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

[@Richard.Atkinson]

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.

[@Josicauc]

Thank you for sharing these videos! I do agree, I don't think it's a double fugue, but that subject (could we call it a counter-subject) is rather prominent! I also heard that "surprise" as an augmentation of the theme! :)Thanks, once again!

[@mtv565]

@Richard Atkinson: You're correct, it isn't a double fugue.

[@hugoclarke3284]

Yeah I was going to comment that. The second subject is a countersubject that is introduced late in the fugue.

[@bahrss]

You have asked for suggestions in the end of the video... So, can you, please, make a video about Bach's Mass in B? For me "Et resurrexit" and "Confiteor unum baptisma" are the most interestimg and appealing choir fugues

[@Geopholus]

What i love about Your analysis is that all the presentation is filled with LOVE, humor, and unfettered reverence, such a contrast to for instance Alan Belkin, who is wise to turn off comments on his nearly mindnumbingly boring lectures on Music Theory. You zip through really profound but simply rendered observations that are (I imagine ) equally revealing to a child, or a seasoned maestro. Your commentaries put me into Bach's Universe, in outer space, floating around weightlessly, as does this other version of the piece , with the prelude : kzbin.info/www/bejne/m2TRYYScoc5ljNk

[@grahambob64]

You really love counterpoint, man. I love it

[@steven21ys]

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.

[@paxwallacejazz]

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.

[@abundance6692]

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

[@johannsebastianbach3411]

Damn, I am the man!

[@dmitrishostakovich2822]

Nice to meet you, bro

[@Richard.Atkinson]

I did a video about one of your fugues too...

[@dmitrishostakovich2822]

It's a nice one ;)

[@jackminto7062]

@@dmitrishostakovich2822 OOH the D flat major and A major are my favourites, Shosty!

[@jendadabings1202]

@@dmitrishostakovich2822 Hey Shosty! When is your new symphony coming? Cant wait!

[@douglasjensen8986]

I hope you keep posting these, so wonderful.

[@VianoMusicAcademy]

I wish they taught theory like this in school!

[@steffen5121]

I wish I knew more composers that composed like Bach did.

[@steffen5121]

Todd Tolson thanks I will

[@Geopholus]

@@steffen5121Somewhat similar: Vincent Lubeck, Jan Dismas Zelenka, George Friderich Haendel, Johann Ludwig Krebs (student of Bach), Jan Pieterszoon Sweelinck (inspired Bach), Johann Pachelbel (who taught Bach's brother (look beyond the Canon)), and there is a young composer living today, Nicholas Papadimitriou, who has written several Fugues that could fool many experts into thinking they were by Bach. Check my channel for lists of video's uploaded by others on the general subjects: "Great Baroque", and "Art of Fugue" for many fine examples.

[@steffen5121]

@@Geopholus Great. I will look into them.

[@eryeryeye5787]

@@steffen5121 Especially Zelenka!!!

[@m.calloway2624]

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

[@michaelp4657]

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 KZbin analysis videos were like this - I don’t know if it could be any clearer than you make it.

[@julieyoo6538]

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.

[@Geopholus]

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.)

[@artje123]

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

[@Hidden_Frames]

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.

[@muchenli]

I'm super interested in what you have mentioned. Do you have a source for the earlier versions and/or academic articles related to this? I'd love to read and analyse them.

[@Hidden_Frames]

@@muchenli Sure! David Ledbetter's book on the 48.

[@muchenli]

@@Hidden_Frames Thank you! Just ordered it. I need more academic music books in my life ^^

[@TheApostleofRock]

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.

[@leonhardeuler6811]

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

[@natalijadrazovic5104]

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

[@Kralperri]

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

[@steffen5121]

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.

[@frenchimp]

It is full of humour and playfulness. That's what makes it so attractive, I think.

[@steveedelen3251]

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

[@1969Chronos]

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

[@David_Goza]

Bravo! What a lucid approach!

[@blueamber5311]

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.

[@MasonIshida]

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

[@lalahohoable]

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

[@markhughes7927]

So wonderful! Breathtaking!

[@derik2nicolai584]

Very well done and perfect way!

[@rogelio2ify]

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.

[@johnbouttell5827]

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

[@vspianist]

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

[@channelelectronique]

beyond incredible! one of my favs too.

[@CharlesAustin]

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

[@trevjr]

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.

[@PushkaryovVsevolod]

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!

[@alexshih3747]

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.

[@ronmor2004]

Great video! Thank you very much!

[@peterlindauer6370]

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

[@FougarouBe]

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 !

[@FougarouBe]

Happy New Year to you and your beloved ones, Richard ! :)

[@jeffrylangford1936]

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

[@RandallDark]

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

[@naumprihodyaschy8629]

a little bit

[@웁쓰-u4d]

thank you!!

[@Waterboy2211]

Amazing thank you

[@enrico_piano]

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!!!

[@georgemarshall5226]

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

[@mckernan603]

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

[@mr.trashbin307]

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.

[@claudefazio]

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?

[@AnthonyMondon]

Good work as always. What's next !?

[@C720L]

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

[@handavid6421]

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 )

[@hanaoshimapiano]

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?

[@Richard.Atkinson]

Another great stretto fugue! I will try to do it at some point, but there are others that need to be done first.

[@gracelee9437]

Lovely!

[@quaternion-abicjdk]

2:04 entire fugue

[@MichaelRosin]

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.

[@Erinnmnn]

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

[@andrewtessman9921]

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!

[@Richard.Atkinson]

I see what you're saying. But your rule that it needs to have a third in it to resemble the original motive is arbitrary. Part of what makes this fugue difficult to analyze is that the 4-note motive is present in so many variants. For example, some might argue that the left hand in measures 12-13 is playing variants of the motive (and they fit your requirement because they contain thirds), but I didn't consider them close enough to highlight. Certainly the "surprise" that I mention at the end resembles the original motive at least as much as the one I highlight at the ends of measure 33, for example. Maybe I should have also included a question mark for the "surprise," but I did make it clear that it's a stretch to call it a real entry.

[@andrewtessman9921]

I see what you're saying. True, the end of m. 33 (as a "?" entry) does make a good case. I think I didn't accurately convey what I originally meant, though. For subject entries: the initial interval (between the 1st and 2nd eight notes) is either a 2nd or 3rd (tonal or real or inverted), and the last interval (between 3rd and 4th eighth notes) is either a 4th or 5th (tonal/real/inverted). But the second interval (2nd to 3rd eighths) is, as far as I can tell, always a 3rd. Therefore I would deem the between-voices augmentation a coincidence (albeit curious). But true, I certainly don't deny that the bass line in 12-13 is derived from the subject in fragments... although curiously, one could also argue that the "2nd subject" occasionally contains an ornamented variant of the subject (beats 2 and 4 of m. 10), but that's also not consistent throughout the fugue. Then again, that's one of the beauties of the fugue that makes it, as you say, "unorthodox and remarkable". :)

[@TheGuggo]

I’d love to be able to understand half of what you guys are saying :-) I just love this music and JSB’s works in general. Anyway thank your contributions in making this educated and informed conversation.

[@magnuspires6501]

Remarkable

[@brianbernstein3826]

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.

[@Richard.Atkinson]

I didn't read this carefully at first (I try to read all my comments, but sometimes I struggle). My pinned comment was in response to someone else's comment on my C# minor fugue video. Now I see that you did make the point (I think?) in the second to last sentence that there is no second exposition for the second "subject," which is the reason I later mentioned in my comment above. I don't really agree that the two subjects are variants of each other, though, which I thought at first was the only reason you were giving for why it isn't a double fugue (which is why I didn't post a correction at the time).

[@MarcJohan2009]

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?

[@caterscarrots3407]

I don't think so. Both the Bb major Fugue and the C minor Fugue from Book I are easier than this fugue.

[@LionKing-mv2uk]

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

[@dpmalfatti]

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

[@peterjongsma2754]

I'm happy with Row Row Row Your Boat.

[@krismariasy9728]

You should do analysis of polyphonic works by Tallis and Byrd

[@rlunger1]

Hard for me to follow but fantastic !

[@TheDirkplas]

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

[@diegosatori5718]

Nicee video

[@Richard.Atkinson]

Thanks!

[@rosiefay7283]

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

[@Richard.Atkinson]

Rosie Fay What makes something an invention instead of a fugue (if we ignore what Bach chose to call it)? Other than being limited to 2 or 3 voices, I’d say the main difference is that inventions are usually much less contrapuntal and rarely venture beyond rudimentary imitation. The E minor fugue from Book I (the only one with only 2 voices) is the most invention-like of the fugues, in my opinion. This fugue, on the other hand, is one of the most complicated, so I wouldn’t call it an invention.

[@mikahkilgore4972]

“A well-behaved fugue” 😂

[@minkyunglee1286]

WOW

[@minkyunglee1286]

...

[@JimHantis]

W counterpoint

[@enochy6586]

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

[@Sam-tj9np]

usually the countersubject appears immediately after the first statment of the subject. In this case, the subject kinda forms the countersubject.

[@GuillermoPSKrebs]

#SiempreBach

[@robbes7rh]

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

[@felixmendelssohn4301]

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

[@Richard.Atkinson]

You can ask, but I can't answer. I don't see anything wrong...

[@MKimberViola]

@@Richard.Atkinson Maybe "Felix" is wondering why the F# in the treble staff's key signature is an octave lower than usual. I think it looks rather nice that way, the sharps in both staves appearing to be in "parallel motion." Does that mean I have a contrapuntally biased brain, too? I do love writing counterpoint, an unusual predilection for a 21st-century composer.

[@caterscarrots3407]

@@MKimberViola And it is a very common thing in the Baroque era to have accidentals on multiple places in the staff. A lot of D major Baroque pieces for instance have both a lower and an upper F# in the treble clef's key signature. This double accidental key signature, I find to be especially common amongst string instruments in the Baroque.

[@Bod_users]

and the chromatic fuge please

[@ferdburfle7320]

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

[@kurtisburtis]

ferd burfle: indeed, it would; but it seems that he (Bach) was also making a point about the usefulness of the well-tempered tuning.

[@sophiagilmson7481]

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

[@chrysanthos7265]

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

[@3gc42bx]

"Contrapuntally biased brain"

[@louisemattice-raab5513]

Das war WUNDERBAHR GANZ GANZ WUNDERBAHR DANKE SCHOR

[@RealHogweed]

wouldn't a harpsichord be better for this?

[@hugoclarke3284]

for the purpose of this video the piano is actually more suitable for emphasising melodies hidden in the texture. It does sound lovely on the harpsichord or clavichord too.

[@gracelee9437]

Lovely!