The Art of Fugue – Contrapunctus I (2021) | Hacker News Reader

The Art of Fugue – Contrapunctus I (2021)

ethanhein.com

133 pointsxeonmc62 comments

Every once in a while I get a giant traffic bump on an old post, and it's because someone shared it here. It's always a nice surprise. Thanks for reading!

Thank you for the wonderful post. I was humming the Nomai leitmotif from Outer Wilds[0] when two earworms came up simlutaneously: this, and the Little Fugue, and for some reason they comingled in my mind that I couldn't remember which subject was which, so I went googling which was how I found your post.

[0] https://youtu.be/zHm-GAuy8CI?si=8iSgsn_D5g0LFovt&t=72

Excellent article and great analysis of the state of the fugue - your insight has motivated me to dig out some Bach from the old piano bench and give things a bit of a bash.

As a musician, stuck in a bit of a rut of late, this kind of thing really helps get the juice flowing again. I’ve spent 15 minutes churning through some fingering and activating old muscle memory I’d forgotten about completely since the piano lesson days, and tonight’s jam session with my band is going to have some new flavours to introduce.

Good stuff, thank you!

The Netherlands Bach Society is trying to record all the works of Bach and make them available:

* https://www.bachvereniging.nl/en/allofbach

Their Art of the Fugue is a multi-instrumental joy. Here's where Contrapunctus I starts: https://youtu.be/N6sUlZa-IrU?t=7

wow. thank you.

The visualizations here remind me of the old Bach WTC analysis and commentary website that used David Korevaar's performance (and some others for the ones on organ or harpsichord) and Tim Smith's analysis. Problem was, they were all done using Flash.

Some amazing person uploaded video versions to Youtube. I would highly recommend them: https://www.youtube.com/playlist?list=PLYwl4jo5DoXTTPY0P8Tlc...

This one in particular is beautiful: https://www.youtube.com/watch?v=g9ShwIrMJlU

Here is a free recording of a piano performance of the Art of the Fugue by Kimiko Ishizaka:

https://kimikoishizaka.bandcamp.com/album/j-s-bach-the-art-o...

This artist also has a free recording of her Goldberg Variations available:

https://opengoldbergvariations.org/

Her bandcamp page also has the Well-Tempered Clavier, and two of her own albums:

https://kimikoishizaka.bandcamp.com/

Thank you! Just listened to some of the Art of the Fugue & enjoyed it very much

Since no one else has done it, I'll plug the Canadian Brass recording -- it's one of my favorite recordings of the Art of the Fugue, and (among many other things) just shows how flexible and instrument-agnostic this music is.

I adore the Canadian Brass' recording, and also the other Bach pieces they have transcribed.

I'd also like to plug the album released by the Academy of St. Martin in the Fields, who did a double album of the Art of Fugue and the Musical Offering, and used a variety of different scorings for each movement.

This and their Pachelbel's Canon were what ignited my love for classical music as a child.

Except nobody would call "The Art of the Fugue" classical. It's baroque.

For what it’s worth: plenty of people would refer to it, broadly, as classical music.

https://en.m.wikipedia.org/wiki/Classical_music_(disambiguat...

It’s not music from the classical period. Indeed, it’s from the baroque period. But in my decades of talking about and performing classical music, the term has never led to confusion.

That comment is mind boggling. I've spent a large fraction of my life playing in classical orchestras and also never heard anyone get confused. Yes, classical music is a genre and a period. Bach is in the genre, but not the period.

I hope the commenter learned something from their attempt at pedantry.

You're replying to someone who did, and plenty of others do. Language is fluid and flexible.

There are two uses of classical in modern parlance: classical as in the classical Mozart period, and classical as in anything that spans from Baroque to the late romantic Rachmaninov era and other composed music that uses largely traditional harmony or atonal music along the lines of Shoenberg.

I love this one too, and spent an incredible amount of time identifying the particular recording from audio memory as a kid in the 90s when my dad used to play it. Really excellent renditions, and I'm no classical music buff, it's just almost objectively brilliant regardless of musical tastes.

Bach's fugues are amazing, they sound great on harpsichords and organs, whereas some piano music sounds very wrong when it is payed without all the volume modulation, the fugues are carried by the interactions between the melodies, the counterpoint.

Bach in general is amazing in terms of surviving all sorts of transcription and mutilation. Compare the Little Organ Fugue as originally intended:

https://www.youtube.com/watch?v=ddbxFi3-UO4

to the a cappella version by the Swingle Singers:

https://www.youtube.com/watch?v=uhU7euFPWwo

Some music is very much tied to a particular instrument, but Bach is more or less universal.

I much prefer the art of fugue on strings. The Delme Quartet is the best rendition I've found.

The two pauses in contrapunctus 1 are, in my opinion the two best pieces of silence in the whole musical canon. I always think of the chords that come after theme as 'from his mother's womb untimely ripped'. They can make me weep when I'm in the right mood. (sorry for the over-sharing...)

Nothing to apologize for.

The Art of Fugue itself was unfinished but if as the story goes, he died as he was penning the last bar of fugue 15, then he kind of signed himself out in the sense that the notes corresponding to the letters (in German) BACH are spelled as a motif as B flat, A, C and B natural in the 8th to the 5th bar before the final bar which is unfinished. I have no idea if this true. We do know that this unfinished fugue was the last piece he wrote.

This is a tall tale told by one of his sons to pump up the mystique (=> market value) of the unpublished work at the time of his father's death. Common sense and technical analysis tell a different story.

By all means,there's no way anyone, even the great Master himself, could have undertaken a project of 14 fugues with various subjects, with the final one (14, not 15) being a quadruple fugue that combines four of them together, without being certain of what the subjects were and that ultimately they could indeed be combined.

Bach scholars have analyzed the paper and the device used to draw staff lines to show that a completed version likely existed, now lost.

Wow! Each recording is better than the other!

As a non-musician sometimes I have difficulty on following Bach's contrapunctus, particularly on orchestral and organ works.

I like how most recordings here slow down the tempo, allowing us, the ignoramus, to follow the melodic lines.

If you like this approach I highly recommend a few recordings of the Brandenburg Concertos with slower tempo made by an orchestra in St. Petersburg under a maestro called Alexander Titov.

For the last week I've been listening to the recordings by The Academy of Ancient Music under Egarr, and by the Concerto Italiano under Alessandrini. The latter is fun and raw and jaunty — it feels much more alive than the Academy of St. Martin in the Fields / Sir Neville Mariner recordings.

Will check out the St. Petersburg Opera Orchestra / Titov recordings today — thanks for the recommendation!

You can enjoy them either way: you can try to follow the individual voices, or listen to the overall texture, and you can switch too. It's all about enjoying the music as deeply as you can. Listen to it again, listen to other performances or re-arrangements, and see what you like best. There are people who don't like the organ, but many have been transcribed. Some organ pieces work even better on piano than organ.

But it's not for everyone. I had a colleague who called the violin double concerto tedious and long-winding, whereas I think of it as a fantastic piece which by itself is enough to put Bach in the top tier.

To be quite frank, as a high-trained musician, I like almost all of Bach's works played slower. You can almost always slow them down more than whatever you think is too slow and find new things to appreciate. Paulstretch to the rescue!

I fell in love with this piece hearing Michael Winograd play it on clarinet: https://www.youtube.com/watch?v=mTsQ-TbQReI

Ah yes, Vulfmon! Jack Stratton seems to love his Fugues.

In case you haven't already: check out Vulfpeck /// Bach Vision Test; a really nice visualization of Contrapunctus IX a 4 alla duodecima.

https://youtu.be/vJfiOuDdetg?si=GF1mbszFHOky2QVd

Fugues are still being written. Here's one from 2016, although a bit controversial:

https://m.youtube.com/watch?v=RZxCAqCUgug

I don’t see anything controversial there.

How does an article like this on HN avoid having a comment referring to "Gödel, Escher, Bach: an Eternal Golden Braid"?

https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach

(Yes!)

(EDIT - formatting)

No kidding!

The FIRST thing that came to mind when I read that headline was Hofstadter's Contracrostapunctus in THAT book!

Check it out! Read it! And if you DON'T find the WHOLE hidden message, read it again, because it's spelled out RIGHT in the dialog!

Happy hunting!

Quite right.

An article referring to:

{e ∈ GEB|HN: e := article referring to GEB}

... might be considered rather self referential (especially if I have got my rather dodgy notation right). Note how I leave out several important definitions and leave them to your imagination. I will resort to hand-waving as required.

Hmmm: FIRST, THAT, DON'T, WHOLE, RIGHT. I speak en_GB you monster!

For the J.S. Bach fans, here's a fun site that organizes his cantatas calendrically: https://whichbachcantata.be/

Such a pleasure to read. using beats seemed almost profane at first but it allows for chunking the complexity where it could really help someone get what's going on. I don't listen to the fugues much, and really mainly guitar arrangements of his work I'd like to be able to play one day (allegro assai, lute suite prelude, etc), but it's hard not to get mystical about it. jubilance is the word I'd use for his work. for me the music forms an imaginary navigable space when I hear it, and as everything that lives can hear and count, every piece seems like a meditation on what can be aligned, harmonious, and essentially, True in a universal sense- the awe of a creation for its creator.

I'm an absolute amateur dilettante musician, but for someone just starting to hear his work, I'd suggest the skill is in being able to listen for separate voices and then follow them, and then to practice following them in simple pieces with enough dissonance in them to make you intellectually keep track of what's going on. the simplest possible polyphony someone can use to hone their attention that has analogues to early music may actually be Arvo Pärt's work, as once you can separate voices, the richness of Bach and other composers kind of explodes.

great fan of hein's writing, a pleasure to be reminded of it and to get to comment.

Amazing how Glenn Gould caresses that piano, in a performance that is almost a spiritual act.

Apart from geek toys that often cause more hassle and annoyance than they're worth, the most appreciated material things that I purchased in the first half century of my life are:

• The Art of Computer Programming (purchased the first volume aged 16, decades later I'm still waiting for volume 4 to be completed)

• Encyclopedia Britannica

• J. S. Bach: The complete organ Works on ten CDs.

The Voyager space craft contains a disc with Bach's, The Well-Tempered Clavier, Book 2, Prelude and Fugue in C, No. 1 on it, and the joke among space folks goes, one day a radio telescope will receive a message deciphered as S-E-N-D M-O-R-E B-A-C-H!

Don't waste your life striving to be fashionable, aspire eternal beauty and knowledge!

PS: I like the visualization, thanks for this blog post and bringing the beauty of Bach that is almost out of this world into a bleak Tuesday afternoon [on which nasty people drop bombs on children and people too stupid for the power they carry keep quiet about it]. I would like to see another visualization, which shows the music scores smooth-scrolling from right to left with all tones currently being played highlighted in yellow, and below the scores I'd like to see the hands playing said tones on the organ, all in temporal alignment.

Ad Gould: The phrasing at around 2:40, where he has this voice stepping into the previously dominant legato voices, is tremendous!

How did the Art of Computer Programming help you in those years?

Looks damn good on the bookshelf lol (I say with 3 volumes of the second edition right behind me)

I've used it to settle a few combinatorics arguments over the years too.

BBC Radio 3 has show Record Review (aka Building a Library) where they go over various recordings of a particular work and recommend particular one(s):

* https://www.bbc.co.uk/programmes/b06w2121/episodes/player

The Emerson quartet version blew me away when I first heard it. I recommend it over the piano versions because I think you hear the full extent of the voices better (coming from someone that loves and play the piano).

"It's very hard to perceive counterpoint, and there is a limit to how much we can perceive at once. 2 voices is hard and takes practice, 3 voices is even harder, but you can have these flashes where you hear clearly voices playing off one another and its like getting a glimpse into the divine."

I've always wanted to learn how to listen to counterpoint. Anyone have good tips on how to appreciate it and know what it means to perceive counterpoint?

Ha I've been learning the piano for over 30 years and I still feel the same as that quote and am not convinced I can hear so many voices at once so well, though admittedly I have improved a little recently because a lot of the music I have been playing has three or more voices and to play them you must hear them.

So playing an instrument (usually keyboard) helps - JSBach's inventions and sinfonias were written to teach counterpoint IIRC. If playing is out of scope then I found listening to orchestral music can be helpful because you can latch onto different instruments and learn to interpret what they're doing individually (first) then how they are interacting with other voices after. Strong quartets will similarly allow you to listen to multi-voice music that may sound more distinct than just keyboard.

The other piece of advice is to get very familiar with a particular musical work and listen to it repeatedly. Once the familiarity is there you'll start to pick up different things on repeated listens. If you then start changing the recording/performer you'll also notice how they choose to interpret passages differently and certain voices may sound more prominent which can be a hook for your ear to latch onto...

Just some initial thoughts, hope that helps!

EDIT - Pachelbel's Canon in D is probably one of the most accessible songs to practise listening to. Poor cellists always grumble about playing this one, see if you can hear why

I can understand when there are 2 voices, but when there are 4 independent voices how on Earth does one follow them.

I prefer to simply be taken along.

It happens when you don't think about it.

Practising Bach's music certainly helps.

But yes, just letting it flow and paying attention without trying to learn or remember anything, is probably the best answer.

It's like an orchestra (or the different sections of one), the melodies are written to fit together perfectly.

There are many almost "poppy" feeling fugues in the Well-tempered clavier with four voices.

In comparison, The Art of Fugue feels more academic and dry to me personally. I still like it, but don't feel as connected to it in as to many of his other works.

Tangent ahead: even good pop songs require melodies that are more than just homophonic. Best example in rock, pop, disco for this are good bass lines I think.

Incidentally, "bass lines" are also an important fixture in the history of baroque music.

I'm not preaching here, I'm not good at music theory or playing music. But I think many pop songs also follow counterpoint rules, at least to a degree. There are also varying degrees of strictness regarding these rules in Bach's music.

It doesn't need to be an academic puzzle as many make it out to be, I think the intent was to formalize how to write good music for multiple voices.

All that said ... you are still right :D

But it's even more impressive the way solo keyboard artists can articulate these voices.

Not to mention the organists.

It's a life endeavor that you will never master. start at age 4 playing minuet in G, at age of 90 you'll still be learning new things. The music is beyond us, yet ourselves, to paraphrase Wallace Stevens. All we can do is enjoy the ride.

Also worth reading: https://listenlearnanddo.wordpress.com/2013/02/11/bach-badas...

Also, let us never forget what Laibach have done to it

https://www.youtube.com/playlist?list=OLAK5uy_k0PDQPcIZG5_gJ...

Being able to compose fugues well is notoriously difficult.

Mozart was never able to.

Beethoven on the other hand...

https://en.m.wikipedia.org/wiki/Grosse_Fuge https://youtu.be/hUaziUz4jx0

So you want to write a fugue? https://m.youtube.com/watch?v=8sogUjiqg2c

A music history prof in college described this as "the ultimate raised middle-finger to the audience — Beethoven at his most I'm-writing-for-me-only."

Mozart wrote several fugues considered very good, the most famous of which is the Kyrie from his Requiem, which is a double fugue to boot.

Check out John Mortensen's YouTube channel.

https://www.youtube.com/@cedarvillemusic/videos

He can improvise fugues on the spot. A lot of earlier composers could do so as well because their training from the get-go was improvisation.

I thought I would check out your comment against other opinions: " Mozart’s contact with the mastery of the German contrapuntal tradition opened a completely new musical horizon. He produced a number of stand-alone fugues, and this newly gained compositional skill helped to inform the creation of his final sublime orchestral masterpieces. Words simply can’t describe the jaw-dropping and breathtaking fugal display of quintuple invertible counterpoint in the final movement of the “Jupiter.”

We should all listen to the Jupiter and decide for ourselves if 'Mozart was never able to'.

https://interlude.hk/fugues-and-other-musical-charms-from-ba...

> Mozart was never able to.

* ending of the last movement of the Jupiter Symphony

* Introitus of the Requiem (four-voice ricercare in the instruments, then cascading upward in SATB choral writing, both combined with an operatic-style accompaniment)

Here's a mind-blowing one-- at the end of his String Quartet K. 387 in G major. This is a modified rondo-sonata form where the rising figure of the rondo theme-- normally just a simple, catchy, tune-- is actually the subject and answer of a fugue! I'm fairly certain Mozart is the only composer of his era to substitute a fugal exposition for the rondo theme in a modified rondo-sonata form[1].

Even more impressive, the 2nd theme is a different fugue which continues into the rondo theme for-- you guessed it-- a double fugue.

All of this is so fast, effervescent and seamless that someone like OP could be forgiven for not even noticing the fugue. So now OP must ask-- how many other examples are there of Mozart subtly shifting into and out of first-rate Bach-like contrapuntal textures?

It's a question Beethoven undoubtedly knew the answer to, at least for all the Mozart scores he could get his hands on.

1: Haydn has a great musical joke at the end of the so-called "Lark" quartet-- in the middle of a fast, old-school Rondo he switches to minor and plonks down a thick four voice fugal exposition and development against the fast-flowing figuration from earlier. It disappears as quickly as it came, like Carl Stalling but before the era of cartoons!

It took me until my 40s to really enjoy Mozart. The thing is, if you approach it from the stodgy perspective of a "Classical Music Enthusiast" then it's easy to miss what's delightful about it, but if you aren't trained in listening to classical music, it's not that accessible.

It's like that with a lot of jokes. If they don't make you grin and laugh, it's hard to "get" what's so special about them. Bach you can kinda just zone into and gradually uncover what's special (or not), and just keep uncovering, or fuguing out, or whatever. Mozart, the joke is here and gone, and if you missed it, the whole thing just kinda doesn't seem all that special.

Like a joke, you can have the punchline explained to you, but it won't make it funny, and you'll question the taste of those who do. But if you find yourself grinning, you'll only find more things to grin at the more you listen. As a kid and young adult I kinda hated Mozart. I was really surprised when I started liking it, more and more, and now I can't get enough.

That's been my experience with Mozart, anyway.

Mozart is all charm and jokes and smiles until you realise there are monsters swimming under the surface.

I think I know what you're talking about here, but maybe not. Can you elaborate?

First, I did want to point out that my claim that "Mozart was never able to" didn't mean that I thought he wasn't able to compose fugues, rather I thought he wasn't able to compose fugues WELL--definite emphasis on "well".

Second, what I mean by "composing a fugue well" is to be able compose a piece or movement whereby three or more, usually four, voices are heard in a contrapuntal, not harmonic, manner for an EXTENDED PERIOD OF TIME (i.e., maintaining this for many measures).

I looked closely at some of the examples people brought up like the last movements of both the Jupiter Symphony and his String Quartet No. 14 and nowhere do I see 4 voices simultaneously acting contrapuntally for more than just a handful of bars. Mozart would often write a given voice contrapuntally, but would often quickly revert that voice to a harmonic function. If you look at measures 91 to 106 in the last mvt of Quartet No. 14, that writing is a joke if you say he can write fugally. The second violin, viola, and cello are all mainly serving a harmonic function; they're just playing chords. One part that might look truly fugal would be in measures 112 to 117, but that's just one small part and not extended, as in the great fugues of Bach and Beethoven. Measures 61 to 90 kind of look truly fugal, but he really only has 3 voices going contrapuntally here at any given time, not 4. Look at measures 63 until 68 where the cello is playing an extended rest, for example.

Yes, Mozart wrote fugues. Did he write truly sophisticated, truly "fugal" fugues? I still think not.

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