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.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.
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.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.
It's the intuitive recognition of structure and order. You don't have to have a course in advanced analysis to do that.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....
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.Jeffrey Armbruster wrote: ↑Fri Jun 16, 2017 12:00 amWithout 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.
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.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.
James Boswell: Life of Johnson, Oxford University Press, 1970, p. 911But 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.
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.Jeffrey Armbruster wrote: ↑Fri Jun 16, 2017 4:54 pmWell 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.
You "burst into joyful sums" whenever you hit a "correct", mathematically measurable chord on your guitar. You just don't realize it.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.
If you'd ever seen my efforts in the kitchen, you'd know this was a blessing in disguise.Jeffrey Armbruster wrote: ↑Fri Jun 16, 2017 4:54 pmWell 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.
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.I guess I'm claiming that the "foundation" of music can't be separated from the experiential.
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.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.
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).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 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.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.