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Imagine some structureless music. Music without meter, free improvisation or just a series of random sounds.

What concepts of music theory could we still apply to describe the progression of such music in time?

Here's what I think we could focus on describing:

  • How the pitch of the sounds changes in time, if it does.
  • How the timbre of the instruments changes in time, if it does.
  • We could split the music into arbitrary chunks and compare how many notes or sounds were played in each chunk. I believe the term for that is "rhythmic density" or "attack density". So, we could say at which points the music becomes more or less aggressive/saturated.
  • We could talk about shorter and longer "musical bursts" (e.g. if we're describing the music of Cecil Taylor).
  • We could still describe some repeating patterns in the music, if we can notice any. Even if those repeating patterns don't create any typical musical structure.

However, I don't know the terms for most of these.

Why I'm asking this question

Most music is very structured. And music theory has a lot of terms for describing the precise structure of a musical piece. But I want to talk about musical analogies and musical effects which are unrelated to the precise structure of musical pieces. While being as objective as possible. So, I'd like to know the terminology which could help me. I think even highly structured music could sometimes benefit from a description which ignores most of its structure.

One vague analogy which comes to mind is geometry vs. topology. Most descriptions of music are like "geometry". Are there descriptions of music which are more like "topology"?

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    I'd argue that a music without a meter, free improv or the Cecil Taylor piece you give as an example they all have structure. And even in random sequence of sounds what listener is looking for is any signs of randomly created structure - so pattern, contrast, motivic development etc. For example in Cecil's improv there is a strong motiv and it is being developed throughout.
    – Jarek.D
    Commented Mar 14 at 11:36
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    Yes, our toolbag of theory terminology relies on a cloud of common assumptions and concepts. We dive right in assuming that both we and the reader know what is meant by "tonic" or "meter." And yes, these concepts were birthed by musical convention, and when unconventional pieces go outside of them, theorists are forced to go outside their toolbag. The best approach is to describe things very literally, rather than invent new terms, but if these anti-conventions develop into alternative conventions, then alternative terms solidify, like serial music theory. But... Commented Mar 14 at 13:11
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    ...But it seems to me the difficulty with this present question is that you're looking for a universal approach to exceptional works. Either there can't be one, or you're still restricting your thinking by certain parameters. For instance, who says music is audible? 4'33" isn't (depending on your interpretation). Who says music exists in time? Who says it's humanly generated? etc. Ultimately you might have to resort to describing each piece in the most objectively observational ways. I guess the trouble comes when trying to compare and connect disparate works. And maybe we shouldn't? not sure. Commented Mar 14 at 13:15
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    I think this is too broad. As Andy Bonner mentions, as we look at discussing less structured music we start to have trouble with having a solid definition of what is music in the first place. Assuming we've gotten that far, then we discover there are too many ways to write unstructured music. Even if we restrict ourselves to aleatoric music, we can't easily discuss a short list of ways to understand the structures or lack of structure in such works. What we can do is extend the concept of what constitutes formal boundaries beyond cadences, etc. and understand other types of structure... Commented Mar 14 at 15:34
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    ... but that would only be feasible with specific pieces or fairly narrow categories of pieces. When we do extend analysis in music theory and analysis, we usually apply familiar words in new ways and build new phrases to describe things, and there isn't a lexicon of newer terms that are broadly applicable to unusual type of music. Two whatever extent there is a new lexicon, it's spread out across journal articles and doctoral dissertations and it would be too broad for this site to compile all the terms here. Final note: I have a math degree and the geometry vs topology analogy lost me. Commented Mar 14 at 15:39

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A close reading of your question focuses on your list of possible analysis points. Yes, your list strikes me as some of the things you would analyze for structureless music.

You might think about randomness, for comparison, and look into how randomness is treated in mathematics and computer programming. Sometimes those folks will say you cannot create true randomness. Applied to music I would say watch out for some pattern creeping into the work.

Also, you probably want to be careful to not conflate "structureless" and "random." Math is not my wheelhouse, but from my reading, I imagine those two concepts are not opposite, and the topic of deep discussion.

The 20th century saw the development of musical styles interested in breaking away from predictable patterns, patterns the musicians found too confining.

If you're interested in jazz, looking into free jazz. Ornette Coleman is one famous player in that style.

In "classical" music look into serial and aleatory music. Some might say those are not truly random styles of composition, but part of the 12-tone/serial purpose was to break out of the traditional musical pattern you described in your question - meter, chord progression, etc. - and aleatoric chance was about breaking out of predictable patterns, which is surely related to randomness. For the average listener those styles sound like random noises.

However, I don't know the terms for most of these.

Reading up on avant-garde music styles should give you some of the vocabulary.

We could still describe some repeating patterns in the music, if we can notice any. Even if those repeating patterns don't create any typical musical structure.

I think this will be a particularly important part of digging into the "randomness" idea. Things like tone rows or tone sets are types of patterns. But it probably would get closer to your point if they were called something like musical anti-patterns. As far as musical aesthetic go, I think methods to create the unpredictable, in avant-garde styles, were good enough even if not truly random.

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Imagine some structureless music. Music without meter, free improvisation or just a series of random sounds.

What concepts of music theory could we still apply to describe the progression of such music in time?

You can describe what happens. If no pattern, repetition, development etc. emerges, that's all you can do.

Or maybe there IS a 'structure'?

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Michael Curtis has given you a better answer to your main question than I could. As for "why you're asking this question," if you want to really dig into "musical analogies and musical effects which are unrelated to the precise structure of musical pieces," I'd suggest you have a look at Leonard Mayer's Emotion and Meaning in Music. While it is far from light reading, it's still considered the definitive book on its subject, and is often cited in discussions of other art forms. (Here's a preview from Google Books.)

One comment on it: rather than talking about music that has no structure, it attempts to discuss aspects of music not specifically related to structure, and therefore might be said to ignore structure. This isn't entirely accurate, because Mayer points out various instances of emotional affect that can be attributed to specific musical phenomena, and one may argue than that these phenomena qualify as structure. But in any case I suspect you fill find the book interesting and informative, and it may also give you some of the terminology you're looking for. ("Emotional vectors" is a term that sticks in my mind 40 years down the line.)

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If you want to try and remove the structure from music, then one way might be to try and generalize and generalize until you get to some axiom.

I think the main axiom of harmony is the idea of repetition, for example playing "random" notes is really creating sound waves of different frequency, so you just created a bunch of sine waves, which itself is repeating (just very quickly). Note: you can also add harmonics (sum of multiples of the base frequency) if you want to model instruments more accurately.

Then you can build polyphony as a sum of sin waves such as chords etc.

Then you can enforce that only certain frequencies are allowed using some rule, e.g) check out 12 tone equal temperament (440 * 2^(k/12)).

Then you can start looking at temporal information like during this time interval what frequencies were played, and how many were played, what were there amplitudes.

For example perhaps during a particular time interval the collection of sine waves {4402^(0/12), 440 * 2^(4/12), 4402^(7/12), 440*2^(11/12)} were played simultaneously (A maj7 was played).

With this system you can create "songs", which are sequences of temporal information which specify what frequencies are played, and at what amplitude, etc...

You could then change any stage in this system to create an entirely new music system, and to the listener it would sound "random"/"novel" as compared to what they are used to hearing.


Now given this generalization, you can find things that might hold true regardless of how you change the system, these properties would be facts that are true about the "topology" of harmony rather than the actual notes and chords you'll find in specific songs.

An example of this is roman numerals which abstract away the idea of specific notes, and rather focus on what type of intervals are used in specific tone collections.

In theory we could go and change our rule for generating new notes in our musical system to create music system with N-many different notes. It's just that it would require us to create new instruments to play those notes which aren't as commonplace.


We could also go back and replace the axiom of sine waves with hitting an anvil with a hammer, and in this system we observe how many sparks come off the anvil (frequency).

Next we restrict that the number of sparks allowed to come off the anvil must be an even number (restricting what notes can be played), and we allow multiple hammers to be used at once, and develop hammer theory which gives says that a common spark change would be 2 sparks then 9 sparks then 1 sparks (chord changes) and make hammer spark songs ...

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    Your analogy is very clear. But you frame it as if we always have to be focused on hyper-specific properties of hyper-specific events (the exact frequency of a particular sound, the exact number of sparks from a particular hit). I think we could also generalize in a different way. See the examples in the OP. Commented Mar 17 at 9:45
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I'll quote the first paragraph of text that happens to be on Wikipedia's "Music theory" page right now.

https://en.wikipedia.org/wiki/Music_theory

Music theory is the study of the practices and possibilities of music. The Oxford Companion to Music describes three interrelated uses of the term "music theory": The first is the "rudiments", that are needed to understand music notation (key signatures, time signatures, and rhythmic notation); the second is learning scholars' views on music from antiquity to the present; the third is a sub-topic of musicology that "seeks to define processes and general principles in music". The musicological approach to theory differs from music analysis "in that it takes as its starting-point not the individual work or performance but the fundamental materials from which it is built."

From that, I do not at all get an impression that music theory is a natural science that measures and observes "objective" characteristics and attributes of sound, like a specimen under a microscope.

From the top of my head, in random order and ad-hoc, I'll list some aspects of describing music that are not about the structure of a piece as an artifact.

  • Who makes (or made) the music
  • Where do (did) they make the music
  • Why do they make the music, what goals they have
  • What kind of materials and tools do they use for making music
  • What kind of an impact have they had with the music
  • What lead them to making this kind of music
  • What do they think about when making the music
  • How do they communicate with each other when making the music
  • What kinds of emotions does the music evoke in listeners
  • What kinds of emotions does the music evoke in the musicians
  • What sources of inspiration have they had
  • What kinds of interactions and processes are there between the musicians and their environment when making the music
  • How do the music-making occasions vary, what variables are there
  • What kinds of commercial uses are there with this kind of music
  • What kinds of rules do the musicians have regarding the music
  • What sub-genres of this music are there
  • What kind of an organization do the musicians have, and how does it contribute to the musical outcome
  • What kind of written communication is there about this music, and how is it reflected in the musical outcome

I don't know what kind of "structure of music" the OP had in mind, but I tried to omit whatever it could be. Perhaps I misunderstood the whole thing.

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  • Interesting, this is the kind of sociological approach that I normally think of as the opposite of standard “music theory.” I think of theory as being especially prone, even more than other fields, to treat the work as an “aesthetic object,” divorced from the cultural circumstances of its creation or performance, an abstraction. Commented Mar 14 at 23:24
  • But one of my recommendations to the OP was going to be, when encountering a work that doesn’t lend itself to the conventional language, to focus more on this kind of sociological approach. If I had to write about ASLSP, I’d be much more interested in its reception history, in collecting the experiences and responses of visitors to the church, than in analyzing the boring old score. Commented Mar 14 at 23:28
  • @AndyBonner I think one of the biggest misconceptions about music theory is trying to see it as a natural science, when it is a humanistic science. Music is a part of culture, and studying music is studying culture. Many Western people, particularly those prone to an engineer way of thinking, seem to have this illusion that the conventions of Western music somehow arise from rules of nature, and actually music theory is a theory about nature. And then they try to learn the rules, the structures, the formulas. Commented Mar 15 at 19:06

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