What kind of sequence is music?
Hi, I wanted to ask your opinion, although it may sound trivial to you. You probably agree that music is a sequence (e.g. of notes, frequencies, amplitudes, voltages, etc). But what kind of sequence is it? In mathematics, a very important is the class of convergent sequences --- sequences that have limits. For example, a sequence of points in a topological space is convergent if its limit is some point in the same space. So, in your opinion is music a convergent sequence?
Best Answers
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I am not sure if the answer to your question is definite. Your 'head line' question "What kind of sequence is music" to me begs another question , namely "what is music". Especially in a digital age with the use of sampling all sorts of sound and processing these sounds and using them for 'music' then the term 'music' in itself has become extremely wide.
So to me then before you start trying to define something then maybe narrow down what it is that you want to define ?
Otherwise then my own understanding of language , especially the English , might not initially suffice for me to venture into any deep technicalities about language or deeper philosophical pondering on definitions that might develop into hair splitting discussions.
I don't know if you will find this page of interest - keep scrolling down to read.
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Well, just as with your question, I also provided an answer. Why can an answer not be accepted in the same way as the question? My answer was also just as spontaneous, even if you don't like it also.
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Well, technically it is an answer to the question as you asked for opinions and that was my opinion. Can't simply sweep answers to the side because they didn't fit expectation when asking on a public forum.
It is unclear what you are asking for tho. Are you wanting to dive into the technical maths of what defines "music" as a sequence? What about non-traditional music that has no basis in any sequence or pattern? Or a wind chime that is still considered a musical instrument and would be described as making a musical sound but completely randomised and cannot be predicted by maths alone? If we classify something as a piece of music, does it have to follow a sequence? Does it have to have a way of being reproducible or have an end to it?
The question is almost like asking what is the secret to the universe. Music is far more than a simple explanation of frequencies and amplitudes and well beyond the scope of explanation for a forum post. Maths can be used to explain how music works in the same way it can be used to calculate the size of our universe, maths is at the basis of everything but is not the answer to everything.
Is music a "convergent sequence": sometimes, but other times, no.
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In my opinion, thinking of music in mathematical terms isn't useful. There are mathematical properties to aspects of music, e.g. pitch and rhythmic relationships. But these properties aren't in my opinion useful in understanding or composing music.
In short, you are trying to apply mathematics where it isn't meaningful. It is no more useful than trying to apply the definition of musical frequency ratios (major third, perfect fifth, etc.)—which are useful for building chords and determining musical resolutions—but again, not in a mathematical sense, in a purely musical sense, and within particular musical contexts—to painting.
It's true that all music ends. This is not the same as a convergent sequence. Such a sequence has rules that music does not. And technically a convergent sequence cannot end. It is infinite. It approaches ever closer to the limit but cannot reach it. For practical purposes, all music has a definitive end. You could create a piece that never ends, as theoretical exercise, but it would be an intellectual experiment and uncharacteristic of music in general as written and experienced by composers and listeners. And it still wouldn't need to follow the rules of a convergent sequence. It might never approach anything. As an example: you could write software that plays a single note and holds it down—unvarying—forever (or at least until the software is closed or the computer shuts down). Where is this music going? It is already there.
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TBH, I think music is something to enjoy and not overthink. It's like asking "what is happiness", you may see maths and complex things to resolve into a result, others see a simple escape or window of expression from one to another.
Enjoy it and be thankful we have an atmosphere where music can work.
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Not arguing with the "enjoyment" postulate, but it's not the question. Also, a question often occurs spontaneously whether you like it or not… I've been thinking about it for sometime, and I'd be interesting to hear what others think. Should music have a limit? If not, why? The answer does not have to be mathematical. A guess or intuition sometimes is more interesting.
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Music is art. Everything that is art exceeds definitions, constraints and understanding.
How could we understand feelings? They don’t exist to be understood. They exist to be felt
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I am not sure if the answer to your question is definite. Your 'head line' question "What kind of sequence is music" to me begs another question , namely "what is music". Especially in a digital age with the use of sampling all sorts of sound and processing these sounds and using them for 'music' then the term 'music' in itself has become extremely wide.
So to me then before you start trying to define something then maybe narrow down what it is that you want to define ?
Otherwise then my own understanding of language , especially the English , might not initially suffice for me to venture into any deep technicalities about language or deeper philosophical pondering on definitions that might develop into hair splitting discussions.
I don't know if you will find this page of interest - keep scrolling down to read.
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interesting, but this is already theology, and depends on whether you believe in the afterlife. Let me quote my favorite philosopher on that subject: https://youtu.be/zeUtCxe-xDg?t=251
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Sure, every attempt of a definition will miss something and will not satisfy everyone. My question assumed that you "agree that music is a sequence…", If you don't agree, no problem. Still you'd probably use a sequencer to write it. In math, sequences assume discrete (or countable) time, but if you are not happy with that either, there are so-called "nets" or generalized sequences. Countable or not, time is indispensable component of music, unlike other art forms. So, if you accept that music is some kind of sequence, then regarding convergence there are only two options: 1) it converges or 2) it does not. By the way, your point about an "end" is, in fact, quite crucial observation, because finite sequences are usually assumed convergent in mathematics, because they treat the last element of a sequence as its limit point. This, however, means repeating the last point (a note or beat) indefinitely. But perhaps a more natural way to continue music would be a loop (aka "modulo"), in which case the question about convergence is still open.
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Glad to hear my question provoked another, and such a profound one as "what is music"? This is obviously subjective, which is why I did try to narrow it down to two types of sequences. If you believe music is not a sequence of some events, then that's no problem. I tend to think that it is a kind of sequence, and thinking about its limit, I realized that the answer is not so straight forward even from mathematical point of view, because it depends on the type of space we consider. If you think of it simply as a sequence of numbers (e.g. notes) or their combinations (chord or tuples), then because (most) music does not stay constant or converge to the same note, it appear to diverge (not to infinity, but simply because it does not converge). But then comes the fact that music should end, and so it is a finite sequence, which (as I mentioned before) is usually considered convergent by virtue of treating the last note as its limit (i.e. repeating it forever). To me this does not appear to be very musical. But we also may consider different kinds of spaces where music exists. I personally do not believe that music can exist outside human mind. Someone has to think about it to compose and then someone must hear it to perceive as music. So, if we treat mind as kind of space where music exists or originates, then convergence would imply that music never leaves one person's mind.
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Well, just as with your question, I also provided an answer. Why can an answer not be accepted in the same way as the question? My answer was also just as spontaneous, even if you don't like it also.
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No problem, let's think of it as an answer, but not to the original question.
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Well, technically it is an answer to the question as you asked for opinions and that was my opinion. Can't simply sweep answers to the side because they didn't fit expectation when asking on a public forum.
It is unclear what you are asking for tho. Are you wanting to dive into the technical maths of what defines "music" as a sequence? What about non-traditional music that has no basis in any sequence or pattern? Or a wind chime that is still considered a musical instrument and would be described as making a musical sound but completely randomised and cannot be predicted by maths alone? If we classify something as a piece of music, does it have to follow a sequence? Does it have to have a way of being reproducible or have an end to it?
The question is almost like asking what is the secret to the universe. Music is far more than a simple explanation of frequencies and amplitudes and well beyond the scope of explanation for a forum post. Maths can be used to explain how music works in the same way it can be used to calculate the size of our universe, maths is at the basis of everything but is not the answer to everything.
Is music a "convergent sequence": sometimes, but other times, no.
0 -
In my opinion, thinking of music in mathematical terms isn't useful. There are mathematical properties to aspects of music, e.g. pitch and rhythmic relationships. But these properties aren't in my opinion useful in understanding or composing music.
In short, you are trying to apply mathematics where it isn't meaningful. It is no more useful than trying to apply the definition of musical frequency ratios (major third, perfect fifth, etc.)—which are useful for building chords and determining musical resolutions—but again, not in a mathematical sense, in a purely musical sense, and within particular musical contexts—to painting.
It's true that all music ends. This is not the same as a convergent sequence. Such a sequence has rules that music does not. And technically a convergent sequence cannot end. It is infinite. It approaches ever closer to the limit but cannot reach it. For practical purposes, all music has a definitive end. You could create a piece that never ends, as theoretical exercise, but it would be an intellectual experiment and uncharacteristic of music in general as written and experienced by composers and listeners. And it still wouldn't need to follow the rules of a convergent sequence. It might never approach anything. As an example: you could write software that plays a single note and holds it down—unvarying—forever (or at least until the software is closed or the computer shuts down). Where is this music going? It is already there.
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Your answer, Paul, is the closest to what I was expecting, and glad to hear you and many other seem to agree that music is a divergent sequence, especially because music usually does not stay still or converge to a value that would be its limit. And I agree that even though music compositions usually end, their end point (e.g. the final note) should not be considered as a limit point. So, even though finite sequences are usually considered automatically convergent, this is not natural for music. I also tend to think that music diverges, because it escapes the original space - the mind of its creator - and then travels across people's minds. I also do not like the idea that music should have some limits or even bounds.
Speaking of mathematics, it is also a form of art. I think Russel once said that mathematics "possesses not only truth, but supreme beauty". I did not want to "apply mathematics" to music. Many clever people have already done this. I was working on some topology, and it was a question that simply occurred in my head, and when I started thinking about it, I realised that the answer is not straightforward. I have my opinion, and thank you for sharing yours.
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