Mystical mathematics in Baroque music

[keyboardclass]

What features correspond to the golden section?

Why don't you just get off your arse and have a look?

[nyiregyhazi]

Why don't you just get off your arse and have a look?

I was enquiring as to what I might be looking for. Which specific features are you saying are in line with the golden section? The climax/highest note of the melody, relative to the phrase length? Seeing as no music forms literal rectangles or curves that correspond to the golden section, it would be of interest to know which particular features you feel imply the golden ratio. Depending on the criteria for singling moments out, you could arguably find it in virtually anything- which is why it would be interesting if you were to clarify what in particular distinguishes the moments that you feel imply the ratio in a notable fashion.

[keyboardclass]

Not to do your thinking for you - What would be the most obvious elements to make in the ratio of the golden section?

[nyiregyhazi]

Not to do your thinking for you - What would be the most obvious elements to make in the ratio of the golden section?

Within a theme, I have no idea- hence the question. Structurally speaking, it's far from remarkable to think that the golden ratio might regularly appear if you compare exposition+development to the recapitulation, in a sonata form movement. You'd expect it to occur rather regularly, even if not by design. The nature of sonata form is highly inclined to lead to something resembling the ratio. However, within a single theme I'd be interested to know what features point to the ratio. It's not like a building, where two measurements are staring you in the face. I had a look and saw a rather standard looking 8 bar phrase (comprised of 2 4 bar units). No sign of the ratio there. What features of the theme (that you said is constructed upon this premise) actually point to it?

[keyboardclass]

Within a theme, I have no idea- hence the question.

In that case I suggest you do the maths!

[nyiregyhazi]

In that case I suggest you do the maths!

As I made abundantly clear in my post, I DID do the maths. It revealed a very ordinary theme constructed around a structural ratio of 1:1. If 1.6:1 is implied by any other features of the theme, would you mind demonstrating what features these are?Alternatively if the opening theme is not "the theme" which one are you referring to?

If you're not willing to follow up on what you claimed to have identified, it's pretty evident that you're all mouth and no trousers. I rather suspect that you're simply repeating some kind of misremembered 2nd hand information from a 3rd party. If not, then no doubt you'll be willing to follow up on your suggestion that the theme is founded upon the golden section by illustrating what characteristics you consider to imply it.

It's all very easy to portray oneself as having special inside knowledge. But it's not terribly interesting  when a person can only portray ownership of knowledge, without having the ability to divulge any.

[keyboardclass]

I suggest you do the Maths again then.  You'd also need some knowledge of the context in which it was written.  That may be difficult for someone who can't tell Mozart from Schubert!

[nyiregyhazi]

I suggest you do the Maths again then.  You'd also need some knowledge of the context in which it was written.  That may be difficult for someone who can't tell Mozart from Schubert!

 

The structural ratio of the opening theme remains 1:1- not the golden ratio. Context is what I am asking for- specifically what context implies the ratio that you claim "the theme" (you never said which one, so please clarify if you are not talking about the opening) is constructed upon. If such a context exists, I see no sign of it-hence my questions requesting a clarification of what you are trying to claim and some evidence that might support it.

This empty pretence of possessing personal insight is of no further interest to me. If you're only interested in pretending to know things (then responding evasively to the most basic questions about what you claim to have identified) there is nothing to be learned here. Respond with whatever topic-ducking insult you wish. I have no further interest in this playground tom-foolery.

[keyboardclass]

 This empty pretence of possessing personal insight is of no further interest to me.

Actually it's called research, something else you wouldn't know anything about - and since when is what's of interest to you of any interest to anybody?

[keypeg]

I have been noticing personal attacks in several posts in a row by the same person.  It is unpleasant for all members, let alone the targeted person.  I am surprised that no moderator has acted on it.  Let's hope this stops.

[nyiregyhazi]

Actually it's called research, something else you wouldn't know anything about - and since when is what's of interest to you of any interest to anybody?

Proper research enables a person to follow up on simple questions. Half-remembering having heard something, claiming to know it and then responding rudely to polite enquiry (about the fact that the theme shows no sign of what you claimed to have observed) is something altogether different. If this based on accurate research, this is exactly what I am inviting you illustrate.

[keyboardclass]

If this based on accurate research, this is exactly what I am inviting you illustrate.

Something you singularly fail to ever do, being content to quote the 'Laws of the Universe' as your research!  I think I'll do the same - read your Newton!

[nyiregyhazi]

Something you singularly fail to ever do, being content to quote the 'Laws of the Universe' as your research!  I think I'll do the same - read your Newton!

Indeed, applications of widely accepted knowledge do not require sourcing (the laws of classical mechanics continue to be available in any book on the subject, should you wish to investigate). If the application is in question, the person disputing must provide evidence of false logic or incorrect applications of accepted mechanical law.

So, if you'd like to point out what about the theme implies a 1.6:1 ratio, we'll be in a position to use accepted mathematics to verify whether the golden ratio is implied or not. If your calculations are wrong, it's usage mathematics that will show that- not any external 2nd hand source. I don't greatly care if this is from you or another. I'd like to know issues you are referencing, so can I make my own checks about whether the ratio exists. Why are you being so evasive, if such a ratio exists? You are happy to insist that a theme was constructed on it, but the details are top secret? Show us where.

[keyboardclass]

You are happy to insist that a theme was constructed on it, but the details are top secret? Show us where.

As far as you are concerned the details are top secret.  You add nothing to this forum, just take.  If you can't do your own leg work (and I doubt you can) then go without.

[nyiregyhazi]

As far as you are concerned the details are top secret.  You add nothing to this forum, just take.  If you can't do your own leg work (and I doubt you can) then go without.

I did the leg work- hence my pointing out that I see no sign of the ratio within the theme. Explain which three points you consider significant (and for what specific reasons) within the theme and I will be most glad to concede having missed something, should the golden ratio indeed exist between them. The closest thing I saw is a 2-3 a ratio with the second statement (of 4 bars plus 6), which is hardly close enough to be considered significant. The whole significance of the golden ratio is that it cannot be closely approximated by anything so simplistic or common.

Stop being such a hypocrite and either "add" something to the forum by providing some specifics (by which anyone can either substantiate or falsify your claim) or stop trolling (with this tedious tirade of ad hominems, in response to an extremely simple on-topic question).  If I'm such an idiot, then prove it by pointing to where the golden ratio exists in that theme. If you cannot find it anywhere, then man up enough to hold your hand up and admit to error. If you have nothing to contribute but off-topic insults (in response to a wholly topical enquiry), I suggest that you dig a hole in the ground and shout down that instead.

The difference between intellectuals and pseudo-intellectuals is that intellectuals are willing and able to respond to pertinent questions, whereas pseudo-intellectuals simply wish to portray ownership of knowledge. If you consider yourself to lie in the former category, stop trolling and answer the topical question.

[keyboardclass]

Not reading that rubbish - be grateful I showed you where to look!

[nyiregyhazi]

Not reading that rubbish - be grateful I showed you where to look!

No you didn't. Seeing as you evidently haven't noticed, that is the very point I have been making. I have been inviting you to support a currently unsubstantiated claim (that appears to be most grossly in error), by showing me where to look for the ratio that I see no sign of. Instead of showing me where to look, you favour irrelevant and evasive responses- or "trolling", to use a more pertinent term. Perhaps you have a different "opinion" about mathematics, but in my book a theme that is comprised of two evident four-bar halves implies a ratio of 1:1.  

Seeing as a virtually infinite number of features can theoretically imply structural divisions, if there is a less obvious implication of the ratio in theme, you're going to have to point to what feature you feel defines the significant structural division. If you have genuinely spotted something, it's not terribly difficult to divulge what.

[keyboardclass]

[nyiregyhazi]

Seeing as not a single one of your last 8 posts has made a single point that either expands upon or even relates in any way to the topic (regardless of my best attempts to bring you back to it) you might want to edit them to read the same.

[jesc]

I wanted to avoid this topic but then decided I want to clarify a few things on how they go down.

I'm new to this board and I'm not sure if this is the right category to place this message but I reckoned perhaps the teachers would know enough about musical theory to help me on my way.

I recently started reading this book on Superlearning, that combines rythmic breathing and the slow movements of Baroque music(~60 bpm) to achieve semi photographic memory.

If you want a serious answer, ask a researcher if he's willing to discuss this in front of the scientific community. Each field has a reputable journal that publishes papers regarding new discoveries (to put it simply). If you find a reputable journal that published a paper dealing with this topic, good for you. Read it. If you can't understand it read the references. If you can't understand the references, read the references of the references. If that doesn't work, review your college subjects.

And when listening to music the body automatically synchronizes with the beat, so the heartbeat, brainwaves, breathing all fall in sync. Apparently 60 bpm is the tempo that stimulates memory, whereas 72 bpm makes ppl more suggestible(as studies had shown by marketing companies).

And not just the beat, there's something salubrious about the harmonies in Baroque as well and not just for humans also plants were effected. Numerous studies have shown that plants grew towards the Baroque music, grew much better than without. The same experiments were conducted with Rock(the plants shriveled up and died) and Country(no effect whatsoever).

Most likely under Biology and physics. Do the same as above.

They think it's because the composers of the Baroque age were influenced by mystics like Pythagorus and Hermes Trismegistus who claimed that the same mathematical harmonies that ruled the orbits of the planets, the tides etc, could be applied to music and architecture and that these harmonies and vibrations would effect man like playing the middel C in a room with painos will make the other pianos 's middle C vibrate  in harmonry with it.
Baroque composers were also affiliated with the church so they had ready access to ancient wisdom, the masters of subtle energy
I was wondering if someone here could enlighten me where I could learn more about the mathematics behind baroque music>

I don't know what to say. If you find a mathematical paper from a reputable journal dealing with this topic then good for you. Do the same as above.

I'm being gracious. Personally for the record I'll say, I don't find anything mathematical about your post. Please give me a bone to chew on: Group theory, Topology, Number theory, Galois Theory, Set Theory, Logic, Algebra(see group theory), Functional Analysis, Real Analysis, Complex Analysis, Differential Equations, Probability, Graph Theory...

Further advice: While searching for papers, seriously... remove the word "mystical".

[nyiregyhazi]

I'm being gracious. Personally for the record I'll say, I don't find anything mathematical about your post. Please give me a bone to chew on: Group theory, Topology, Number theory, Galois Theory, Set Theory, Logic, Algebra(see group theory), Functional Analysis, Real Analysis, Complex Analysis, Differential Equations, Probability, Graph Theory...

In compositions by Debussy in particular, there is notable usage of the golden ratio, which occurs widely in nature and in much architecture. There is certainly mathematics in the construction of much music. However, as for the idea that there is notable mathematics behind the reasons why music affects us, I'd have to say that I am VERY skeptical. The big difference between architecture and music, is that the visual effect of the ratio is evident at the very first glance. All it takes is one look. Unfortunately, nobody can truly perceive the structure of a whole composition in a single instant (well, they say Mozart could do so, but this is exceptionally rare). You can construct a diagram to represent proportions, but to actually experience a composition as one (and feel more satisfied by specific ratios than others) is highly doubtful, in my opinion. Far too much good music has nothing to do with it. To assume these "hidden messages" come through in an impartial listening experience strikes me as very much in the realms of mysticism- rather than anything objectively or rationally probable.

Personally, I do not see anything natural about the golden ratio in music or believe that people are affected by it. Some composers knew about it and consciously used it. However, I do not believe it has any notable bearing on the experience of listening. Countless great works have been constructed without it remotely either in mind or in evidence. Even if there's something natural about it in numerous visual patterns found within nature (that are visually satisfying) I believe that applications to music are a synthetic construct, rather than a "natural" thing that has evolved.

[jesc]

In compositions by Debussy in particular, there is notable usage of the golden ratio, which occurs widely in nature and in much architecture. There is certainly mathematics in the construction of much music. However, as for the idea that there is notable mathematics behind the reasons why music affects us, I'd have to say that I am VERY skeptical. The big difference between architecture and music, is that the visual effect of the ratio is evident at the very first glance. All it takes is one look. Unfortunately, nobody can look at the structure of a whole composition in a single instant (well, they say Mozart could do so, but this is exceptionally rare).

Personally, I do not see anything natural about the golden ratio in music or believe that people are affected by it. Some composers knew about it and consciously used it. However, I do not believe it has any notable bearing on the experience of listening. Countless great works have been constructed without it remotely either in mind or in evidence. Even if there's something natural about it, in numerous shapes (that are visually satisfying) I believe that applications to music are a synthetic construct, rather than a "natural" thing that has evolved.

Very skeptical is the right word. In the research journals of mathematics, there is absolutely no room for analogy or anything of the sort. Everything is proven through logic. That's in higher mathematics to put it mildly.

Even something which seems obvious to some as occuring in nature or architecture should be proven through the basic laws of logic. Lay down the definitions and axioms then prove it.

TBH, if I'm carrying my reputation in mathematical research on the line here I won't even be discussing this. Unless some papers are cited of course    

It may sound stuck-up sorry. I just wanted to give some insight on how a part of the scientific community operates. It can be vicious. I'll admit as a pianist and a mathematician, I'm careful to probe their connections. The last research I encountered was a computer algorithm that intelligently composes "music"... to put it mildly (sorry I lost that paper. Will post the link if ever I find it). And that venture kept the discussion within the algorithm and not on the mystical connection between music and math.

[nyiregyhazi]

Very skeptical is the right word. In the research journals of mathematics, there is absolutely no room for analogy or anything of the sort. Everything is proven through logic. That's in higher mathematics to put it mildly.

Even something which seems obvious to some as occuring in nature or architecture should be proven through the basic laws of logic. Lay down the definitions and axioms then prove it.

TBH, if I'm carrying my reputation in mathematical research on the line here I won't even be discussing this. Unless some papers are cited of course    

It may sound stuck-up sorry. I just wanted to give some insight on how a part of the scientific community operates. It can be vicious. I'll admit as a pianist and a mathematician, I'm careful to probe their connections. The last research I encountered was a computer algorithm that intelligently composes "music"... to put it mildly (sorry I lost that paper. Will post the link if ever I find it). And that venture kept the discussion within the algorithm and not on the mystical connection between music and math.

I see where you're coming from. I have very little time for extremely randomised speculation passed off as if it were proven fact (based on nothing more than blind hope that it is true). However, in fairness, I would say that this is neither strictly a wholly mathematical issue nor a wholly mystical one. For example, the reason why plants came to grow in a manner that reflects the golden section may or may not necessarily be grounded in the same mathematical logic that can be used to analyse the pattern. Is the maths merely a description of what happened to occur, in hindsight, or is the same mathematical principle behind the factors that meant it evolved that way? I wouldn't like to speculate. Potential explanations would require extremely advanced linking up of countless different sciences. Pure maths is an absolute, but if there's any truth in this then it's about how people respond to maths- not the internal logic of the maths itself. That makes it much more complex, compared to the clear-cut procedures that occur within pure maths.

Anyway, I do have a suspicion that nature evolved life in a way where this ratio is somehow aesthetically pleasing to man- when visible at once. This would be hard to logically "prove", but I suspect that it could be strongly supported by experimentation. I think we're light years away from touching some of these thing with logic, but there are many things that experimentation points to, regardless of whether logic can prove them- eg. inherently attractive tendencies in a face. I can believe that there is something natural about why man would design buildings in a way that corresponds to occurrence in the natural world. Specifically though, I don't personally believe that a listener (certainly not an untrained one) can perceive vastly less obvious musical versions of this ratio or be affected by them- and I certainly don't believe there's any experimental evidence to imply that they can.