posted on 18 Dec 2020

Strictness of Logic versus Openness of Logic

When the conversation turned to the essence of the symphony, I remarked that I admired its severity and style and that profound logic which created an inner connection between the motives. That agreed with the experience I had come to in my creative work. Mahler was of the opposite view. “No, the symphony must be like the world. It must embrace everything!”[1]

– Jean Sibelius

So let’s think about this. Sibelius & Mahler present highly contrasting, maybe even dichotomous views of the symphony. Well, they talk about the symphony but I think it generalises to any major sort of artwork. I’ve understood both composers better since first coming across this passage. There really is some stringent logic at the core of Sibelius’s symphonies, which, to borrow a phrase from Schopenhauer, seem designed to convey a single thought. And there really is a sense in which Mahler’s symphonies unfold in many different modes & reach for many different subjects.

Below I’ll consider some different dimensions of this thought. But first, a reminder. This is a model for thinking about art. We must look at any model with equal measures wonder & unease. No one work of art will fit neatly on either side of the dichotomy. It’s a generalisation & so will sometimes make wrong predictions. But because it says as much about what an artwork isn’t as what it is, it may help cast light on a variety of material.[2]

Teleological Genesis versus Presentation & Analysis #

(Relates to development & transition – how motives are elaborated & joined.)

Teleological genesis is the phrase James Hepokoski uses to describe a motive revealing itself gradually, starting from a formative seed, until it culminates in its fullest statement, its revelatory telos.[3] “[T]he beginning presupposes the end almost as much as the end presupposes the beginning.”[4] Presentation & analysis is my phrase to describe the composer’s presenting the theme in its model version & then developing it in derived versions that cast new light on the model version.

Schopenhauer uses the terms “organic” and “chainlike” to describe a similar contrast. The first process is organic in the sense that a theme or motive’s full statement grows out of much smaller, simpler versions of it & then disintegrates again, echoing the way organic lifeforms grow until they reach their prime after which they age & die. The second process is chainlike in the sense that it consists of distinct parts that are then welded together in the manner of artificial objects.

The first is like constructing a thesis from first principles. The second is like presenting a thesis & then considering it from different angles.

Content-based, Rotational Form versus Traditional Form #

(Relates to large-scale composition – how sections are arranged.)

Bach’s fugues never had a predetermined form. He let each subject (theme) determine its own form. A simple subject needed only a simple design, but complex & chromatic subjects required longer durations & more expansive designs, because there was more there to develop & work out. The form is generated inside-out. Put differently, the first presentation of a subject poses a varying number of questions to the listener & it is the duty of the remainder of the piece to answer these questions.

Portrait of Jean Sibelius.

I think this is what Sibelius meant when he wrote: “I intend to let the musical thoughts and their development determine their own form in my soul.”[5] Hepokoski calls this content-based form[6] & we can contrast it with traditional forms like sonata, rondo or minuet. These traditional forms can be inspiring because they invite the composer to imagine what content to put in them. That sort of composer starts out with a formal design & proceeds to invent or adapt themes & motives to fit it – the inverse of starting from the motives themselves.

What makes the traditional forms so powerful & durable is their flexibility. You’ll find hardly any pure textbook sonata form in the literature. Nearly every characteristic of each form is negotiable. But the one thing that’s not negotiable is also what most of them have in common, namely the process of cycling through a set of themes, usually in a fixed order. This process is powerful because it simultaneously provides contrast & builds up new expectations. It’s also very salient: most people, when they listen to sonata-form pieces, don’t really notice things like key schemas or development sections or, god forbid, postmedial caesuras; what they notice is themes – themes following one another like seasons over a span of years. Sibelius kept this core feature & jettisoned the rest. Hepokoski calls the result rotational form.[7]

Like Sibelius, Mahler was not a slave to tradition, but unlike Sibelius, his musical language was & always remained that of the Austro-German tradition, at which Sibelius only looked from the periphery.

Centred Tonality versus Progressive Tonality #

(Relates to tonality – which keys the composer chooses & how they are arranged.)

In most symphonies, each movement ends in the key that it began in, & the final movement ends in the key that the first began in. The old metaphor here is that the return to the key of the Tonic – the home key – is like the return home after a long journey: the hero, having seen much abroad, arrives home with new eyes. There is a sense of closure. But many of Mahler’s symphonies end on a different key from the one they started in. That’s like the hero’s journey ending in a remote & unfamiliar place.

Portrait of Gustav Mahler.

I think this – what musicologists call progressive tonality – is a natural consequence of the view Mahler expresses in the quote we started with. If you think the symphony should be like the world, then everything must be of the same importance, all perspectives are equal & there is no room for a single supreme centre. Unlike, say, pictorial art, music unfolds over time & can’t present many different perspectives at once. So by necessity the perspectives need to be spaced out in time. Progressive tonality is one result of this view.

Sibelius, although his music incorporates elements of major-minor tonality, modernist chromaticism & folk-like modal tonality,[8] never abandoned the idea of a definitive tonal centre in his symphonies. His movements & symphonies often return to the Tonic at climactic moments & important themes often return in their original key. Each of his symphonies has a first and last movement that share the same key.[9]

In centred tonality, there’s a gravitational pull towards the familiar Tonic. In progressive tonality, the final destination is always unknown.

Strictness of Logic versus Openness of Logic #

(Relates to the general compositional process.)

When I write music, I usually follow a process of

  1. putting down some notes,
  2. listening,
  3. (usually) removing/editing &
  4. going back to step (1) or (2).

This is essentially an adversarial process, not unlike that of a GAN, where the composer alternates between creating & judging. There’s a sense in which the composer proceeds algorithmically. The important thing here is that, on steps (1) to (3), the composer moves forward using a set of (explicit or implicit) rules & preferences.[10] The stricter these rules & preferences are, the more focused & coherent the resulting music is; the more open these rules & preferences are, the more varied & wide-ranging the music is.[11]

The all-embracing composer must by necessity let their music take many different shapes & present it in many different idioms. For that to be possible, they can’t have a small set of stringent rules & preferences. Different idioms are governed by different rules. The more single-minded composer, however, happily sticks to their native language, so to call it, because to them it’s a wellspring of inspiration & meaning that cannot be exhausted.

This is the dimension that ties it all together, because it is the source of those others. What I think Sibelius meant when he talked about the “profound logic” & “inner connection[s]” of the symphony is just this, that the stricter the rule set a composer works with, the more closely related the resulting music’s parts will be, just as countries with stricter & more strongly enforced laws & norms produce more uniform populaces. And so it is no surprise that a symphony by Sibelius seems to express the essence of a thing, whereas one by Mahler seems to express its relation to other things.


  1. Ekman, K. (1936). Jean Sibelius : en konstnärs liv och personlighet. Helsingfors: Schildt. ↩︎

  2. It was in reference to his essay The Hedgehog and the Fox, which draws a similar distinction, that Isaiah Berlin said: “Every classification throws light on something”. (Berlin, I. & Jahanbegloo, R. (1991). Conversations with Isaiah Berlin. New York: Scribner’s Maxwell Macmillan International.) ↩︎

  3. Hepokoski, J. (1993). Sibelius, Symphony no. 5. Cambridge England New York: Cambridge University Press. ↩︎

  4. Schopenhauer, A., Norman, J., Welchman, A., & Janaway, C. (n.d.). Preface to the first edition. In Schopenhauer: The World as Will and Representation (pp. 5–10). Cambridge University Press. ↩︎

  5. Hepokoski, J. (1993). Sibelius, Symphony no. 5. Cambridge England New York: Cambridge University Press. ↩︎

  6. ibid. ↩︎

  7. ibid. ↩︎

  8. Hepokoski, J. (2011). Modalities of National Identity: Sibelius Builds a First Symphony. In The Oxford Handbook of the New Cultural History of Music. ↩︎

  9. You can argue about the 4th, which is his most chromatic & tonally ambiguous symphony, but even that one kind of begins & ends in A minor. The 7th is of course in a single movement but begins & ends in C major. ↩︎

  10. Of course, there’s an exception to every rule. But a rule with an exception is still a rule, only more complex. ↩︎

  11. This doesn’t necessarily affect quality. Quality is just one aspect you take into account when judging. There are many others that have more to do with your biases & preferences. So a composer with a more lenient rule set may still have the same demands on quality as one with stricter rules. ↩︎