with the final close E to Am so the key is A minor.

The D♯ of the opening two bars is a decorative figuration of an Am chord. The chord tones are highlighted in the image above in blue, while the non-chord tones are circled in red.

Non-chord tones can be found in diatonic and chromatic forms. The D♯ could be called a chromatic auxiliary or chromatic neighbor tone, being an auxiliary or neighbor of the Am chord tone E.

The B and D natural imply some kind of dominant chord on the third beat which would lead to the Am chord, but we can skip of that particular detail as it isn't directly about the D♯.

Chromatic non-chord tones are a common way to encounter tones from outside of the key signature. Some other ways to find chromatic tones are:

• the raised sixth and seventh scale degrees in minor keys
• secondary dominant harmony
• borrowed harmonies (usually chord borrow from the minor mode when the main key is major)
• certain chords that usually are in the "advanced" part of a harmony textbook like augmented sixth chords, neapolitan chords, or fully diminished seventh chords, those chord tend to precede the dominant chord

...an augmented fourth above the tonic of A...(I'm beginning to suspect that this part of the song is actually in E Phrygian, and that the D♯ is a leading tone

It's interesting that you describe the D♯ as an augmented fourth (A4) above the tonic A. Of course that is true, but I think there is a subtle distinction between relating the D♯ to the tonic A or the chord tone E. Speaking of an A4 above a tonic suggests, to me, an alteration of the diatonic P4 above the tonic, and alteration of the subdominant scale degree, which could possibly be functioning as a leading tone to E provided the harmony actually reflected that function.

If that were the case we would expect the D♯ to be part of a B, B7, or D♯dim, a type of dominant chord, moving to a E or Em chord. You could really make that particular harmonic function, and the A4 relationship, and subdominant alteration, by harmonically sounding the A and D♯ together, resolving it to G(♯) and E.

But, that does not actually happen. Harmonically it is just an Am chord with decoration. In this case the notable relationship is simply the half-step below the chord tone.

There is nothing phrygian going on, but that is another matter altogether. It would require a discussion of modal harmony. Suffice to say our harmony is clearly tonic/dominant and the mode is clearly minor. It's in A minor.

It seems strange that you know terms like augmented fourth, phrygian, natural minor, diatonic, leading tone, etc. but don't understand where chromatic tones come from. Don't take my comment the wrong way. I'm a little suspicious of your theory sources. You might want to get a good college level harmony textbook. Kostka/Payne, Harmony is a well known text. Piston, Harmony is another. There are others you could use, it might depend on what is locally available for you. Do some research. Find a well cited book from an author who is a professor of music.

Answer 3

For starters, it's entirely feasible to use non-diatonic notes in a piece - we get so many questions which pre-suppose it's 'against the rules'.

That D♯ note features many, many times, and is simply a chromatic use - nothing more, nothing less.