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Science Music & Mathematics 101 

Science

Written for Canadian Community News by Mike Sterling

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My new friend Dr. Eli Maor and his wonderful wife Dalia (without the h) have influenced me a great deal. (Click Here). 

One of Dr. Maor's writings moved me to try to understand music from a mathematical foundation.  It's been a rewarding journey

From time to time when people ask me:

"Mike, what are you working on this year?"

Over the past 18 months I've answered by saying:  "I'm working on another  instrument based upon some beautiful mathematics that has not been exploited before in a musical sense.  I'm hoping to have it be visually beautiful and functionally interesting." 

The questioner usually does not want me to go much further because it can be time consuming for both of us.  It's not a good elevator conversation.

Most of the time as an aside say:  "Music is highly Mathematical" Both of us leave it at that for another day. 

It's a good line to shut me down as they cautiously back up, reaching for the door handle behind them.   The next line often is "I've got to let you go"  Ditto!

It often puzzles me.  What do they mean? What exactly do they think is mathematical about music?  Is there a secret they've found taking  guitar or piano lessons or something?

I've found that most don't mean anything at all by saying what they do.  They've just heard it from from others and picked up hints along the way.  Sometimes they mean timing and beat.  Sometimes pitch and harmonics.

It really does not matter because they enjoy what they enjoy.  We can't study everything in depth.  In fact I can't think of a single thing that gives as much pleasure with less effort than music.  It would be good, if we all had a bit more of a grasp, however.  I think we all can learn a bit more.

Dr. Maor in his next book will probe the real meaning of the connection between mathematics, physics and music.

The manuscript is at his publisher's now beginning an 18 month journey to bookshelves.  His last book concerned mathematics and art.

His books get peer reviewed by experts enlisted by Princeton University Press.  When they come out, they are devoured by a loyal readership.  They set a high standard.

He gives some hint as to why he is writing a book on Mathematics and Music in his gem 'The Pythagorean Theorem, a 4000-year history.' (to purchase this book or Dr. Maor's many books click here)

Dr. Maor gives us some hint of things to come in chapter 16.  Here is what he says:

Click the orange arrow to read the second column

"So what is mathematics, really?  I think the essence of it is the search for pattern, for structure and regularity, and for connections between seemingly unrelated objects, whether "real" or abstract.  In this sense it is quite akin to art, to music in particular."

He illustrates this by showing a table of Integrals. (a part of Calculus).  Calculus is kind of the gate keeper to further study in physics, engineering and mathematics. To the trained mathematical eye, patterns and variations leap off the page of Integrals.

He then shows the opening page of W.A. Mozart's Piano Concerto no. 16.  To the trained musical eye patterns and variations indeed come forward.  I can see what he means, but I don't have a trained eye.  I don't see what the expert sees.  I've devised my own methods of seeing and I'll go into that further. The Integrals are clearer for me.  In fact they simply jump out at me.

What triggered me to write this article comes from the desire to know more about music.

I've been working on a harp like instrument.  I was curious about the shapes of classical harps of which mine is not an example.

So, not resisting the urge to know more, but hoping to enjoy it, I asked myself this morning:  "What is the reason the harp is shaped like it is?"

Google might know.  I got levels of response with degrees of nonsense mixed in with truth.  We'll explore that question in #102.  Stay tuned.


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Sunday, January 04, 2015