Learning the art of fugue with J.S.Bach's The Art of Fugue: Analysis of Contrapunctus I

TRO analyses the first fugue in J.S.Bach's Die Kunst der Fuge, looking at the construction of the subject and answer, form, and the use of motives.
BIBLIOGRAPHY/FURTHER READING AND WATCHING:
Bach, J.S. Handwritten score: ks.petruccimusi...
Bach, C.P.E. 1752 edition: conquest.imslp....
Cobussen, M. Deconstruction in Music [Contrapunctus I, para. 4]. Interactive Dissertation, Department of Art and Culture Studies, Erasmus University Rotterdam, The Netherlands: www.deconstruct...
Couprie, P. (2009) A nice graphic analysis (in French), with an edition that helpfully points out deviations from the handwritten score: • J.S.Bach - The Art of ...
Graeser, W. (1926) The Art of the Fugue. Bach Gesellschaft Augabe. Leipzig: Breitkopf & Härtel: ks.imslp.net/f...
Hook Theory - a great community-sourced theory site: www.hooktheory...
Mondrup, C. (2018) Edition of The Art of Fugue used for this video, based on an edition by Werner Icking: ks.imslp.info/f...
Sokolov recording used in this video: • The Art of the Fugue, ...
Tovey, D.F. (compiled 2013 from original 1931 OUP publications) Bach's The Art of Fugue & A Companion to The Art of Fugue. New York: Dover Publications

[@trocomposition4216]

Erratum: Bar 56 in bass should read p5 (perfect 5th) rather than p4.

[@Geopholus]

perfect fifths and fourths,.. have a certain equivalence if they are in the same octave and one transposes one of the elements up or down an octave. for instance , moving upward, "F" to "C" =fifth, "C" to "F" =forth. A simple symmetry, very useful to be aware of when composing. Shifting the reference of "what is the root key", sort of the same effect, Bach, Mozart, and Beethoven, often used the trick of using an ambiguous metrical figure to change the beat emphasis, in a work, to make us think the key has moved to the dominant or subdominant, by this kind of strategic use of 4th and 5ths ... up or down ?...

[@zacharykeenan7723]

Thank you so much for a brilliant and heartfelt analysis! As a 17 year old, I was a fan of mostly metal and classic rock. I was fortunate (and uniquely blessed) to take a music theory class in high school with a teacher who introduced the class to Bach and his genius. I'm now 50 years old and for the last 33 years, Bach has been my musical mainstay. This video has reinforced and taught me afresh the unsurpassed genius of Bach. Rarely can something simultaneously move both the heart and the mind. Thanks again.

[@trocomposition4216]

Thank you for the kind words, Zachary! Metal in particular has learned a lot from Bach so I can see how your 17 year old self would have responded to it so positively 👍

[@mattwilliams8582]

As a teenage rocker into Metallica I accidentally came across Zoltan Kocsis' rendition of this. Threw the disk into my Alpine CD player. Sounded like jumbled notes the first time, second time my brain went "what?, wait, there is a complex pattern here". I became fixated on the entire work trying to understand the pattern and structure and at the same time falling in love with the tonal beauty. It was like I was in possession of some form of extra-terrestrial machine that no one else could see. Tried getting all my friends into it. None took to it. If fact it was annoying to them. Anyone have a hypothesis as to why some people can understand and enjoy this music but assumingly most cannot?

[@Adar195]

I totally agree with you and i have the same question?What limits most to not "get" these pieces?I expect a certain level of musicianship is necessary even to start grasping these masterworks and this also explains the immense popularity of pop and popular songs/pieces,but it is yet to explain it fully.

[@fatitankeris6327]

@@Adar195 It's the idea that there's a harmony, but it's not just chords, it's counterpoint, and it is a combination or layering of several voices that have EACH THEIR OWN MELODY, though they enter into the group by the means of the original, first melody, known as the subject. That means that it is incredible complexity to behold in many of these fugues, but as with all things, complexity isn't always enjoyed, in most cases people don't like it... Yet some people have an appreciation for it, imagine a complex clock or machine, that has so many parts, yet it does something beautifully smooth when they all work together. Some will be consumed by amazement, others will get confused and turned away, often most...

[@Adar195]

@@fatitankeris6327 thank you very much.

[@Geopholus]

As to why so many people don't "get" Art of Fugue, and why do those of us who do, find it so sublime. I think all the answers of the other commenters are hitting on the right ideas, and maybe there is also something more. Long ago I attempted to list all the Rock pieces/songs that either made it into "top 40" or were on an Album that did, that either were directly lifted from Bach, or were a development/variation of something he wrote. There are about 30 ! Most of them emphasize a nice lyrical melodic line,... Art of fugue is all about interweaving and interleaving different lines that still, in the end, seem to present a unity of purpose.... it is much more difficult to comprehend, or even, just plain hear it, in terms of melody. It is difficult often because the "melodiousness" can be a long slow simple pattern, or a fairly busy quick changing pattern, and so many things can be happening simultaneously in Art of fugue ! A lot of musicians L O V E Bach best, but also many people in the sciences (especially physicists ) and other creative people. Surely it has something to do with recognizing complex patterns that are based on fundamental principles, and the joy of seeing into the secret thicket deep in the weeds. For those who can't hear what is going on, it is frustrating,... they throw up their hands in disgust,... what the hay. They can hear something is happening but they just can't get the hang of it.

[@frenchimp]

My answer would be: a form of open-mindedness. You listened to it twice, you gave it a chance. You perceived that there was something there you couldn't grasp all at once, and instead of putting you off, this stimulated your curiosity. I think you have the mental attitude of a researcher; Bach was a researcher. Many people are mentally lazy, they only enjoy what's familiar to them, they're looking for things that look like them - like the person they are, not like the one they could become, if they gave a chance to the infinite potential that's in them...

[@Mymusicaldream]

One of the best Pieces Ever written!

[@Kurtlane]

Please, please, please, no Derrida! No Foucault! No Adorno! No Karl Marx, Friedrich Engels or Vladimir Ilyich Lenin! I have been forced to listen to the last three since I was born 62 years ago. Can't I at least escape from them here through the divine music of Bach?

[@hanztimbreza6217]

I am very glad that youtube recommended this video to me. I am not a musician nor do I play any instruments but I love listening to Bach. This analysis, which is understandable for a non-musician like me, makes me appreciate Bach's genius even better. I didn't even notice that this video is 29 minutes long. One suggestion though: after concluding the detailed analysis, play the whole piece uninterrupted, while displaying all the coloured annotations in the score. This will help the viewers recall the analysis next time we listen to the piece on our own.

[@trocomposition4216]

Thanks, Hanz. Glad you found it interesting! Good idea re playing the full piece at the end 👍

[@Geopholus]

@@trocomposition4216 Yes please play the entire piece at the end. That was also especially what I was hoping for though I have heard this piece close to 1,000 times and indeed have played it. Your analysis is beautiful and delightful.

[@PushkaryovVsevolod]

Увлечённо рассказывает. Сразу видно, - человек любит музыку и знает о чём говорит. Вот бы услышать из его уст рассказ о том как построены французские сюиты И. С. Баха.

[@trocomposition4216]

Спасибо! Я хотел бы когда-нибудь снять видео о французских сюитах 👍

[@canman5060]

You may need a two hour video for the unfinished Contrapunctus 14 with three subjects !

[@trocomposition4216]

Be careful what you wish for! 😂😂

[@aniruddhvasishta8334]

24:35 - "Used judiciously, silence is one of the most powerful weapons in the composer's armory"

[@gregbowden7786]

This was wonderful. I hope you do more from Art of the fugue.

[@trocomposition4216]

Thanks, Greg. Glad you liked it! Yes, more on its way 😊

[@jelonec4585]

And I second this. Absolutely gripping! Bravo and thank you for your excellent work!

[@neilsaunders6009]

Prout rhymes with "shout", but he wasn't a lout (and, to judge by the photo, not terribly stout).

[@robbes7rh]

I totally agree. Even with this unassuming opening fugue Bach demonstrates his Midas touch with musical notes giving us this perfectly proportioned gem of extraordinary beauty. Imagine what things must follow from his fecund musical mind as he embarks further on this monumental work.

[@VaughanMcAlley]

Contrapunctus I is amazing. Basic ingredients done perfectly, like an espresso from a middle-aged Italian barista. Good on its own, or as the starting point for something more fancy.

[@CristianRettigBianchi]

Nice coda in your video btw. Congrats.

[@ban9nas177]

“Technique only has value when it serves an end that transcends the means” How beautifully said! Thank you for this wonderful video dear sir. This piece lives in a deep place within my heart.

[@trocomposition4216]

Many thanks! ☺️

[@spiritualpolitics8205]

This was a fabulously deep and detailed musicological lecture; I don't think I've ever heard anything like it. Please keep up your fine analyses, particularly of the AoF! It helps me in my compositional aspirations, and I suspect these lectures will become preeminent on that greatest of contrapuntal works...

[@trocomposition4216]

Thanks! I definitely need to get back to AoF soon - it’s such a treasure trove of musical wisdom ☺️

[@loganbarnes8621]

You madman, you're already tackling the Art of the Fugue!? What a strong start you are giving your channel haha. Terrific work!

[@trocomposition4216]

Haha! Thanks, Logan 😉

[@samaritan29]

can't wait for contrapunctus XIV!

[@blakec.s.franchetto9522]

Great analysis, very clear and well presented. Look forward to hearing more from you. Insightful

[@trocomposition4216]

Thanks, Blake. Much appreciated!

[@roberthubbard5696]

This is just what I have been looking for! AoF is my favorite musical piece but I wanted to understand why it is so deeply moving. I’m not a musician but your analysis gets even to me. Wonderful, unique, and very much appreciated!!

[@trocomposition4216]

Really glad you to hear that! 😊

[@riverstun]

Thank you. I've been waiting for something like this for a long time. I especially like your descriptions of what he's doing in g minor and why. All too often, I just dont uniderstand Bach's accidentals. So for example the F# at the beginning of the piece just seems random. But when you describe it as prefiguring the much later entry in G minor, it makes sense. Also, the weird (in a good way) accidentals in the Coda also make sense now.

[@riverstun]

Love to see a deep analysis of the first 4 bars of the B minor Kyrie, btw; I have no idea of how he achieves most of what he does.

[@trocomposition4216]

Thanks, riverstun. Glad you found it useful 😊 Bach's harmonic control is indeed amazing!

[@Geopholus]

Riverston, so nice to see You here,.. it's been a while... I find that Bach almost always prepares us a little, to be on our guard for a journey into distant lands. He often begins a piece, off the down beat, introduces a slightly off balance idea before he has finished making his first statement, and there is always a suggestion that something deeper is going on. I never liked the term "accidental", as there is nothing accidental about them,... they always fit perfectly into the pattern being described...if the piece is in, one of the more formal idioms. In Bach this is always the case. I don't think Bach ever wrote a piece that stays strictly in one key, but he always modulates in a completely organic way. One of his biographers (perhaps Christoff Wolfe (spelling?)) mentioned that Bach seems to use "scales" that are combinations of different modes or scales before he has even spanned an octave, or borrows elements suggesting a different mode or key certainly before going the distance of 2 octaves.

[@gunnarharaldsson5317]

Thank you very much! This is fantastic. Hope you do more analysis of Bach!

[@trocomposition4216]

Thanks, Gunnar! More on its way 👍

[@RinzePrins]

fantastic analysis, you have ' transcended' the sometimes dry analysis to compositional insights. As a viewer I could feel that you are a composer. If you ever were to get round to it, more content like this would be very welcome.

[@trocomposition4216]

Many thanks for the kind words! 😊

[@nathaniellevy7956]

Thank you for the terrific analysis of this piece. Incredibly thorough and very useful. If I may make one suggestion, please feel free to play the sections you're discussing more often, even twice. It's always helpful to the brain to put the words right next to the phrases you're discussing.

[@trocomposition4216]

Thanks! Noted for next time 👍

[@raycasbierd]

When ever I get lost in a tangent of miss information I come back to this video it's brilliant, I love how bach utilises the accents on 1 & 3 of his concomitent parts by using smaller lead in notes to emphasise the strong beat or creates space at these points for another voice to do it. It's Magical and Marvellous work can we expect any more videos please? Ray

[@trocomposition4216]

Thanks! I’ve been busy with my own composition and the day job recently but definitely need to get back to this soon 👍

[@OfficialDanieleGottardo]

What a great lesson!!!

[@robbes7rh]

Quick comment just to let you that returning to this video 7 months later I had an even more rewarding experience letting the ideas sink deeper into my ever evolving musical imagination. There is depth to Bach perhaps nowhere more evident than in the Art of Fugue and in this very opening fugue that you’ve done a wonderful job explicating in your analysis.

[@trocomposition4216]

Thanks for the generous words! Really glad you’re finding the video rewards repeated viewing 👍

[@AndreasMartinLaute]

Thank you so much for this wonderful explanation. I’ve been listening to this masterpiece of human genius since my early childhood now being a lutenist mainly performing works for the Renaissance lute but also the few pieces Bach wrote for the Baroque Lute. I particularly like your last statement of your video concerning the “means”. You have a new subscriber - all best wishes! Andreas Martin, Lute & Guitar

[@trocomposition4216]

Thank you for the kind words, Andreas! It means a lot ☺️🙏

[@rogerramjet6615]

Great work thanks.

[@ittaimazor9154]

Loved your analysis, it was clear and detailed. I"m singing this piece in the format of a mixed vocal quartet and this will help us allot to lead the interpetation much more. Thanks allot!

[@trocomposition4216]

Thanks! Wow, that sounds challenging - good luck with the performance! 😊

[@raycasbierd]

Hi Tom, could you explain the using an out of key note like C# to confirm d minor, also the unusual voice beginning is just a standard authentic and plagal use of voices? Oh yes thanks for the video

[@trocomposition4216]

Hi Ray. Although C# is not in the key signature for D minor, it is sharpened in the D harmonic minor scale because the semitone/half-step to D leads more strongly back to the tonic note (than a C natural would). For this reason C# is known as the leading note in D minor, and harmonically the movement from leading note to tonic implies the key-defining progressions V-i or vii-i. Hope that clarifies! 😊 I'm not quite clear what the latter part of your question is referring to?

[@raycasbierd]

@@trocomposition4216 hi Tom thank you for clarifying, was this common back then or unique to Bach? Did he invent it or use it as a rhetorical device so to speak? I assume this is a common technique/standard practice nowadays. In your video you mentioned at the start how he changed the upper voice to start with a leap of a 4th rather than A 5th I remember reading before his time and before the use of minor, major scales things were more about modes etc and back then they used to single out voice entries using authentic and plagal technique. Hope this makes sense sorry for long message. Curiously Ray

[@trocomposition4216]

@@raycasbierd Hi Ray. Yes, spot on - the authentic/plagal scale system is indeed the origin of the tonal answer 👍 However, by the high baroque period, composers like Bach and Handel were much more flexible in their approach to the rules that had been derived from this authentic/plagal scale system, because the predominance of the maj-min system meant that harmonic considerations took priority, and these are the considerations we look at in the video. Regarding the other point, yes, sharpening the leading note in minor keys was fundamental to the maj/min system and was standard practice by Bach’s time; it originated in the practice of sharpening the 7th at cadences in earlier music (musica ficta). Hope that helps 😊

[@juankliss]

This is a very serious channel that should break into the algorythm's spiral and get some larger attention. keep it up! Composing my own 4 part fugue in tango style right now! greetings from argentina.

[@trocomposition4216]

Muchas gracias, Juan! A tango fugue sounds like a fun challenge 😊 Good luck with it! 👍

[@SpaghettiToaster]

@@trocomposition4216 There‘s a very nice one by Piazzola in case you didn‘t know!

[@trocomposition4216]

@@SpaghettiToaster Loved it! Thanks for the recommendation 😊

[@albarylaibida1214]

Excellent video! I wonder if it would be possible for you to make a video composing a fugue of your own. I think that would be amazing. Congratulations! Once again, the video is superb!

[@trocomposition4216]

Thank you for the kind words, Albary. Great minds think alike! I'm currently writing a fugue modelled on this one and will be making a video on it in the new year 👍

[@albarylaibida1214]

@@trocomposition4216 First, I would like to thank you for the compliment. Secondly, I can't wait for your fugue. This indeed will be a great new year's gift.

[@rengsn4655]

25:09 "D-tour" .... I see what you did there

[@trocomposition4216]

Ha! Unintentional but a good spot 😉

[@InsaneCarville]

Countless arrangements I've been listening to for a few months and couldn't put my finger on why I loved it so much... until NOW. Thank you so much for doing this!

[@trocomposition4216]

You’re very welcome!

[@russellshanahan8810]

This is a fantastic analysis thank you for the time and effort.

[@trocomposition4216]

Thanks, Russell! Glad you’ve found it useful 👍

[@Tylervrooman]

Great work! Can't wait to see more!

[@petermole3872]

8:04 You seem to have gathered a lot of admirers with this video. Let me join them. I have come back to Contrapunctus I in recent weeks and having watched again, I am sure I shall play better tomorrow. Thank you very much

[@trocomposition4216]

You’re very welcome, Peter! Thank you for the kind words 😊

[@m.calloway2624]

Superb analysis. I particularly like how you deal wirh all aspects of the music, including artistry, and in an integrated fashion. Would love to have your analysis of Beethoven's Grosse Fuge quartet. Many thanks.

[@trocomposition4216]

Thanks for the kind words! 😊 If you haven’t seen it yet, I highly recommend Richard Atkinson’s analysis of the Große Fuge: kzbin.info/www/bejne/gYLGeYOejqqigLs

[@andreslka]

Thank you. That's Sokolov recording, right?

[@trocomposition4216]

It is! 👍

[@canman5060]

Love this anaylsis.

[@omarsalcedodelatorre6255]

Thank you for your analysis! It helped me a lot!!👍😉

[@trocomposition4216]

You're very welcome, Omar! I'm glad it helped 😊

[@AntonioLarizza]

Nice job dear friend, thank you!

[@trocomposition4216]

You're welcome, Antonio! 👍

[@NN-rn1oz]

Good mythical morning, Link. And thanks for the great lesson!

[@AnaPaula-np5rq]

Would it be possible for you to include subtitles in Portuguese, Spanish or German?

[@trocomposition4216]

Hi Ana Paula. You can get auto-translations by going to the settings wheel in the bottom right corner, clicking 'Subtitles', then 'English (auto-generated)', then selecting subtitles again and opting for 'auto-translation'. From there, you can select the language. It won't be perfect but hopefully should help! 😊

[@AnaPaula-np5rq]

@@trocomposition4216 The only translation option here is englisch, has no other language. No problem. My understanding of English is primitive. I like to write comments and have to use translator. 😢

[@canman5060]

This is like integral calculus in Mathematics !

[@doctor78212]

Excellent observation. Music theory is beautiful math.

[@ValzainLumivix]

Nice

[@rogerperry2182]

Thanks to you I love Bach even more !

[@trocomposition4216]

That's great to hear! 😊

[@evangelos6509]

This is so nice, thank you!!!

[@trocomposition4216]

Thanks, Vangelis! More AoF to come 👍

[@luciangabrielpopescu]

Truly amazing analysis: 28:14

[@trocomposition4216]

Thanks, Lucian! Much appreciated.

[@janetsoskice8461]

Hi

[@donbroni]

do you teach privates near or in london would love some assistance on learning this fugue

[@trocomposition4216]

Hi Donald. I’m afraid I don’t, but very best of luck with learning this masterpiece! 👍💪

[@donbroni]

@@trocomposition4216 Thanks for the encouragement your resources here will help alot

[@dawsonstearns]

EXCELLENT thank you for this exquisite analysis

[@trocomposition4216]

Thanks, Stacy! You're welcome 😊

[@mustuploadtoo7543]

i love these videos. please keep making them :)

[@trocomposition4216]

Thanks! Will do 👍

[@mustuploadtoo7543]

@@trocomposition4216 i have got notifications on so i wont miss it 😎

[@ZephaniahL]

Are you Tim's brother?

[@trocomposition4216]

I am 👍

[@oboista6963]

What is the name of the book?

[@trocomposition4216]

The book I referred to by Ebenezer Prout is just called ‘Fugue’. Highly recommended! 👍

[@oboista6963]

@@trocomposition4216 thank you!!!

[@lukegregg5944]

Fascinating, could you perhaps do a video covering an impressionistic piece? I'd like to see how you tackle analysing and understanding something like that compositionally. But more content of anything like this would be great.

[@trocomposition4216]

Thanks for the suggestion 😊 I've got a few things lined up for the immediate future but will definitely add this to the list.

[@talastra]

No, not the impressionists. Shostakovich's 24 Preludes & Fugues, and the Shchedrin's *heeh* [no seriously] :)

[@johannesbrahms3322]

Your channel is gold! Keep it up!

[@trocomposition4216]

Thanks, Severin! Appreciate it 😊

[@Rocksssfull]

"BaK"