Try to restart, reframe and remove the discussion that started in the Mahler thread.
ISTM that there are two unsupportable positions on the topic:
A) the Quantophiliac, who looks for deterministic mathematical relationships to aesthetics, forgetting that music is art and therefore cannot be fully defined by the sum of any set of empirical observations.
B) the Quantophobe, for whom mystical inspiration is all and ignores the fact that math is often a useful tool in achieving and describing aesthetic objectives.
Certainly composers have taken direct inspriation from mathematics. Bartok w/ golden mean proportions, Ligeti with strange attractors and other fractal phenomena etc. Music is not math any more than architecture is math, but as Monk sez, all musicians are subconsiously mathematicians.
In which case one needs to find the "Golden Mean" between the two positions! 8)
Which, oddly, will not be an even path! :o
I have also wondered if there is not a musical connection to playing chess via a (subconscious ?) mathematical ability: e.g. Prokofiev apparently was a very good player.
And mathematicians have remarked upon proofs, etc, with the words "elegant" and "beautiful," with some openly suspicious of any series of equations that shows too much sweat and not enough grace as being on the wrong path.
I have, however, been bored to tears by articles in scholarly musical journals going through "permutations of sets" blah blah blah! For an elite who might claim they can actually hear such things in a work and follow them, fine! If that floats your boat to the Isle of Musical Bliss, fine!
But I'm jumping off that boat: throw me a life preserver! Cherry preferably!
Interesting thread! And I entirely agree that neither A. nor B. is tenable.
Quote from: bwv 1080 on May 04, 2007, 06:50:56 AM
Certainly composers have taken direct inspriation from mathematics. Bartok w/ golden mean proportions, Ligeti with strange attractors and other fractal phenomena etc. Music is not math any more than architecture is math, but as Monk sez, all musicians are subconsiously mathematicians.
To this I partly assent. Artists get inspiration from a wide range of Stuff Out There; there's certainly no reason why some mathematical something cannot be part of the stuff of inspiration.
I don't really think, though, that all musicians are subconsciously mathematicians, beyond the relatively trivial matter that (for instance) the complex of events in an orchestral score are plotted on a kind of graph, and that individual players count in order to keep their place. A lot of what goes on in the music, in the sound, can be measured with and expressed in numbers, sure. But I do not think this makes musicians as a class "subconscious mathematicians" any more than fifty other vocations.
My 2ยข
Quote from: Cato on May 04, 2007, 07:05:38 AM
I have, however, been bored to tears by articles in scholarly musical journals going through "permutations of sets" blah blah blah! For an elite who might claim they can actually hear such things in a work and follow them, fine! If that floats your boat to the Isle of Musical Bliss, fine!
Yes; whatever tools a composer finds to make the best music he can, he is welcome! Why not?!
But heaven help
Webern if you need to study a set of five graphs in order to "understand" (let alone "enjoy") his music! (I believe no such thing.)
Hey. What about the Hamhockophiliacs (of which I am one) who are wholly inspired by ham hocks.
(http://onokinegrindz.typepad.com/ono_kine_grindz/images/SmokedHamhocks-thumb.jpg)
what i'm interested in is the relationship between musical mathematics and how they affect one psychologically- it's hard to find any info at all about it, but here's something:
http://pom.sagepub.com/content/vol28/issue1
it has an article titled "Psychological Connotations of Harmonic Musical Intervals", except it looks like you have to subscribe or something ???
i might have to begin a study all by myself
Quote from: greg on May 04, 2007, 07:22:19 AM
i might have to begin a study all by myself
Go for it! Don't forget the hamhocks!
Quote from: karlhenning on May 04, 2007, 07:24:23 AM
Go for it! Don't forget the hamhocks!
aye aye cap'n 8)
i just found a good article:
http://mediatheque.ircam.fr/articles/textes/McAdams96a
looks like it might help me with some of my many questions
leave it to IRCAM to deal with interesting stuff! :)
Quote from: sonic1 on May 04, 2007, 07:12:11 AM
Hey. What about the Hamhockophiliacs (of which I am one) who are wholly inspired by ham hocks.
(http://onokinegrindz.typepad.com/ono_kine_grindz/images/SmokedHamhocks-thumb.jpg)
As they say in Guadalajara:
El grosso profundo!Is there music in them thar hamhocks, or any kinda 'rithmetic? 8)
"Hamlet" is no doubt derived from such appendages through a Boolean subset of Poincare derivatives!
Along with the economic theories of Alexander Hamilton!
And I'm betting David Hockney's photographs can be analyzed the same way!
Music is organised sounds.The organisation process is
economic. First we define musical scales etc. Then we construct higher level objects, thematic material (themes, melodies, harmonic ideas etc.). Finally we have constructed movements of larger works and complete works.
Lower level objects are easy to define mathematically. Music scales are based on simple math. Equal temperament (http://en.wikipedia.org/wiki/Equal_Temperament) is 100% pure simple math based on simple equations like:
(http://img163.imageshack.us/img163/6053/9bfcf4448e5ef69cbc03369jr1.png) (http://imageshack.us)
Harmony is based on math too. Consonance and dissonance (http://en.wikipedia.org/wiki/Consonance_and_dissonance) is related to how simple or complex relation there is between the fundamental frequencies of the notes in chords.
High level objects are difficult/nearly impossible to define mathematically. Clever statistical analyse of "good" melodies perhaps gives interesting results about how melodies follow certain complex rules. Anyway the math starts to be extremely complex. Trying to define complete symphonies with math would be insane. The math needed would be beyond anything mankind can understand I am afraid. However, the smaller blocks in music can be described with at least some kind of statistical logic.
Hey, where is pink harp? I thought for sure we would get a diatribe from him by now regarding this subject.
Quote from: 71 dB on May 04, 2007, 08:06:23 AM
[snip]
High level objects are difficult/nearly impossible to define mathematically.
Clever statistical analyse of "good" melodies perhaps gives interesting results about how melodies follow certain complex rules. Anyway the math starts to be extremely complex. Trying to define complete symphonies with math would be insane. The math needed would be beyond anything mankind can understand I am afraid. However, the smaller blocks in music can be described with at least some kind of statistical logic.
Thank you for demonstrating the pointlessness of your own post.
Quote from: 71 dB on May 04, 2007, 08:06:23 AM
Music is organised sounds.
The organisation process is economic. First we define musical scales etc. Then we construct higher level objects, thematic material (themes, melodies, harmonic ideas etc.). Finally we have constructed movements of larger works and complete works.
Lower level objects are easy to define mathematically.
Music scales are based on simple math. Equal temperament (http://en.wikipedia.org/wiki/Equal_Temperament) is 100% pure simple math based on simple equations like:
(http://img163.imageshack.us/img163/6053/9bfcf4448e5ef69cbc03369jr1.png) (http://imageshack.us)
Harmony is based on math too. Consonance and dissonance (http://en.wikipedia.org/wiki/Consonance_and_dissonance) is related to how simple or complex relation there is between the fundamental frequencies of the notes in chords.
High level objects are difficult/nearly impossible to define mathematically.
Clever statistical analyse of "good" melodies perhaps gives interesting results about how melodies follow certain complex rules. Anyway the math starts to be extremely complex. Trying to define complete symphonies with math would be insane. The math needed would be beyond anything mankind can understand I am afraid. However, the smaller blocks in music can be described with at least some kind of statistical logic.
You are acquiring wisdom, grasshopper! Especially in that last paragraph!
There are complex, near infinite calculations for which one would need a computer with more atoms than the Universe contains: in fact at such a point at least one physicist throws up his hands and names any such computer "God". QED
Quote from: karlhenning on May 04, 2007, 08:11:30 AM
Thank you for demonstrating the pointlessness of your own post.
Ouch.
Quote from: Cato on May 04, 2007, 07:54:43 AM
As they say in Guadalajara: El grosso profundo!
Is there music in them thar hamhocks, or any kinda 'rithmetic? 8)
"Hamlet" is no doubt derived from such appendages through a Boolean subset of Poincare derivatives!
Along with the economic theories of Alexander Hamilton!
And I'm betting David Hockney's photographs can be analyzed the same way!
As Schoenberg's rejection of tonality coincided with a rediscovery of his Judiaism, can we say that atonality is a rejection of 400 years of hamhockery in Western music but perhaps a more kosher alternative?
Quote from: karlhenning on May 04, 2007, 08:11:30 AM
Thank you for demonstrating the pointlessness of your own post.
You don't understand the point of my posts (lack of scientific insight?) so you think I demonstrate myself wrong. Who would be so stupid?
Math doesn't always mean exact things like 2 + 2 = 4. I may also mean things like:
"When you throw a dice you get number 6 statistically one time out of 6 tries."
"The estimated value for f(7.1) is between 11.2 and 11.7."
Quote from: bwv 1080 on May 04, 2007, 08:17:12 AM
As Schoenberg's rejection of tonality coincided with a rediscovery of his Judiaism, can we say that atonality is a rejection of 400 years of hamhockery in Western music but perhaps a more kosher alternative?
Oy! Your timing is off a wee bit, but who knows? Schoenberg was something of a
farbisener ! $:)
Quote from: 71 dB on May 04, 2007, 08:38:37 AM
You don't understand the point of my posts (lack of scientific insight?) so you think I demonstrate myself wrong. Who would be so stupid?
Math doesn't always mean exact things like 2 + 2 = 4. I may also mean things like:
"When you throw a dice you get number 6 statistically one time out of 6 tries."
"The estimated value for f(7.1) is between 11.2 and 11.7."
As a Mathematics major here at the University of Chicago, I confess not to be able to follow any of your theories. What are you trying to accomplish exactly? Are you trying to create a mathematical model for ideal musical compositions? If, so, then how are you using statistics? Are you simply studying great works, and modeling their sound with a function? If so, what kind?
Gosh, Steve; perhaps I'm not deficient in scientific insight after all! 8)
Quote from: karlhenning on May 04, 2007, 12:06:34 PM
Gosh, Steve; perhaps I'm not deficient in scientific insight after all! 8)
I've already emailed one of my Professors the url to this thread. Perhaps, he can make some sense of this for the two of us. :)
More likely, though, he will use 71db's theories, as a bit of comic relief after our final, next class. :)
Quote from: Steve on May 04, 2007, 12:05:10 PM
As a Mathematics major here at the University of Chicago, I confess not to be able to follow any of your theories. What are you trying to accomplish exactly? Are you trying to create a mathematical model for ideal musical compositions? If, so, then how are you using statistics? Are you simply studying great works, and modeling their sound with a function? If so, what kind?
as a physics/engineering major at University of Washington, i am afraid that i ALSO can't make any sense out of just about everything 71 db says.
I think it is rather clear what 71 dB is trying to say. In fact, it is so utterly obvious as to be self-evident, and thus superfluous.
Much like this post, actually.
Quote from: Cato on May 04, 2007, 08:14:00 AM
There are complex, near infinite calculations for which one would need a computer with more atoms than the Universe contains: in fact at such a point at least one physicist throws up his hands and names any such computer "God". QED
Possibly the size you are thinking of is that of the googol, 10 to the power of 100
Or maybe the googolplex, 10 to the power of a googol.
For me the proof of music is in the music itself. Listen and it is revealed.
Quote from: sonic1 on May 04, 2007, 08:08:56 AM
Hey, where is pink harp? I thought for sure we would get a diatribe from him by now regarding this subject.
ok, i'll fill in for him:
"Wubba wubba wubba wubba.......
Debussy 0:) ...............
.......
....
Wubba wubba wubba wubba........
Wagner 0:) clk ahhhhhhhhhhh"
Quote from: Daidalos on May 05, 2007, 12:40:20 AM
I think it rather clear what 71 dB is trying to say. In fact, it is so utterly obvious as to be self-evident, and thus superfluous.
Much like this post, actually.
I
like your sense of humor!
Quote from: greg on May 05, 2007, 04:54:20 AM
ok, i'll fill in for him:
"Wubba wubba wubba wubba.......
Debussy 0:) ...............
.......
....
Wubba wubba wubba wubba........
Wagner 0:) clk ahhhhhhhhhhh"
We mustn't forget an ode to Elgar ;D
philosophy aside, I enjoy listening to music while doing my calculus homeworks, so music and math do go very well after all.
I find Schoenberg ideal for improper integrals. ;D
Quote from: Steve on May 05, 2007, 08:16:57 AM
I find Schoenberg ideal for improper integrals. ;D
haha, but seriously, when you are doing difficult stuff like that, you are just begging for John Cage's 4'33 to help you to concentrate.
Quote from: MahlerTitan on May 05, 2007, 08:36:58 AM
haha, but seriously, when you are doing difficult stuff like that, you are just begging for John Cage's 4'33 to help you to concentrate.
oh no, here come the 4'33" jokes...........
.............
Quote from: greg on May 05, 2007, 01:52:40 PM
oh no, here come the 4'33" jokes...........
.............
...
...
;D ;D ;D
First off, on the fundamental relationship between math and music: yes the chromatic scale is based on simple geometric ratios, but beyond this (and a few other things perhaps), I think saying "Music comes from math" or "Music is founded upon math," or anything of the like, are more subtle statements than one might let on. It's very philosophically grounded in whether one thinks math can "be" there without having defined it first, or whether one sees math as a lens through which physical and theoretical phenomena can be analyzed. Certainly math has played an important part in serialism, which utilizes set theory and algebra, but can we say it has played a similar role in either the creation or "essence" of a Beethoven piano sonata? Certainly we can analyze the music in a mathematical fashion, but does this make it fundamentally an object of math?
Quote from: 71 dB on May 04, 2007, 08:06:23 AM
Music is organised sounds.
The organisation process is economic. First we define musical scales etc. Then we construct higher level objects, thematic material (themes, melodies, harmonic ideas etc.). Finally we have constructed movements of larger works and complete works.
Lower level objects are easy to define mathematically.
Music scales are based on simple math. Equal temperament (http://en.wikipedia.org/wiki/Equal_Temperament) is 100% pure simple math based on simple equations like:
(http://img163.imageshack.us/img163/6053/9bfcf4448e5ef69cbc03369jr1.png) (http://imageshack.us)
Harmony is based on math too. Consonance and dissonance (http://en.wikipedia.org/wiki/Consonance_and_dissonance) is related to how simple or complex relation there is between the fundamental frequencies of the notes in chords.
High level objects are difficult/nearly impossible to define mathematically.
Clever statistical analyse of "good" melodies perhaps gives interesting results about how melodies follow certain complex rules. Anyway the math starts to be extremely complex. Trying to define complete symphonies with math would be insane. The math needed would be beyond anything mankind can understand I am afraid. However, the smaller blocks in music can be described with at least some kind of statistical logic.
Those are some sketchy generalizations. What do you mean by "high level objects"? If a symphony is a "high level object," what do you make of Quantum theory, Chaos theory, or General Relativity? These are highly complex fields that are mathematically framed. One can even make a case that complex things are often mathematically simple. Then again, if you think "high level objects" are simply things that cannot feasibly be mathematically defined, you are using circular logic (or rather, you are simply stating tautologies).
--CS
Quote from: CS on May 07, 2007, 06:20:48 AM
First off, on the fundamental relationship between math and music: yes the chromatic scale is based on simple geometric ratios, but beyond this (and a few other things perhaps), I think saying "Music comes from math" or "Music is founded upon math," or anything of the like, are more subtle statements than one might let on. It's very philosophically grounded in whether one thinks math can "be" there without having defined it first, or whether one sees math as a lens through which physical and theoretical phenomena can be analyzed.
Interesting. And, of course, the music does not "reside" in the physical phenomena which are so readily measured by mathematics. As to the theoretical, the relation between theory and the music is never otherwise than porous and ephemeral.
Quote from: CSCertainly math has played an important part in serialism, which utilizes set theory and algebra, but can we say it has played a similar role in either the creation or "essence" of a Beethoven piano sonata?
The role is certainly somehow different; but I do not think that math "drives" either any more than the other.
Quote from: karlhenning on May 07, 2007, 06:52:23 AM
The role is certainly somehow different; but I do not think that math "drives" either any more than the other.
At the very least I think it can be said that the direct application of some mathematics in serialism has an effect on the music in the way it is created; it is more of an apparent inspiration and component of its "style" than many other styles music (or compositional techniques). But like you say, this does not mean serialistic music is more of a mathematical "object" than music with classical harmony. (Am I reading you right? If so, I agree.)
Quote from: CS on May 07, 2007, 07:40:07 AM
But like you say, this does not mean serialistic music is more of a mathematical "object" than music with classical harmony. (Am I reading you right? If so, I agree.)
Yes, indeed.
I'd be careful about the whole music and math thing: there is a big difference between what is inspired by math, and what is simply able to be translated into math. I am not saying that music is not mathy at times, depending especially on the composer, but just that math is more a tool of organization, a way of interpreting natural phenomena than necessarily a source.
You can interpret anything mathematically (with probably mixed results) but what is the point? You can interpret things however you want, and call it a world view. But that would be ignoring the world, and the various ways that people experience existence, let alone art.
There are composers who probably use a math like mindset for composition. But there are plenty of composers who probably couldn't give a rat's arse about such methods.
Quote from: sonic1 on May 07, 2007, 08:15:10 AM
I'd be careful about the whole music and math thing: there is a big difference between what is inspired by math, and what is simply able to be translated into math. I am not saying that music is not mathy at times, depending especially on the composer, but just that math is more a tool of organization, a way of interpreting natural phenomena than necessarily a source.
You can interpret anything mathematically (with probably mixed results) but what is the point? You can interpret things however you want, and call it a world view. But that would be ignoring the world, and the various ways that people experience existence, let alone art.
There are composers who probably use a math like mindset for composition. But there are plenty of composers who probably couldn't give a rat's arse about such methods.
Well, music, like any other sort of value based system, can be translated into a mathematical strucure quite easily. With that information one could develop certain models for 'the ideal' in music, based upon analysis of canonical composers. It can actually be quite interesting. As to ever obtaining a mathematical paradigm for perfection in music, that is ridiculous. Mathematical anaylis of music can be quite useful, actually. I would personally like to see how one might go about looking at the relationship.
Quote from: Steve on May 07, 2007, 10:28:36 AM
. . . Mathematical anaylis of music can be quite useful, actually.
I agree, though my own math is fairly primitive (and I am content thus).
Quote from: Steve on May 07, 2007, 10:28:36 AM
Well, music, like any other sort of value based system, can be translated into a mathematical strucure quite easily. With that information one could develop certain models for 'the ideal' in music, based upon analysis of canonical composers. It can actually be quite interesting. As to ever obtaining a mathematical paradigm for perfection in music, that is ridiculous. Mathematical anaylis of music can be quite useful, actually. I would personally like to see how one might go about looking at the relationship.
Mathematical analysis could go so far, agreed. Some of it might be interesting. But much of what I really love in music couldn't be measured that way. And i am not saying that in the Pink Harp kind of way. I just think aesthetics are so complicated that the amount of mathematical analysis it would take to be successful would be ridiculous. This is what words and poetry are for. Really, if you don't get it, no amount of math will help you.
Quote from: sonic1 on May 07, 2007, 09:01:38 PM
Mathematical analysis could go so far, agreed. Some of it might be interesting. But much of what I really love in music couldn't be measured that way. And i am not saying that in the Pink Harp kind of way. I just think aesthetics are so complicated that the amount of mathematical analysis it would take to be successful would be ridiculous. This is what words and poetry are for. Really, if you don't get it, no amount of math will help you.
I couldn't agree more. Conveying subjective experience with formal logic is about as helpful as trying to rate the perfection of a Donne sonnet on a graph. Well said. :)
Cato, on the first page you said that Mathematicians follow beauty and elegance... I just wanted to say that they also have been known to use computers to solve problems, and that includes number theory and group theory.
I especially recall that a few weeks ago the representations of a Lie group were found that took 60 gigs to store!
Beauty is an aesthetic that although many mathematicians follow, as do musicians, is not a necessary part of either. It's confusing a discipline with an aesthetic held by many (but not all, and not even a majority) that work in the discipline.
<edited> deleted the argumentative part of my post
Quote from: DavidW on May 08, 2007, 07:23:44 AM
Cato, on the first page you said that Mathematicians follow beauty and elegance... I just wanted to say that they also have been known to use computers to solve problems, and that includes number theory and group theory.
I especially recall that a few weeks ago the representations of a Lie group were found that took 60 gigs to store!
Beauty is an aesthetic that although many mathematicians follow, as do musicians, is not a necessary part of either. It's confusing a discipline with an aesthetic held by many (but not all, and not even a majority) that work in the discipline.
Right! Why exclude anything which could aid in finding a correct answer?
Well, maybe it might cause more confusion than actually help. I am not saying this is absolutely the case, but maybe people feel like icy cold statistical analysis of music is not the sort of analysis that would help them be better listener/music makers.
Quote from: sonic1 on May 08, 2007, 02:58:12 PM
Well, maybe it might cause more confusion than actually help. I am not saying this is absolutely the case, but maybe people feel like icy cold statistical analysis of music is not the sort of analysis that would help them be better listener/music makers.
I'm not sure that I can agree with that last response,
sonic1. Any relevant external information is certainly no substitute for subjective experience with music, but it does have it's uses. Knowledge of the untimely death of Robert Schumann and his kinship with Brahms is hardly musical information, but it certainly can give someone the perspective with which to understand the mood of his Piano Concerto. Cultural information and other historical tidbits can often enrich the entire listening experience.
How math is used in conjunction with music also matters a great deal. Searching for objective standards in music, which can be expressed quanatively is entirely useless, and unlikely to aid the listener in any significant manner. However, if we confine our use of math to study our favourite pieces, we may find information that can enrich our experience in the same fashion that some useful historical fact pertinent to the composer's life might do the same.
What I had in mind, was more of a tool to help listeners study the music they so often enjoy. Instead of trying to determine why certain pieces are great and others are not, I would be interested in simply comparing pieces from the canon in order to find common structures that seem to find pleasure among listeners. It's at best, another tool for our study of music, and could never replace the importance of repeated listening.
I've noticed, but haven't been able to wrap my head around, a currently fashionable branch of music theory called "neo-Reimann analysis". It employs a pretty imposing mathematical apparatus to describe music of Brahms and other traditionally tonal music.
Is there someone here who knows, and can explain to me, what this is about?
Didn't Shoenberg write "Heart and Brain in Music." ??
;D
Quote from: Steve on May 09, 2007, 12:42:37 PM
I'm not sure that I can agree with that last response, sonic1. Any relevant external information is certainly no substitute for subjective experience with music, but it does have it's uses. Knowledge of the untimely death of Robert Schumann and his kinship with Brahms is hardly musical information, but it certainly can give someone the perspective with which to understand the mood of his Piano Concerto. Cultural information and other historical tidbits can often enrich the entire listening experience.
How math is used in conjunction with music also matters a great deal. Searching for objective standards in music, which can be expressed quanatively is entirely useless, and unlikely to aid the listener in any significant manner. However, if we confine our use of math to study our favourite pieces, we may find information that can enrich our experience in the same fashion that some useful historical fact pertinent to the composer's life might do the same.
What I had in mind, was more of a tool to help listeners study the music they so often enjoy. Instead of trying to determine why certain pieces are great and others are not, I would be interested in simply comparing pieces from the canon in order to find common structures that seem to find pleasure among listeners. It's at best, another tool for our study of music, and could never replace the importance of repeated listening.
It might be helpful to a composer, or a very serious listener, but to the average person I am skeptic that such information would help anyone.
I love science, but sometimes I think mathematical analysis as applied to even health, causes more confusion than not, let alone trying to analyze something like music or art. Can you get results? Maybe, but it seems a lot more work than just relying on your ear and your gut. I am sure most of the greatest composers had no need for such things. Musical analysis in the standard way was enough for them, and is enough for me. Just regular musical analysis is a lot of work. I think we are often, in modern times, a little tech happy, and it takes away from the art itself. I say, screw all these new mathematical ideas, and go back to combing over bach cantatas...you will find enough knowledge there to keep you busy the rest of your life-and probably with better results. But maybe I am old-fashioned.
Quote from: sonic1 on May 10, 2007, 11:39:57 AM
It might be helpful to a composer, or a very serious listener, but to the average person I am skeptic that such information would help anyone.
I love science, but sometimes I think mathematical analysis as applied to even health, causes more confusion than not, let alone trying to analyze something like music or art. Can you get results? Maybe, but it seems a lot more work than just relying on your ear and your gut. I am sure most of the greatest composers had no need for such things. Musical analysis in the standard way was enough for them, and is enough for me. Just regular musical analysis is a lot of work. I think we are often, in modern times, a little tech happy, and it takes away from the art itself. I say, screw all these new mathematical ideas, and go back to combing over bach cantatas...you will find enough knowledge there to keep you busy the rest of your life-and probably with better results. But maybe I am old-fashioned.
'just relying on you ear or gut' - Once again, I am not advocting the substitution of listening with mathematical anaylsis, just that it can be a useful way to understand the music we love. As a Math major, I am reluctant to ever accept the notion that 'math makes things more confusing'. For me, whenever I am able to analyze a system with Mathematics, either statistical modeling or using some other branch of math, I find that I am able to enrich my understanding of that system. While I would never be so foolish as to try and reduce my experience of Mahler, for instance, into a series of data, I understand that mathematics can often lend a deeper eye into the inner workings of various systems, math not excluded. Just because many great composers were not mathematically inclined, does not proclude those that are from applying their studies to music. I am very interested, after attending a wonderful Philospohy of Science confrence last summer in using mathematics to enrich our theories of asthetics.
While you might not see the possibilities in such a relationship, I do. While my research would in no way resemble 71db's - arbitrary scales of subjective qualities (perfection, sophistication, etc), looking at various musical structures with mathematical models would.
Quote from: sonic1 on May 10, 2007, 11:39:57 AM
It might be helpful to a composer, or a very serious listener, but to the average person I am skeptic that such information would help anyone.
I love science, but sometimes I think mathematical analysis as applied to even health, causes more confusion than not, let alone trying to analyze something like music or art. Can you get results? Maybe, but it seems a lot more work than just relying on your ear and your gut. I am sure most of the greatest composers had no need for such things. Musical analysis in the standard way was enough for them, and is enough for me. Just regular musical analysis is a lot of work. I think we are often, in modern times, a little tech happy, and it takes away from the art itself. I say, screw all these new mathematical ideas, and go back to combing over bach cantatas...you will find enough knowledge there to keep you busy the rest of your life-and probably with better results. But maybe I am old-fashioned.
Don't mean to be pedantic, but mathematical analysis (http://en.wikipedia.org/wiki/Mathematical_analysis) is perhaps not the field we're talking about here (are we? ???), but rather statistical analysis, or "analysis using math" ::) ;D. I just point it out because I just started studying Analysis and wouldn't know how in hell it could be used for music! It seems there may be ways however... (as Mark mentioned "neo-Reimann analysis"? Sounds very intriguing...)
Quote from: CS on May 10, 2007, 02:13:12 PM
Don't mean to be pedantic, but mathematical analysis (http://en.wikipedia.org/wiki/Mathematical_analysis) is perhaps not the field we're talking about here (are we? ???), but rather statistical analysis, or "analysis using math" ::) ;D. I just point it out because I just started studying Analysis and wouldn't know how in hell it could be used for music! It seems there may be ways however... (as Mark mentioned "neo-Reimann analysis"? Sounds very intriguing...)
I was, indeed referring to statistical analysis. However, the results could be use to form a mathematical model. I suppose that's what caused the misnomer. Aptly noted, CS.
Quote from: Steve on May 10, 2007, 02:37:28 PM
I was, indeed referring to statistical analysis. However, the results could be use to form a mathematical model. I suppose that's what caused the misnomer. Aptly noted, CS.
Well I wasn't quoting you, but it wasn't really directed towards anyone specific anyway. Was just making the distinction since we're throwing around the terms anyway.
BTW Mark, do you have any information about that "neo-Reimann analysis"?
I 'did' Riemann analysis at university; can't say I remember much about it apart from the liberal sprinklings of quadruple flats on his charts; and I'm not sure if what I did was distinct from neo-Riemann. Fat lot of use I am, huh?
Had any thoughts on Barber? I know I sent you a lot of stuff, and I don't want to pressure you into a judgment - just interested if you've made any progress with him?
I thought it was intensively math-related because of the name Riemann -- but I think I found it has to do with Hugo and not Bernhard. :P
Composing music is simple:
http://ccrma.stanford.edu/~blackrse/algorithm.html
Maths may in fact be of more use in demonstating what is not in music rather than disclosing esoteric structures. A famous case in another field was the discovery of lay lines connecting telephone boxes in the Cotswolds thus showing that the whole concept of lay lines is a figment of man's imagination that arose because the chance of apparantly significant lines appearing through a completely random selection of points is very small.
The Greeks had The Quadrivium, which was geometry, astronomy, arithmetic, and music. So music has always been a part of math. sound is physical vibration, and can be quantified. Musical intervals are expressed as ratios.
If this is all too complicated, do like Alban Berg did, and just use arbitrary numerological sequences to compose with.
Hoo-boy.
Jeez-Marie.
Astronomy is not math, neither is music
Quote from: bwv 1080 on May 03, 2017, 08:59:34 AM
Astronomy is not math, neither is music
The very point.
Quote from: bwv 1080 on May 03, 2017, 08:59:34 AM
Astronomy is not math, neither is music
You need to read about the quadrivium, then.
Quote from: millionrainbows on May 03, 2017, 12:16:04 PM
You need to read about the quadrivium, then.
No i dont. Ancient greeks are not an authority and whatever was in the quadrivelum means nothing
It's easy to see how music is geometric. The 12 notes get divided up into symmetrical groupings, based on the number 12 rather than the tonal way, which is asymmetrical.
Tonality was/is based on sensual constructs: major/minor chords are not symmetrical, and the octave is "divided" at the fifth, which is the way tonality works best, with the IV and V.
Geometrically, the modernists have divided the octave at 6, or the tritone, which is not harmonically derived, and even sounds dissonant, especially when compared to the fifth. All the intervals except 7 (fifth) and 5 (fourth) are symmetrical: 1, 2, 3, 4, and 6 (the rest are inversions).
The fact that there are 12 notes did not always exist, and everything (7-note scales) was based on the sound of the fifth and major third. "12" was arrived at through Pythagoran procedures (not Pythagoras himself, who did not need 12 notes). This "twelveness" itself is an arbitrary, geometric quality.
...arithmetic was pure number, geometry was number in space, music number in time, and astronomy number in space and time. Morris Kline classifies the four elements of the quadrivium as pure (arithmetic), stationary (geometry), moving (astronomy) and applied (music) number
Beethoven was so mathematically incompetent that he never even properly learned how to multiply and divide. (He could add and subtract.)
Apparently this caused a lot of trouble with his personal finances.
He probably didn't care what was in the Quadrivium, either. Although his life probably would have been easier if he had.
The idea was that the mathematical subjects should be taught/learned in ascending complexity: arithmetic deals only with "one dimension" (numbers"), then plane geometry, then threedimensional geometry, then movement in three dimensions (and celestial mechanics was the only well described regular natural movement until the late middle ages/early modernity). Music theory deals with proportions (of chord length), it was therefore seen as the more complex partner of arithmetic.
"The Pythagoreans considered all mathematical science to be divided into four parts: one half they marked off as concerned with quantity, the other half with magnitude; and each of these they posited as twofold. A quantity can be considered in regard to its character by itself or in its relation to another quantity, magnitudes as either stationary or in motion. Arithmetic, then, studies quantities as such, music the relations between quantities, geometry magnitude at rest, spherics [astronomy] magnitude inherently moving." (Proklos)
https://en.wikipedia.org/wiki/Quadrivium
(It is not completely different from today when one starts with arithmetic and plane geometry in middle school and in college physics point mechanics in three dimensions will usually be taught before elastic continua with the vibrating string as the simplest case.)
well, ever since I saw intervals expressed as ratios, I've been a believer.
Quote from: Florestan on May 03, 2017, 01:32:12 PM
A progression which is directly inherited from, and heavily influenced by, the quadrivium of yore. Dismissing the latter as meaningless for today's world is either ignorant or provocative.
Why should I respect the ancient philosophical construct of the quadrivium any more than, say, Aristotelian concepts of science?
Quote from: Florestan on May 03, 2017, 12:30:38 PM
Math without astronomy, aplenty --- astronomy without math, hardly if at all. Just saying.
Math is a tool, one is that is essential to astronomy and sometimes useful for some composers. Go back and read the OP - just realized I started this damn thread a decade ago
Quote from: bwv 1080 on May 03, 2017, 06:32:13 PM
Why should I respect the ancient philosophical construct of the quadrivium any more than, say, Aristotelian concepts of science?
You should not respect it as some "higher truth" but as a historical reality that was important and influential for education for at least 2000 years (from the 5th century BC or if the Pythagorean tradition is plausible even earlier until at least the 17th century when Kepler tried to fit the planetary orbits into "harmonic proportions") and the deeply entrenched idea of the connection (NB not identity) between music and maths is expressed in it quite clearly.
It's like asking "why should one respect the golden ratio when it is just some stuff the ancients came up with" and ignoring how it has dominated parts of aesthetics, architecture etc.
Quote from: millionrainbows on May 03, 2017, 01:37:13 PM
well, ever since I saw intervals expressed as ratios, I've been a believer.
This composer begs your pardon, as he did not come dressed for church.
Quote from: k a rl h e nn i ng on May 04, 2017, 01:12:48 AM
This composer begs your pardon, as he did not come dressed for church.
Oh, I see. Care to elaborate?
Meanwhile, the "wholesale resurrection of ancient threads" continues...
Quote from: millionrainbows on May 15, 2017, 12:34:34 PM
Meanwhile, the "wholesale resurrection of ancient threads" continues...
I refer you
here (http://www.good-music-guide.com/community/index.php/topic,15504.msg1062545.html#msg1062545).
Quote from: bwv 1080 on May 04, 2007, 06:50:56 AM
Try to restart, reframe and remove the discussion that started in the Mahler thread.
ISTM that there are two unsupportable positions on the topic:
A) the Quantophiliac, who looks for deterministic mathematical relationships to aesthetics, forgetting that music is art and therefore cannot be fully defined by the sum of any set of empirical observations.
B) the Quantophobe, for whom mystical inspiration is all and ignores the fact that math is often a useful tool in achieving and describing aesthetic objectives.
Certainly composers have taken direct inspriation from mathematics. Bartok w/ golden mean proportions, Ligeti with strange attractors and other fractal phenomena etc. Music is not math any more than architecture is math, but as Monk sez, all musicians are subconsiously mathematicians.
I can save you a lot of time.
Mathematics is not an art.
Science is not an art.
Music is not mathematics.
Music is not a science.
Music is a fine art: music is only
"like unto" maths and science in that it is an abstract discipline, that overlap but slight.
Any one involved in any of the three disciplines can be said to have an interest in a type of
order.Bartok did use the ratios of the golden rectangle to determine
the number of measures of sections in a piece. I.e. section 'a' was so many measures long, 'b' so many, etc. This was about
segment durations in linear time, no longer about a rectangle: he did this in several
short pieces, rather like just a few studies. He did not apply it all the time, or in any of his larger-scale pieces that I know of.
If that same ratio of number of measures per section of a piece had been used by a 'bad' composer, the golden rectangle ratio would have done exactly jack-shit to make a bad piece any better. I.e. a skilled and talented composer can make that set of related duration segments
work (they could also make other non-golden rectangle ratio segments
work): it is not the set of ratios itself that has any 'artistic magic.' or intrinsic worth.
It was GMG member North Star who sagely pointed out that maths
are used to such a near universal effect in delineating and quantifying so much of our world and universe that mathematicians are going to be prone to believe that there must be a lot of quantifiable maths in music. For the acoustics department, sure (its a science, after all, that uses a lot of maths:-) For the 'art' part?
Well, Timothy Leary's description of the brain's very most basic impulse is good here. For the sake of illustration, let us agree the oceans in this quote are 'art,' and specifically, the art of classical music.
"Imagine your mouth, actual size, adrift on all the oceans of the world. That mouth is calling out, "Order."As Karl Henning has already said,
a musician's imagination can by catalyzed by any number of things, a mathematical premise included. A la the example of Bartok and the golden rectangle, the inspiration (math or other) is rarely applied or carried out literally... it was just a premise to springboard an idea.
If there were some tried and true set of maths as applied to music to 'make pieces work,' wouldn't there have been several hundred tomes on the subject by now -- and wouldn't more people, using those tomes as teachers and guides, be writing stunningly good pieces?
The modern human has a very poor imagination.
Edit: The modern human, on average, is also extremely bad at mathematics, or so says lots and lots of personal experience.
Quote from: nathanb on May 16, 2017, 06:37:44 AM
The modern human has a very poor imagination.
Edit: The modern human, on average, is also extremely bad at mathematics, or so says lots and lots of personal experience.
"It is said," that "Musicians" are often adept at maths, languages, and they are also quick to learn how to fly an airplane.
Well, "It is said." lol.
Quote from: Monsieur Croche on May 16, 2017, 06:30:13 AM
I can save you a lot of time.
Mathematics is not an art.
Science is not an art.
Music is not mathematics.
Music is not a science.
Music is a fine art: music is only "like unto" maths and science in that it is an abstract discipline, that overlap but slight.
Any one involved in any of the three disciplines can be said to have an interest in a type of order.
Bartok did use the ratios of the golden rectangle to determine the number of measures of sections in a piece. I.e. section 'a' was so many measures long, 'b' so many, etc. This was about segment durations in linear time, no longer about a rectangle: he did this in several short pieces, rather like just a few studies. He did not apply it all the time, or in any of his larger-scale pieces that I know of.
If that same ratio of number of measures per section of a piece had been used by a 'bad' composer, the golden rectangle ratio would have done exactly jack-shit to make a bad piece any better. I.e. a skilled and talented composer can make that set of related duration segments work (they could also make other non-golden rectangle ratio segments work): it is not the set of ratios itself that has any 'artistic magic.' or intrinsic worth.
It was GMG member North Star who sagely pointed out that maths are used to such a near universal effect in delineating and quantifying so much of our world and universe that mathematicians are going to be prone to believe that there must be a lot of quantifiable maths in music. For the acoustics department, sure (its a science, after all, that uses a lot of maths:-) For the 'art' part?
Well, Timothy Leary's description of the brain's very most basic impulse is good here. For the sake of illustration, let us agree the oceans in this quote are 'art,' and specifically, the art of classical music.
"Imagine your mouth, actual size, adrift on all the oceans of the world. That mouth is calling out, "Order."
As Karl Henning has already said, a musician's imagination can by catalyzed by any number of things, a mathematical premise included. A la the example of Bartok and the golden rectangle, the inspiration (math or other) is rarely applied or carried out literally... it was just a premise to springboard an idea.
If there were some tried and true set of maths as applied to music to 'make pieces work,' wouldn't there have been several hundred tomes on the subject by now -- and wouldn't more people, using those tomes as teachers and guides, be writing stunningly good pieces?
Dont see that you saved me any time, just obfuscated what I said back in 2007 without contradicting any of it. To try to add some real clarity I would add that music theory is not math in the sense that there is no axiomatic foundation such as exists in statistics, computer science or other fields in applied math. However, I do like the Monk quote
Quote from: Monsieur Croche on May 16, 2017, 06:51:14 AM
"It is said," that "Musicians" are often adept at maths, languages, and they are also quick to learn how to fly an airplane.
Well, "It is said." lol.
My professor for Flight Performance & Stability was both an ardent lover of unconventional aircraft design and, apparently, a fair cellist.
But extreme minority cases are rarely useful, lol.
Quote from: bwv 1080 on May 16, 2017, 06:51:49 AM
Dont see that you saved me any time, just obfuscated what I said back in 2007 without contradicting any of it. To try to add some real clarity I would add that music theory is not math in the sense that there is no axiomatic foundation such as exists in statistics, computer science or other fields in applied math. However, I do like the Monk quote
Way back in 2007, eh? I must have missed that class ;-)
Of course, I over-reacted, not to your post but to the usual floating in the ether plethora of those who think that some ordering of music and its basic materials can be done near to solely via maths, which is, unfortunately, a fairly commonplace recurring premise (a premise almost always put forth by non-composers, btw.)
And of course I would think it more than obvious and needing no further qualification that
Music Theory is, by its very title as definition, neither a math or a science.
Best regards
Better Music Through Science!
Quote from: k a rl h e nn i ng on May 17, 2017, 08:38:29 AM
Better Music Through Science!
Karl, are you old enough to remember the post-war 1950's promotional campaign / propaganda slogan
"Better Living Through Chemistry?" (The 60's generation took it to heart, used that slogan with a wink, in a way the 50's set would never have imagined:-)