Magnificent Counterpoint in the Finale of Mozart’s Jupiter Symphony

Magnificent Counterpoint in the Finale of Mozart’s Jupiter Symphony


Hi. I’m Richard Atkinson. This video will analyze the magnificent counterpoint in the finale of Mozart’s “Jupiter Symphony,” # 41 in C major, K. 551. The movement has been celebrated for more than 200 years as one of the quintessential examples of craftsmanship in Western music. In this analysis, I will discuss its many incredible contrapuntal passages, culminating in the coda, during which five of the previously introduced themes are combined at once in five-part invertible counterpoint. The sonata form movement begins with a simple homophonic statement of theme number one, which consists of four whole notes. It will be highlighted in red for the remainder of the movement. It is answered by a frequently recurring rhythmic motif that I will highlight in gray since it does not play a role in any of the future contrapuntal passages. Theme number two immediately follows this, and consists of a dotted figure followed by a descending configuration of eighth notes. It will be highlighted in green. The first significantly contrapuntal passage occurs now, when theme number one (or at least the first three notes of it) enters as the subject of a fugal passage, with this short underlined figure acting as the countersubject. After this forceful statement of theme number one, theme number three (highlighted in blue), consisting of three staccato notes followed by a trilled dotted figure, makes its first appearance as a stretto between the first violins and the cellos and basses. “Stretto” is the fugal term for when the entries of the subject are squeezed together such that the second enters before the first is finished. Although it does not strictly apply to anything in this movement, I will use it to describe moments when the themes enter in such close succession. The stretto involving theme number three begins the modulation to the dominant key, and is immediately followed by a stretto involving theme number two. In this case the second entry occurs only one beat after the first, with a third, abbreviated entry in the horns of just the dotted rhythm, giving the appearance of three-part imitation. With the dominant key of G major now firmly established, this is the moment in a normal sonata movement when old or new thematic material would enter in the new key. In this movement, it consists of a fourth theme played by the first violins (highlighted in orange), a fifth theme played by the oboes (highlighted in yellow), the previously-mentioned third theme (played by the bassoons), and the previously-mentioned second theme (played by the flute). This is followed by another stretto of theme number three between the flute and bassoon, and then by an incredible stretto of the newly-introduced theme number four. The stretto involving theme number four begins with imitation of just its first three notes, with entries separated by the space of one measure. Subsequently, the entirety of theme number four is played in a remarkable four-part stretto, with each entry separated by the space of only one beat. Most of the orchestra now plays fragments of theme number four. This is followed by a passage featuring the recurring motif that was highlighted in grey, and another three-part stretto including variants of theme number two, including the original theme played by the violas and cellos, a syncopated version in the flutes and oboes, and a non-literal inversion of the theme played by the violins. An inversion is the [VERTICAL] reflection of the original music. In this case the overarching direction of the theme is inverted, but it is not a literal inversion (which actually does occur later in the development section). The exposition ends with two final statements of theme number two, first from the solo oboe and then from the solo bassoon. The development section of a sonata form movement typically explores distant keys while subjecting the material from the exposition to further development often by treating it more contrapuntally. In this movement, Mozart has already treated the material in an extremely contrapuntal manner, so the development section is relatively short. It begins with a statement of theme number one, answered by theme number two, followed by theme number one in a new key, answered by the literal inversion of theme number two. This is followed by a four-part stretto of variously truncated versions of theme number two, and then by alternating statements of a rhythmic variation of theme number one in the winds, and strettos involving theme number two and its inversion. The development section ends with statements of theme number two and its inversion, followed by a wonderfully elegant modulation back to C major, using entries of the dotted beginning of theme number two in the first bassoon, second bassoon, horns, and finally the entire theme in the first violin. As we’ve just heard, the recapitulation section begins with theme number one, followed by the recurring gray highlighted motif (much like in the exposition). Suddenly, the violins enter with modulating statements of theme number one in C, D, and E. At this point theme number one has its first stretto, between the first and second violins, modulating back to D, then back to C. Now listen to the remainder of the recapitulation section, which is similar to the analogous sections in the exposition. We’ve finally arrived at the famous coda, which continues with a stretto of the almost literal inversion of theme number one, between the high and low strings. This stretto is almost M. C. Escher-like in its configuration, since lining up the inversions of theme number one in this manner, creates additional instances of the non-inverted theme. This leads to the crowning moment of the symphony: an incredibly complex passage that features five-part invertible counterpoint. Invertible counterpoint occurs when contrapuntal lines are interchangeable among instruments of different registers. This passage begins with a simultaneous statement of theme number four by the violas, and theme number one by the bassoons, horns, and cellos. With each successive repetition a new theme appears. First, theme number three is added; then theme number five; and finally theme number two. Now all five themes are played together, interchangeably among the different parts. The symphony ends with statements of the recurring grey highlighted motif and theme number two, in a majestic conclusion of one of the most magnificent movements in the symphonic literature.

100 Replies to “Magnificent Counterpoint in the Finale of Mozart’s Jupiter Symphony”

  1. Correction: an inversion is the VERTICAL reflection of the original music (for mathematics purists out there). I meant that it is reflected over the horizontal (x) axis.

  2. Thank you for sharing this brilliant analysis of a phenomenal piece of music. Just to add another observation, theme 1 appears against itself in retrograde at the beginning of the recapitulation. The theme enters in its original form in the first violins at bar 225 and is answered by its retrograde in the violas at bar 227.

  3. I just posted on Instagram and Facebook my sense of being admiringly overwhelmed by the complex construction of this movement. A follower alerted me to this analysis of yours. Wonderful – congratulations and thanks. (My only caveat is that the word “incredible” is overused and perhaps always inappropriate here; your work is making Mozart’s composition credible.) I’ve watched and listened twice, and shall return. And I look forward to more of your work.

  4. As a preteen I somehow ending up with a box set of all the Mozart Symphonies. This being the last one I listened to it quite a bit. Especially when I found out that Mozart was Einstein's favorite composer. My mom (I guess) made sure I had access to a broad spectrum of European Art music as a child. I might add we were working class in the 60s but my mom was deeply influenced by a college music apreciation class when she arrived from Asia as an exchange student in the early 50s. I seem to remember All the Beethovan Symphonies as well as a Box set of all of Bachs Organ works. But really Jazz was the thing for me as soon as I heard Modern Jazz Quartet and Vince Gauraldi's Charlie Brown music. But hearing this now is like seeing an old friend. Also for great harmonic analysis of #40 Gminor "1st movement" go to my channel and checkout Bernstein on Mozart.

  5. The dialogue between the strings and the woodwinds in the development is very haunting in its contrast when the woodwinds quietly answer.

  6. I am translating a book on great composers from English to Korean and I am here to figure out what the author was saying specifically about this movement as the contrapuntal culmination of Mozart's music. And I couldn't be more grateful for your hard work. It really enlightened me. Thank you very much.

  7. Hi Richard,
    Terrific analysis as I've mentioned before. I have some difficulty with the grey theme since it seems to occur somewhat frequently during the movemrnt
    Is it the character of the theme that led you to not include as a major contrapuntal theme? We know it occurs at the end of the coda leading back to the homophonic texture that ends the movement. If it was included, as Adler does in his book on orchestration, then he probably is not included one of your major themes. I will look this up and get back to you (I believe I said I would do this before in another post. I'll get back to you on this this time)
    There seems to me to be an excellent chromatic section that's not very long but creates some great tension.
    Thanks for your comment to me concerning Haydn.

  8. This only made more confused. Start picking at the surface and you’ll soon discover a dozen more layers that will take a lifetime to understand.

  9. We know that the last three symphonies were not performed in Mozart's lifetime. Did he make comment about these three symphonies in his letters?

  10. Brilliant explanation of the brilliance that was Mozart. This music gives me chills; it was nice to see a glimpse of what makes it so interesting. Thank you!

  11. Mozart is the bridge between the Classical and Romantic styles. It is a pitty he only lived 35 years. Luckly is a sense Beethoven finished what Mozart started.

  12. Richard, I have watched this a number of times.  your patient analysis is wonderful to behold.  thanks for taking the time to reveal a little bit of what has bewitched us for so many years!

  13. Love this recording! Been listening too much to period performances of this. It's great played by a classic chamber orchestra.

  14. Mr. Atkinson, you analyses are marvelous! Thank you for publishing this and all of your other studies of the literature!.

  15. Es interesante constatar la impresionante evolución de la obra sinfónica de Mozart, desde sus alegres pero relativamente simples sinfonias de juventud hasta este último tiempo de su última sinfonía : la cima del Clasicismo Musical ! ( siendo todavía joven 1788 ).

  16. This is such a magnificent piece. When I hear this, I get a feeling of transcendence and uplift. Thanks for the analysis.

  17. The color delineation of the passages (the analysis) discussed must have taken many hours
    And is sensational, I have been reading scores for 60 over years, I am 89, and have never seen such a thorough job well completed.
    Now set to work and do the same for your new copyright printed edition of JS Bach’s 48 . !!!!!! I would love to relearn them
    being told with the colors what I should tell my listeners, and myself as I play. Lovely. Lovely. Have just finished
    Learning another 48 set by the Russian composer SHCHEDRIN , Bach would have been astonished, intrigued and disgusted at the same time.

  18. Apart from the vocal comments could you post a super slow motion movie of that movement with
    Links back and forth so one can repeat each passage until known like passage practice on the piano.
    Just add the links and film your existing movie in super slow motion. I have no idea how to do it. I hope you have started a whole new fashion in printed music.

  19. Thank you for a brilliant analysis, sir. Your color codes provided an excellent guide to remarkable ability of Mozart to weave them into this amazing finale without sounding scholarly. That of course is magic. There are a few questions asked by unexpected entrances in unusual entrances in remote keys. Mozart makes the question mark then sound logical with wit, nobility, humanity and a sense of joy, exuberance to launch the human spirit.
    Thank you, sir, for adding to our love of Jupiter Symphony.

  20. Major differences in mozart fugues and Bach's. In name only. There is the gallant. Style here that Bach might have found foreign

  21. Mozart is much more Melodic than Bach.
    Bach is Architectural Mathematically.
    Mozart is Architectural Melodically.
    Much prefer Mozart.

  22. Orchestras in the late 18th century were much smaller, more like a chamber ensemble. Hearing this played by a modern orchestra makes the intricate counterpoint IMO harder to hear. One should really listen to the "Jupiter" played on period instruments, where the themes really "pop" instead of becoming muddled.

  23. Hello, Richard Atkinson- we at the Community-Fusion Network are holding a competition for the greatest string quartet from any living composer in the world we can find, and the Ensemble Odeon will play it in live concert.

    I understand this is a bit abrupt, but would Richard Atkinson like to be the 5th judge of the "CFN International Composition Competition: String Quartets" as an obvious expert on counterpoint? We'd love to have you!!😊😊

  24. Mozart was more talented than Bach. Mozart started writing fugues at 12. Bach didn't even write his first composition at 20.
    MOZART'S FUGUES (number inside brackets indicate the age he wrote them)

    Missa solemnis in C minor "Waisenhausmesse" KV 139 Gloria (12): https://youtu.be/vnxH8M31F3g?t=1023

    Missa solemnis in C minor "Waisenhausmesse" KV 139 Credo (12): https://youtu.be/vnxH8M31F3g?t=1851

    Mass in C major "Dominicus Messe" K66 Gloria (13): https://youtu.be/rlQJ2bgK3RQ?t=979

    Mass in C major "Dominicus Messe" K66 Credo (13): https://youtu.be/rlQJ2bgK3RQ?t=1869

    Miserere in A minor, [4-part contrapuntal study] K.85 (14) https://youtu.be/_PxqQOUn1v0

    KV125 – Pignus Futuræ Gloriæ (16): https://youtu.be/dQ77xyyffjA

    Missa in honorem Sanctissimae Trinitatis in C major KV 167 Gloria (17): https://youtu.be/X9T_URjVl5I?t=167

    Missa in honorem Sanctissimae Trinitatis in C major KV 167 Credo (17): https://youtu.be/YvCnr15hh78?t=584

    Missa in honorem Sanctissimae Trinitatis in C major KV 167 Agnus Dei* (17): https://youtu.be/g2teM5WckzA?t=175

    String Quartet No. 8 in F major K. 168 (17): https://youtu.be/3JDrlCG-y_E

    String Quartet No. 14 in D minor K. 173 (17): https://youtu.be/q5MVDsqIqCY

    Litaniae de venerabili altaris sacramento K243 [double fugue] : VIII Pignus (19): https://youtu.be/U-PDJozhBLI

    Misericordias Domini in D minor K.222* (19): https://youtu.be/lEBYufTXJQk

    Missa Longa in C K262 Gloria (19): https://youtu.be/yCDFfN7g_Bk?t=408

    Missa Longa in C K262 Credo (19): https://youtu.be/yCDFfN7g_Bk?t=1020

    Vesperae solennes de confessore in C, K.339 – 4. Laudate pueri Dominum (24): https://youtu.be/c3rDwFFQ6bQ

    Missa solemnis in C, K.337 – 5. Benedictus (26): https://youtu.be/ghAa3BJ4b5I

    Praeludium and Fugue KV 394 (26): https://youtu.be/m9vVu8rNON4

    Suite in C K.399 – I. Overture K399 (26): https://youtu.be/UHgs7-u7wGQ

    Sonata for Keyboard and Violin No. 29 in A Major, K. 402: II. Fuga (26): https://youtu.be/mMe4MCsH2WY
    Trio (Fuga a 3) in G Major, K. 443 (27): https://youtu.be/UtLOtTDk848
    Fugue In G Minor KV 401 (27): https://youtu.be/tXpV-gpgkQw

    Fugue In E Flat Major KV 153 (27): https://youtu.be/_2rpWr3etWo

    Fugue In G Minor KV 154 (27): https://youtu.be/2t42ZCeLxlk
    Grosse Messe in C minor KV 427 Jesu Christe — Cum Sancto Spiritu [double fugue] (27): https://youtu.be/97Twh_q8lQs?t=1719
    Grosse Messe in C minor KV 427 Sanctus — Osanna [double fugue] (27): https://youtu.be/97Twh_q8lQs?t=2696
    Adagio and Fugue for String Orchestra in C Minor, K. 546 (32): https://youtu.be/PFXF0Aysh4w

    Fantasia for mechanical organ in F minor K594 (34): https://youtu.be/Qka_HMc2ajc
    Fantasia for mechanical organ in F minor K608 (35): https://youtu.be/Jkh8Re4JUCw
    Overture to Die Zauberflote K620: https://youtu.be/c2TGbfzTx2A
    Der, welcher wandert diese StraBe voll Beschwerden (35): https://youtu.be/kB56nw1zx-o
    Requiem in D minor K626 Kyrie [arguably the greatest double choral fugue not written by Bach]
    (35) https://youtu.be/8ybTabIfLgY
    Requiem in D minor K626 Domine Jesu (35): https://youtu.be/i4DyyUvZws4
    there's more

    + tons of classical counterpoint in string quartets, quintets, symphonies, concertos

    + tons of choral, vocal, instrumental canons and canonic minuets

    Magnificent Counterpoint in the Finale of Mozart's Jupiter Symphony: https://youtu.be/YTxYykhQZbI
    The Ingenious Fugal Finale of Mozart's G Major Quartet, K. 387: https://youtu.be/uoXDHOyfJ-k
    The Incredible Finale of Mozart's K. 590 Quartet in F Major: https://youtu.be/nkbdUjjfRTQ
    Invertible Counterpoint in the Finale of Mozart's D Major String Quintet, K. 593: https://youtu.be/IQbxsGtyc2g
    Mozart: Canon for four voices, in C major, Anh. 191, K 562c: https://youtu.be/YC9bKfzXC18

    *Beethoven wrote his 9th symohony choral parts from studying these two choral works of Mozart

  25. Wonderful analysis; the contrapuntal climax in the coda is breath-taking. Mozart the symphonist went out with a bang. Lots of Bach study behind it.

  26. Listened to this gem for 45 years and never realized the 5 themes or the remarkable counterpoint between them. Thank you for an added great Mozart enlightenment!

  27. Thank you very, very much Richard! Up to now, this magnificent part was too complicated for me, because I didn't understand at all what was happening. This vid gives me much more understanding of the techniques Mozart used. I play clarinet in an amateur symphony orchestra in Deventer, the Netherlans, but I bet our conductor wouldn't dare to put this piece on our desks!

  28. One comparison is where six themes – some rhythmically amended – come together at a ting on a ‘triangle’ in the mastersingers overture by wagner.

  29. With all due respect to Mozart and yourself, this is a great piece and you do great work Richard, but it's really just imitative counterpoint with simple countersubjects; your analysis while fantastic, just dresses up simple ideas in highfalutin language and technical jargon, all the words make it sound more complex and impressive than it really is. And with further due respect, musical analysis
    is more of a description of what was done, it does not usually explain why it was done. But of course one cannot read the composer's mind, we only see the product of their ideas in what's likely an imperfect representation of what we might call a more perfect underlying form, and for most of us it would be a feeble and useless attempt to make sense of the mind and thoughts of a genius.

    What I'm saying is that calling this "magnificent counterpoint" (which while it may well be and probably is) is like saying a simple 4-part round of Row, row, row your boat or Frere Jacques is a great piece of music. Yeah, it sounds interesting enough because the "ear is dumb compared to the eye" and I think we have difficulty making sense of things aurally if they are of any degree of complexity, but I'm not sure how many people would call either a masterpiece. Sure, Mozart adds some further complexity, he adds things which aren't an exact imitation/repetition of the main themes, but as a composer, particularly one of his stature and ability, that is to be expected.

    I would also say that I think the reason people like this work is precisely because it's simple, this is one of Mozart's more accessible works because it has a relatively simple structure and form, it has themes and counter-themes which can be easily identified and followed. Of course the fact that it's lively and energetic doesn't hurt either.

    In regards to musical analysis and theory, I would argue that the most important ideas, those that are purely creative and form the basis of composition, of writing/composing a piece of music, cannot be fully analyzed and understood. I mean, if/when we analyze a poem, especially a great poem, or a great piece of music for that matter, do we uncover its beauty, inspiration, and origins, or are we merely dissecting the goose laying the golden eggs in an attempt to find out what's inside, trying to figure out the technical reasons how and why something works? I would suggest that such a technical understanding, even if complete, would still miss the magic which is the music itself. There's just something about when it all comes together, how it's truly greater than the sum of its parts which cannot be fully realized or understood through musical/technical analysis no matter how sophisticated.

    P.S. With everything I've said, I do want to point out that I dearly love this piece, I just don't consider it the most magnificent, masterful, or complex examples of counterpoint(but I do realize that that was not your assertion).

  30. Excellent, very lucid and well presented. Would you consider the idea that the counterpoint in the bass at the recapitulation should be regarded as a retrograde inversion of the first theme?

  31. Putting five themes together at once and making it easy and pleasant to listen to…Now that is mastery of the craft of writing classical music. Well done Mozart!

  32. La fameuse superposition des cinq thèmes de la strette finale de la symphonie Jupiter est un hapax dans toute l'histoire de la musique symphonique. Comment décrire cet instant exceptionnel que Mozart nous donne le privilège d'entendre ? Ce tour de force hallucinant ressemble à une sorte de mise en abîme vertigineuse où notre regard, furtif et éperdu au dessus d'une organisation sonore d'une complexité transcendante, peut entrevoir cependant, non sans peine, l'espace d'une paire de secondes, dans cette épaisseur mathématique tourbillonnante, quelques détails des entrelacs arachnéens, quelques thèmes reconnaissables mais superposés en millefeuille savant. Un esprit sans égal a pesé ici chaque note de ce système sonore d'une perfection insondable. Ce passage, qui ressemble à une brèche dans l'espace-temps, ne dure sans doute que quelques secondes, mais ces secondes d'ici-bas suffisent à toucher un instant l'éternité divine, celle qui se trouve au-delà du Ciel empyrée.

  33. POWER. You can clearly see it now. In green, pink, violet & yellow. And sometimes, oranges. It turns out to be grey in sections.

  34. This entire movement feels like an ending finale that just keeps getting better and better.
    And when you think it's just going to do the typical ending, it does something amazing.
    Remember hearing just a portion of it the first time a small audio clip. I thought it was the ending portion of the movement. When I finally got a download of the entire movement back in '98 or '99 (remember dial up?) I realized it as just the first section of the piece. Then the ending, I didn't know anything about fugue, so I remember thinking: you can do this with music? It sounds like like an infinite wall of interchanging melodies that compliment each other, not a bunch of noise but like a buffet that you can hop your ear around to which ever melody or stand back and listen to them together.
    Since then, I'm always hoping for a finale that goes even longer with this fugue awesomeness.
    Ode to Joy's fugue is pretty cool. I wish a Swedish orchestra that performed a Zelda medley would have done a fugue of as many themes as possible at the end.
    It's like all time exists at once. Something amazing and special.
    With today's composition software, it probably helps a lot to make such things.
    The ending sounds like the making of a fugue but it's not 🙁
    https://www.youtube.com/watch?v=YrpWBgB6oz8

  35. This is not music. This is another dimension altogether. Mr Atkinson has helped us understand better this timeless masterpiece. Thank you for your extraordinarily lucid and clear contrapuntal analysis.

  36. Dear Richard, this finale is a revelation to me. I am not musically educated and you have deepened my understanding of this great work. Thank you dearly. Einar, Reykjavik Iceland.

  37. I'm embarrassed that I am so late to the party in discovering this channel. A wonderful and clear analysis. Well and delightfully done!

  38. I don't agree much with the terminology of calling "theme 2" what I consider an arpeggio with passing and neighbor tones, but I loved that Richard found a similarity with Escher.
    Also, the legend says that Alexander Glazunov told Shostakovich that Mozart's Jupyter Finale was like the Koln cathedral. If you ever have the opportunity to visit it, you'll know why.

  39. Richard, this is amazing. Could you help me with something, and sorry for the ignorant comment. I have always thought that one of the most astounding things about the coda is that it reveals that when themes 2-5 on played top of each other, they together reproduce the CDFE pattern of theme 1. That is, Mozart gave us themes 2-5 without us realizing until the Coda that they were all conduits for theme 1. I think I see it in the sheet music, but I admit I don't read orchestra scales well. What do you think?

  40. I am not a musician. Classical music has always seemed like magic to my uneducated ears: This video makes me more incredulous that any human being could put all this together so that it seems as if it just grew as a product of Nature. It is astonishing that in addition to the compser's genius, an orchestra can play this flawlessly. What a gift good recordings have been to a schlubb like me!

  41. Your pedagogy is very good. Through your interplay between visual and audible identification of ideas, something notoriously complex is rendered relatively easy to comprehend. San Jose Mike is correct that Mozart was exposed to fugue as a child, but this work and others, I believe, reflect his exposure to the great works of Bach and Handel at the salon of Baron Von Swieten in 1782. That changed his life, and his way of thinking. It's not just fugue. It's Bach, and Handel. It is notable that this movement does not feature any formal fugue. Is Mozart demonstrating that such rapid geometric transformations of ideas, should inform not just fugal writing, but all of music, and for that matter, creative thought? In ths movement, voices engaged in complex contrapuntal interplay merge into powerful unison statements of a classical theme. It seems like the strengths and discoveries of two very different traditions, "baroque", and "classical", will interact to mutual benefit.

    Any thoughts?

    Again, thanks for your presentations, and keep up the good work.

  42. I have had a problem with not understanding sheet music and especially not understanding where the logic comes from, why Mozart sounds so good. Your explanation is amazing, chunking information that would look like only random individual notes to me if there wasn't for your videos! THANK YOU!!!

  43. Thank you for your detailed explanation of this masterpiece which in my personal opinion, and everyone has their own opinion, is the greatest movement in symphonic music. There are comments in this section of Mozart having to work hard to achieve his work. I have been a believer more in the view of the music flowing out of him more naturally than in his hard work pondering. His output for his short years is astounding and much more per year of life than Bach or Beethoven, or anyone else I can think of for that matter. What's more, while it took Beethoven a lifetime to produce 9 symphonies, most of them masterpieces, Mozart produced his last three symphonic masterpieces (39, 40 and this one, 41) in a miraculous 6 weeks in the summer of 1788! That does not seem to have left much time for hard work pondering.

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