music and mathematics

[pnoom]

I have often realized what math teachers are very interested in music. And a lot of musicians, especially composers, conductors or organists, have good knowing in math. Than I imagine it is not by pure chance.

Not at all by pure chance. Understanding mathematics thoroughly helps you understand music thoroughly.

 

[Pacific 231]

Not at all by pure chance. Understanding mathematics thoroughly helps you understand music thoroughly.

Completely agree with you.

 

[Oneiros]

IMO Music goes way beyond maths. Numbers may form the structure of sounds, and even works of music, but one can't reduce music to this. It has far too much mystical power.

Formulae and such might stimulate the mind, but can they also illuminate the soul? Music can.

 

[Gustav]

there's no music without math

please explain why some if not all indigenous cultures, even though lack the most rudimentary mathematical knowledge. Yet, they still created songs, and played instruments.

Furthermore, there was music long before the development and discovery of Mathematics.

 

[Gustav]

I have often realized what math teachers are very interested in music. And a lot of musicians, especially composers, conductors or organists, have good knowing in math. Than I imagine it is not by pure chance.

essentially you are making up things, please, do not mislead people by providing wrong information.

If what you say is true, please provided me with some "official" statistics, otherwise, only a fool would believe what you say.

 

[pliorius]

well, gustav, they didn't need to have formalized mathematical language like we know it now, yet it doesn't deny that they used maths, but not formaly or so consiously as we do. more over it could be said that their music was more of a singing kind, yet they worked by mimesis or ,well, feelings. both of them are not mystical powers, but operations.
and yes, i thouht of that while writing the other post, and for instance i thought that they didn't have understanding of notion 'subject' as we do, so their music would be both - maths, unconsciously, and singing, which was not the voice of a particular subject, but of collective. so it seems that when time goes on, we get clearer mathematics and more subjective subject but not necessary each of them dependent on one another. for voice is something diffrent than maths.
so beyond math in music, there must be voice - that's why i'm not still sure if rytis mazulis is a true composer..

 

[pnoom]

essentially you are making up things, please, do not mislead people by providing wrong information.

If what you say is true, please provided me with some "official" statistics, otherwise, only a fool would believe what you say.

You don't really need "official statistics." It should be clear that because music is so reliant on math, understanding math would help to understand music.

You want a specific example: I am very advanced in math (I'm taking a college math course but I'm still in high school). I'm also in a music theory course. I entered with no significant musical knowledge, but I still grasp the concepts faster than any of my classmates.

 

[Gustav]

You want a specific example: I am very advanced in math (I'm taking a college math course but I'm still in high school). I'm also in a music theory course. I entered with no significant musical knowledge, but I still grasp the concepts faster than any of my classmates.

well, in terms of knowledge, i am a 2nd year university student. I have taken all the required calculus courses, as well as physics, and basic music theory. Yet, i fail to see any explicit relationship between mathematics and music.

You don't really need "official statistics." It should be clear that because music is so reliant on math, understanding math would help to understand music.

well, without evidence, all these talks are "empty" and meaningless. Furthermore, people seem to believe that math and music are somehow related in a "Big" way. Such beliefs has yet been justified in a convincing fashion. In a simple sentence, if you want to convince me, you'd better give me some hard empirical evidence. Because, i can say that music is absolutely unconnected to math, because all the musicians i know all do poorly in that subject.

I hope this discussion can go beyond just stating our "beliefs", but to somewhere more meaningful, where the real knowledge is at.

 

[pnoom]

Time signatures only work if the fractional note values add up to the fraction representing the time signature.

That is math, pure and simple.

 

[Rune Vejby]

Music is math.

Time signatures are math. Note values are math.

This is an interesting argument. But then I can argue that music is discourse. Intonation is discourse, tonality is discourse. Now I have argued that music is belonging to the linguistic sciences and that it is no longer math...

But you are right bro', unfortunately music has become math. That is why most people do not consider music to be art anymore. Ask a young person in any country this question: What discipline contains the highest artistic value: Painting, Writing or Music?
The boy will no doubt tell you "Painting and Writing", yeah?

This is because music has been arranged (according to mathematical princples) to suit a specific consumer need. The people want tracks with a max. of 8 chords, min. 120 bpm and a maximum duration of 3,5 minutes... There are even computer programs which claims to be able to analyze the "hit potential" of a tune...

So our equation looks like this now:

Music is math
Music is not art
Math is not art

Now it makes sense, yeah?

Fortunately some composes still value the abstract and impressionistic character of music. We don't give a I love this forum about rythm, time signatures and note values. About duration and structure... We don't make any funds, but hell, it doesn't matter, because art is so much more than money bro'.... Its the meaning of life

 

[pliorius]

i wholy agree with the statement that music is language, which i meant by arguing about music source as a voice and becoming subjet. and music is made true art not by math, yes. yet i don't believe that getting rid of all of its mathematical features is a way of making it an art. noise to me is not an art form. as well as silence.

"This is because music has been arranged (according to mathematical princples) to suit a specific consumer need. "

this doesn't deny the fact, that music can be arranged according to mathematics to suit no one else, but the work and composer in question. as true mathematics isn't about technological achievement, but about true beauty of thought movements in number. art can be decadent as science.
music is about thought movements(embodied in sounds). both, math and music is about thought movements. if pop culture use trivial maths to get fast acknowledgement and money, that doesn't mean math is trivial - it only means they are thinking base.thinking false movements.

 

[Corno Dolce]

Hi Pliorius,

I totally agree with your last sentence - it sort of informs my thinking in regards to the pop movement in general.

Cheers,

Corno Dolce

 

[methodistgirl]

How many of us though enjoy tinkering with some kind of gadget or
gizmo. I will always be doing that my ownself. Instead of just fixing
something to eat, knit, and other hobbies; I like to tinker with other
gadgets. I even put the tab back on one of the organ stops. It fell
off when I found the organ after one of the top musicians got off of
the organ. I felt like I really fixed something! I know one thing where
music meets mathematics and that is geometry. Look at the different
organs, pianos, and other hand made instruments. Look at the designs.
Not all pipe organs look like boxes with buttons and keyboards. They do
have a design. You have to get the different panels of wood on the
instrument just right or it wouldn't match at assembly. The same goes
for the brass instruments. You wouldn't be able to fit a 1/3 inch pipe
with a 1/2 inch pipe to make a sound it would'nt fit.
judy tooley

 

[Pacific 231]

How many of us though enjoy tinkering with some kind of gadget or
gizmo. I will always be doing that my ownself. Instead of just fixing
something to eat, knit, and other hobbies; I like to tinker with other
gadgets. I even put the tab back on one of the organ stops. It fell
off when I found the organ after one of the top musicians got off of
the organ. I felt like I really fixed something! I know one thing where
music meets mathematics and that is geometry. Look at the different
organs, pianos, and other hand made instruments. Look at the designs.
Not all pipe organs look like boxes with buttons and keyboards. They do
have a design. You have to get the different panels of wood on the
instrument just right or it wouldn't match at assembly. The same goes
for the brass instruments. You wouldn't be able to fit a 1/3 inch pipe
with a 1/2 inch pipe to make a sound it would'nt fit.
judy tooley

Very good description!

 

[pnoom]

At some point, I plan on composing a piece of music using the digits of pi. I'll let you guys know how it sounds.

I haven't figured out how to deal with the fact that pi has 10 distinct digits but there are only seven distinct notes (if I want to use key signatures, which I probably do).

PLEASE: no suggestions from you guys for how to do it, I want to figure this out myself.

 

[Gustav]

At some point, I plan on composing a piece of music using the digits of pi. I'll let you guys know how it sounds.

I haven't figured out how to deal with the fact that pi has 10 distinct digits but there are only seven distinct notes (if I want to use key signatures, which I probably do).

PLEASE: no suggestions from you guys for how to do it, I want to figure this out myself.

atonal music eh? i challenge you to compose "Tonal" music using Pi.

 

[Corno Dolce]

Hi Gustav,

*Compose "tonal" using Pi* - whoa dude, that could be a never ending work - Pnoom would probably be employed for all eternity. :grin::grin::grin:

Cheers,

Corno Dolce

 

[John Curtin]

Mathematics is really more an art than a science. Science is about observable phenomena; mathematics has little to do with observation. A good mathematician needs to be creative, able to think laterally. Anything less makes you little more than an accountant. (No offence to any accountants out there.)

Mathematics is essentially the purest form of thought. Some people say that music is the purest form of emotion. But I'd like to think that we've come a bit further than the ancient Greeks in that we no longer think of emotion and rational thought being antipodal. They are really just different ways of approaching things, and they aren't really separable at all.

There is "beauty" in mathematics, on just as abstract a level as we say there is "beauty" in music. On a more "rational" aesthetic level, we like mathematical systems that are balanced and symmetrical, just as we music that has symmetry and balance on the same rational level of aesthetics. Mathematics and music are both highly abstract. This is probably why musicians are often more proficient at mathematics: both pursuits involve abstract thought that can't be expressed in images or language.

Music expresses more "raw" emotions, however this has more to do with the physiological and/or cultural effect it has on us. Of course it is more effective at communicating emotion, because everybody can listen to music, whereas the vast majority of people can barely remember high school algebra. It speaks to a wider audience, and has developed a language that is effective at expressing emotions. Whether this is an inherent property of music is highly questionable. There is no objective emotional content in music; it is found only in listeners who impute it. Whether the response is fundamentally ingrained or purely cultural is an interesting question, but I prefer not knowing, because I would prefer the magic to remain.

There are of course 'mathematical' elements in music, as many of you have pointed out. We speak of melodic and harmonic 'formulas', chord changes that are as guaranteed to evoke the "right" response as certain as a mathematical theorem. The composition process isn't as subjective as we would like to think; there are rules that everybody follows, rules that some people choose to follow, but I think we can agree that if the composer is not writing based upon any rules then s/he is no longer creating music: a computer can create white noise more efficiently.

I'm not necessarily saying that the emotions imparted by music are reducible to mathematical formulae (this is the 'magic' I was talking about), but to say they are totally different is really an unsupportable claim.

 

[pnoom]

Two thumbs up for that post, John.

 

[Oneiros]

Mathematics is really more an art than a science. Science is about observable phenomena; mathematics has little to do with observation. A good mathematician needs to be creative, able to think laterally. Anything less makes you little more than an accountant. (No offence to any accountants out there.)

Mathematics is essentially the purest form of thought. Some people say that music is the purest form of emotion. But I'd like to think that we've come a bit further than the ancient Greeks in that we no longer think of emotion and rational thought being antipodal. They are really just different ways of approaching things, and they aren't really separable at all.

There is "beauty" in mathematics, on just as abstract a level as we say there is "beauty" in music. On a more "rational" aesthetic level, we like mathematical systems that are balanced and symmetrical, just as we music that has symmetry and balance on the same rational level of aesthetics. Mathematics and music are both highly abstract. This is probably why musicians are often more proficient at mathematics: both pursuits involve abstract thought that can't be expressed in images or language.

Music expresses more "raw" emotions, however this has more to do with the physiological and/or cultural effect it has on us. Of course it is more effective at communicating emotion, because everybody can listen to music, whereas the vast majority of people can barely remember high school algebra. It speaks to a wider audience, and has developed a language that is effective at expressing emotions. Whether this is an inherent property of music is highly questionable. There is no objective emotional content in music; it is found only in listeners who impute it. Whether the response is fundamentally ingrained or purely cultural is an interesting question, but I prefer not knowing, because I would prefer the magic to remain.

There are of course 'mathematical' elements in music, as many of you have pointed out. We speak of melodic and harmonic 'formulas', chord changes that are as guaranteed to evoke the "right" response as certain as a mathematical theorem. The composition process isn't as subjective as we would like to think; there are rules that everybody follows, rules that some people choose to follow, but I think we can agree that if the composer is not writing based upon any rules then s/he is no longer creating music: a computer can create white noise more efficiently.

I'm not necessarily saying that the emotions imparted by music are reducible to mathematical formulae (this is the 'magic' I was talking about), but to say they are totally different is really an unsupportable claim.

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.

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?

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.

These are just some ways in which maths and music differ, IMO.