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The image above shows, from Bach 371 Chorales, No. 3 "Ach Gott vom Himmel sieh darein" in E Minor.

I think my analysis is totally wrong, but I just wrote it down on the image to try it out.

1. I can't figure it out why F#(G) in the first red box is used

I think that this F# is not for a secondary dominant, secondary diminished, borrowed chord, or modulation. Can you use a chromatic passing tone like that? I think not. So I don't know why that F# came out (As a reference, 'F natural' didn't appear before.)

2. Second red box

I believe there is modulation in this part, but I cannot be sure.

If there is no modulation, I can't explain the progression in the last measure.

If there is modulation, can you use A melodic minor chord as a pivot chord? Because there seems to be only the A melodic minor chord that can be the pivot chord. (for exactly 'ascending melodic minor')

I can't figure it out. So I would be very grateful if you could help.

  • Bach didn't write chordally. He wrote separate lines, some of which do translate that way, but trying to dissect his work harmonically won't work too succssfully.
    – Tim
    May 20, 2022 at 6:52
  • @tim lot of people here say like that and i kinda get it.. But I'd like to know if there's a way to proceed that I'm not aware of.
    – guss2222
    May 20, 2022 at 7:01
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    It may help to follow each line of music (satb) and decide why Bach wanted those notes to follow.
    – Tim
    May 20, 2022 at 7:53
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    @Tim harmonic analysis of Bach chorales is bread and butter of music theory. You're right that not everything fits nicely into common practice tonal harmony, but it's not correct to say that Bach didn't write chordally -- rather, the Bach's chordal theory was somewhat different (principally, it didn't include the modern concept of inverted chords, so D-F-A and F-A-D were considered to be distinct chords). I'll post an answer in a little while.
    – phoog
    May 20, 2022 at 8:26
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    Partly based on the chat for the accepted answer, I have reason to believe that the Bach 371 Chorales, No. 3 "Ach Gott vom Himmel sieh darein" is, in fact, not in E minor as claimed, but in A minor with the "Dorian" key signature picked (see the Toccata and Fugue in D minor, BWV 538, "Dorian" for an infamous example of this tendency).
    – Dekkadeci
    May 20, 2022 at 16:05

2 Answers 2


I can't figure it out why F#(G) in the first red box is used

There should be no accidental, since there's an F♯ in the key signature. Both the Bach-Gesellschaft edition and the Neue Bach-Ausgabe print this F♯ without an accidental. (Both are available at IMSLP; note that this chorale, unusually, appears at the beginning of the cantata.)

F♯ is diatonic to E minor, so this is just a regular passing tone.

For the note to be F-double-sharp, it would have to be a double-sharp sign, which looks like a small x. Accidentals are not additive; this sharp sign is just a notational redundancy that doesn't change the music.

Second red box...

I would analyze the entire second phrase, starting on the fourth beat in the example, in A minor. Lutheran chorales often have each phrase cadencing on a different degree of the scale, and it's frequently useful to consider the entire phrase relative to that scale degree. The first chord of that phrase comprises the pitches G♯-B-D-F♮, so it is vii°7/iv.

Analyzing the phrase relative to A minor means that the E major chords are not i (which they can't be because i is minor) nor even I, but V/iv. Similarly, the chord comprising B-D-F♮ is ii°/iv. The E in the bass is an accented passing tone; the structural root is D. This leads us to an analysis of the cadence, ignoring suspensions and other contrapuntal details, as ii♯6/iv - V/iv - iv, which can hardly be more standard.

If you're looking for a pivot chord, you might consider that the I chord at the end of the first phrase (beat 3 in the example) is reinterpreted as V/iv.

Finally, a word on terminology. "Melodic minor" is a scale. There's no such thing as a melodic minor chord, melodic minor key, or melodic minor tonality. "Melodic minor" arises from the tendency for the sixth and seventh scale degrees to vary in minor keys -- sometimes one sees the major sixth or seventh and sometimes the minor.

It is also interesting to note that the melody here is in B phrygian, even though the harmonization is in E minor. This provides another explanation for the frequent appearance of E major.

  • so you mean, (EDF♮B-DDF♮C-DDF♮D) is 'ii♯6/iv', (EG#EC) is V/iv, (EAEC) is iv64?
    – guss2222
    May 20, 2022 at 10:11
  • what is '#' in ii♯6/iv?
    – guss2222
    May 20, 2022 at 10:11
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    @guss2222 1: yes, the E and C are passing tones that you can ignore for the harmonic analysis. 2: ♯6 indicates that the sixth is raised. I was a bit confused when I added it, though; it's a major sixth but it is diatonic, so it isn't raised and the figure just be a plain 6. I will take it out. 3: ii/iv is followed here by V/iv, but yes, I am suggesting that it's better to analyze the entire 8-beat phrase using X/iv symbols; alternatively you can use iv: and then analyze in A minor. 4: there could be a source somewhere with F♯, though I can't imagine that it's anything other than a ...
    – phoog
    May 20, 2022 at 11:11
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    @guss2222 ... mistake. The only question is where the mistake first occurred. It doesn't change the music; it's just redundant. Accidentals are not additive, so it is not an F-double-sharp and therefore not a G. 5: but we don't talk about chords being "in a scale"; they may be "in a key." So E minor is a chord in the key of A minor, and E major is also a chord in the key of A minor. The same is true of D minor, D major, G major, and G♯ diminished. All of these chords could be found in pieces in A minor for centuries before the melodic, harmonic, and natural minor scales were invented.
    – phoog
    May 20, 2022 at 11:19
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    @guss2222 my point is that we don't speak of "pivot with A melodic minor scale." A pivot chord is a chord that exists in two keys. There's no "melodic minor" about it anywhere.
    – phoog
    May 20, 2022 at 12:00

This section is more easily analyzed if one works backward from the end. The piece ends on an A minor chord preceded by a V, i64, and V yielding a common perfect cadence (as your analysis shows). While the notes are offset with each other (the first eighth note in the bass causes a bit of rhythmic displacement.) The final bar is V-i64-V-i; the i64 I a double suspension of a V7 and this pattern occurs quite often. (As a matter of terminology, "melodic minor" isn't used to describe a key, only a scale pattern within the minor-key complex.)

Because the piece is primarily contrapuntal in texture, there are lots of chord changes happening in a hurry. No real modulation occurs. (To have a "true" modulation, there needs to be an extended section that is clearly in another key with significant use of notes outside of A minor.) So the whole piece should be analyzed using A minor as the tonic. The music consists of four independent voices (as noted in the comments), a harmonic analysis may look rather complicated. It's not wrong though and may be helpful in understanding the way Bach used combinations of melodies to produce harmonic effects.

Note that analyzing the piece in A minor simplifies things though. The first measure starts with a V chord followed by V7 (the eighth note D creating a seventh chord.) The chords up to the first fermata are E6, E65, a, D43, E. In Roman Numerals, V6, V7, i, IV43, V. The sixth and seventh scale steps in minor are mutable; in the key of a minor, the lower forms F and G or upper forms F# and G# may be used as long as good voice-leading (i.e., "sounds good" in this style) is followed. Thus the harmonic analysis isn't affected by the D major chord instead of a D minor (IV43 rather than iv43.) Similarly for the VII to i63 that follows.

There are a couple of places (left as an exercise) where the movement in eighth notes is best analyzed as using a non-harmonic tone, usually creating a suspension.

One more notational funny (at least I did a double-take). The piece is in 4/4 (probably written as C) time but he last measure with the repeat sign has only 3 beats. It seems as if this is the (older?) notational style wherein the last measure is shortened if there is a pick-up measure. I'm guessing this piece starts with a 1-beat pickup measure.

  • you talking the modulation happened in the first measure? Or do you not know this Chorales in 'E Minor?'
    – guss2222
    May 20, 2022 at 9:02
  • The cadence shown in the example is not the end of the piece; it's the end of the "A" section -- the chorale is in bar form.
    – phoog
    May 20, 2022 at 9:08
  • I don't know the chorale. I just analyzed the posted section from the cadence backwards. If this is the tail of an E minor composition; I'd go with the A minor from the last beat of the first (posted) measure, as suggested above.
    – ttw
    May 20, 2022 at 13:01
  • maybe i posted all wrong in the first place . actually this chorale start 'EEG#B'. first i saw this i think that just secondary dominant, but maybe just start as a A minor.
    – guss2222
    May 20, 2022 at 14:51

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