DawgTalkers.net Forums DawgTalk Everything Else... Music and Math

Some of you know that I was a Mathematics teacher and love the discipline. Others know that I enjoy music, but am completely ignorant of the discipline.

I listen to music almost all day long. I have always heard the "math" in music, but never pursued it. Anyway, I did a bit of research and came across this right off the bat. Tell me what you think.........Oh, and you experts--guys like Clem, ddub, lamp, Portland, Diesel, etc.....please help educate me and anyone else who wants to know more.



Here is one more:



I find this fascinating. I am a bit apprehensive about posting this because Clem and the other guys might laugh at me for my ignorance on the subject. I mean, this might be common knowledge and I am making a big deal of it.

Oh well.......I just think it is really cool. And if anyone else enjoys mathematics, I will post more interesting things about the subject, such as prime numbers and how they relate to the universe.

I do think it is interesting with all the places that math turns up.

Unfortunately, Intuitive Calculus is killing what little enjoyment of Math that I had. Trying to learn implicit differentiation with a professor that uses the general power rule and then calls it the chain rule was rather confusing there for awhile.

Sorry to hear that. A lot of college profs are the worst teachers. I remember the old phrase from them: "it's a great place to work except of the students."

Most are there for to research and publish. Don't let them get you down. Math rocks!!! Heck, collegiate learning is awesome. I really miss those days. Massaging the mind was so invigorating. Sure beats the rut that everyday working life presents.

Vectoral Calculus here. I had to take it twice. The first class had 200 people in an auditorium. The instructor was Viet Namise, and sounded like he just got off the boat. As I have a sort of hearing problem, it took me three weeks to understand him. By then, I was too far behind to fully recover.

The 2nd class had about 30 people, and the instructor walks in. He looks to be the average white guy, so I was relieved I'd at least be able to understand what he was saying. The guy was from the Highlands of Scotland, and sounded like he just got off the boat. After figuring out the burrs, growls, and spits, I was only two weeks behind. I managed to pass the class, but just barely. The final was a (insert words I can't type here), but I got most of it right. The test had one question, and you had to show your work.

I understand the mathematics in music, as I also played. I wasn't that good, but I understood it all.

My late father was a college math professor who taught at both the bachelor and doctorate level. I never got into higher math, but basic math has always come rather easily to me, so I imagine I may be genetically predisposed to understanding math. I chose other roads, however.

Later in life, I am finally pursuing my lifelong fascination with astronomy, and I wonder if, had I pursued math and science when I was in college, could I have been part of the explosion of knowledge that is currently happening in cosmology. I try to keep up with all the latest discoveries, but alas, I don't understand the math that drives it.

One of my Science profs was from Vietnam. He used to tell us how dumb Americans were and I can still hear him say: "Not my problem."

Edit: Hey, I would appreciate it if you wanna educate us on any of those topics.

Did your dad's mathematical prowess intimidate you? My dad was very old-school. I was always the best kid at math in school, but my dad made me feel dumb. LOL...Amazing.

You mentioned that math came easy to you. My kids and I were talking about math this weekend. Both are better at it than I am, but anyway, we all think that society makes math harder than it is. For example, it's perfectly acceptable to say: "I suck at math," and people say, "me too." The patterns in math have always amazed me. It really helps simplify math. I realize that the higher level math fields are complex, but basic number sense is really easy. Like I always told my students: "numbers are your friend."

Anyway, this thread probably wont have much life. Too geeky and not controversial enough, I guess. I just think it's really cool how math influences so much of our lives.

My calculus professor is Eastern European. His accent is pretty understandable to me, but at the same time you can tell he can't always find the right words to explain something the way he wants to. He makes me think of Count von Count from Sesame Street.

I have always been good at math, but then it always made sense. Now I'm being given formulas, but not being shown the proofs that would really make them understandable.

The fact that I took a 10 year break from math/school and am probably taking too many courses this semester (while spending way too much time on the draft) most likely doesn't help.

No, my father had a way of making things logical. In the summer of 1967, when I was 12, my father took me with him to work on several Saturdays. He was in charge of Western Reserve University's (one and only) computer which took up the entire 2nd floor of a wing of a building and was less powerful than your cellphone. He spent about an hour programming the beast with punch cards so that I could play a (text only) baseball game against the computer. (Yes, I was playing computer games in 1967!!)

My problem wasn't that I was intimidated, my problem was that other things in life fascinated me more. Studying bored me, so I didn't do much of it.

Interesting thread. I was always really good at math and I'm not really sure where it came from. This was during a time where I was not a good student, I wouldn't do my homework or pay much attention in class. I was one of those talented but maddeningly frustrating students for a long time.

It's interesting where math turns up. For example, poker really took off in popularity a little over ten years ago. Many people think the most important things in poker are having guts and making big bluffs while maintaining a good poker face. Those things do play a part but at its core, poker is fundamentally about game theory and that's basically just another way of saying math. A person with a good intuitive grasp of math has a huge advantage in poker even if they are not explicitly working on odds in their head at the table (usually the underlying problems are so complex that doing so would be impractical anyway. Pot odds and such are easy enough to keep track of but knowing exactly what to do with them becomes a lot more tricky).

Or take football. One of the reasons I find teams' 4th down strategy to be so aggravating is that it is so obvious that coaches overvalue field position and undervalue offensive possessions. This is a unanimous or near-unanimous position among people who are really good at game theory and has been shown to be accurate time and time again with analytics, simulations, game models, etc. and the teams still lag behind. Even simple intuition should tell a smart person that punting on 4th and inches is almost always moronic.

There was some talk about the importance of nutrition in another thread. 'Nutrition' covers a wide range of topics although I'd argue that for somebody who is obese, the most important thing is to simply get that weight down. This requires some knowledge of Calories, macronutrients, etc. I'm no fan of counting Calories myself although many people really do need to do it just to get a grasp on what they are eating. Fat is ~9Cal/gram, Carbs are ~4cal/gram, Protein is ~4Cal/gram and a moderately active person might maintain their bodyweight at about 14Cal per lb. bodyweight. Fat loss diets would usually be 12Cal/lb. or less. This requires some degree of math to figure things out although my experience is that only a small percentage of people have both the knowledge and the ability to apply it. That knowledge could help a lot of people though.

A random thought: I question the math curriculum in schools where the subject usually gravitates to calculus. I think it should gravitate toward probability/statistics as the latter is more useful across a wider range of subjects. Of course that's not universal; some careers depend upon an understanding of calculus.

Thanks for the videos. It's at least somewhat plausible that people would go "math and music, how does that work together?" although it's obvious once you see it plainly.

What shocks me is how many computer programmers I work with tell me they hate math. Especially video game programmers. The whole point of a video game, or movie special effects, or architectural visualization is to take something from 3 dimensions and plot it to 2 dimensions. As an exercise a few years ago, I decided to perform this in a web page so my colleagues could understand how modern graphics architectures work: https://dl.dropboxusercontent.com/u/41766532/rasterizer/rasterizer.html

If you right click in the white area in Google Chrome and select "View Page Source" you can see the code for how the triangles are drawn. I'm sure as a math teacher you may have come across terms such as barycentric coordinate spaces, matrix determinants, etc. In a more simplified sense, all 3d graphics (games/movies/etc) do something like this:

- Given a triangle in 3D space:
-- Transform vertices from 3D space into viewport space using 4x4 matrices (3x3 for rotation and scale, with a position encoded in the final row)
-- For each potential pixel on the screen, determine if the pixel should display the triangle
--- We optimize this and test for depth, to ensure triangles don't draw on top of each other incorrectly
-- If the triangle is at this pixel, calculate barycentric coordinates and pass these coordinates to a shader
--- I use these coordinates in my example to place a 2D image onto the triangles, giving additional detail.

My day job tends to offer a fair bit of linear algebra

NRTU:

Good stuff, guys. Thanks for sharing. Just a few comments:

--Someone mentioned theory and abstract thinking. I love that type of thinking, but as a teacher, I have come to realize that many don't see things that way, so I have really made an effort to use more concrete and representational examples before moving to the abstract.

--Then, there was the comment about calculus vs Probability/Stats. I really like that idea because of the practical side they bring. Statistics were always my favorite classes in college. Well, that and literature. LOL

--I hope some more of our musical friends will weigh in on this topic.

--Gage! I'll shut-up and you keep talking!!!

Along those lines, in college my calculus prof. was from Costa Rica. I could tell you his name to this day.

Nice enough guy. (he did have 2 thumbs on his right hand - it was kind of distracting - but, short of surgery, nothing he could do about it, I know).

20 kids in the class. His accent was so unbelievable - seriously, often times after class, he'd walk out and 20 of us would sit there asking "So, what did he say? What are we supposed to have done for next class?" etc.

On the last day a student could withdraw from a class and get a "W" for a grade (instead of an actual grade), he told a number of us: You are failing, and I don't see how you will get anything but an F. This is the last day you can withdraw."

And trust me, it was all we could do to even understand him on even THAT.

I went from that class to the Dean's office and withdrew, as did the others.

Turns out that was the last class he taught. The college learned of the language barrier and pretty much told him he needed to become better in English.

Now, I wasn't ever "great" at math, and I certainly don't blame him for me withdrawing.

This wasn't college .... but back when I was in High School, (9th grade) I had a math teacher who previously taught advanced math in college.

He walked into the classroom, and lost the entire class from the word go. He threw up formulas, never explained a one of them, and acted exasperated when we just didn't understand what he was teaching. Not one kid passed his 1st or 2nd exam. We all failed. He was teaching advanced college math to 9th graders, and none of us were prepared for that.

Most of us kids complained to our parents, and many called the school, but it got nowhere until every kid in his class got an F on their 1st report card.

IIRC, he left after that 1st year to go back to college.

Especially early on in IT, a lot of programmers were pulled from the music department due to the correlation.

Then why do we have so many really bad, annoying musical themes on our computers?

Because that was a long time ago. Musicians tend to stay in the music department now... lol

Some of the early video game music was pretty darn awesome for the limitations they had to work with.

Patterns, analogies, rhythm, sequence, compare/contrast and categorizing are skills that are everywhere in life!

It's almost like life was created that way .......

I lost my rhythm twice... hence two kids

I know its not math but I had a childhood friend that could play any instrument, he could pick it up and start playing it.. I asked him once how it was possible and he said it came to him once in a dream that all music was like a wheel and always came back on itself.

Actually it is like math (geometry)

ye old 'circle of fifths.'

ah, the memories...

I was always great at math, but when it comes to music I have two left ears.

I have read this a few times before. What is the connection there? Like what skills from music transfer over to programming? Those are genuine questions btw

I'm not a music guy in the sense that we are talking about here. I just seem to listen to music and know what I like, for example I think that Metallica sounds awesome but I couldn't really tell you why. It just gets me going.

I'm an awful singer and dancer though-- I guess you could say I don't have good rhythm. Then again I have not put in any effort or been in any formal music classes since middle school, so that probably plays into it some. It seems like it comes naturally to a lot of people though so I don't know.

Back to programming-- learning programming was actually a hobby/side project of mine for months and I picked it up quickly. I understand how things fit together if you will. I've gotten sidetracked on that but I will pick it up again. I guess I'm curious how an understanding of music would affect and benefit that pursuit.

Skills I'm not entirely sure, but I can see some relation between music and programming. My programming background stretches for roughly 20 years, while I only played guitar in high school, so I may not be the best for this.

- Both music and programming deal with a very abstract concept.
- Both programming and music are lessons in failure long before they are lessons in success, limiting the number of people who would commit to either task.

And a common thread from an outside point of view: Most people don't care if a popular game or app was made by good programmers, and most people don't care if a popular song was written by a good musician. Yes people in the industry care, but we've already drank the kool aid Is a businessman or plumber going to care that one song was sung in a difficult octave? Not really. They just want to know if it sounds good to them. Just like those same people won't care if I wrote my game in C++ or C# or Javascript, as long as the game is fun to play. There's a large disconnect between actually "doing" music and programming and those who consume the medium.



Keep at it, it's a lucrative field and good programmers are in very high demand. A company 30 minutes from here for instance wants to pay someone $195k a year to manage their software team. Maybe not wall street money, but that's huge cheddar IMO, especially for northeast Ohio. I get anywhere from 6-10 headhunters a month contacting me, so the demand is definitely out there.

You're the first person who ever called me an expert on anything lol but I won't be able to offer a lot of insight. A lot of of the stuff in those videos was above my head, but I do think that math can apply to most everything. BTW the guy in the second vid had a sweet-sounding guitar. If my wife ever lets me buy another guitar it'll be a hollow- body similar to his.

I know some music theory but never really thought of mathematics as it would pertain to music. Instead I hear the notes, and think of it as a language, notes being strung together to form a "thought" much like words form a sentence. Hit a bad word - or note - and the message is jumbled.

If we are in the key of C, I know where to find the third, fifth, seventh and so on haha. And I also count in my head a lot when I play, but much of it is feel when I play, but try to match experience with instinct: in other words, when I know where I'm going I know how to get there (mostly).

I always disliked math in school but I have can do basic math very fast - not that it matters much.
I have enjoyed reading this thread.

When I was a li'l kid (grades 1-3), I HATED math. It was just too esoteric for me to understand. I was befuddled by it. It never made sense at all. When I hit 4th grade, we started to learn fractions...and I was totally lost. I started 'checking out' during Math section, because I couldn't grasp the concept of "parts of a whole."

I felt stupid.
I felt like: "I'll never get this- I'll NEVER understand it. What's the use of trying to get this crap?"

Until then, I'd always been attracted to the 'smart kids' at Roosevelt Elementary... and they were cool with letting me hang around them. I learned almost as much from hanging out with Kevin Lowry and John Jensen on the playground as I learned from Miss Sortland, Mrs. Jenkins or Miss Neely. (Kevin's Mom was a 6th grade teacher at our school. John Jensen was a 'child savant'- an intellectual heavyweight far beyond my intellectual acumen. Both were social leaders in our little social sphere). When I got to 4th grade... the gap started to widen.

I began distancing myself from the academic-minded friends I'd always enjoyed in grades K-3. I was becoming one of "The Dumb Kids"... right before my eyes- and it seemed that my dye was cast. The 'Smart Kids' were moving on... and I was getting stuck in the mud. I just couldn't keep up, no matter how hard I tried. On the playground, I started gravitating toward guys like Kenny Hughes and Terry Robinson, instead of Kevin and John... and they didn't seem to miss me. (Kenny and Terry were budding 'hood rats,' Both ended up "doing (major) time" at state institutions. Both lived within 3 blocks of my house, and we all played together as kids.)

Miss Henry (my 4th grade teacher) didn't help things at all, when she called me out in front of the entire class on the first day of school, and said: "I already know about you from the teachers who had you before me. I'm going to make an example of you for all your classmates."

Mary Henry's public proclamation (in front of the entire 4th grade class) was 1 month before I went to a general assembly, and saw some big kids from the local Senior High School play some string instruments in our Gymnasium. The instant I heard that high school kid play his notes on a cello, my life changed forever. I instinctively knew that I just HAD to get my hands on that magical thing.

(There is an entire thread's worth of personal anecdotes/stories around my acquisition of that first, cheapass plywood cello- but that's a story for another thread/time...)

My main point in all of this:
Within 2 months of taking up the cello, I'd discovered the concept of making music in 4/4 time. 3/4 time. 6/8 time. All of a sudden... FRACTIONS made sense to me- and 4th grade mathematics wasn't such an intellectually daunting hurdle.

Music-making became the instinctual, physical, 'hands-on' link between what I couldn't intellectually grasp (at the hands of Mary Henry) to what I COULD understand (at the hands of Bert Blair.)

Some kids learn perfectly well by being taught in a classroom by autocratic, simple-minded, dictatorial, uninspired "Johnny One-Note" teachers. Other kids learn by doing... while being guided by nurturing, insightful, thoughtful mentors. I was lucky enough to find the right teacher, with the right message... at exactly the right time. Math made sense to me ONLY after I found Music.

I was one of those li'l kids who actually had to literally put math in his hands to make sense of it.


Vers: It's entirely possible that you & I might not even know each other, had those circumstances not slammed together- at exactly the perfect time in my life.

______________


At a pivotal time in my life, Music saved me.
It yanked me from casual associations with kids who later became recidivist members of 'The Incarcerated Class' of American citizens... and led me to a path that landed me on the steps of the American Capitol, a shared stage with some of Classical Music's all-time luminaries, and an exalted place on the stage of Carnegie Hall.

And, hey: I've also been some places that Kevin Lowry and John Jensen have never been... some of those places are well above what they ever could have dreamed for themselves- and some far below. Bringing oneself up from the fringes of society makes for a lively story, with many twists and turns. I should write a book, Dawg.

_____

I learned fractions because I took up the cello. And I'm speaking to you now (from a place of victory) because Music & Math came together... for a child of Parents who were too poor to even buy a ticket at Carnegie Hall.

Good thread, Vers.
I'll talk about "Math & Music" in my next post(s).

Tonight, I thought it was more important to talk about the intersection of Math & Music, as it pertained to my own Real Life's Experience. I hope you don't mind.


Perhaps later, I'll talk about Mendelssohn, Johann Sebastian Bach and Arvo Pärt.... and how their use of 'numbers in music' led to some of the most beautiful music Mankind has ever written....

And maybe- just maybe- I'll tell you Dawgs how My "Mary Henry Saga" came full-circle, when I was 17 years old....


...but for now, let me tell you this:

There is a very real and personal story attached to the significance of 'Math In Music'... and my entire life is living proof of that connection.

It would be cool if we ever met. You could explain some of the nuances of music and I could then help you w/math because I can almost guarantee that they are connected and I bet the light would go on for you. Plus, I would get to learn all kinds of cool stuff.

Sorry if those videos were too high brow. Do your own search on it. I bet you'll find it interesting.

Clem, you never cease to amaze me. I have so much respect for you as a person, a writer, and a teacher. I am hoping you--and others--continue to educate people like me that love to learn. I want you to teach me--and others--as much as you have time for.

I'm going to jump off track [just a bit] and respond to a comment you made. I have some experience there and I'll share, but I don't want to change the premise of the thread. It's just a connection and an aside.



Man Clem. That's awful. We are about the same exact age and we both know that a lot of teachers back then were harsh and actually discouraged critical thinking rather than celebrating it.

I was kind of a rebel in school. Imagine that? LOL I remember often being shut-down when I tried to get the class to look at things from another perspective. For example, I would question if the "Indians" really were the savages during the expansion of America. That was not acceptable thinking when I was a kid. I thought it was wrong for women to be burned at the stake for not following the Puritan way. I thought that it was hypocritical for white plantation owners to have relations w/black women and then go in and read the bible. I thought it was more important to know why the Romans built Hadrian's Wall and what were the consequences of the wall being built as opposed to what year did the constructing of the wall begin. Dawg, you know that my line of thinking was out there in the early 70s in Small Town, Ohio. LOL

I remember sitting in class one day after being scolded for not being a true American for siding w/the "Indians," and thinking that if I were to ever become a teacher, I would welcome opposing opinions, encourage debate, embrace diversity, and motivate my students to strive for critical thinking.

Not long after that, I was in Algebra class and my teacher hated me because I had long hair and I was a jock. I didn't fit the mold. He would mock me by calling me The Little Drummer Boy because he said I beat to my own drum. Anyway, a girl next to me was struggling w/one of the formulas. She whispered that she needed help. I started explaining it to her and all of a sudden, someone jerked my hair HARD from behind, snapping my neck back. I jumped up and saw it was Mr. M. I laid him out w/one punch. I was so scared. Unsure of what to do, I ran to the Vice Principal's office and started yelling that I knocked Mr. M down. LOL.....I was punished big time, but I knew then that I was going to be a teacher if my NFL career [I yi yi yi] didn't pan out. I swore to motivate kids rather than kill their spirit.

Which leads me to:



Yeah, that's awesome.

Like I said before. I love abstract thinking and it comes naturally to me. However, I know that many people need concrete and then representational examples before moving to abstract thinking.

I also try to find what interests kids. I had one kid who loved baseball but struggled at geometry. Man, I had him research major league baseball stadiums. We discussed how the diamond shape of the field was created. Wall angles, especially at Fenway Park. How the bases form angles. The curvature of the infield dirt and outfield grass. The shape of the plate. Pitching rubber. Etc, etc.

Other kids loved who struggled w/fractions, percentages, decimals, mean, median, mode, and range... were allowed to investigate sports in areas such as free throw percentage, batting average, yards per pass attempt, etc.

I encouraged cooperative work rather than pulling someone's hair for helping other students. I wanted kids to think about a situation from every possible angle rather than just playing follow the leader. Learning through inquiry rather than rote memorization. Student led discussions rather than lectures. There is not one teacher in the room. Instead, there are 25 teachers in the room. I want kids to have to justify their answers and explain how they arrived at an answer. I want others to analyze and evaluate what the other student is saying and then either support that answer or critique it in a constructive way. The key is to get the class to feel comfortable enough to express their opinions and ideas w/out feeling threatened.

It's so freaking amazing to see these kids grow academically and socially. To see the shyest kids challenge the most popular kid's ideas and not feel threatened. To see them so accepting of each other's ideas, opinions, and challenges. Man Clem, I am tearing up just thinking about it.

I feel the passion in your writing when you speak about music. I have the same passion for education. Helping a young person grow has got to be the most rewarding thing on the face of the planet. No offense to anyone else's profession.

Bro, wouldn't it have been great to have you visit my classroom and we could have down an integrated lesson involving math, music, and history? And then have them write songs and essays about what they have learned? Man.......how sweet would that have been?

I did similar things w/the Harlem Renaissance, Latin music, Native American chants, etc........but to have an expert like you come in would have been grand.

Sorry for the diversion. I'll shut up now and you guys PLEASE continue to educate me on the topic. I do love to learn.

Too tired to write tonight. Instead, I'll share an example of math in music. It's a piece I just started working on. "Fratres," by the Estonian composer Arvo Pärt. It's a set of variations all based on the same 8-chord sequence.

Some variations (like the first one) are quite frenetic... and run 4 times faster than others. Some are slow and almost tortured-sounding.

And then, there's the section at 8:44, that takes the cello from its low notes to pitches in the ultra violin range, using those same harmonics that were mentioned in your first video. The section at 10:00 is astounding. It's done by a technique we call 'artificial harmonics." The cellist stops the string HARD with his thumb or first finger, then touches the string very lightly (like brushing a loose eyelash from a baby's face) a Perfect 4th above the stopped note. What comes out is the stopped pitch- but TWO FULL OCTAVES HIGHER!

I think it's just beautiful... and it doesn't take a degree in music theory to easily hear the mathematical relationships at work.

Turn your speakers up
turn you lights down
And take a 12-minute trip into something that you've never heard before. It's hypnotic and deeply satisfying.

https://www.youtube.com/watch?v=FkHEjiuYBuM

(for some reason, my browser won't embed the video here... I've been having problems with it for about a week or so)