What is Digg?66 Comments
- ivosilva, on 07/11/2008, -1/+13Math is everywhere...
Should have studied it more. Damn. - MrFurious2k, on 07/11/2008, -0/+9While the article addresses melody and harmony (and the relative tonality), it can't be understated that rhythm and percussion (while still inherently mathematical) greatly affect the pleasurable nature of one's listening experience.
An interesting experiment might be to set a bunch of rules up using mathematical theory and let the computer "auto-generate" a piece. I recognize the software necessary to do this would be quite complex, but it'd be interesting non-the-less. - Phyltre, on 07/11/2008, -0/+5I read through this slowly and found myself largely unable to parse it. I'm not sure I automatically agree with the idea that because musical principles adhere to geometric rules, they must therefore be somehow governed by these rules and their effects must be a property of that system. Correlation versus causation, and what have you.
- irishjays, on 07/11/2008, -0/+4I got to page 2!
- elscorcho717, on 07/11/2008, -1/+4Interesting, although I think the author is trying to read more into his whole theory than is really necessary. That math and music are inherently related is nothing new -- and so it shouldn't be surprising that there are ways of expressing musical ideas mathematically. But it's a leap of faith to say that music is governed by these rules. In fact, the concept of deceptive resolution is a good example of why this doesn't work and it's not handled in any depth by the author for a reason. Yes it's true that many times when considering a chord progression a composer will try to use chords with similar chord tones but that is not the only kind of motion possible in music (and hasn't been for a long time). Much of the concept of cadence is setting up an expectation and then satisfying it but what is even more satisfying is a deceptive resolution. This is not governed by the neat rules described in the article for "mapping" music.
- SevasTraSi, on 07/11/2008, -1/+4not rocket science or "quantam theory"...no. Maths.
- analogkid01, on 07/11/2008, -0/+3Buried for pop-culture racism.
- Jelfish, on 07/11/2008, -1/+4No matter how you try to describe it, be it with chord symbols or complicated geometric spaces, music is, and always will be, defined by humans and tied to the human condition because it is interpreted/listened to by humans. We interpret music likely on a fundamental level according to consonance and dissonance of frequencies, but also based on what is already familiar to us. That's why jazz enthusiasts can listen to and enjoy stuff that most others might consider musical nonsense, and why song-writers can write a chart-topper using the most tired chord progressions.
I hate to be cynical, but this comes off as little more than intellectual self-gratification. - DayTripper47, on 07/11/2008, -0/+3I've always thought it wouldn't be that hard to create a program that would auto-generate Baroque music, since there are so many fixed rules to go along with it (no parallel 5ths, large jumps, common chord progressions). I could do my music theory homework in seconds.
- johneffort, on 07/11/2008, -0/+2Funny, I always already thought that most of the science branches are very related to each other. I even think it is very possible that you can solve specific math problems with translating it into music and then looking into it as a musician. When you find the musical solution, you translate that back into math. If the world is indeed so related, than it's very possible that on a lot of other scientific fields there are already solutions to other field's problems.
- usbcd36, on 07/11/2008, -3/+5They go into the mathematics of music, but don't explain equal temperament?
- geoken, on 07/11/2008, -0/+2Half of the article was talking about the uselessness of equal temperament, or at best branding it an approximation based on insufficient knowledge of math.
The point of the article was that every note represents a specific point where frequencies achieve a certain harmony. Equal temperament basically takes a range of sound and splits it up into equal pieces then plops the note at the beginning of each one of those pieces. It may be a good approximation, but that's just luck.
- SevasTraSi, on 07/11/2008, -0/+2That is one opinion but what if it was shown that you were wrong. Would you be willing to except evidence that all "successful" music since the baroque era followed similar sets of geometric properties on these non cartesian coordinate systems!
I'm not saying its purley maths I'm just saying have an open mind. - HonestAbe, on 07/11/2008, -0/+2"In two dimensions (when there are two notes in each chord), we first wrap around each axis, x and y, so that they become circles rather than lines."
Uhhh.... some pictures would complement this article very nicely, buddy. - mrrealtime, on 07/11/2008, -0/+2quite the opposite actually. Many musicians find themselves in math related fields later in life, like programming. I havent conducted a study personally, but I wouldnt be surprised if the majority of computer and math related consulting jobs are held by former members of bands and musical groups because the combined "entrepreneurial" skills involved in running a band with the ability to recognize, duplicate and enhance patterns particularly as a cover band musician would lend themselves well to the career of programming.
- sg7791, on 07/11/2008, -0/+2And you're making music majors everywhere sad. D:
- mrrealtime, on 07/11/2008, -0/+2wrong. Science is all about discovering why things work and how we can quantify "listen" and "feeling". You are free to crawl under a rock and pretend that knowledge is unknowable, but the intelligent folks will try to understand the facts and apply them in ways you seem too lazy to try to understand.
- Jelfish, on 07/11/2008, -0/+2I whole-heartedly agree with you about rhythm. Rhythm is the absolute foundation of music and, in my opinion, the most human aspect.
- geoken, on 07/11/2008, -0/+1Basically, pleasing tones can be mathematically defined.
Furthermore, groups of notes which sound pleasing adhere to some mathematical rules. - Twenty, on 07/11/2008, -0/+1Well, acevoncash, what you're saying I'd imagine is true. People were dicking around with notes, and came up with a couple that sounded good together, and the next thing you know, chords, key signatures, and the musical language was formed. However, this was in each culture. Asian and African music use different languages. There's a huge number of combinations of notes which produce harmonious products outside of common, and even fairly advanced knowledge. Hey, another example. Power chords sound great (root-C fifth-octave) on a distorted guitar. I knew this for a long time, but it wasn't until I actually looked it up that I found out it was because of the way the harmonic frequencies interacted with the distortion (clipping) effect.
Also, I realized that your post had no point about halfway into this, so there's nothing to argue against.
-- math major / musician + composer - 4321234, on 07/11/2008, -1/+2Why are you being such an ***** about it?
- Jelfish, on 07/11/2008, -0/+1That's an interesting point. Although the author would probably argue that it has more to do with mapping harmonic and melodic progression on a quantized space rather than the specific frequencies to which those points represent. The consonance and dissonance due to frequency ratios is built into the system by defining common chords.
- lp66, on 07/11/2008, -0/+1The author, Dmitri Tymoczko, is a professor at Princeton. He had a cool web app demonstrating all this dense prose, but it seems to be gone. It's nice to see another theorist/mathematician, in the vein of Milton Babbitt.
Oh, I found a movie of a Chopin piece he made.
http://www.princeton.edu/pr/media/chopin/chopin3_3 ... - likeyehokwhatev, on 07/11/2008, -0/+1People have been experimenting with this. I heard a computer generated piece in one of my counterpoint classes based off the work of Bach- basically, the programmer analyzed the works of Bach set rules based what he found commonly occurring in each of the pieces.
This may have been the guy, interesting none the less
http://news.bbc.co.uk/2/hi/science/nature/240642.s ... - presidentnixon, on 07/11/2008, -0/+1"Ray, pretend I don't know anything about metallurgy, engineering, or physics, and just tell me what the hell is going on."
- remo2012, on 07/11/2008, -0/+1Homophonic music
http://www.youtube.com/watch?v=i_kDHqQVOpo - SevasTraSi, on 07/11/2008, -0/+1Thank you! Starting September I'm dong a third year university model (I'm studying Comp Sci and Maths at Manchester Uni (England)) to write a program which studies the geometry of musical chords. This is exactly the research I will be studying and hopefully writing a program which will help composers use this to assist compositions.
Wish me luck!
BTW there is a definite link between music and maths, as a pianist and a student of maths I find the two skills highly complementary. - Jelfish, on 07/11/2008, -0/+1Equal temperament is far from useless. In fact, it was developed because an instrument tuned to Pythagorean temperament will sound bad when played on certain keys.
More info: http://www.hpschd.nu/tech/tmp/pythagorean.html
Equal temperament was developed so that you can tune your piano (or any other quantized instrument) to one set of frequencies and every key that you played in would sound good (enough). Just about all music today is played on equally tempered instruments, and certainly it doesn't sound bad, so I don't think it's a big deal. - inactive, on 07/11/2008, -0/+1the overtone series was discovered very early in music and the division of notes into equal 'divisions' only came in around the time of bach with the invention of the pianoforte (literally 'softloud')
if this artificial adjustment was not made you could never have orchestras and symphonies - geoken, on 07/11/2008, -0/+1The variances in percussion from one popular song to another are so minor that I don't even think the program would have to be complex.
Put a snare on the 4th and 12th note, a kick on 1,6,10 and then randomly throw in hats and I think 3 out of 5 times the computer program will generate a drum loop that listeners will find pleasurable.
Furthermore, if you've ever used a drum synth that gives you precise controls over all parameters you'd see that these rules hold true when you're tweaking the snare settings to get that perfect sound.
- Twenty, on 07/11/2008, -0/+1I'm a math major now, and I wish I'd study it more.
On another note, harmony and melody are overrated. Grating dissonance is where it's at. /Metal - pnunn, on 07/13/2008, -0/+1No one here is substituting science for talent. You keep assuming dumb ***** to justify your lack of training. You're just ***** ignorant man. If you don't know the math in it your improv is ultimately *****. Maybe you've got some good runs- or maybe you've got that one pentatonic run you play in different keys- but you clearly have no idea what the hell you are doing and I imagine you fare horribly outside of your comfort zone.
If anyone here is driving the wrong way...
...well...
Or rather- I'm there "dude"- but I don't see you here anywhere.
A whole human history you willfully ignore- maybe I'm way off and you're a dumb luck player- but I bet you are as limited as can be. - marx2k, on 07/11/2008, -0/+1Wow, you sure put a lot of energy into replying to a joke.
- pnunn, on 07/13/2008, -0/+1Oh- excuse me- I didn't realize I was talking to a professional. I'd love to have a pissing contest over how long each of us have been in "the biz" but I don't need that to qualify myself- nor does it influence the unchanged outcome of your oversight.
The math in music is inherent to the systems that create it and as such are the results and according timbres. Determining that the scientific nature of any art is specifically limited to the concept you can call to mind readily does not disqualify anything the author of the article said nor anything I have said. You make an assumption that to think what you said was absurd I have to be approaching the creative process all wrong, but I venture that in being so aloof to academic and mathematical concepts in music and willfully ignorant of principles beyond intervals (apparently) that you miss the bus on all kinds of ***** -so I doubt I can correct all of that here.
I will ask you- since you have enough figured out as to have delivered a verdict on my question of who the ***** was: if arts and sciences are so divisible- why is it that educational systems as far back as the ancient Greeks keep lumping them together? I think you are reacting and not thinking. Yes- it is true that I could happily bang away on my guitar and play the blues and solo from "my soul" or whatever (and do when appropriate)- but even applied in that format, there is an inherent math in the structure. The number of bars, the progression it self and the scale degrees within that determine the harmonic content of each chord. I feel like going on to explain the relationships all of this shares with other instruments is redundant- my point is, whether you know it or not- there is a science- don't expect me to be beholden to your experience because you conjure up a 2 decade history of willful ignorance.
And in these twenty years of experience it would surprise me that it hasn't struck you in the studios you've no doubt spent a lot of time in that art and science are quite merged with regards to the finished product that is a studio recording. Anyone can run equipment- but understanding it tends to produce a more "musical" result.
Whether the world finds me to be an ***** here or not- your statement was (and remains as such despite elaboration) incorrect and no matter how you personally choose to approach things, there is a science to any of the arts. It seems odd that you are so angry and eager to divide the arts and sciences when so many of my contemporaries seem to embrace it. I stay working for my will to embrace it and I would recommend such an attitude to anyone in the field- ***** or not.
As for the actual subject at hand- I don't think the concept the author is working at is bulletproof and I do think that intuitive elements are being overlooked- My disagreement with both of you is specifically that the elements should not be too readily separated. Knowing the science frees the intuition to paint in broader strokes with brighter colors. Don't fool yourself into thinking you've got the whole thing knocked just because you are good at what you do.
Frankly, I imagine your defensiveness to the very notion exposes to you and anyone reading this that there is a great deal you don't know and you are bristling as anyone does when confronted with a concept they cannot readily refute because they have a good deal of homework to do before they can understand it. - acevoncash, on 07/12/2008, -0/+1agreed.
- Twenty, on 07/11/2008, -0/+1No, it IS math -- that's why there are such things as harmonies and visual aesthetics. It's all math and psychology, but you don't notice it. It's not until recently that we've looked into WHY melody exists and why some photographs look really nice. Music sounds nice because your mind recognizes the the mathematics in it, somewhere deep in all that gray matter. Oh and I was agreeing with you, music didn't stem from math at all. But melodic sounds are rooted in math, whether we know it or not.
- SevasTraSi, on 07/11/2008, -0/+1wtf "university model"
I think model = module = project - kenplaysviola, on 07/11/2008, -0/+1I was in his class a few years ago at UC Berkeley when he was teaching music theory. Very down to earth guy and very energetic.
- acevoncash, on 07/11/2008, -0/+1wooooooah there buddy. i know just as well as the next guy that if you understand how a chord works you can get the intonation to be perfect. I know what its like to play in an ensemble that matches perfectly and gets overtones. I have played with division one drum corps. thats not what im getting at.
I absolutely agree, its probably as best its going to get, the notation system. However, I was trying to point out that the way it was created was slightly archaic and although is related to math doesn't really have a grounding in it. You don't have to know math to understand how to bring a note into perfect harmony.
I'm pointing all this out because its like saying a painter is a great mathematician because of the wonderful understanding of geometric shapes, three dimensional depth and curves. Yes there is math in it, yes there is a correlation however a painter doesn't do computations to make his latest work. (at least most of the time)
I'm not trying to ***** on western music. on the contrary. I'm just trying to say it isn't exactly math either. - acevoncash, on 07/11/2008, -0/+1I know the math is in the music. i don't think the music stemmed from the math is all I'm getting at. Mozart wasn't thinking about non Cartesian coordinate systems. However, if you came up with evidence proving me wrong I'd be more than willing to accept it. I don't know if i could 'except' it or not.
- thorie79, on 07/11/2008, -0/+1http://xkcd.com/435/
- clarient, on 07/11/2008, -0/+1Way to ***** on the history of western music! If you know a better way of notating music, please, elaborate. Notation is not and never will be a completely accurate representation of sound. There is no way to commit to paper what real music sounds like.
There's nothing wrong with the way our tonal system evolved, and it doesn't make musicians poor mathematicians. It's actually quite the opposite - musicians that grasp the relationship of individual notes within chords, phrases, and ensembles often have an innate aptitude for logic and order. But they know that a note is never exactly the same note every time, and it allows them great flexibility in creating ART and not just sound. - Twenty, on 07/11/2008, -0/+1It really needs that octave though to give it such a fuzziness and warmth.
- acevoncash, on 07/11/2008, -0/+1for the record, a power 'chord' isn't a chord at all - its only two notes.
- pauleric, on 07/11/2008, -1/+2You were unable to parse the article because it was horribly written. He (the author) rambles without really explaining what is meant by the big words, but if you're already familiar with both music theory and math, doesn't say anything much that is startling.
He should've started by explaining that (in modern tuning) each half-step increases the frequency by a factor of 2^(1/12), so an octave doubles the freqency. And while consonant intervals are rational numbers (with small integers), this is only approximated very closely by a piano tuned in this way. And then gone on to explain lots of stuff he only talks about.
You can argue correlation vs. causation all day, but it's not like most physics. This has to do with the way the brain works and our perception, and until we make a *lot* more progress in that area were going to keep arguing about it. - ATLien74, on 07/13/2008, -1/+1Nothing makes someone look more like a pompous ***** than to over intellectualize something that is rooted in human feeling and emotion. Sure there is math involved, I'm perfectly well aware of the concept of musical intervals, but if you are trying to approach music from a mathematical stand point you are missing the most important part, the human emotional element and feel. That's NOT something you can understand with math. This is why computer generated music sounds so stiff, and fake. There's no emotion of feeling in it.
Music is NOT science, it's ART. Sound is science, big difference.
I'm not being short sighted or ignorant at all, I'm speaking from 20 years of experience playing professionally....and yes, you are the ***** *****. - SlamCam, on 08/01/2008, -0/+0good article.
i had always heard there is a connection between math and music but never had it explained to me.
awesome. :) - gabrielconroy, on 07/25/2008, -0/+0Who says musicians aren't any good at maths? High quality musical composition shows an awareness of latent patterns, and the ability to manipulate and arrange those patterns to create sound structures amenable to our tastes.
There's an interesting discussion here: http://www.bbc.co.uk/radio4/history/inourtime/inou ... on the relationship between maths and music. - dstz, on 07/11/2008, -0/+1As a musician I'm nearly as math inspired as it goes. I use the minimalist tools (repetition and iteration,) and obscure software to work on the geometry of my home scales.
That said, I'm well aware that it's only a backdrop, a way to make my mind work in a constructive way when the /real/ inspiration isn't here. When inspiration is here, I don't give a damn about ratios and measures: what works, works. -
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