music and mathematics

[John Curtin]

Nice post - some very interesting ideas here. I agree that music and mathematics are similar in that they cannot be expressed in terms other than their own. But I don't see music as being nearly as abstract as maths. Rhythm, for instance, is grounded in our most fundamental expression of life (breathing). And I've never heard of mathematics inducing the soul to dance, or moving someone to ecstasy. I think there is mystical power in music which goes beyond thought and abstraction, and strikes at our heart directly.

You obviously don't know many mathematicians. It's rare, and obviously quite different to a response to music, but I have had thrills from mathematics; both from learning new theorems (it all just fits together!) and from just applying mathematical skills. I hope I don't sound like too much of a geek!

It's strange isn't it, to talk about music as if it's a 'thing'. Probably language just lacks the capacity to describe / define music's essence. Like you say, there is basically no content in music apart from what we ascribe to it. So what do we actually study, when we approach music? It's more like trying to figure out our own position on music, rather than the music itself. To me, it's about gaining understanding of the self. Is higher level mathematics like this?

Higher level mathematics, in fact all mathematics, is really about gaining an understanding of mathematics itself, so, no not really. This is obviously where the analogies break down the most.

I guess you're right about the rules. When composers write music based on principles which are completely unfamiliar to the listeners, no-one will understand it. Again it must come down to social / cultural conditioning. The wonderful thing about creative thought, though, is that certain rules can be broken to the effect of opening the mind of others in a way which couldn't have been previously imagined. Think of the effect of Beethoven's music on his contemporaries. It was unprecedented, but there was enough familiarity there for them to relate to.

That's one of the things about mathematics though. The development of mathematics, just like the "development" of western music (if you want to call it that), has to quite a great extent been based on breaking established "rules". If we'd stuck with saying "two into three does not go", we'd never have got fractions. If we'd kept saying "you can't take three from two", we'd never have got negative numbers. If we kept thinking that every number can be expressed as a fraction of two whole numbers, well pi and the square root of 2 would have quite a difficult time. If we kept saying "you can't take the square root of minus one" we'd never have discovered imaginary numbers. If we stuck with what the Greeks thought and said you can't add an infinite number of things together, we wouldn't have calculus.

However, I would suggest that all of human endeavour and innovation is based essentially on breaking the established rules of what can be done, so it's not exactly unique to music and mathematics.

I like this thread; we've got some good discussion going here .

 

[Rune Vejby]

This is a strange discussion heh.... but I guess it just shows how people wish to deconstruct art and make it understandable.... too bad yeah... If people can't understand it, they don't like it. So yes, music and science are interrelated, sadly.

 

[Oneiros]

You obviously don't know...

Ah, the maths thrills which come from understanding sound as though they're intellectual. I suppose music can do this too, in the sense that it opens one's mind to different ideas, but the ideas aren't rational / logical like maths - they're intuitive or emotional. Although you may be right - drawing a clear line between them may be somewhat naive... Perhaps music contains a fusion of intellectual and emotional ideas? Of maths and mood...

Fully agree with the rule-breaking comments. Like you say, in this way maths really is like music - the inventive mathematicians would need to be fairly creative. This has given me a new respect for maths as a "creative art"... Or is that going a bit too far?

This is a strange discussion heh.... but I guess it just shows how people wish to deconstruct art and make it understandable.... too bad yeah... If people can't understand it, they don't like it. So yes, music and science are interrelated, sadly.

I don't understand what you're saying here... Do you think it's a bad thing to talk intellectually or scientifically about art? I do think that the most valuable in art is beyond explanation / discussion, as it strikes a deep level of experience, but discussion can bring certain ideas to light which enhance one's perception of it.

 

[pliorius]

yes,i'm happy to have started such an interesting thread, sincerely hadn't expected such a nice responses and conversation. alain badiou, french philosopher, wrote that scientist (mathematician) needs only one other scientist to approve of his results, while artist ultimately needs no one (nevertheless, work of art has an adress, such being the nature of all language). plus it's good to remember that math has it's riddles that are waiting to be solved for centuries,a s with ferma's (hope i wrote it right) equations, and we all know of musical riddles as that of old bach. as for emotional/intuitive part we can remember mozart words, which sounded smth like this - ordinary people will admire this music not knowing why, while professionals will see it's structural beauty. it could seem that math lacks its "ordinary people", yet when one learns and starts to understand new (to him/her) math, threre's really a big emotional or intuitive change. they might not seem, but numbers and sequences are unique. all odd numbers versus/together with numbers like 2,4,6,8,10. having diffrent relations, diffrent taste. and it's not too far to claim, that 17 is quite diffrent from 4. i had a discussion with mathematician, who, when i used to stay that it's just calculating, it's just computation, would completely deny my words and response with something like - you don't know how much imagination and intuition as well as a brave choice is needed for good mathematician. yes, for us, not exceptional in maths, it is hard to see, whre the beauty comes in, but it is as well with people, who don't understand some music - they really don't see how some sound sequences and layers can be beautifull.

 

[methodistgirl]

You are talking about digital music and here is an example:
C7th,E7th,G7th--C08. That's a C chord or something like that.:smirk:
judy tooley

 

[JLS]

It's strange isn't it, to talk about music as if it's a 'thing'. Probably language just lacks the capacity to describe / define music's essence. Like you say, there is basically no content in music apart from what we ascribe to it. So what do we actually study, when we approach music? It's more like trying to figure out our own position on music, rather than the music itself. To me, it's about gaining understanding of the self. Is higher level mathematics like this?

Higher level mathematics, in fact all mathematics, is really about gaining an understanding of mathematics itself, so, no not really. This is obviously where the analogies break down the most.

We search for in music the same thing we search for in mathematics: internal coherence and consistency, without which both would be cacophony.

 

[Corno Dolce]

Hmmm - *Internal coherence and consistency*. Somewhat off-topic: I wish that mankind could likewise search for internal coherence and consistency within their own soul and being. We too often see mankind *wigging out* and the cause is lack OF internal coherence and consistency.

 

[JLS]

Hmmm - *Internal coherence and consistency*. Somewhat off-topic: I wish that mankind could likewise search for internal coherence and consistency within their own soul and being. We too often see mankind *wigging out* and the cause is lack OF internal coherence and consistency.

It is exactly what we do when we create mathematics, music, language, logic, science, philosophy, religion...

We attempt to bring coherence and consistency to the phenomenal world. We integrate what we receive with our selves(our modes of experience) in coherent and consistent ways. In doing so, we facilitate our existence and our coexistence. We create an intersubjective world in which we can have meaningful communication; where we can connect with others and attempt to extinguish that ever nagging fear of solipsism.

 

[methodistgirl]

The only math I notice in music is geometry. The shape of notes are lines
circles, and more. It takes geometry to build these instruments and make
them persise so that they can fit. You notice how a different length in a
pipe will create a different pitch and sound. That is geometry.
judy tooley

 

[Serassi1836]

Music is math.

Time signatures are math. Note values are math. I'm in a music theory class, and as the teacher said at the beginning of the class, people who are good at math tend to be good at music and vice versa.

Music and math both rely on patterns. Of course they should be combined!

And in Bach's "Goldberg variations" there are 10 canons (the 3, 6, 9, 12, 15, 18, 21, 24, 27, 30) and in them there is the simmetry and the translation.

Sound has a frequence, which it's a number. Sounds are numbers.

Isn't music maths?

 

[Muza]

I have to say, I find this thread to be one of the most interesting ones I have taken a part in lately. I will most certainly come back and read through it more carefuly when I get a chance!!!

 

[NEB]

But where does maths drop away and artistry take over. Maths cannot explain that indescribable something that makes a difference between a great musical performance, and a metronomic reproduction (which would inevitably be soulless). It is the very imperfections that make music most beautiful.

 

[Mahlon]

"But where does maths drop away and artistry take over. Maths cannot explain that indescribable something that makes a difference between a great musical performance, and a metronomic reproduction (which would inevitably be soulless). It is the very imperfections that make music most beautiful."

ah but what is the soul? I know this may sound pessimistic, but in reality, "Music" isn't emotional itself, Humans perception of music is, just something to think about. My proof, if you play a chiwa wa a piece of music, will they have the same response that a human does? I actually found a fascinating paper online about how music in many ways mirrors the workings of the brain itself. Here's the paper if any of you are interested. And then theres' studies done to develop computers which can compose.. although fairly unsuccessful at the moment. This isn't the exact article i was talking about .. tho looks interesting . I cant find the specific one at the moment http://www.musicandmeaning.net/issues/pdf/JMMart_1_3.pdf

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Here I have found the article!!
http://www.psych.unito.it/csc/cogsci05/frame/poster/1/f656-mauro.pdf

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may be off topic. but fascinating nonethless http://www.compositiontoday.com/forum/44_939.asp

 

[Serassi1836]

I think that music is art, and maths isn't art. But a lot of music's elements are based on maths and physichs. Are you agree?

 

[John Curtin]

Mathematics is an art. The problem is that they don't present it in this way when you learn it at high school, which is a mistake.

 

[Serassi1836]

Yes, I know. I think that find a new good dimostration of a theoreme is art. My last post was only a resume of all this thread. It's only try to solve diplomatic this thread.

 

[C5Says]

How about if I say music is code?

Don't mind me...just thinking out loud...

 

[Serassi1836]

Yes, music is a code.

Secret codes are often on mathematical bases, but if you want to write a message you must be good at writing. And if your secret code is beautiful, and what you write is terrible, the message is terrible.

If you want to write music, you've a code, and you must combine symbols, notes' frequences, instruments' sounds...

 

[kierantk]

Still, without mathematics, we would have no harmony, and we all understand how boring monophonic music is.
Harmony is produced through the number of corresponding points on the superposition of multiple sound waves, which allows us to calculate which chords our ears will like to hear.

Also, look back at the history of music. The twelve semitone scale was created by the famous Pythagoras, the very same who made the important geometric theorem. JS Bach's creation of the equal temperament system used fairly advanced maths, using the twelfth root of 2^x, to give the different frequencies of different notes, and thus the pipe lengths of different pipes on an organ, or tensions on string instruments.

Maths and Music go hand in hand

 

[methodistgirl]

Think about timing your music. It's in either in 4/4 time or 3/4 for a waltz
including 6/8. This is another place where math fits in.
judy tooley