Amazing Counterpoint: Analysis of C-Sharp Major Fugue from Bach's Well-Tempered Clavier, Book II 

Correction: even though this fugue defies classification in many ways, it's incorrect for me to have called it a "double fugue," since that term is reserved for fugues that have two separate expositions (one for each subject), or for fugues that begin with simultaneous entries of both subjects.

You really love counterpoint, man. I love it

Damn, I am the man!

I remember as a child being completely awestruck everytime I heard Bach counterpoint. It's funny how all of these highly considered and informed deeply embedded structural components register with an interested child's mind as pure fascination and affection.

I wish they taught theory like this in school!

Omg I just started learning this piece this morning and your video has opened up a whole new horizon of understanding, thanks a lot! I didn't notice many of the clever counterpoint in the middle voices, the inversions and the augmented bits. The whole thing is like one giant sudoku.

"My contrapunctually baised brain" Lovely expression! Your videos are very interesting and worthwile!

Thank you for providing this marvelous resource. There was a time when people could access Timothy Smith's visually illuminating analyses of Bach's counterpoint in the WTC (I and II), the Goldberg Variations, and other works; sadly, it is no longer anywhere to be found. Your website is a most welcome rectification of that vacuum.

I noticed this fugue was really strange when I first heard it! Immediate stretto. I sought it out because, if memory serves, Aaron Copland mentions it in his book, “What to Listen for in music” as his favorite fugue from the whole WTC. Really outstanding video work. I wish more RU-vid analysis videos were like this - I don’t know if it could be any clearer than you make it.

Bravo! Great analysis of one of Bach's most complicated fugues. You pack a lot of information into a very short time.

Thank you! The Prelude to this is a favorite, especially as played by Glenn Gould. But now I will have a deeper appreciation of the fugue.

I hope you keep posting these, so wonderful.

Wow this is great, thank you so much , I love this fugue (and the prelude) so much and I was so eager to see such a wonderful analysis.

Wonderful. I especially like the way you highlight the score.

Great analysis. Very informative. You've pointed out interesting spots that I have missed in my own analysis.

Bravo! My mind is blown away by this great analysis!

Wow so much packed into such a short piece. Also I find it fascinating how the performer is able to make the slowed down variations of the theme pop out amidst the "colorful sea" of other things going on.

Your videos are really addictive to watch. So much to learn, helping my admiration of Bach to keep growing. Thank you 😊

Your analysis enhances what is already a great musical experience. Mr. Atkinson, you have the gift.

The last bar has fragments of the scalar portion of the main theme. Nice video! This must be my hundredth time watching this!

Very well done and perfect way!

This is the education I’ve been looking for. Subscribed.

One of my favorite fugues, and played brilliantly by Andraes Schiff, with impeccable touch and timing. Also love the prelude . (wish I could hear it too.)

So wonderful! Breathtaking!

Thank you .. so enlightening !! A great joy to hear !!

This is one of my if not my favorite fugue of both WTC-works! The first second I heard this piece years ago, I fell in love with it and still am. I don't know why, I just did. It maybe the incredible density of fugatos in this piece. I do also love the unbroken optimistic vibe it emits.

great video, thank you.... please keep posting the Well-Tempered Clavie 2

Bravo! What a lucid approach!

Thanks Richard, this will help me for the competition Im preparing for.

I like your phrase “well behaved fugue”. Great video/analysis by the way!

Great video! Thank you very much!

beyond incredible! one of my favs too.

Great, thank you! Some additional thoughts: In this fugue Bach uniquely captures his own compositional process. He "tries out" ideas until he "lands" on a suitable one (measure 17). This is not just a subjective interpretation: extant earlier versions of the piece validate this palimpsest theory. To my ears only the harpsichordist Scott Ross captures the delirium of this moment of discovery. The 32nd notes near the end confound everyone. They're an "open problem" much like open problems in mathematics. Listen to Schiff's uncertain rhythm, for example.

Please Analyse WTK 2 Fugue in C sharp Minor! That would be awesome

Love this fugue, great job on the analysis. Of course I prefer Gould's much slower tempo and xray vision bringing out every entry and false entry. Again Bach showing off that he can make a fugue out of anything, breaking the subject into pieces and using them like some great kind of cake.

Amazing thank you

thank you!!

Who are you? You super brain! Keep up the good work! Although I do not know English, but the graphics allow me to understand what it is! You're great!

Always so interesting :) It is nice to see the "theory" behind something I can feel but not explain ... if you see what I mean ;P Thank you !

All of these videos are really great, but could you maybe combine the commentary into bigger sections? Like maybe explain the exposition, then play the clip of the exposition, then explain the first episode, then play the clip, etc.? A lot of the time the flow of the video feels really obstructed, especially in Bach fugues where there's an extremely high density of musical thought.

I really enjoy your videos. I look forward to the next one!

Lovely!

this is so awesome, thanks so much for sharing. There used to be a page called Analyzed Fugues (index of?) and it had all the WTC fugues analyzed, it was VERY unfortunately taken down... luckily I saw systematically a couple of times... do you think you could do something like that? -I mean all the fugues analyzed, even the Art of Fugue, there was never any systematic analysis online that was convincing (that I found). I would be willing to help or at least I would be delighted to learn and would be regular visitor if something like that would be documented on video. I'm also a composer and my final goal is fugue writing. Thanks and REALLY looking forward to more Bach fugue analysis!!!

Good work as always. What's next !?

I'd say the two voice augmentation is a beautiful coincidence... remarkable of someone to hear that ( but it is beautiful once you notice it huh )

Have you looked at any of the Mendelssohn String Symphonies? All of them are full of brilliant counterpoint

Brilliant! Could you do the totally insane A minor fugue?

Thank you so much for posting this analysis!! Would you be willing to do it for Bach's E Major prelude and fugue from Book 2?

I have always wondered about that stretto in the exposition, so I'm glad that you pointed that out. I can't think of any other fugue that has such an unorthodox exposition by J.S. Bach or other composers. Was was that a first in fugue writing?

Have you considered doing an analysis of the finale of Verdi’s Falstaff? An unconventional and ironic use of fugue.

I see what you mean at the end, but the subject would go up to the 3rd instead of a second, so it is close.

Remarkable

Hi Richard, I admire your work. You have a great channel. What determined when you put a "?" or not? Was it whenever there was an intervallic altercation to the original subject motif ('Up-3rd, down-3rd, up-5th')? Thank you.

Woah. At 2:56 did anybody else get flashbacks to Duel of the Fates from Star Wars for a brief moment?

You should do analysis of polyphonic works by Tallis and Byrd

Beethoven’s op 110 sonata in a flat major has a terrific fugue in the third movement, could you look at that ? (The first fugue in it). Also, terrific videos

Nicee video

Hard for me to follow but fantastic !

Excellent video! I really love your channel and all your work, it makes the concept so easy to understand and the graphics are really well done. With respect, I believe you are mistaken about it being a double fugue, as the second subject is actually the first in disguise. look at the first entry of what you call the second subject, the 10 notes between the A# and F# (your analysis considers B the first note, which I totally understand, but hear me out). notes 2, 4, 6, and 8 are all passing notes and can be ignored. Look at just notes 1, 3, 5, and 7 - this is the tonal answer of the first subject, the only difference being note 5 is E# when it "should" be an A#. now look at just notes 3, 5, 7, and 10, this is the original subject, only once again, the third in the group (note 7) is changed. in this case, instead of C# it's a 32nd note whip between G# and E#. the changes in counterpoint these substitutions cause are just as consonant and invertible as before for the following reasons: any diatonic scale (such as what you call subject two) contains two instances where a major 3rd is followed by a halfstep, such as in a C major scale where you have CEF and GBC. that's the tonal answer of this piece. looking at what you call second subject, the chord tones create two superimposed triads between notes 1 3 5 and 3 5 7. that's the subject of this piece. finally, according to your analysis, the second subject enters on B twice then G# twice. even disregarding the chromatic alterations of the second entry, this is a very very far cry away from the C#, G#, C# ,G# we'd expect from a subject exposition in this tonality. it's very rare that Bach strays from I V I V entries in a four voice fugue.

I (respectfully) disagree with your "surprise" at the end of the video. Although it's a lovely coincidence; any other (tonal) entries of the subject at least have some sort of third, where this is 2nd-2nd-4th (as opposed to, for example, Measure 4: 2nd-3rd-5th; no other entry has two consecutive 2nds.) Another point of argument (again, very respectfully) is that I wouldn't classify the semiquavers as a 2nd subject. I view it as though Bach introduces it as a new tail to the subject (similar to measures 1-3), and continues this added fragment as a motiv. But as always, you do amazing work clarifying the passages in your videos, and the color scheme makes it wonderful to follow!

Great video. I would like so see a complete analysis of every bar! I know it’s not the subject of this video, but this must be one of the easiest fuge from WTC I,II to play. Am I correct?

WOW

Anyone hear that huge overtone on the C# in the bass clef?

Could the last three notes of the bass be a possible fragment entry?

I get a minor nice headache when i hear and see this, the wizard of music

I'm happy with Row Row Row Your Boat.

Interesting analysis. Although this piece is nominally a fugue, would it be fair to call it a three-part invention?

2:04 entire fugue

Perhaps due to the shortness of the subject Bach felt the need to give it some flare with this unusual treatment.

#SiempreBach

Isn't this "second subject" called a "countersubject," or is there a distinction that makes it not a countersubject?

and the chromatic fuge please

I love your site! Wish you could come to my concert. Respectfully, Sophia Gilmson

Can I ask what's wrong with the key signature ?

“A well-behaved fugue” 😂

This would be easier to read if he would have notated it in d flat! Haha Seven sharps? Doesn't happen very often. Fortunately

What a quaint fugue! It sounds very disjointed at first listen. I will have to go deeper into it.

"Contrapuntally biased brain"

Das war WUNDERBAHR GANZ GANZ WUNDERBAHR DANKE SCHOR

wouldn't a harpsichord be better for this?

Lovely!