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I'm playing the prelude in Bach's d-minor suite. My teacher and I were wondering what the third to last chord is. We didn't find that A, E and D form a chord, but do they? Is the D maybe a "queuing" note that resolves to the C#? We found that this chord was the climax of the phrase and that's maybe because it is so exotic.
All info is appreciated.
It is actually misleading to think about this music in terms of chords as we know them, as the system we use to identify and speak about vertical harmonies was still under development during Bach's time. Bach had no concept of a "suspended chord" for instance. Bach did not think of chords the way a guitarist does (moveable stacks of exact intervals, with major/minor system names), as that outlook on harmony was a product of the 19th century, and not a prevalent theory in his day. As strange as it sounds ideas like chord names (G minor chord, C major chord) would have been alien to him. That's not saying his music can't be seen from that lens, but it doesn't help you understand how both performers, and composer's saw the music in his day, and the music makes far more sense when you see it on its own terms.
It is true that the "chord" you have found as an example of a contrapuntal suspension (http://en.wikipedia.org/wiki/Nonchord_tone#Suspension), but to really get inside Bach's head, you have understand that he saw stacks of intervals which were the incidental consequence of good counterpoint, rather than purposefully constructed vertical harmonies.
For Bach, creating the movement from D, to C# and back to D again was the most important goal, and suspending the D from the previous chord allows him to do this quite gracefully.
Why?
Because it allows him to resolve the final contrapuntal movements correctly. You see, it was considered desirable to end a contrapuntal line with 7th-Root in the top voice, and 5th-root in the bottom voice. Everything before that point is just (artfully) setting up the voices so they made gracefully enact that moment.
Try to think of the music as individual, independent melodies.
It's an Asus4 chord, which is a suspended chord where the third (C#) is replaced by the fourth (D). The fourth is carried over from the previous chord (D minor), and - as you've suggested - resolves to the third (C#) of the next chord (A major).
The accepted answer is patently ridiculous...
...but to really get inside Bach's head...
How about looking at Bach's manuscripts?
Here is an example from the Klavierbüchlein für Wilhelm Friedemann Bach which shows a figuration prelude where the completion of the prelude is written out in chords. The idea of chords wasn't alien to Bach or his contemporaries. The answer seems to be mistaking the concept of chords and harmony with the idea of fundamental bass (chord root and inversions) introduced by Rameau which was a new concept for the time. But the suggestion that harmony was not thought of in homophonic terms, as vertical chords, is false. That time period combined contrapuntal and homophonic approaches.
...stacks of exact intervals...that outlook on harmony was a product of the 19th century...stacks of intervals which were the incidental consequence of good counterpoint, rather than purposefully constructed vertical harmonies...
Rameau's Treatise on Harmony describes chords as stacked thirds so the concept is not a 'product of the 19th century.' The figured bass of Bach's time actually is stacking intervals above a bass part. The written figures literally stack intervals over the bass. Realization could be block chords or various figures and textures, but conceptually it was stacked intervals. Here is an example from BWV 151...
But regarding the original question...
We didn't find that A, E and D form a chord...
That is because the chord is actual an A chord, but the D note is a suspension.
This passage is actually a perfect textbook example. The previous measure is the "preparation" where the D is introduced as a chord tone in Dm a i6/4 chord, followed by an A chord V with the D note suspended, which then resolved down to C# for the proper V chord.
"Queuing" does capture the essence of the function and handling of the D note, but the technical term - which the teacher should have known - is suspension.
Bach certainly both knew and applied suspensions. The modern use of suspended chords is a heritage from classical music and it dates many hundred years back. It is certainly well known in baroque music. The usage of a sus chord has changed, but the term "suspension" has stayed.
Yes Bach made a lot of music based on linear counterpoint, but it is plain wrong to claim that he didn't make music based on chords. There is a chord system developed in baroque music with baroque chord symbols known as basso continuo also called figured bass. For a keyboard player the bass line was given for the left hand. Included with the bass line were chord symbols, figures, mostly numbers. Based on that it is up to the keyboard player to decide which chords to play with the right hand.
Examples: The bass note itself indicates which triad to play with the bass note being the root of the triad, and the type of triad (major or minor) given by the key signature. Thus if the key signature is 3 sharps (A major) the bass note E means an E-major chord. If you want an E minor chord there is a natural sign under the bass note E. In case the bass note is not the root of the chord it must be indicated with a figure. The figure "4" under a bass note means suspended fourth within root-position triad. Thus the bass note E with the figure "4" underneath actually means Esus4.
If the composer wants to write precisely what should be played he would do that instead of course. Bach has both written music with a basso continuo part for the keyboard and music with precisely written notes for the keyboard.
Today continuo parts for keyboard are often published with precisely written notes even though the composer actually only wrote the bass line with figures. So that is someone's suggestion of how to play it in order to help those who have not learned how to interpret a figured bass.
This is actually a Asus (a,e,d) V4 with suspended 4th resolving to the 3rd of A (a,c#,e).
It can quite clearly be proofed that each bar here is in a certain chord:
I don‘t agree at all with an other answer that denies this conept, as a lot of Bach‘s music and especially his suites are obviously composed and invented by vertically and harmonically “thinking”.
(Ernst Kurth is one of the theorists that emphase the linear-counterpoint development and horizontal approach to Bach‘s harmony. This also correct - but not exclusive.)
