Eric Whitacre and the Golden Ratio

Many of you have heard of Eric Whitacre, but how many of you know of the strange connection many of his pieces have with the Golden Ratio? If you don't know what it is, then look it up on Wiki. I first heard of this connection on this interview, and it's really fascinating how that turns out. The climax, or some other major point in the piece tends to occur at this point. The golden ratio is equal to (1+√5)/2, or about 1.618.

Times are approximate. The Golden Ratio is approximated by dividing the total time by the point in which the climax occurs. You have to convert seconds to minutes (or vice versa) to get it to work. All pieces except The Stolen Child, The Kangaroo, and The Seal Lullaby come from the BYU Singers recording. Those three exceptions are posted on his website. If anyone has either of the BYU Singers recordings, feel free to check my work.

A Boy and a Girl – Key Change (2:48/4:28)?

Cloudburst – Soprano Solo (5:09/8:12)

The Cow - Climax (0:39/1:02)

Go Lovely Rose – Climax (2:43/4:17)

The Kangaroo - Climax (0:24/0:38)

The Panther - Climax (0:31/0:48)

Her Sacred Spirit Soars – Key Change (3:56/6:36)

The Seal Lullaby - Final Phrase (2:18/3:45)?

Sleep – Climax (3:33/5:40)

The Stolen Child - Massive Crescendo (5:30/8:40)?

When David Heard – Climax (9:10/14:54)

This is really a weird phenomonon. I had thought that all belief in the magic of the Golden Ratio had died out hundreds of years ago, but there still seems to be something to that number. Does anyone else know of any other songs/artists where this occurs?

Wow! Amazing.

Whitacre wouldn't be alone in using this. Wikipedia lists it is being present in the works of Debussy, Chopin and Bartok, and I remember a lecture in which we were shown Bart

Other composers simply find that the most effective point for a climax is approx 2/3 of the way through the piece without realising they have used this proportion.

That's what I think Whitacre was getting at in this interview (it's been some time since I listened to it, so I might be wrong here) - it was like, someone ELSE did a study of his pieces and found the phenomenon just happened to occur at the golden ratio, which he found interesting. And I don't think you can use time to find the ratio, since time can and will vary from performance to performance - not to mention if rubato is in use. Better way would be to use beats (since measures are usually uneven in Whitacre music).

By the way the actual ratio part wasn't explained very well in the OP, so for those interested:

if "time after climax"= a

and "time up to climax" = b

Then a/b should equal b/(a+b)

Or in words;

small piece:big piece = big piece:whole thing

That's what I think Whitacre was getting at in this interview...was like, someone ELSE did a study of his pieces and found the phenomenon just happened to occur at the golden ratio, which he found interesting.

Unless a composer is actively attempting to do something like this, there really not much point in saying this is anything more than rooting around for stuff to write papers on.

It's so easy to simply let coincidence and confirmation bias put meaning where there really is none.

under 'not interesting nor relevant'>

If anyone else thought, as I did, upon reading this thread, "Gee, I wonder just how close these numbers really are to the golden ratio," no need to think further. I have no idea if it interests anyone (probably not), but I already did the number-crunching, so I might as well post the results here.

title			climax	total	ratio	1/ratio
			(seconds)
A Boy And A Girl	168	268	0.627	1.595
Cloudburst		309	492	0.628	1.592
The Cow			39	62	0.629	1.590	
Go Lovely Rose		163	257	0.634	1.577
The Kangaroo		24	38	0.632	1.583
The Panther		31	48	0.646	1.548
Her Sacred Spirit Soars	236	396	0.596	1.678
The Seal Lullaby	138	225	0.613	1.630
Sleep			213	340	0.626	1.596
The Stolen Child	330	520	0.635	1.576
When David Heard	550	894	0.615	1.625

The actual golden ratio			0.618	1.618
[/CODE]

Make your own conclusions. Based on the data alone, I think it seems close enough to be interesting, but if you want to draw conclusions beyond "it's interesting", you have to take into account first the selection of pieces (is it random? Were other "measurements" taken that didn't fulfill the criteria? How large is the collected body of Whitacre's works?), and then the definition of "climax" (may well be very difficult--or might not be).

Also, with the data itself you might also think about what kind of deviations can be expected in the compositions themselves (due to climaxes out of necessity falling on specific points in a phrase or bar), and in the recording (rubato, silence at the beginning or end of tracks), in order to gauge how far off the ratio can be and still count as a hit.

Although I believe this subject doesn't hold much [i]musical[/i] or artistic value, I'm not quite as inclined to dismiss this as wholly coincidental or uninteresting as flint seems to be. Still, points like the above need to be taken into account if any scientific conclusions are to be drawn.

Am I the only one who finds Whitacre's music overly cliche? I know how popular he is, but I've never been into any of his compositions, with the possible exception of 'Cloudburst'. He and Lauridsen just sort of bore me. Maybe this typical golden ratio climax is why?

@Flint: I just posted this here to see if anyone else is interested. I don't see it as particularly musically significant, mostly just an interesting topic.

@c7music: Some of his music is indeed very similar, but I see a vast world of difference between The Stolen Child, Leonardo Dreams, and little tree. To each their own. But most of his pieces do not climax near the golden ratio. AFAIK just the ones I listed do.

@Dev: The composer also probably had the Rubato and such in mind when he wrote the pieces. A simple sheet music analysis wouldn't reveal the tempo changes or length of fermatas. I actually think that it's more striking to find these things in live performances. What would be really intriguing would be to see how much the ratio varies between performances.

@EldKatt: I only posted those pieces that fit the criteria. None of Whitacre's other pieces that I checked had this connection (some 20 songs). The climaxes/key changes are all pretty obvious, though some pieces have more than one (When David Heard, Her Sacred Spirit Soars, etc).

I'd appreciate someone else checking my timings if they also have a CD. Don't use MP3s if they're encoded in VBR as you never know if 4:23 is going to be 4:23 all the time.

I took the total time and divided it by the golden ratio to approximate where that point would lie, and if there was a very significant point in the song there, I wrote it down. It's really sketchy (maybe no connection with the Golden Ratio, at least in these performances; I need to recheck) with The Stolen Child, A Boy and A Girl, and the Seal Lullaby) but someone should seriously listen to When David Heard with the Golden Ratio in mind (BYU Singers version). Simply amazing, especially when you punch the numbers in and see how close it gets.

@EldKatt: I only posted those pieces that fit the criteria. None of Whitacre's other pieces that I checked had this connection (some 20 songs).

This is cherry-picking.

You're attempting to find meaning where there is none.

Unless a composer is actively attempting to do something like this, there really not much point in saying this is anything more than rooting around for stuff to write papers on.

It's so easy to simply let coincidence and confirmation bias put meaning where there really is none.

I agree with that last sentence. I too am highly sceptical of such musicological "research" and I think that very often "discoveries" are made in music that come more from a biased observer than the actual observed object.

But that doesn't mean such research is totally useless. First, there are scientific principles which can make a study more or less unbiased if applied correctly. You need to establish a clearly stated hypothesis first (such as: Most of Whitacre's pieces have their climax at the golden ratio), define each part of this hypothesis (i.e. to how many it needs to apply to be relevant, how closely it must match the golden ratio to be relevant, what exactly constitutes a "climax" etc.). And only after you have established these things you actually look at a large number of pieces and start counting, and then draw conclusions from that.

The problem with a lot of "musicological research" of this kind is that it's done really sloppy. They don't state what they want to research first, they just start "looking for golden ratios" everywhere and ignore everything that -doesn't- fit. Nor do they often worry about statistical relevance etc.

Of course, in practice all of this isn't so easy. First of all, almost no composer has written enough to create any statistically relevant sample size. Then it's hard even to define temporal proportions in pieces where there aren't exact metronomic marks and no rubato/fermata's etc. And hardest of all is defining what things like "climax" mean in a piece of music, since music is almost always a very ambigous thing that can be looked at from many sides with the same validity. But still, I think with a bit more "scientific thooughness" one could gain much clearer results.

The other aspect however is that not every discovery that doesn't doesn't show an object in an unbiased way is necessarily just bad. (As long as it doesn't pretend to be objective and scientific). There's almost never just one clear "truth" about a piece, and even an analysis that "discovers" something that comes more from the method of the analysis than the piece itself can be very enlightening. Sometimes, an analysis that doesn't really focus on hard facts but takes a more artistic and free route can even be much more suitable for a piece and give the reader a much better approach.

I think both the "hard scientific" and the "free artistic" form of analysis are highly important and definitely have their place. I only have a problem when one is sold as the other. (Which of course doesn't mean there can't be mixtures between the two - as probably most analyses are.)

This is hardly remarkable. Composers sometimes decide where the supposed 'climax' will be in relation to the golden ratio whilst they are composing a piece. It's not really a revelation or a discovery, so much as a compositional device.

As for Mr. Whitacre, to quote my Aural Lecturer (the revered conductor Paul Brough)

'Well, put it this way. Do you know the choral composers Eric Whitacre and Morten Lauridsen? They're sort of in vogue at the moment. Which is fine as long as you don't call it music.'

This is cherry-picking.

You're attempting to find meaning where there is none.

Well, maybe. But I just find that when his pieces do approximate it so precisely), then there has to be something there. A good 29.03% of the pieces I checked show a definite connection (9/31), with a variance from the golden ratio of around .012 to .07 . I have also stated repeatedly that I'd welcome checking of my timings and data, if anyone else has a copy of either CD.

@rautavaara: Mr. Whitacre has stated that none of this was planned. Also, he happens to be one of my favorite composers, and I'll call his stuff music if I want to. To each their own. But that's not really part of the topic.

This is hardly remarkable. Composers sometimes decide where the supposed 'climax' will be in relation to the golden ratio whilst they are composing a piece. It's not really a revelation or a discovery, so much as a compositional device.

As for Mr. Whitacre, to quote my Aural Lecturer (the revered conductor Paul Brough)

'Well, put it this way. Do you know the choral composers Eric Whitacre and Morten Lauridsen? They're sort of in vogue at the moment. Which is fine as long as you don't call it music.'

I don't personally care much for Whitacre's music either, but I don't think statements like that are helpful at all (even less so when they're just random, unfounded quotes by someone else). I think we've had enough "X is not music"-threads to know where such statements tend to lead here.

I don't personally care much for Whitacre's music either, but I don't think statements like that are helpful at all (even less so when they're just random, unfounded quotes by someone else). I think we've had enough "X is not music"-threads to know where such statements tend to lead here.

It was hardly random. The OP seems to think that the Golden Ratio's supposed presence in his works is a 'phenomenon' which acts to deify Mr. Whitacre in a way which I do not agree with.

'Well, put it this way. Do you know the choral composers Eric Whitacre and Morten Lauridsen? They're sort of in vogue at the moment. Which is fine as long as you don't call it music.'

What a stupid goddamn man. I really really hate this popular=not legitimate notion that a bunch of "learned" people have regarding any sort of art. What the hell WOULD he call music? 4'33''? (I know we've had that topic - let's not get into it again. That's just the best example I could come up with).

I personally don't think the golden ratio has any merit towards anything, it's really just a coincidence based on the fact that Whitacre probably likes having just this much music, a climax, and then just this much music after it.

Also, I disagree about some of the supposed "climaxes" - in Her Sacred Spirit Soars, for example, I'd say the climax is at the very end. So that's out.

EDIT: hopefully "goddamn" and "hell" aren't horrible enough words to break the code of conduct

What a stupid goddamn man. I really really hate this popular=not legitimate notion that a bunch of "learned" people have regarding any sort of art. What the hell WOULD he call music? 4'33''? (I know we've had that topic - let's not get into it again. That's just the best example I could come up with).

I personally don't think the golden ratio has any merit towards anything, it's really just a coincidence based on the fact that Whitacre probably likes having just this much music, a climax, and then just this much music after it.

Also, I disagree about some of the supposed "climaxes" - in Her Sacred Spirit Soars, for example, I'd say the climax is at the very end. So that's out.

EDIT: hopefully "goddamn" and "hell" aren't horrible enough words to break the code of conduct

It is okay... he's European...

Makes sense now, right?

It is okay... he's European...

Makes sense now, right?

What do you mean by that?

You know... the intellectual type in music.

The judging intellectual type. The type that makes the rest of the smart composer-types, look like ridiculous snots.

You know... the intellectual type in music.

The judging intellectual type. The type that makes the rest of the smart composer-types, look like ridiculous snots.

How exactly, then, does being European have anything to do with it?

Does anyone else know of any other songs/artists where this occurs?

Look up "My loving Life" by Nikolas Sideris in the chamber music forum. ;)

(nothing to do with climaxes, the golden ratio is used in a completely different (and more interesting, in my opinion) way)

That's where snotty intellectualism comes from.

That's why America has Steve Reich.

That's where snotty intellectualism comes from.

That's why America has Steve Reich.

And Elliott Carter?!

And Elliott Carter?!

He's a WASP. European roots... especially musically.

It was hardly random. The OP seems to think that the Golden Ratio's supposed presence in his works is a 'phenomenon' which acts to deify Mr. Whitacre in a way which I do not agree with.

I wasn't replying to this part. What I was referring to as "random unfounded quote" was your last sentence about it not being music, which really has nothing to do with the topic and just leads to stupid arguments like the one displayed in the last couple of posts.

Steve Reich? Oh yay.

John Adams on the other hand...

And Elliott Carter...

Europe vs USA? More like The UK vs rest of Europe vs USA?

Back on topic: (So the post is justified)

Golden ratio ... is interesting.