What is music?

Talk about things that are not necessarily related to music or the guitar.
Jeffrey Armbruster
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Re: What is music?

Post by Jeffrey Armbruster » Thu Jun 15, 2017 9:41 pm

"The reason they don't is not because maths doesn't describe motion correctly but because mathematical descriptions are difficult for human beings to latch on to."

Well then maths should be on the curriculum so that instrumentalists will at last have a rigorous and calculable way of expressing what the composer wants. All the major composers were fluent in maths, right?

No? and yet they somehow managed to compose. I wonder which of them described their work as doing sums. When Beethoven was spotted marching through a field waving his arms in transport while hearing an inner music, I doubt he was making calculations.

Yes of course there's a mathematical element to music. But if you reduce music to math, as Leibniz seems to , then the best way you would describe one of Beethoven's late quartets would be with equations. And this was my point. To a certain mind set, phenomenon are only truly understood when you reduce them to calculable formula. There's a mathematical element in poetry as well, in terms of rhythm. Same thing with painting, in terms of formal relations withing a composition. I wonder how far math gets us in appreciating one of Donne's sonnets? Well, you say, anyone who's fluent in maths will understand. Sure; except for most of what's important. Who goes to a symphony and is transported...by the math? Leibniz, apparently.

I grant that I'm riding a hobby horse and am exaggerating. Math can describe aspects of beauty quite well. It's one method among others.
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ddray
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Re: What is music?

Post by ddray » Thu Jun 15, 2017 10:03 pm

Jeffrey Armbruster wrote:
Thu Jun 15, 2017 9:41 pm

Yes of course there's a mathematical element to music. But if you reduce music to math, as Leibniz seems to , then the best way you would describe one of Beethoven's late quartets would be with equations. And this was my point. To a certain mind set, phenomenon are only truly understood when you reduce them to calculable formula. There's a mathematical element in poetry as well, in terms of rhythm. Same thing with painting, in terms of formal relations withing a composition. I wonder how far math gets us in appreciating one of Donne's sonnets? Well, you say, anyone who's fluent in maths will understand. Sure; except for most of what's important. Who goes to a symphony and is transported...by the math? Leibniz, apparently.
I don't know where you're getting this "all or nothing" sort of thing. The Leibnitz quote from what I can tell has to do with an intuitive sense of mathematical qualities ("hidden") within a work of art. And a composer doesn't have to be a mathematician to employ things like symmetry, retrograde movement etc. But yet they're there. As for Donne's sonnets, yes there are mathematical constraints that sonnet form itself imposes: 14 lines of iambic pentameter with a repetitive syllable stress pattern of short-long.
Ultimately it's about imposing order on chaos, and order can be expressed mathematically, whether we're aware of it or not.

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Re: What is music?

Post by Jeffrey Armbruster » Thu Jun 15, 2017 10:34 pm

" As for Donne's sonnets, yes there are mathematical constraints that sonnet form itself imposes: 14 lines of iambic pentameter with a repetitive syllable stress pattern of short-long."

Well of course, that's what I meant when I said that there was a math element in poetry--although few poets would be likely to consider it that way. The poem isn't the metrical scheme, which all classical sonnets alike share. And don't forget the rhyme scheme.

I took Leibniz to be saying, 'yet they're there' and that's what music essentially is. Maybe not. Again: "Music is the hidden arithmetical exercise of a mind unconscious that it's calculating". Hmmm....
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Re: What is music?

Post by ddray » Thu Jun 15, 2017 11:36 pm

Jeffrey Armbruster wrote:
Thu Jun 15, 2017 10:34 pm
" As for Donne's sonnets, yes there are mathematical constraints that sonnet form itself imposes: 14 lines of iambic pentameter with a repetitive syllable stress pattern of short-long."

Well of course, that's what I meant when I said that there was a math element in poetry--although few poets would be likely to consider it that way. The poem isn't the metrical scheme, which all classical sonnets alike share. And don't forget the rhyme scheme.
Without the metrical scheme and the constraints of the sonnet form there would be no poem. Which answers your question about math coming into play in appreciating the sonnets.
I took Leibniz to be saying, 'yet they're there' and that's what music essentially is. Maybe not. Again: "Music is the hidden arithmetical exercise of a mind unconscious that it's calculating". Hmmm....
It's the intuitive recognition of structure and order. You don't have to have a course in advanced analysis to do that.

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Re: What is music?

Post by Jeffrey Armbruster » Fri Jun 16, 2017 12:00 am

Without the metrical scheme and the constraints of the sonnet form there would be no poem.

Read one of Donne's holy sonnets. Now read another. And another. Each follows the scheme of a sonnet. Now read a sonnet by Shakespeare. All of these would be almost entirely indistinct--almost, because of a variable rhyme pattern--if the metrical scheme defined them. You would always end up saying the same thing about each poem: 14 lines of iambic pentameter. Period. That's all the counting and calculating to be done. Strangely, people find these poems to be each one unique. An identical metrical (math) formula, and yet not reducible at all to this formula. I suggest that you leave out most of what's important and telling and beautiful about any of these poems, if you reduce them all to their metrical scheme..."the hidden arithmetical exercise of a mind unconscious that it's calculating". Except these poets are quite conscious of the form they're working with.

Oh and yest there is some slight variation in emphasis within iambic pentameter; it's not strict. that changes nothing.

You may be right in how you interpret Leibniz. I still think that finally he's saying, scratch a melody, find a mathematical calculation. Math is the fundamental reality of the melody and harmony.
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Re: What is music?

Post by ddray » Fri Jun 16, 2017 12:20 am

Jeffrey Armbruster wrote:
Fri Jun 16, 2017 12:00 am
Without the metrical scheme and the constraints of the sonnet form there would be no poem.

Read one of Donne's holy sonnets. Now read another. And another. Each follows the scheme of a sonnet. Now read a sonnet by Shakespeare. All of these would be almost entirely indistinct--almost, because of a variable rhyme pattern--if the metrical scheme defined them. You would always end up saying the same thing about each poem: 14 lines of iambic pentameter. Period. That's all the counting and calculating to be done. Strangely, people find these poems to be each one unique. An identical metrical (math) formula, and yet not reducible at all to this formula. I suggest that you leave out most of what's important and telling and beautiful about any of these poems, if you reduce them all to their metrical scheme..."the hidden arithmetical exercise of a mind unconscious that it's calculating". Except these poets are quite conscious of the form they're working with.

Oh and yest there is some slight variation in emphasis within iambic pentameter; it's not strict. that changes nothing.
They're ringing their individual changes within a set structure. There are rectangles too that can be filled with all sorts of things. Without those 14 lines it's no longer a sonnet, is it.
You may be right in how you interpret Leibniz. I still think that finally he's saying, scratch a melody, find a mathematical calculation. Math is the fundamental reality of the melody and harmony.
What if it is? I don't see how that's so horrible. Math is bound up with existence. You sound like someone who was traumatized by a calculus course. ;)

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Re: What is music?

Post by Jeffrey Armbruster » Fri Jun 16, 2017 12:34 am

You sound like someone who was traumatized by a calculus course. ;)

I was traumatized by much easier math than that!

I'm just trying to point out everything in music that gets left out of the mathematical reduction. By which I mean, the stuff that Bream, say, points out to a student in a class in order to breathe life into a phrase.
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Rasputin
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Re: What is music?

Post by Rasputin » Fri Jun 16, 2017 8:11 am

I think your underlying point is that a mathematical description will inevitably fail to capture the qualitative features that make music worthwhile.

If so, I disagree - that's not to say that I think all of the qualitative features we care about can be captured mathematically, just that I don't think the idea is a non-starter.

To go back to rhythm, someone might say it boils down to counting and it doesn't get much more arithmetical than counting, but that would be a very superficial description of rhythm. It would totally overlook the qualitative differences between the beats - yes 2/2 goes 1-2, 1-2, but the 1 feels different from the 2, and the 1 of bar 8 will typically feel different from the 1 of bar 1. Saying that it's counting seems to strip it of these differences, when they are half the point.

Hierarchical theories of rhythm like Lerdahl and Jackendoff's capture the differences by saying that beneath the basic pulse there are pulses moving twice as slowly, four times as slowly, etc. The beats of the basic pulse that feel meatier are those that coincide with a pulse at a lower level - so 1 feels different from 2 because it coincides with a pulse at the next level down, and the 1 of bar 8 feels typically feels different from the 1 of bar 1 because it typically coincides with pulses at 3 lower levels, whereas the 1 of bar 1 only coincides with 1.

There's obviously a lot more to be said about rhythm than that, but I think this mathematical approach does account for the difference in feel. If that can be done for a basic aspect of music like this, then maybe it can be done for others too. With that in mind I don't think it's right to assume that a mathematical description would necessarily "leave out the stuff that Bream, say, points out to a student in a class in order to breathe life into a phrase". This is more of an assertion than an argument.

Another undercurrent seems to be that music can't be based on maths because communicating the mathematical structure doesn't give you the feeling of the music - but this is like saying that cakes can't be based on recipes because reading a recipe doesn't give you the taste of cake. What is meant by saying that music has a mathematical structure (at least, what I mean by that) is that the features of music that give rise to the qualitative effects we care about lend themselves to being described in mathematical terms. The qualitative effects themselves are always experiential, just like the taste of the cake,

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Andrew Fryer
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Re: What is music?

Post by Andrew Fryer » Fri Jun 16, 2017 9:35 am

Maybe Leibnitz was Aspergic. Autistic, even.
I began a book on Chaos theory yesterday, so I know nothing about it, but it strikes me that even for those of you who can't tell the difference between "maths models x" and "x is maths" music is perhaps represented by maths with rather a lot of mathematically inexplicable "noise" and it's the noise that you should be worrying about?
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Re: What is music?

Post by Francisco » Fri Jun 16, 2017 3:54 pm

Samuel Johnson is supposed to have said, according to his biographer, that sometimes things may in fact become "darker by definition". It is an interesting observation which he made on Tuesday, 7 April 1778
But sometimes things may be made darker by definition. I see a cow, I define her, Animal quadrupes ruminans cornutum [a quadruped that chews the cud and has horns]. But a goat ruminates, and a cow may have no horns. Cow is plainer.
James Boswell: Life of Johnson, Oxford University Press, 1970, p. 911
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Re: What is music?

Post by kertsopoulos » Fri Jun 16, 2017 4:11 pm

Each different rythmical structure in music, if it is successful in its function, gives us at the time of hearing another conception of the time as we experience it without hearing any music. Music can be defined symbolically as a "time conception therapist" because this effect can be many times therapeutic, for the listener.

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Re: What is music?

Post by Jeffrey Armbruster » Fri Jun 16, 2017 4:54 pm

Well yes if you lay some flour and eggs and sugar out before me and say, have some cake, I might object that you're offer is half baked. (sorry). Giving me everything that's required for a cake without giving me cake cheats me of what's essential.

"What is meant by saying that music has a mathematical structure (at least, what I mean by that) is that the features of music that give rise to the qualitative effects we care about lend themselves to being described in mathematical terms. The qualitative effects themselves are always experiential, just like the taste of the cake,"

This is a fair point. I still wonder if you can take away the experiential--the cake--and call it music. I guess I'm claiming that the "foundation" of music can't be separated from the experiential. We don't burst into joyful sums when we think of our lover. Well, most of us. But then we wouldn't call it singing. More, I wonder if math 'founds' music and gives birth to its qualitative effects. Rather, isn't math just an instrument we use to analyze music? We apply it from outside, so to speak.


there may be the scientific 'changes in quantity give rise to changes in quality' reasoning at play. Quality is the epiphenomenon, quantity is the solid (material) foundation. If you want to understand, go to the quantitative foundation and start calculating, says modern science.

If a mathematical definition of music leaves out of account the 'qualitative' aspects of music, it's a poor definition. In fact math can't give an account of those things. To repeat myself, such a definition leaves at least much of what music is out of account. It's like defining a quarter of a cat and still calling it a cat.
Last edited by Jeffrey Armbruster on Fri Jun 16, 2017 8:53 pm, edited 1 time in total.
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Re: What is music?

Post by ddray » Fri Jun 16, 2017 6:13 pm

Jeffrey Armbruster wrote:
Fri Jun 16, 2017 4:54 pm
Well yes if you lay some flour and eggs and sugar out before me and say, have some cake, I might object that you're offer is half baked. (sorry). Giving me everything that's required for a cake without giving me cake cheats me of what's essential.
Yeah but if you don't have the flour, eggs and sugar there's no cake at all. What is produced from mixing those ingredients is a cake. Experientially you may think it's delicious or terrible. But the ingredients are still there.
We don't burst into joyful sums when we think of our lover. Well, most of us. But then we wouldn't call it singing.
You "burst into joyful sums" whenever you hit a "correct", mathematically measurable chord on your guitar. You just don't realize it.

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Re: What is music?

Post by AndreiKrylov » Fri Jun 16, 2017 6:32 pm

wow! what a discussion!
mathematics... or mix of it with ...?
Music is a reflection of us an our life but - Is our life mathematics?
Isn't it a total absurd, full of irrational ideas, events and history?
And why we are talking about "chord" here?
What chord? In what tonal system?
Standard Tonal? Microtonal or any other?
If Music is something which consist from "perfectly measured chords" why many of us including me - do not like perfectly sounding computers which could make "precise music"?
We certainly could consider if this type of computer generated sounds are music too, because pop-music which bombarding us from every radio , tv etc. in 90% computer generated music, but is it music really?
What kind of ears are necessary to determine - what is music? Any ears?
What kind of brains? Any brains?
How could we decide what is it - by opinion of majority?
By something which will be presented to us as "opinion" but in reality is just financial interest of big corporations?
What is music?
It is a language describing us and our lives, therefore it is in some way mathematical, but it is also absurd...
I'd better speak by music...Please listen Andrei Krylov at Spotify, iTunes, Apple Music, Amazon Prime etc. Thanks!

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Re: What is music?

Post by Rasputin » Fri Jun 16, 2017 6:37 pm

Jeffrey Armbruster wrote:
Fri Jun 16, 2017 4:54 pm
Well yes if you lay some flour and eggs and sugar out before me and say, have some cake, I might object that you're offer is half baked. (sorry). Giving me everything that's required for a cake without giving me cake cheats me of what's essential.
If you'd ever seen my efforts in the kitchen, you'd know this was a blessing in disguise.
I guess I'm claiming that the "foundation" of music can't be separated from the experiential.
Well, it's only the foundation of music because it founds musical experience, but I think you can separate them analytically as long as you don't go thinking that your description of the structure of music is itself music.
More, I wonder if math 'founds' music and gives birth to its qualitative effects. Rather, isn't math just an instrument we use to analyze music? We apply it from outside, so to speak.
Well, what interests me is the suggestion that when we apply it from the outside, we find it on the inside. Music - or at least rhythm - seems to yield to mathematical analysis, which seems to carve it at the joints. This implies that the mathematical structures in music are an important part of what the brain latches onto in carrying out the processes we experience as music.
there may be the scientific 'changes in quantity give rise to changes in quality' reasoning at play. Quality is the epiphenomenon, quantity is the solid (material) foundation. If you want to understand, go the quantitative foundation and start calculating, says modern science.
I don't think it needs to be nearly as narrow as that - if I can hark back again to the hierarchical theory of rhythm, the qualitative difference that meter imparts to successive beats is not explained in quantitative terms; it is explained in terms of the relationship between beats at different levels of the hierarchy. Maths is not just about quantities (that would be arithmetic, maybe).
If a mathematical definition of music leaves out of account the 'qualitative' aspects of music, it's a poor definition. In fact math can't give an account of those things.
I agree wholeheartedly with the first sentence. For me the jury is very much out on the second. I think that it can give a compelling account of at least some of the qualitative aspects and would be interested to see how well it could handle others.

PS: Some of the other attempts to explain musical phenomena in mathematical terms (for example the explanation of dissonance that equates it with beating) are failures in my opinion - but I wouldn't be surprised if they could be fixed up. In the case of dissonance, the problem as I see it is that what the theory is actually explaining is an auditory phenomenon, whereas - as Scruton insists - there is an important difference between auditory and musical phenomena. That is not to say they are not related, just that they are not the same. It may be me that we actually need more maths here - the maths that describes the relationship between the two.

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