piano and math

[rosie]

How many people in this forum consider themselves good at math? Like, not just a good memorizer and test taker, but can you actually figure things out that haven't been explained to you? I was chatting with a number of pianists, and they are not good at math, and also do not like it. Jon Nakamatsu is one. Got good grades, but didn't really understand it. Me too, but everyone thinks pianists are good at math. Why? Because of counting out rhythms?

[xvimbi]

A disprotportional number of mathematicians, chess players, but also scientists, particularly physicists, are very good musicians. Of course, it's not about keeping rythm. That's trivial. It's rather about grasping the inner structure of music. All scales, chords, chord progressions, etc. can easily be expressed in mathematical terms (group theory). If one is able to grasp complex and abstract ideas, one can also grasp a lot of music, particularly the kind of music that is very mathematical, such as Bach and Mozart.

Of course, the reverse is not necessarily true: not all musicians are good at math. Most musicians are happy with reproducing what's written in the score, but rarely attempt to analyze the mathematical aspects of an entire piece, let a lone an the entire work of a composer.

[Motrax]

Einstein played violin, Heisenberg played cello, and Bohr played piano, off the top of my head. But the converse is true too, in many cases.

I'm majoring in physics and piano (or at least I'd like to - college hasn't quite started yet). Horowitz was an amateur physicist. And a pianist I talked to, Orli Shaham, said she was going to study physics but decided on piano during college.

[Tash]

well i'm pretty good at maths, not like omg you're a freak type, but i did extension maths for my final year at school and did pretty well in it. i'd like to do some at uni but don't have that choice sadly. however the other 7 girls in my music class all hated maths and weren't that great (no offence to them) but they were singers and trumpeters and flautists and oboists rather than pianists, and the girls who were really good at maths did play an instrument but not that seriously.

[Rach3]

senior year math major here

[monk]

Piano playing (on a decent level) requires a certain intelligence.

And anyone with a certain intelligence can understand math and be good at it.

The only cause that some intelligent pianists are not good at math is that somehow they never had real INTEREST in it. The were simply bored in school.

And some people were scared away from math because from early on they were told that math is difficult and boring. And if you really believe that, you will be bad at math, it's that simple!

Another possible reason is that among normal pupils every geek is sneered at. And if you're interested in math and good at it, your "geek coefficient" rises. Many pupils regard social acceptance as more important than to be good in school, so they decide (mostly on a unconscious level) to be equally mediocre or bad as the others in class.

Best Wishes,
Monk

[rosie]

Thanks for the replies.

It's great to hear other ideas on this.

rosie

[glamfolk]

I've often thought that, although the math connection is probably accurate, it's just as likely that musicians are proficient in language.  Music theory describes the inner workings of music the same way that language theory does, and music is a language (or a series of languages) after all,  although that doesn't guarantee any kind of conversational facility.

Maybe it's just that musicians are smarter in general.

That's probably it.

[Egghead]

Piano playing (on a decent level) requires a certain intelligence.

And anyone with a certain intelligence can understand math and be good at it.

The only cause that some intelligent pianists are not good at math is that somehow they never had real INTEREST in it. The were simply bored in school.
...
Best Wishes,
Monk

This thread is v. interesting. Monk: What kind of problems do you think require so much intelligence in piano playing (and what is the level you are talking about?)?

Are you implying the same "certain intelligence" REQUIRED to be good at piano playing automatically enables you to be "good at" math? And vice versa?

So, now I wonder about the level/kind of math you are talking about. If you are talking about the professionel level, than I think that is a rather daring statement!

If you are talking pre-university stuff, it requires v. little effort to be v. good at math given a certain intelligence, whereas to play the piano properly you must actually practice.

On a purely anecdotal basis, I do agree though, that at university level there seems to be a higher correlation between math/music or physics/music activity than, say, engineering and music.
So there is a significant correlation (maybe, again anecdotal) for people being INTERESTED in both math(or physics) and music.

Egghead

[Egghead]

A disprotportional number of mathematicians, chess players, but also scientists, particularly physicists, are very good musicians. Of course, it's not about keeping rythm. That's trivial. It's rather about grasping the inner structure of music. All scales, chords, chord progressions, etc. can easily be expressed in mathematical terms (group theory). If one is able to grasp complex and abstract ideas, one can also grasp a lot of music, particularly the kind of music that is very mathematical, such as Bach and Mozart.

Of course, the reverse is not necessarily true: not all musicians are good at math. Most musicians are happy with reproducing what's written in the score, but rarely attempt to analyze the mathematical aspects of an entire piece, let a lone an the entire work of a composer.

Yes, I fully second this whole post, apart from the group theory bit. I am not sure I get this. Would you care to explain, xvimbi?

Also, physicists like taking things apart, understanding them and putting them back together. Reminds me vaguely of (pre-)practicing (analysis) of a piece.

Egghead

[xvimbi]

Yes, I fully second this whole post, apart from the group theory bit. I am not sure I get this. Would you care to explain, xvimbi?

Taken from a dictionary: "Group Theory is that branch of mathematics concerned with the study of groups.  A group is a set, together with a binary operation satisfying certain axioms."

In a nutshell, a group consists of a set of elements and a set of rules how to manipulate these elements. The result of these manipulations must be elements of the group itself (closed group).

In terms of music: the group elements are the 12 notes. The binary operations are the rules that tell us about the relationships between these notes, e.g. the definition of intervals, scales, chords (minor, major, diminished, augmented, etc).

[monk]

Hello egghead,

I'm from Germany, so my English is not perfect ;-)

With "certain intelligence" I meant: "a certain amount of intelligence"!

There is no evidence (although many people claim that) that there are different intelligences, different talents "pre-wired" in our brains.

Anyone who really is intelligent can learn anything complex - be it math, piano playing, chess playing, computer programming etc.

The factor which determines whether one really learns a subject and becomes good at it is INTEREST (and following the interest, diligence!). That of course varies vastly; but the "hardware" (the brain, nervous system and body) required to become good is there.

Best Wishes,
Monk

[dlu]

I was the top of my class in math. Got an A++ both on the exam and in the class. No, I am not boasting, you asked if we were good at math. I love math but would never chose it as carrer (or science, ewww I hate science). Well, I am just entering high school next year, so, we'll see how that goes.

[ivoryplayer4him]

A disprotportional number of mathematicians, chess players, but also scientists, particularly physicists, are very good musicians. Of course, it's not about keeping rythm. That's trivial. It's rather about grasping the inner structure of music. All scales, chords, chord progressions, etc. can easily be expressed in mathematical terms (group theory). If one is able to grasp complex and abstract ideas, one can also grasp a lot of music, particularly the kind of music that is very mathematical, such as Bach and Mozart.

Of course, the reverse is not necessarily true: not all musicians are good at math. Most musicians are happy with reproducing what's written in the score, but rarely attempt to analyze the mathematical aspects of an entire piece, let a lone an the entire work of a composer.

Just a little extra thought here...but maybe all mucisians (serious ones) ARE good in math?  I mean...maybe there is a more complex math invovled in the structure of music that isnt taught in school.  I mean i know that some of it is.  But i mean.....ok i suck at math.  I mean i love math, but when it gets into the complex math, i just hate it.  I can do it, but ihate it.  THere are a lot of times that i just think that i cant do it.  But maybe music is math, in a complete since and society (being school and education) has taken that meaning out.  I know this sounds weird lol but its something to ponder.  I believe it was aristotle (maybe plato) who believed that life was created using math and music.  Math being the structure and music moving it along.  If we look at everything in respect to mathematics, then WE KNOW MORE THEN WE THINK WE KNOW!  I mean, i just believe that there are several ways to concieve the idea of Math Knowledge.  There is a lot of upper theroy that if you asked me about it, i couldnt explain it to you and would probably think that i didnt know it, but its actually been pointed out that i can play it, and somewhere i have an understanding for it, but briniging it out audibly there is a barrior.  Maybe thats the same for all of the less fortunate in the math area?

Its really late lol so if some of that didnt make since, then i'm very sorry lol.  I have a book called "development of western music" and there is talks about greek and european ancient believe in this type of philosophy.  I havent completed studied it, but some of it i'm taking for my own.

[xvimbi]

Just a little extra thought here...but maybe all mucisians (serious ones) ARE good in math?  I mean...maybe there is a more complex math invovled in the structure of music that isnt taught in school. ... But maybe music is math, in a complete since and society (being school and education) has taken that meaning out.  I know this sounds weird lol but its something to ponder.

Keep in mind that math is entirely man-made. There are many different ways to do trivial calculations, but somehow, we have agreed on doing most of it in the decimal system (computing is done to a large part using binary and hexadecimal systems). The notes in Western music follow certain mathematical relations, they are not derived from nature. Yes, some people will object to this, but hey, we don't live in Medieval times anymore.

The point is that all musical systems, like math, are man-made and completely arbitary. There is no universality to it, not even "globality" as the Western system sounds awful to many oriental people and the other way around.

Music can be expressed in mathematical terms, and anybody who undestands those principles will be able to understand a lot of other mathematical concepts as well.

[blindmouth]

Keep in mind that math is entirely man-made. There are many different ways to do trivial calculations, but somehow, we have agreed on doing most of it in the decimal system (computing is done to a large part using binary and hexadecimal systems). The notes in Western music follow certain mathematical relations, they are not derived from nature. Yes, some people will object to this, but hey, we don't live in Medieval times anymore.

The point is that all musical systems, like math, are man-made and completely arbitary. There is no universality to it, not even "globality" as the Western system sounds awful to many oriental people and the other way around.

Music can be expressed in mathematical terms, and anybody who undestands those principles will be able to understand a lot of other mathematical concepts as well.

you wouldnt happen to be a philosopher (or into it), would you? if you arent, i asked this question because many (or is it some?) philosophers deny that mathematics is an objective feature of reality. also, you must be really clever to think that way if you arent into philosophy!

[Tash]

on a completely non-philosophical note, is there any other place in the world that calls it 'maths' rather than 'math'? i find calling it 'math' really weird...

[xvimbi]

you wouldnt happen to be a philosopher (or into it), would you? if you arent, i asked this question because many (or is it some?) philosophers deny that mathematics is an objective feature of reality. also, you must be really clever to think that way if you arent into philosophy!

Yes, I'm a philosopher, because I'm a scientist! Philosophy and science was once the same thing ("Ph.D." means "Doctor of Philosophy"). Anyhow, no, I am not really a philosopher in the modern sense of the word.

I don't know if one has to be clever, but to a scientist, it is fairly normal to view math as a tool, not as a fundamental property of the Universe. Math has nothing to do with the Universe. It is merely a set of man-made conventions that has been put together to describe natural things, such as the motion of the planets, etc. Math is a language and often a pretty lousy one.

[Spatula]

Piano playing (on a decent level) requires a certain intelligence.

And anyone with a certain intelligence can understand math and be good at it.

The only cause that some intelligent pianists are not good at math is that somehow they never had real INTEREST in it. The were simply bored in school.

And some people were scared away from math because from early on they were told that math is difficult and boring. And if you really believe that, you will be bad at math, it's that simple!

Another possible reason is that among normal pupils every geek is sneered at. And if you're interested in math and good at it, your "geek coefficient" rises. Many pupils regard social acceptance as more important than to be good in school, so they decide (mostly on a unconscious level) to be equally mediocre or bad as the others in class.

Best Wishes,
Monk

I'm quiet surprised.  I thought normally, well at least for us asians anyways, that good grades would somehow be corelated to being somewhat popular and friends would think you'd be successful in life.  But that's just me.  

[blindmouth]

Yes, I'm a philosopher, because I'm a scientist! Philosophy and science was once the same thing ("Ph.D." means "Doctor of Philosophy"). Anyhow, no, I am not really a philosopher in the modern sense of the word.

I don't know if one has to be clever, but to a scientist, it is fairly normal to view math as a tool, not as a fundamental property of the Universe. Math has nothing to do with the Universe. It is merely a set of man-made conventions that has been put together to describe natural things, such as the motion of the planets, etc. Math is a language and often a pretty lousy one.

scientist? wut did you get your phd in? im majoring in industrial engineering (we work on efficiency/process improvement/people/business for those who are wondering) and minoring in philosophy (though not successfully!) also, did you know  that philosopher can be translated from the greek as 'lover of words' ? many ancient greeks (hericlitus comes to mind) delved into multiple subjects dealing with our world (geometry, ontology, physics, blah blah i think you got it.) however, they werent scientists in the empirical sense.

ok i was really digressing with that so, aight ill get to the point. im surprised by your viewpoint because most people i have met feel that math is the 'truth' because it is never wrong (2+2 is ALWAYS equivelent to 4, 2+2 never equals anything else.) i believe that Plato was the first to equate the realm of mathematics as an existence of a perfect God. (help me out if i got that wrong.) anyways, i want to rebut what i just said about the entity '2+2'. that 'interpretation' can be labeled both subjectively and objectively.

example:
1. 2 apples and 2 oranges make 2 pairs of fruit.
2. 2 apples and 2 oranges makes 4 pieces of fruit.

which one would be incorrect? if im right, neither answer would be candidates for an error.  so then is interpretation the only candidate for right or wrong? if math isnt a truth, then what is? the emotion, that what music strives to sway?  ive completely lost concentration i dont even know what  my contention is !

addressing the subject of the thread,  i would have to say im not a great 'amateur' pianist and even less so with math! i shoulduh minored in music performance to get some help with my piano playing abilities.

[Pumpkinhead]

wow, I thought that music really helped the math. I mean, maybe music is an easy afterthought for someone great in science in math. And maybe not the other way around. Who knows? I'm taking AP Calc and chem my Junior year(this year), but maybe I'm just good at math.

[xvimbi]

im surprised by your viewpoint because most people i have met feel that math is the 'truth' because it is never wrong (2+2 is ALWAYS equivelent to 4, 2+2 never equals anything else.)

2+2=4 is "true", because man decided that it was. Math is based on so-called axioms, which are simply a set of assumptions and rules that people made up during the past few thousand years. It was DEFINED that 2+2=4, that's why it is "true".

By the way 2+2=4 is only "true" when using the decimal system. Just like PI (the ratio between the circumference and diameter of a circle) is 3.1415... only for flat circles. If the circle is constructuted on the surface of a sphere, PI will be different. So, what is "true"?

i believe that Plato was the first to equate the realm of mathematics as an existence of a perfect God.

There have been many people over time who thought math was divine (oooh that does rhyme...). That's a matter of belief.

[Spatula]

2+2=4 is "true", because man decided that it was. Math is based on so-called axioms, which are simply a set of assumptions and rules that people made up during the past few thousand years. It was DEFINED that 2+2=4, that's why it is "true".

By the way 2+2=4 is only "true" when using the decimal system. Just like PI (the ratio between the circumference and diameter of a circle) is 3.1415... only for flat circles. If the circle is constructuted on the surface of a sphere, PI will be different. So, what is "true"?

There have been many people over time who thought math was divine (oooh that does rhyme...). That's a matter of belief.

God is THE mathematician.

[mozartgonebad]

YES!!! my 25th post...anyway...
i consider this math and music think very intersting, it uses the opposite halves of the brain...
i, myself am considering a double major in piano and chemistry or biology, so  

[Spatula]

YES!!! my 25th post...anyway...
i consider this math and music think very intersting, it uses the opposite halves of the brain...
i, myself am considering a double major in piano and chemistry or biology, so  

GOOD4U!

[schmetterling]

My high school is highly academic ( It has been the highest achieving academically in NSW for the last 10 years) -and also highly Asian, Spatula! The student who came first in science and math last year is also the best pianist in the school. Unfortunately, it's not me =(

My previous piano teacher always said there was a link between mathematics and music, and I believe quite a lot of research has been conducted, so to speak, on the topic.

[super_ardua]

I think it is because math and piano require one to use what one has,  and not what one wants to do.

[scarbo87]

Well we at least know that our beloved Ludvig Van "Hated math"

and Rubienstein did as well

[paris]

i think math is such a waste of time!!!!!!!!!!
it is so stupid, all that...ugh... i need math only because i don't want to be cheated in supermarket  

and i'm so bad at math...but very lazy in solving tasks, calculating...boring...boring...boring...boring...boring........................BORING



(yesterday i had 2 hours math in class, i become a zombi! )

[ted]

I actually do agree with xvimbi on this. Here are two little connections I came up with myself and published in various places years ago.


I have never understood why books discussing equal temperament spend hundreds of pages of meandering historical reasoning on something which seems to me very simple. Cannot the whole thing be summarized as follows?

We desire to find divisions of the octave which contain as many close approximations as possible of the type 2 to the power of (a/b) = c/d, where a,b,c,d, are integers and c and d are integers as small as we can make them.

In fact, a moment’s thought tells us that it suffices to find a close approximation for 3/2, the next simplest ratio after ˝. A few minutes with a hand calculator soon reveals that 12, 19, 24 and (bit of a surprise) 29 are the lowest divisions of the octave containing a very close approximation to 3/2.

12 is the obvious, indeed probably the only, choice for a practical manual instrument. 24 gives the quarter tone scale. Why is any more analysis needed ?

As an exercise I experimented with 19 and 29 using an Amiga and found that the first embeds the diatonic scale as the partition 3,3,2,3,3,3,2 and the second embeds it as 5,5,2,5,5,5,2. I didn’t try what 19 sounded like, but the division of 29 sounds great. It also yields “almost” symmetric scales of 4,7,5 and 6 (hence 2 and 3 ) notes. I recorded a simple sequence modulating around the circle of 29 keys and tried it on musicians. It surprised me that even professional musicians couldn’t tell they were actually hearing 29 keys instead of the usual 12 !

The second topic which seems to me to be burdened with needless complexity is analysing how many chord types there are ignoring pitch and position (i.e. major, minor, diminished etc). Seeing the chromatic scale is a cyclic group of order 12 and a chord type is therefore just a partition of 12, a quick application of the Polya Burnside theorem (or by just counting) tells us that including a silence there are 352 chord types (or scales, regarding a scale as a chord) playable on the piano. Further, a second application of the theorem gives an obvious way of looking at the chords within each partition. For example the partition 4,3,3,2 has three permutations corresponding to the seventh chord (4,3,3,2), the sixth chord (4,3,2,3) and the minor sixth chord (4,2,3,3)

The whole thing has a pleasing unity to it which I used to imagine would appeal to serialists. I couldn’t find it in any books so I published it myself many years ago in the New Zealand Mathematics Magazine (Vol 16, No 2) because no musical publication I could find would accept it.