 The Clarinet BBoard
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Author: BlockEyeDan
Date: 2004-12-06 17:00
Hello all,
I have been doing some research on the connection between mathematics and music. As I go through my music theory classes, it amazes me how much music theory is a form of symbolic reasoning (the department heads have been trying for several years to allow music theory courses fulfill the College's numerical and symbolic reasoning requirement). My questions are numerous: does anyone here find that learning musical theory helps them with understanding traditional mathematics? Does one use the same parts of one's brain when processing music and mathematical equations? Also, I have heard that those people who are naturally gifted at mathematics have an innate understanding and mastery of music theory. (Two of my professors started college as math majors, only to switch gears later on.) Are there any mathematicians here who can shed light on this matter?
Thanks,
Dan
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Author: John Stackpole
Date: 2004-12-06 18:16
Well, you could start with Pythagoras, but don't spend too much time learning Greek to do so.
Instead jump forward a few years to John R. Pierce ("J.J.Coupling" for you elderly science fiction fans out there) "The Science of Musical Sound" (1992) and if that's not enough try "Measure for Measure - A Musical Hisory of Science", Thomas Levenson (1994).
And then for your graduate studies go look at the Australian web pages dealing with woodwind acoustics:
http://www.phys.unsw.edu.au/~jw/woodwind.html
A google search will turn up others as well.
Math and music theory, and "music appreciation", seem to be well correlated. I'm not so sure about ability to make music, rather than just making notes (even in the right time), however.
JDS
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Author: Rene
Date: 2004-12-06 18:18
I am a mathematics professor and a musician (good non-professional singer, and somewhat mediocre clarinet player). I have seen lots of mathematicians that are rather inclined to music and lots that are not. E.g., we have a very good piano player in our department. We have also teacher students that study musics and mathematics. Some of them are good in both subjects, most are not.
It has been said often that musics and mathematics have some relation. But frankly, I do not quite believe in that. Maybe people are surprised when mathematicians are also inclined to music and make a fuzz about it. I doubt there is a statistical evidence for any positive relation.
Good music is nothing you can compute. Maybe an abstract understanding of scales is easier for a mathematical trained, but that is about all. However, I never had problems with transposing.
If you allow me to say that, mathematicians are rather clever people in general. No surprise they have lots of different interests!
Rene
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Author: george
Date: 2004-12-06 18:55
I am a mathematics professor ( now retired) and a not-very-good amateur musician. I cannot prove this with any hard data, but my experience tells me there is a much higher percentage of reasonably talented amateur musicians and people with a modest knowledge of music theory among professional mathematicians than there is among the general population. What this proves, I guess I don't know.
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Author: Don Poulsen
Date: 2004-12-06 20:07
I have have degrees in math and engineering and am a dedicated amateur musician. You'll find that a great number of non-professional musicians on this board are engineers or mathematicians. As one is considered a left-brain activity and the other a right-brain activity, some would find a positive correlation surprising. However, those who purposely study higher level math realize that there is a strong creative (problem-solving) element involved, plus a desire to find an aesthetically pleasing elegance. Making music is another means of satisfying the need to create an aesthetically pleasing elegance. At this point, I would hypothesize that the majority of those musically inclined mathematicians have a much greater appreciation of classical music than, say, hard rock, as the former typically offers more elegance.
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Author: supernova_khr
Date: 2004-12-06 21:18
My daughter's school is a math and music focus school. At least a few people in education recognize some relationships. It's very true that one can play music without understanding mathematics. But, if you really want to understand harmonics, you need to understand mathematics. And I'm not surprised that folks with a mathematical bent have an easier time with music theory. (chord progressions are a bit mathematical too.) Note, however, that a full understanding of music theory doesn't necessarily make one a good performing musician.
Anyway, here's a web page discussing some relationships between math and music
http://www.math.niu.edu/~rusin/uses-math/music/
If you do a google on math and music, you'll find lots of web pages come up.
I'm personally a research physicist, and have lots of musical colleagues, including a few who also play professionally as a second job. As far as whether they're prefer classical to hard rock, only one of my colleagues is actively playing in a symphonic orchestra. These rest are all playing rock, blue grass and jazz.
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Author: Don Berger
Date: 2004-12-06 21:43
I view myself as a "reasonably good chem engineer and inventor", a "fair" mathematician, several patents have math basees, and a semi pro musician, no real training in the last. Thus I see at least a fair correlation, and have wondered how deeply math concepts are/were involved in musical composition and arranging , and perhaps in the choices of instruments for certain parts based upon "harmonic character", ? another can of worms ? A Very Interesting Thread !! Don
Thanx, Mark, Don
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Author: Neil
Date: 2004-12-06 23:58
I have read that right-brained children have a natural affinity for music. It would seem to me that they should be more attuned to its abstract qualities and less able to grasp the rigors of scales and time signatures but I have no professional experience in the area. Is anyone else familiar with it?
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Author: diz
Date: 2004-12-07 01:37
Supanova said:
My daughter's school is a math and music focus school. At least a few people in education recognize some relationships.
Based on what research? thanks.
Without music, the world would be grey, very grey.
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Author: clarinetist04
Date: 2004-12-07 02:03
Interesting. For any of you out there into reading rigorous books on the subject, I encourage the devourment of "Godel, Escher, Bach: An Eternal Golden Braid". It is a pulitzer prize winning book that examines the similarities between Escher's paintings, Godel's mathematics, and Bach's music, mainly his fugues, but not completely. It is very sophisticated and took me over a year to get through it.
I am a chemical engineering and composition/clarinet student in college and I definitely think there is a corelation. I can't prove it, but I honestly believe it. When I consider my previous math teachers, I recall that every one of them had musical ability, whether it be writing symphonies to playing the harmonica (both cases I encountered). Look at Borodin, a fantastic composer and chemist. Other Examples?: John Dunstable, Peter Tchaikovsky (yes, he was a mathematician), Fletcher Henderson, Charles Ives (Acctuary, very math intensive), Victor Ewald, etc.
Quite an intriguing topic isn't it!
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Author: LeWhite
Date: 2004-12-07 05:07
Actually, my sight-reading and rhythm imroved almost as soon as I got a new job, working in an office - lots of alphabetical filing and quick adding up of figures. Hopefully there's a correlation between the two!
__________________
Don't hate me because I play Leblanc! ![[down]](http://test.woodwind.org/clarinet/BBoard/smileys/smiley23.gif) Buffet
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Author: jez
Date: 2004-12-07 10:40
I recently attended a lecture given by a mathematics professor about the influence of 'magic squares' on the music of Peter Maxwell Davies, in the presence of the composer who admitted to this obsession and explained how it affected his thinking in some compositions. It was very thought-provoking and gave an insight into what can inspire a composer of such complicated music to create it.
jez
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Author: BobD
Date: 2004-12-07 13:24
Congratulations to anyone completing reading GEB...it is fascinating.....I equate the task to listening to the complete Einstein on the Beach. I'm not convinced on the correlation of music and mathematics as far as personal likes or abilities go. I never did get as much satisfaction from any of my math studies as I did from music. But, maybe I'm missing something.
Bob Draznik
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Author: ginny
Date: 2004-12-07 15:00
The relationship, if there is one, is possibly that musical training enhances math ability rather than the reverse. I have seen a few studies in children that would indicate this, however I didn't bookmark them. Interestingly but not surprizingly, it seems that musical training may alter the brain physically.
"Schlaug and fellow researchers used magnetic resonance imaging to compare the brains of 32 right-handed musicians with 24 right-handed men who did not play instruments. They found a 5 percent difference in the volume of the cerebellum.
"Finding evidence like this is sort of remarkable. The structure seems to adapt" to early years of training and practice, Schlaug said. "Musicians are not just born with these differences.""
I have removed the reference, because it spread along the page and I need to get working...
In any case it would appear that brain structure is altered (at least in men per the article) The study size is fairly small, and they don't give the confidence levels or other statistical information.
I am in Charles Ives line of work, actuarial analysis, having degrees in math and music.
Post Edited (2004-12-07 15:05)
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Author: ginny
Date: 2004-12-07 15:08
In reference to music theory being a substitute for a math class:
Having done both I don't think music theory would hold up to an intermediate math class, much less a higher level. Many types of analysis are math based, but don't count as a math class, such as those done for chemistry. The calculations lack the rigor of proof as well.
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Author: sfalexi
Date: 2004-12-07 18:44
I'm a math major, and not to bad at math.
That being said, I breezed through music theory I and most of music theory II (before I dropped because it was progressing a little slow and I figured I'll just retake it later, especially since I don't need it to get my math degree right now).
I found that I had a very easy time figuring out intervals, basic triads and chord formations, and any other 'technical' aspect of music. Where my downfall was, was memorizing the terminology (a weakness of mine). I still can't tell you which steps in a scale are the tonic, subtonic, subdominant, dominant, leading tone, etc. etc. etc. (but I did know them for the test)
However like I said, hearing intervals and looking at a piece of music I could (more quickly than the average classmate) tell you whether it was a certain inversion of a triad, what the interval was and what the inversion was, and things like that.
Alexi
US Army Japan Band
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Author: David Spiegelthal ★2017
Date: 2004-12-07 18:51
Well, let's see........my Dad (deceased) was a mathematician and a pretty good (but not great) classical pianist. I'm not a mathematician but I'm probably at least as good a musician as my father was, although my knowledge of music THEORY is practically nil. My semi-boss at work is a brilliant mathematician (with a PhD) and an amateur musician with very little talent. So, take these three random data points and factor them into your theory, for what they're worth.
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Author: sfalexi
Date: 2004-12-07 19:08
I also heard another theory . . .
That in order to 'stronger' correlate math and music, take a look at people who can do mathematical operations versus people who can do mathematical theories.
For instance, meaning if you can do math in your head, you'd be better at music.
Whereas if you know proofs and geometry, that may not factor in.
I heard someone talking about this the other day. I can do some math operations in my head as well as figure out the intervals. Whereas another person who maybe could memorize theories and plug'n'chug with a calculator would not be good at music theory . . . . I wonder how that would play in . . .
Alexi
US Army Japan Band
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Author: diz
Date: 2004-12-07 20:04
Don't get me wrong ... I think there are somethings in life where people are very talented in more than one area. In this case we happey to be discussing mathematics and music.
I cannot remember where I read this (possibly not Groves' Dictionary however). But J.S. Bach was rather the mathematician. His fugues are certainly works of perfection in their form and balance, unsurpassed by anyone since.
Even Mozart stated that fugues were just a little beyond his technical skills (sorry I can't remember where I read that quote either) and he found them a challenge ... hence didn't bother to write many.
Without music, the world would be grey, very grey.
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Author: Ron Jr.
Date: 2004-12-07 20:19
I think the connection between mathematics and music is a one way street. Many mathematicians study music because it appeals to their powerful and highly intellectual minds. Most musicians I know can't stand math.
I argue that music is more rigorous than mathematics for several reasons.
Both have an intellectual or theoretical aspect. Some may argue the point that math theory is much more complicated than music theory, but essentially both have a huge base of knoweledge that must be assimilated and understood.
Yet music has a physical component that mathematics lacks: the coordination of the hands and notes.
Music has a sensory component: one's hearing, sensitivity to tones, note lengths, tonal qualities, and tonal relationships.
Music has a performance component that mathematics lacks.
Music has an expressive or emotional component that mathematics lacks.
I would further argue that playing the piano engages more of the brain than a single line instrument. And certainly playing the piano engages more of the mind, body and emotions than solving a mathematical equation.
Beethoven's quote: "Music is a higher revelation than Philosophy," supports the idea that music will always engage a much larger part mind, senses, body, and emotions than any purely intellectual pursuit, mathematics included.
Ron Jr.
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Author: Sylvain
Date: 2004-12-07 20:55
I believe that the initial topic was about the connection between music THEORY and mathematics. Thee I tend to agree that a mathematically inclined mind can have facilities in recognising and studying the patterns of the harmonies making a piece of music.
Certain composers have established a lot of different set of rules on what should or should not be done in order for something to sound sad or fast or dissonant or...
I believe that a good mathematical mind wlll help in the analysis of a piece, however, its interpretation is something a little bit different. First you have the physical aspect of playing which can demand athlete like abilities, then you have the emotional value of the piece, a certain "controlled let go" that has nothing to do with how well you can dissect the harmonies of the piece.
These last 2 points are to me completely uncorrelated to mathematics.
-S
--
Sylvain Bouix <sbouix@gmail.com>
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Author: Don Berger
Date: 2004-12-07 21:13
I've been hoping that Dan Oberlin, Prof of Math, FSU, a long time friend, Solo chair in the Tallahassee Winds would "chime in" with his thots from our two points of view. Don
Thanx, Mark, Don
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Author: george
Date: 2004-12-07 22:00
I say Amen to sfalexi's comments about music terminology. And also, am I the only one offended, for instance, by the fact that when one goes up, say, a third and then another third, one has gone up not a sixth, but only a fifth? Most everybody else in the world starts counting at zero.
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Author: BobD
Date: 2004-12-07 22:50
Hmmm.....are we comparing music theory and mathematical theory. Which lfield of mathematics? And....are we considering Western music theory and diatonic scales? Or is all this irrelevant?
Bob Draznik
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Author: clarinetist04
Date: 2004-12-08 00:18
I was playing at a district band festival with Jack Stamp of IUP and he told us that in Math, one can get a 95% and pass the course, but if we get only 95% of the notes on a page of music we'd get booed off the stage.
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Author: claclaws
Date: 2004-12-23 08:57
Confessing I was a lousy math student, I cannot but feel again lousy about my inability in transposing string scores for my A and Bb clarinets.
Here's the quiz for those of you who are strong in maths and intervals etc.
I've transposed a 5-#(sharp)ed score for my A cla. It became C maj. (thus no # or b) I was happy.
Now I have a 4-#ed score for the Bb cla, and want to transpose for A cla, to make life easier, of course . Will it become G maj on my A cla?
Does anybody have a easy-to-understand transposition table or something? Have we dealt with this before in this BBoard?
Happy holidays.
Lucy Lee Jang
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Author: GBK
Date: 2004-12-23 11:16
claclaws wrote:
> Now I have a 4-#ed score for the Bb cla, and want to transpose
> for A cla, to make life easier, of course . Will it become G
> maj on my A cla?
The key signature becomes 1 flat (F major/D minor)
> Does anybody have a easy-to-understand transposition table or
> something? Have we dealt with this before in this BBoard?
http://www.grahamnasby.com/misc/clarinet_transpositionguide.shtml
...GBK
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Author: Pappy
Date: 2004-12-23 12:00
Not sure it adds anything, but my anecdotal evidence:
My wife is a physician who's undergrad is in Math and she is not "musical" (played cello in H.S. but nothing since then). She "appreciates" music, knows the symphonic repertoire as a consumer, etc. but does not play.
My sons are both VERY gifted in mathematics (one just finished a computer engineering degree) and are also quite good musicians, playing Cello and Violin.
I am a software engineer (actually a manager of developers at this stage) and competent in math but not a gifted mathematician. I don't know how gifted a musician I am but I am an obsessed musician .
So in our family the most gifted mathematician (son #1) is a middle of the road musician. The most serious musician (me) is a middle of the road mathematician. And the most gifted musician (son #2) is very strong in maths but not "brilliant".
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Author: sfalexi
Date: 2004-12-23 14:13
Quote:
So in our family the most gifted mathematician (son #1) is a middle of the road musician. The most serious musician (me) is a middle of the road mathematician. And the most gifted musician (son #2) is very strong in maths but not "brilliant". And Who's on first base, and What is on second base . . . .
US Army Japan Band
Post Edited (2004-12-23 14:13)
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Author: claclaws
Date: 2004-12-23 20:21
GBK,
Thanks a million! I immediately printed out the 'how to sight-transpose clarinet part' post.
May you have a wonderful Christmas - and you deserve it, because you've helped so many people on this board!
Lucy Lee Jang
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Author: John Noecker
Date: 2004-12-23 22:20
Clarinetist04.... Any chance that was the PMEA District 10 Festival last year? I was there too... Too bad I didn't get to meet you, most of the people around me (other clarinetists) were slightly unfriendly to say the least.... Dr. Stamp was a very interesting fellow to say the least!
John
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Author: sfalexi
Date: 2004-12-24 14:09
EEBaum wrote:
> "And Who's on first base, and What is on second base . . . ."
>
> And who's on first bass?
Exactly.
US Army Japan Band
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Author: Ron
Date: 2004-12-24 15:57
First, I am not a mathematician though I was an above average math student in high school but mediocre in college. I have played the clarinet professionally and currently play in an outstanding community concert band composed of around 65 dedicated volunteer musicians. In this group, there is a fair number of retired or practicing physicians, dentists, lawyers, chemists, teachers, etc. I do not know of any mathematicians in this group.
Music is a language. It has 13 notes in our system to spell chords and create intervals. Along with the lengths of notes and rests, different articulations and dynamics, we have little else to pull out of our bag of tricks to make real music.
Understanding that music is a language, I don't believe we could say that there is a correlation between those who are excellent in learing different languages with those who have an affinity for music; or that great writers make great musicians or composers. I have a friend who is a phenomenal flutist who cannot keep a rhythm to dance - more like three left feet.
Of course there are similarities to music and mathematics. What then is the explanation for so many physicians and dentists being excellent amateur musicians?
This is just another thought on the subject.
Happy holidays.
Ron
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Author: Contra
Date: 2004-12-24 22:36
I prefer to think of math and music as two seperate activities with just a little crossover when transposing. Any more makes my head hurt.
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Author: Bart Hendrix
Date: 2004-12-24 23:53
I have read a couple of studies (sorry, I don't remember the references) that show a positive corrolation between students who participate in music classes and their general academic performance. That would match with my anicdotal experience starting in elementary school, through college, and now through nearly thirty years of teaching high school. Unfortunately, there was nothing specifically relating to math skills in the studies. My own experience is that high achieving students tend to be high achieving in most or all areas. That may open another can of worms about attitude, family support, etc. that does not belong on this BB.
On the other hand, I have a very good friend who is a retired high school music teacher and former professional musician (second income) and one of his college classmates of similar background (my own high school music teacher) who are/were nearly illiterate when it comes/came to anything mathmatical. Although I have never been in a class of the former, the latter insisted that we learn a significant amount of music theory (enough that the class in college became a piece of cake) and conveyed many concepts that could easily be viewed mathmatically without ever viewing them that way himself.
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