Infinity, Part 1

I love endings. I so adore placing that double bar at the end of a piece that I used to consistently hie with undue haste towards that goal, creating final cadences that felt rushed. As soon as I felt that I had composed the main ideas of a composition, I would push towards the first vaguely satisfying stopping point. When I was still a student, I met a slightly younger composer who tried to be helpful by informing me that endings should be loud and fast, because that was the best way to get dates. (Adding to the awkwardness of this conversation was the fact that he was talking with me and my soon-to-be wife.) However, I’ve always been drawn to music that ends with a sigh instead of a bang; music that attempts to transcend the finality of the page and to evoke the possibility of continuing into infinity.

Beethoven, Op. 132, Mvt. 3, final cadence in F Lydian

Beethoven, Op. 132, Mvt. 3, final cadence in F Lydian, a transcendent sigh

I will never forget the first time I heard Beethoven’s Op. 132 string quartet. As the players reached the glorious end of the third movement, the song of thanks in the Lydian mode (see above), I felt that I finally truly understood the mystery of Beethoven: why his music had lasted so long and why it needed to continue to be heard in live performances. I was emotionally sated and wanted nothing more than to go to a quiet place in order to meditate for a while in an attempt to understand what I had just heard. When the next movement began, it felt like such a strong slap to my face that I almost stood up and shouted for the players to stop. I understood that the conventions of his day required continuation, necessitated that loud and fast ending, but I also viscerally felt how wrong this was. I wanted nothing more than for the gently rising fade into the aural distance to be able to stand on its own.

From the very earliest discussions of music, cadences were defined as formulas. The various modes were distinguished by their ranges, emphasized tones, and especially by their cadential gestures. Musicians writing monophonic modal church music also produced compendia of the correct melodic closings for these chants. When other melodic voices were introduced, contemporaries compiled lists of the correct contrapuntal endings (hint: thirds were out, perfect consonances were in). Eventually, these stock musical fragments began to be defined by their harmonic nature, with the dominant and tonic polarities reigning over the tonal hierarchy.

In the 19th century, life on the cadential front became significantly more fun. Composers wanted to create highly original music that avoided formulaic gestures, therefore they began to re-think the ends of their pieces. No matter how many times I hear it, I always find myself unprepared for the ending of Chopin’s Opus 17 set of Mazurkas (see below). We’ve been in A minor for a while at this point, and at the final cadence A is firmly established. But what kind of A? After giving the listener four measures of pure tonic, Chopin returns to the opening figure of the movement, one with an undulating middle voice surrounded by A and F. So at the very end, the implied harmony is … F Major over A? A minor with an added sixth? It’s many things, none of which are a simple A chord. As the music dies away, we are left with a new type of closing, an ending that implies continuation and that invites the listener to imagine further sounds completing what the score leaves unresolved.

Chopin, Op. 17, No. 4, final cadence for a set of Mazurkas

Chopin, Op. 17, No. 4, final cadence for a set of Mazurkas

The last piece of music that Chopin completed was another Mazurka, which was published as Op. 68, No. 4. Throughout this dance, the music constantly moves forward, with falling chromatic lines leading from tonic (here, the F minor chord with an Ab in the bass seems to imply F tonic whereas the F major chord with A in the bass from the previous example implied A tonic) to dominant (see below). We never get any real resolution in F minor. Instead, the music cycles back to the original chord and the melodic lines keep descending.

Chopin, Op. 68, No. 4, opening

Chopin, Op. 68, No. 4, opening

Chopin, Op. 68, No. 4, opening

In this piece, the only real stability is a brief passage in A Major, the parallel major of the mediant of the parallel major of our original F minor (see below). That’s right, I said the parallel major of the mediant of the parallel major. I wanted to write out this relationship in these terms in order to point out how distantly related these keys are, and also it’s a fun party game to describe tonal relationships that involve mode mixture (your resulting amounts of “fun” may vary). Once we reach the chord of A Major, the bass remains static for a few measures while typical predominant to dominant to tonic progressions quickly unfold above it. But the static bass leaves us without a cadence in A.

Excerpt from the most stable part of Op. 68, No. 4

Excerpt from the most stable part of Op. 68, No. 4

When we reach the last written notes at the end of the page, we find Chopin’s marking “D.C. al segno, senza fine” or “return to the sign just after the beginning, without ending.” Stop and think about that for a second. Chopin is asking for the performance to continue into infinity. While this wasn’t the first time he used this device, the fact that he did for a composition that continually descends without any lasting stability in the home key, which also happens to be his last composition, gives this Mazurka added weight. He avoids good cadential formulas throughout this piece. Every recording I’ve ever heard opts to stop at the same spot, the one place where Chopin provides a nice predominant to dominant to tonic progression in the original key (see below). But even here, he immediately subverts the tonic by changing the C to Cb on the last beat, adding instability that needs to resolve into the next measure. I don’t understand why performers feel the need to create a sense of “good” closure here, when Chopin went to great lengths to avoid just that. I’d love to hear this piece on a recital repeated dozens of times, ending in the middle of the chromatic descent or just before it reaches A Major, or really anywhere other than at the typical spot.

Typical ending spot for Op. 68, No. 4

Typical ending spot for Op. 68, No. 4. Note how an editor even added a “Fine” marking here despite Chopin’s explicit request for “senza fine”

I have an ironic fantasy in which a famous pianist dies, at which point the devil offers him a bargain: perform one Chopin piece to the best of his ability and he will be allowed to ascend into paradise. To his horror, after agreeing to this Mephistophelean trick the pianist realizes that he’s been sentenced into an eternity of performing a single two-page composition when he finds the final Mazurka on the music stand. But the more important aspect of this non-cadence is that Chopin found a way to transcend the limits of the written page, to create a sense of infinity, of music without end.

To be continued….

2 thoughts on “Infinity, Part 1

  1. David MacDonald

    I too am a big fan of “small” endings, the sigh rather than the shout. However, one problem I often have when listening to small endings is that they don’t always sound final. A composition teacher told me a long time ago, “The audience should know that the piece is over for some reason other than the performer stopped playing and walked off stage.” I think there’s a delicate balance to be struck in which the piece is clearly over, but the sound (or maybe the idea) of the piece continues on into the silence.

    Side note: I also have an infinite music fantasy. It involves a piece of music written on a single, very long mobius strip, which is mounted on a device that gradually, at a pace appropriate to the composition, scrolls through the music. There is no final barline. There are no repeats or “roadmap” indicators. Just one single system continuing forever.

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  2. Benjamin Smith

    Thanks for this article and the examples provided. I feel the end of the piece is the lasting impression and I always liked the memorable endings and maybe things that aren’t resolved. Like the last lied, Der Leiermann, in Schubert’s Winterreise for example (this whole song feels like it is over a drone). Though it is technically resolved the two chords just shift back to each other so there’s not the usual sense of chords moving to cadence.

    There are many other examples, one’s without the resolution at all but it is more the effect rather than technical means, the feel of the work reaching a close rather than definitive specific end, that one is left with.

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