# Asymmetry in music.



## aleazk (Sep 30, 2011)

It is a fact (that has been studied scientifically) that some music is particulary appealing when it has some sense of 'symmetry' (for example, the famous 'golden ratio'), it sounds very 'natural'. It has been argued that by biological and evolutive reasons, the brain tends to appreciate things with the golden ratio. On the other hand, there's a lot of 'asymmetry' in some music (particularly modern music), but they are masterpieces as well, and they are very appreciated. Why, if there's some biological and evolutive reasons to like 'symmetrical music', we love 'asymmetry'?. I find this a particularly human phenomena, and maybe one of the reasons of the power of arts. We like to push things, we are quickly bored with the 'natural' and we want next the 'unnatural'. In that sense, I think that the so called 'disorder' (in its popular meaning), and others features of modern music, are a natural way to express things that are inexpressible through other means (this is only an example, I'm not trying to do a 'defence' of modern music with this thread). Of course there's a lot of 'grey areas' in all this (what's ugly and what's beauty in arts?), what seemed interesting to me is that this thing of the 'golden ratio' at least provides (although in a very superficial way) some 'objective' framework to discuss this subject. So, for me, it's obvious that we like both symmetry and asymmetry in music, the question is, what do we find exciting in each of the two and why?, also, what are 'good' asymmetries and 'bad' asymmetries?.


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## Renaissance (Jul 10, 2012)

Modern works can also use symmetry. Bartok's SQ are a good exemple in which symmetry can occur. I think there are some books that reveal some hidden symmetries of classical tonality in Schönberg's dodecaphonic compositions too. Anyway, I don't know about the music of the late 20th century and its relation to symmetry.

https://ccrma.stanford.edu/~jchrsmt/Papers/bartokno5v6.pdf


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## Andreas (Apr 27, 2012)

I think the ABA kind of symmetry is very powerful. You find it not only in the ABA song form, but also in the exposition-development-recapitulation structure of the sonata allegro form, and, a little more streched-out, in all cyclic works where themes from the beginning reappear at the end.

I think most arch-like structures (ABA, ABCBA, etc.) provide these neat symmetries. They mirror some kind of going-away and coming-back-home.


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## norman bates (Aug 18, 2010)

i have some difficulties with the idea of simmetry in music, because while in a picture the symmetry it's immediately perceivable, you don't perceive with the same obviousness a palindromic piece of music as something symmetric. You can try to apply a spacial concept to time but there are many differences.


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## aleazk (Sep 30, 2011)

norman bates said:


> i have some difficulties with the idea of simmetry in music, because while in a picture the symmetry it's immediately perceivable, you don't perceive with the same obviousness a palindromic piece of music as something symmetric. You can try to apply a spacial concept to time but there are many differences.


Symmetry is not necessarily a spatial concept. Also, a palindromic piece of music is only a special kind of symmetry that can appear in music. In this context, when I'm talking about 'asymmetry', I'm referring to anything that can be seen as 'unnatural', where the 'natural' is represented in some sense by the golden ratio. In general, I'm skeptical about this kind of relations between arts and mathematics. I'm trying to understand this more deeply to see if it really is useful for a better understanding of the arts.


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## Ramako (Apr 28, 2012)

I think symmetry is a really important concept to grasp a hold of in music, unfortunately I have not done so yet 

I once wrote a piece which had certain passages with a rhythmic structure of 1 beat, 2 beats, 3 etc. or corresponding ones with 4,3,2... The effect was quite interesting, because so much of rhythm is made of the harmonic series (1,2,4,8 etc.) that going 1,2,3... created a lagging effect which I attempted to exploit with limited success.

Rosen argues in The Classical Style that the mind is conscious of the 'weight' of a phrase, or whatever, and so I suppose a similar weight would be necessary to balance it, perhaps a greater weight to gain momentum, or a lesser one to release tension. I wish I understood this better. Symmetry and balance are certainly related concepts.

As for the golden ratio, it is an unfortunate reality that it does have aesthetic qualities, but I do not believe (in music anyway) it is any more natural than the ratio 1:2 (or 1:1 for that matter). I think it is more relevant on a structural scale anyway.

This is all very difficult anyway.


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## SuperTonic (Jun 3, 2010)

When it comes to harmony, tonality actually requires asymmetry. Within tonal harmony, symmetrical harmonic constructs tend to be tonally ambiguous, and in fact are often used as pivot point to modulate to new keys. I'm talking about combinations of notes that evenly divide the octave, ie the whole-tone scale, the fully diminished 7th chord, the augmented triad, and the tritone. All of these are considered highly unstable in traditional tonality because they can be resolved equally well in different ways. This is particularly true of the tritone and fully diminished 7th chord in traditional tonal harmony during the common practice era.


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## aleazk (Sep 30, 2011)

Ramako said:


> I think symmetry is a really important concept to grasp a hold of in music, unfortunately I have not done so yet
> 
> I once wrote a piece which had certain passages with a rhythmic structure of 1 beat, 2 beats, 3 etc. or corresponding ones with 4,3,2... The effect was quite interesting, because so much of rhythm is made of the harmonic series (1,2,4,8 etc.) that going 1,2,3... created a lagging effect which I attempted to exploit with limited success.
> 
> ...


Yes, that's what I'm referring. An 'asymmetry' in this context, for example, would be a 'climax' 'out of place' in a piece.


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## aleazk (Sep 30, 2011)

SuperTonic said:


> When it comes to harmony, tonality actually requires asymmetry. Within tonal harmony, symmetrical harmonic constructs tend to be tonally ambiguous, and in fact are often used as pivot point to modulate to new keys. I'm talking about combinations of notes that evenly divide the octave, ie the whole-tone scale, the fully diminished 7th chord, the augmented triad, and the tritone. All of these are considered highly unstable in traditional tonality because they can be resolved equally well in different ways. This is particularly true of the tritone and fully diminished 7th chord in traditional tonal harmony during the common practice era.


Hi, if your response was motivated by my use of the word 'dissonance', I have rectified it by 'disorder', it was a bad choice of words. In any case, you are right in your considerations about harmony.


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## Ramako (Apr 28, 2012)

aleazk said:


> Yes, that's what I'm referring. An 'asymmetry' in this context, for example, would be a 'climax' 'out of place' in a piece.


Yes. I suppose a climax requires a certain amount of tension raising before it, and some padding afterwards to prepare for the next one. However, symmetry on a small scale exists as well - particularly in the Classical period. The whole question-answer idea of a repeated, or similar, phrase often gives the impression of symmetry, by going down where the previous phrase went up.

Ultimately, they know that music's going to have problems with symmetry when they realized that the basic octave and fifth are asymmetrical. I bet Pythagoras was pretty unhappy when he discovered that.


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## Klavierspieler (Jul 16, 2011)

Good asymmetry:


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## NightHawk (Nov 3, 2011)

Very interesting thread - Anyone interested in the application of the 'Golden Section'/'Golden Mean' should find a copy of Erno Lendvai's book on Bartok and the analysis of his music:

http://books.google.com/books/about/Béla_Bartók.html?id=37GlAAAACAAJ

It is a fascinating study and also involves Bartok's use of the Fibonacci Sequence (1,2,3,5,8,13, 21....) - both it, and the 'Golden Section' are found in nature and are as inexplicably profound as the value and applications of pi.


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## rrudolph (Sep 15, 2011)

I think asymmetry can be satisfying in any artistic form as long as the basic idea of the work in question is clearly expressed. We enjoy symmetry because it presents a closed form to us and that closure lends cohesiveness to our experience. That same sense of logical closure can be achieved with asymmetry as long as it is artfully used. For me, asymmetry becomes disturbing when it seems like the asymmetry is caused by something missing; take, for example, the Milhaud Concerto for Percussion. It has a standard fast opening movement then a slow movement...and that's it. It just peters out. Milhaud lived another 40 years after he composed the work and it was published and performed many times during his lifetime. He had plenty of opportunity to write another movement but didn't, so we must assume that that's how he wanted it to be. To me, it seems truncated, like it was never finished. Because of that it is rather unsatisfying to me. Same with the Schubert 8th. Two great movements, but when I listen to it or play it I always wander what the whole thing was supposed to sound like. The missing movements deprive me of an understanding of the overall scale of the piece, which I consider essential to my listening experience. That's why it really irks me when somebody starts something and then


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## LordBlackudder (Nov 13, 2010)

i suppose they're all symertrical


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## mmsbls (Mar 6, 2011)

I'm used to thinking of symmetry with respect to something (e.g. bilateral symmetry in vertebrates). I can imagine symmetries in music (ABA form was mentioned), but most parts of music seems devoid of symmetry to me. This thread seems more about order and disorder. Is that correct? If there are symmetries in music, can someone give examples?


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## Philip (Mar 22, 2011)

I also have a hard time with the term asymmetry... i know of works that make use of _symmetry_, but isn't asymmetry just everything else? On the other hand, isn't it possible to find symmetry in everything, on some level?


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## aleazk (Sep 30, 2011)

mmsbls said:


> I'm used to thinking of symmetry with respect to something (e.g. bilateral symmetry in vertebrates). I can imagine symmetries in music (ABA form was mentioned), but most parts of music seems devoid of symmetry to me. This thread seems more about order and disorder. Is that correct? If there are symmetries in music, can someone give examples?


well, in any case, I think that it's somewhat clear my use of the word here (as you say, is more related to order and disorder). Maybe I have taken some liberties with the word, my apologies. Next time I will mention the _Lie group_ and the _Killing vector fields_ which generate the symmetries, if people want punctilious definitions.


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## aleazk (Sep 30, 2011)

rrudolph said:


> I think asymmetry can be satisfying in any artistic form as long as the basic idea of the work in question is clearly expressed. We enjoy symmetry because it presents a closed form to us and that closure lends cohesiveness to our experience. That same sense of logical closure can be achieved with asymmetry as long as it is artfully used. For me, asymmetry becomes disturbing when it seems like the asymmetry is caused by something missing; take, for example, the Milhaud Concerto for Percussion. It has a standard fast opening movement then a slow movement...and that's it. It just peters out. Milhaud lived another 40 years after he composed the work and it was published and performed many times during his lifetime. He had plenty of opportunity to write another movement but didn't, so we must assume that that's how he wanted it to be. To me, it seems truncated, like it was never finished. Because of that it is rather unsatisfying to me. Same with the Schubert 8th. Two great movements, but when I listen to it or play it I always wander what the whole thing was supposed to sound like. The missing movements deprive me of an understanding of the overall scale of the piece, which I consider essential to my listening experience. That's why it really irks me when somebody starts something and then


Thanks for your examples, that's the kind of things that I was looking for.


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## violadude (May 2, 2011)

I don't know if symmetry in music can always be easily or naturally perceived in music.

For example, the beginning of this is very symmetrical:





Although, I don't think a lot of people sense an inherent naturalness about it.

Most people do, however, sense an inherent naturalness in the progression I-V-V-I. I guess it depends on context.


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## Sid James (Feb 7, 2009)

aleazk said:


> ...So, for me, it's obvious that we like both symmetry and asymmetry in music, the question is, what do we find exciting in each of the two and why?, also, what are 'good' asymmetries and 'bad' asymmetries?.


What I find exciting is if a composer uses these in a creative way. Eg. Bartok with his string quartets, as has been mentioned. Or Mahler in his 5th symphony, with a similar 'arch' form. Also Beethoven in his late quartets. & even Haydn in some of his string quartets. It goes way back and they all do it uniquely, they rework the forms uniquely.

With asymmetry, I still like some sense of something to hang onto. Eg. in Varese's music there is little or no literal repetition, but what he does do is sometimes make small changes to the same phrase or rhythmic idea, and that small change makes all the difference in terms of guiding me as a listener. There's a similar thing going on with other experimental composers I like who do this, esp. the Americans like Ives, Carter, Partch.

But for me its not a matter of 'good' or 'bad.' Just things that grab me and 'work' for me as a listener (or have potential to after more listens, tries) or 'don't work.' So ultimately its subjective, and these things are often hard to notice or perceive upon just one or two listens. It takes time.


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