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In Beethoven's Moonlight Sonata 3rd movement, I'd like to understand the Fx (double sharp) in measure 8.

excerpt

Measure 8 has a bass of A and an arpeggio with the notes C# E Fx C# which sounds like an A7, but the Fx can't be the seventh, since otherwise it would have been written as a G. If it's not, it serves a specific purpose that I don't get.

With Fx, this chord would be more like an A6, but with an augmented sixth... which I think is unusual.

Is there a reason to avoid the dominant 7th by keeping the "F" name?

Putting measure 8 in context: the previous measure 7 is F#m, and the next measure 9 is G#. I'd like to think that this may be a II-V-I chord progression, and I would expect in that sense a C#m chord. A7 would be the relative major so that would fit...

Would it be the C#m I expect, but with an "augmented sus4" (that sounds like G natural...) and on top of an A bass?

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    "which I think is unusual": not in the 19th century! In fact the augmented sixth chord has its roots in the early baroque. It's enharmonically equivalent (and typically functionally equivalent) to the tritone dominant seventh substitution of jazz theory.
    – phoog
    Sep 22, 2023 at 19:54

3 Answers 3

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This is an augmented sixth chord. Whereas an A7 chord would be expected to resolve to D, an Aaug6 chord resolves to G# — as can be seen in the score.

Augmented sixth chords arise from the b6 of a minor key and contain b6 and #4. Given that this movement is in C# minor, the b6 is A, and the #4 is Fx. The interval of an augmented sixth resolves "outward", to the octave (G#), giving the V chord, which then typically resolves to the I chord.

This particular chord is known as a "German" augmented sixth. The name is traditional and has no known connection to the region. There are three types of augmented sixth chords:

  • German: b6-1-b3-#4 (sounds like a dominant seventh chord)
  • Italian: b6-1-2-#4
  • French: b6-1-#4
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    Does the German look like a dominant seventh, or does it sound like it?
    – Richard
    Sep 21, 2023 at 10:04
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    @Richardissteppingdown thanks. I was picturing a piano keyboard.
    – Aaron
    Sep 21, 2023 at 10:17
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A supplementary answer here, let's consider the voice leading in this harmonic motion:

  • A C# F#
  • A C# E F##
  • G# B# D# G#
Voice leading

There's only one note which really moves between the first two chords: the submediant (scale degree 4) F# getting raised up a half step to F## and then again to the dominant (5) G#. This is a really common voice-leading pattern, 4 - #4 - 5, and you see it in many common chromatic harmonies of this style.


Functionally equivalent chords

As you may notice, this crops up in every type of augmented 6th chord, and this voice leading movement explains the funky spelling of the augmented 6th interval formed over the chord root. It also appears in the common secondary dominant V/V, where the major 3rd of the chord is the #4 of the key. Same with the vii°/V, spelled off of the #4 degree since by definition that's the leading tone to the dominant. Incidentally, in jazz, the tritone substitution sub(V)/V has the same notes as the classical German augmented 6th, but spells it as the key's b5 because the note tends to resolve down to the chordal 7th (scale degree 4) of the dominant.

Often times, complex harmonies can be best understood from the horizontal voice leading perspective; if you understand why certain notes lead to others, strange-looking chords will sort themselves out quite handily.

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  • "because the note tends to resolve down": I always figured it was because A7 is a much more straightforward chord symbol to write than whatever you'd write for a "properly" spelled augmented 6th (and I've assumed that this led to tritone substitution theory rather than the other way around).
    – phoog
    Sep 22, 2023 at 19:58
  • That's also a fair point. Personally I like the resolution-based spelling because it's a nice instructive principle about chromatic spelling, but the actual jazz history might have been more about simplicity.
    – user45266
    Sep 25, 2023 at 18:44
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Look at the following chord, which is G# major. So the F## has some sort of secondary leading note character. This means that chord should be some variation of a D# dom. chord. Given we have the notes c# and f## we have 7th and 3rd. We also have e (m9th). This form a classic diminished 7th chord on the leading note as substitute for the dominant (just leaving out the 3rd (the 5th of the dominant chord)).

The A in the bass works as a second phygian leading tone and is the diminished 5th of the dominant chord. So this should be seen as a D# b5 7 b9 chord without the root note.

Regarding II - V - I: This does not work out exactly. Basically this is a not that uncommon progression IV - #IVø - V, so reaching the dominant chromatically from the subdominant by sharpening the IV into a secondary leading tone. As already elaborated this is functionally equivalent to a IV - II7 - V progression.

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    The downvote is probably because the secondary dominant is a less convincing explanation than the Ger+6 explanation... or possibly because this answer talks about a diminished 7th chord built on the F## leading tone where there is none (the A would have to be A#). Nevertheless, the comparison to the secondary dominant D#7 is interesting, both serve similar function to the jazzier tritone substitution concept.
    – user45266
    Sep 21, 2023 at 17:49
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    @Lazy - Weird, I've read "'root position' augmented 6th chords should be treated as inverted" more often than "augmented 6th chords are dominant(-function) chords with omitted roots". In fact, your post is the first time I've read the latter.
    – Dekkadeci
    Sep 22, 2023 at 5:43
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    @Dekkadeci There’s a first time for everything :). The said reading can be found e.g. in Schönberg’s treatise on harmony.
    – Lazy
    Sep 22, 2023 at 8:25
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    Augmented sixth chords do not have a dominant function; they have a pre-dominant function.
    – Aaron
    Sep 22, 2023 at 9:20
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    @Aaron Not dominant, secondary dominant. The dominant of the dominant.
    – Lazy
    Sep 22, 2023 at 15:24

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