"The Golden Ratio"

I recently found some information about "The Golden Ratio" in another thread, and found it fascinating. So, I immediately went to the manuscript of my Op. 4 symphony, and found that in the final movement, according to the measure numbers, the big climax occurs on 1.6! I'm now going to look at a lot of my own works and works by other composers to see how often this occurs.

Does anybody have any thoughts about this? Have you seen this in your own works?

I don't think I've ever heard of this Golden Ratio. I'm new to composition and analysis, but I'm curious to what it entails... can you satisfy my curiousity?

Absolutely.

After my works I always calculate

to see if the Climax hits at 1.6, and

I seem to able to get the climax there

everytime without much effort.

Although, one should be careful not

to get to mechanical with this though.

Let your natural feeling put the climax

where it will above conscious effort.

More than likely it will hit in the area

of 1.5 - 1.7 though.

But yeah, I have mentioned on this site

before how its common in Bach's works.

Like BWV 1052, 1st movement, which I

consider to be one of Bach's best climaxes.

The climax hits at 113/190 and of course

190/113 = 1.6. In Brandenburg concerto

no 4, 3rd movement Bach interestingly

put the Climax backwards at 1.6, so you

only see it at 1.6 if you start from the end

and go backwards. Another one of his best

climaxes.

The Golden Ratio is used daily without

consious effort and is a true marvel no

doubt. Like say the walls in your room

were 10 feet from floor to ceiling and you

wanted to put a border around the room

for decoration. More than likely you would

without thinking put it 6 feet from the ceiling

and 4 feet up from the floor making 1.6,

10/6 = 1.6.

But yeah... Its pretty cool stuff and you'll

find it all over in music. You can even draw

out a exposition and structure for a work

using it and then fill in the notes on the

structure. Although, it may get a bit

mechanical, maybe not.

Jeremy

Dude, are u nuts? What you are doing is that you are making connections, if so, I can also make alot of connections,there are plenty of things in nature, or in our lives that comes close to 1.6 or 3.14, or 2.57, whatever... Read "The Golden Ratio" if u fantasize about an relation ship between Aesthetics in music and math, I certainly don't think aesthetics in music has anything to do with a number, my EW overture was based on the Fibonacci sequence for a reason, to disprove it's relation to music, bottomline, mathematicians don't write music, only artists do.

Dude, are u nuts? What you are doing is that you are making connections, if so, I can also make alot of connections,there are plenty of things in nature, or in our lives that comes close to 1.6 or 3.14, or 2.57, whatever... Read "The Golden Ratio" if u fantasize about an relation ship between Aesthetics in music and math, I certainly don't think aesthetics in music has anything to do with a number, my EW overture was based on the Fibonacci sequence for a reason, to disprove it's relation to music, bottomline, mathematicians don't write music, only artists do.

Phi does occur a lot, not only in music but in art. Music has a lot of mathematical properties. For example, the way we view scales and the notes we have in our music are based on mathematical ideas. I agree that only a musician who thinks about music aesthetically or at least with a purpose are people who would be able to write good music. For some reason, on purpose or not, a good chunk of classical works do work around phi. For example, I believe some of mozarts and a lot of bachs music does. If it was an effort or an accident is debatable.

I don't think you should be criticizing Inv.

Artist= what?

Mathematics can be an art.

Art is about passion and craft.

What is art? :)

Like I said, phi comes up naturally a lot. In art and music. I think in our inner mind we like phi. I don't suggest trying to reach phi but you'll find you end up there a lot for some reason(if you are not writing random notes)

Saying that there is a lot of mathematics in music is like saying there is a lot mathematics in a newspaper article or anything else

If you are to find any mathematical formula in your music, its all coincidental really, and it just turns out to be 1.6 or whatever, than congratulations.

But if some wacky formula arises from your symphony or whatever, it just turns out that way unconsciously. you shouldn't worry about it.

Dude, are u nuts? What you are doing is that you are making connections, if so, I can also make alot of connections,there are plenty of things in nature, or in our lives that comes close to 1.6 or 3.14, or 2.57, whatever... Read "The Golden Ratio" if u fantasize about an relation ship between Aesthetics in music and math, I certainly don't think aesthetics in music has anything to do with a number, my EW overture was based on the Fibonacci sequence for a reason, to disprove it's relation to music, bottomline, mathematicians don't write music, only artists do.

I disagree. To completely deny the influence of mathematical order and logic within music is, in my mind, to deny music distinction from unordered noise, and downright naive. One needs only to look at the proportions of the scale and harmonic series (indeed the only discovery of Pythagoras for which we have historical evidence), to see quite clearly that mathematical proportions and ratios underpin music in a fundamental and undeniable way. It is also notable that many distinguished mathematicians also have an affinity for music, and vice-versa (certainly within my school this seems to be a trend). Surely you do not deny at least mathematical characteristics like symmetry within music (e.g.. form has a type of symmetry not unlike that of mathematical functions). The golden ratio (not 1.6 btw, but nearby), plays a fundamental role in more complicated types of symmetry. It seems to me surely logical that such a ratio might also have an influence on musical aesthetics.

I certainly don't think aesthetics in music has anything to do with a number

Well, bearing in mind that it is scientifically accepted that the golden ratio, playing a big part in the mechanics of the natural world, has a role in visual aesthetics, also over time as well as space, would it not be reasonable to assume (or at least consider it likely) that the aesthetics of music (sound distributed in time) might be similarly affected, given that all aesthetics are governed by the same class of entity (namely, the human mind).

my EW overture was based on the Fibonacci sequence for a reason, to disprove it's relation to music

Well, I know mathematicians have a tendency to be very pedantic and stringent about the use of the word proof, but by composing a single composition based on the Fibonacci sequence that didn't work I fail to see how you prove there to be no connection. I could compose an awful piece of music not based on the Fibonnaci sequence, but it would be stupid of me to then say "ergo, all good music must use the fibonacci sequence".

Sorry to have a go at you Mahlertitan, but your post was fairly aggressive and I felt it warranted retortion (or maybe it's because I'm not a big fan of Mahler's 1st...). I am both a mathematical Olympian and a keen composer, so I naturally value the very definite link between mathematics and music.

All the above points made, it would of course be highly foolish for me to start composing my next symphony with a calculator on my desk to check the spacings between my climax points (not least because, if the above theory is true, I will create such proportions by instinct and the conductor will automatically adjust tempi, etc. to create the aesthetically correct ratio). To sum up, while it's nice theory to look into, I don't think it should affect the compositional process, which, by its nature, is governed by the unique inspiration, emotion and (I believe mainly) pathos of the composer, and not by a universal mathematical constant (hence why music is interesting, as opposed to aesthetically perfect - in fact the best music surely is not.

I agree with KneeKo

do u have any solid proof?

Music isn't about proving anything. It can, however, be an intuitive search for Truth and Beauty. The evaluation of whether a particular piece of music has scratched upon the surface of Beauty is of course subjective, though the search may be for something permanent and objective.

That doesn't mean, however, that it is unreasonable to draw analogies between music, which is one sort of search for truth, and another search for truth, math. One of these is largely subjective, though it may have an objective basis (music). The other is ENTIRELY objective (math). There is absolutely nothing like "I believe the square root of two is irrational." it IS irrational. Though there are many ways to prove absolute truths about numbers, some of these proofs are simpler than others, and in fact have greater aesthetic appeal. That is the only aspect of math which is subjective, but it is external to what math is actually doing. Music doesn't do or accomplish or prove anything---reaction to it and evaluation of it is all subjective---BUT the presence of true Beauty may in fact be part of it.

If the presence of a certain ratio can be found in a large number of compositions, it seems to me reasonable to assume there must be some sort of underlying objective basis upon which most composers base their work. They are truly searching for Truth and Beauty via music. That is, many of these composers who include this ratio probably do so unwittingly. This is what makes the whole discussion interesting! I doubt many composers actually include mathematical ratios in their music CONSCIOUSLY.... that would introduce decidedly non-intuitive elements into their music, hence defeating the purpose of their search altogether.

It wouldn't make sense to take the analogy so far to say that music is based upon axioms and derivations and theorems. Of course it isn't. But the search for something real and true is there. Hence why this discussion about the Golden Ratio in music is perfectly reasonable, and it is UNreasonable to rail against it in such a virulent manner :ninja:

do u have any solid proof?

LOOL! Your avatar and your phrase match incredibly!! It looks like Mahler is saying that... :)

Just to cool off... :wub:

I have, along with others in this thread, set out rational arguments as to why mathematics and music have a tangible connection. From Canzano's other posts on this forum I would imagine he knows a great deal about music, and to propagate a shouting war by insulting him is itself, I feel, immature and (more importantly) unnecessary and irrelevant.

The issue is, can you put forward any rebuttal to the rational arguments put forward by myself and (better) by Derek? If so, let them be posted so this interesting thread can continue in a constructive manner.

On the subject of proof, I had certainly been informed that studies into the apparent lack of structure in some of Debussy's work (specifically Prelude a l'Apres-midi d'un Faune) found that the reason his music was so beautiful despite a lack of conventional structure was on account of the presence of the golden ratio. I read this in programme notes, though, so I don't have much more information unfortunately.

Actually, Google does provide some very good information. Don't be like another elitist university professor Mahler... just because something isn't published doesn't mean that it isn't fact. I point to Wikipedia as an example, which certain studies have shown has BETTER editing and screening techniques then do major encyclopedias such as Britannica or Encarta.

Of course music and math have a direct correlation. Womens have built their world around the concepts of math and therefore systems created within that world are bound to have math influences. (Okay, I didn't read the whole argument, so this statement might not make sense within the larger whole, but it seems to apply to the last couple of posts :thumbsup:).

Peace and love people!

Music is intimately related to mathematics.

E.g.:

the nature of sound

the nature of timbre

the nature of the octave

the notion of tonality

the intricacies of temperament

numerology and symbolism

the proportionality of instrument resonating bodies

There are many more.

However, people do not think consciously think of mathematics in music. The relationship is there though.

For examples of the Golden Mean in music:

http://www.mcs.surrey.ac.uk/Personal/R.Kno...nArt.html#music

As for the Golden Mean, my pet theory is that it is a nice balance between the familiar and the unfamiliar. It is not the exact number of beauty though. Anything around 1.6 will be averaged out to 1.6 by statisticians. So I do not think the Golden Mean should be heralded as a foundation block for music. It may be there, but it is no more than the unconscious desire to balance contrast/variety and repetition/familiarity.

Absolutely.

After my works I always calculate

to see if the Climax hits at 1.6, and

I seem to able to get the climax there

everytime without much effort.[/b]

You've got too much time on your hands [clap clap clap clap] ta ta ta tickin' awayyyyyeahhh!!!

I think a large part of the application of the golden mean in music is due to aesthetics. For example, the climax of a piece of music:

1. if the climax is at the exact end, then there is no room for a "cool down" period afterwards (there are MANY succesful compositions which do NOT have cool-down periods after the climax).

2. if the climax is exactly in the middle, then there can be a sense of pointlessness to the extended music that follows that climx (and again, there are some amazing pieces where the climax is at the exact center of the piece).

3. if the climax is near the beginning, well, see point 2

Some composers very consciously applied these proportions to their music, and got wonderful results from them (then again, they ARE great composers too, aren't they?).

The B Minor Mass of Bach is replete with musical/mathematical symbolism, yet he was also able to make great music while applying those mathematical restrictions on his own music.

There shouldn't be anything surprsing about any baroque or classical composer applying mathematical rules to his compositions, after all during those musical eras strictly 8-measure phrases (for example) were common-place, and regular time signatures were the norm, which makes the application of mathematical structure to the over-all structure of a work considerably easier to camouflage within a classical form.

I don't personally think of anything mathematical when composing, relying on judgement of the overall effect/affect. If I hit a difficult spot I may check basic issues like 'have I got uneven length phrases' measured in quantity of beats and consider adjustment based on what I find out. And, yes, is the climax (if appropriate) too early or late. But I adjust things according to the flow rather than any mathematical precept.

However, I appreciate that others may be very aware of the mathematics because they are there.

M

hi, all. this is my first post. figured i'd start by replying here. anyway, i kind of agree that questioning whether there's math in music is kind of silly. i'd say that math is basically strict rules defined in a quantitative way. just from a quick glance on the boards, it seems that most people here know basic theory and should realize that a lot of that is based on math. there's interval math for example (like a third plus a third is a fifth), etc.

anyway, i think that writing music with or without the consideration of certain "mathematical considerations" could be valid. just like you can write a melody while considering rules or just writing what sounds good (in which case you will, most likely, just inadvertently follow certain rules. statistically speaking.)

if you *are* interested in using math in your compositions, i think it's important to really try to understand the math first. the golden ratio has mathematical properties that makes it "golden". if you don't really understand why it's golden, in my opinion, you're just using it as "magic", and in the end, you'll either end up using it haphazardly, in ways that don't have any value, or in ways that are automatic and obvious. sure, you can keep experimenting until you find something that sounds right . . but you're still just doing what sounds right, rather than something significant.

am i making sense? my point is that if you want to use math in music, i think you should understand it. just like if you want to follow any other music rules, you should understand why you're using them.

Objection, your Honor! Speculation...

I'm not a big fan of classical music, but when music becomes more mathematical than, well, musical, you start having problems.

I doubt that more then half of the compositions ever written use the 'Golden Ratio', but maybe I'm just speculating...

~Kal

Objection, your Honor! Speculation...

I'm not a big fan of classical music, but when music becomes more mathematical than, well, musical, you start having problems.

I doubt that more then half of the compositions ever written use the 'Golden Ratio', but maybe I'm just speculating...

~Kal

Intentionally or unintentionally? I bet I could look at almost ANY peice of music and find a golden ratio somewhere. Now I think that most people who load their music with it intentionally run the risk of thier compositions suffering musically. My argument would be that the GR is something that is found commonly in nature. The word "found" is the operative here.

No doubt that trying to analyse aesthetics mathematically kept a few people out of mischief and gave them the chance to write huge and expensive tomes! Seems pointless unless the aim is to strip humanity of ALL that is human!

I think this golden ratio simply arose from observation. Nonetheless these interlopers discovered that most of Beethoven's big works correspond to the golden ratio. I'd guess that Beethoven didn't start a work by calculating the number of bars, this and that....

Frankly, who cares? If a piece of music or art works, it works; if it doesn't, etc etc.