The Magic and the Math of Music

To be honest, it’s challenging for me to talk about music.  Not because I don’t want to or don't enjoy it, but rather because I struggle to find a balance between two extremes.  On one hand, it feels too mathematical and simplistic to slap concrete images and labels on music and sounds which we can’t smell, feel, taste, or see. "That sounds dark," "this sounds sweet," "make it smoother," "Make it sound like there's peanut butter on your bow!!"


And yet these are the terms that many musicians are forced to use, for ease of recognition and speed of imitation.

Metaphors abound comparing tone to flavors of food, timbre to shades of colors, and harmonization to inclement (or serene) weather. I’ve heard some juicy ones that I still can remember over the years. It also helps that musicians (for the most part) love to eat and drink. So I often instinctually describe music as “marinating,” “sizzling,” and I look forward to hearing “what’s on the menu.”

On the other extreme, nothing grinds my gears more than the box office blockbuster movies that ascribe WAY too much emotion and potential to the power of music. These movies are usually really heavy handed on the emotions, and skimp on the practicality and grind of becoming proficient. I mean music is amazing, but you still need to eat, sleep, and pay the rent. And also mental disorders are not going to get better by practicing more Ševčík (it will probably make things worse!)

via MEME  (No musician was consulted in the writing of this script)

The point of all this is that despite the sand in my gears and the mouth watering distraction of some tacos in my near future, I came across a quote by Alexander Barantschik, the concertmaster of the San Francisco Symphony that beautifully captures both the art and science of music making. 

“A great violin widens a player’s horizons and creates the possibilities of producing different sounds and shadings. The value of the instrument is in inspiring each player to search for wider possibilities. Compare a painter who has 20 colors to use with one who has 200 different shades—you can imagine how the two paintings they produce might be different.” 

Photo Courtesy of the San Francisco Symphony



I enjoy imagining what you are picturing right now-what your painting with 20 colors vs. 200 colors would look like. This invitation to dream about what you would create is so compelling, and that spark of creativity.

And yet, Barantschik is completely practical and recognizes that the tools we use play an important part as well.  Why use 20 colors when you could use 200? Why drive a VW bus when you could drive a Lamborghini? Sure, it’s easy for you to say, Mr. Moneypants!

To fill in some context, Barantschik has the insanely good fortune to play the Guarneri Del Gesu of 1742 that was played by Ferdinand David (who premiered the Mendelssohn concerto), Sarasate, and was the main instrument played by Jascha Heifetz. This violin is not only dripping in violin lore, but it’s also one of the most scientifically studied and replicated instruments.   

Violin makers all over the world use the recorded dimensions of the “David” Guarneri as a template for their modern instruments. While there are far too many variables to completely duplicate the instrument, that’s not really the point. 

I believe these replicas of iconic instruments have to be enjoyed from both perspectives. The measurements of the wood, the varnish, and the craftsmanship all matter. But the creative history and homage to the masters has value too. Can you imagine what would it be like to own the same violin that played the Mendelssohn concerto for the first time?

So yes, playing and talking about music requires a little woo woo-just believe and listen to the colors of the rainbow all around us.

But and it also takes some scientific and measured consideration for what’s working, what’s not working, and how to fix it.

But it also requires that you close your eyes, through your inhibitions to the wind and let the music flow through you. 

But do that with your tuner and metronome going.

Well, you get the idea.

Be well and practice well




Michael O'Gieblyn

@VT You’re very right, and I should have mentioned more about the actual math, and the actual science of the Pythagorean tuning system. Thank you for including that.


Thank you! Beautiful!

Mark Cobb

Very well thought out essay Mr. Gibbles. Very nicely done.
I was raked over the coals by a music teacher for telling an online group of new learning violinists not to compare themselves to the teachers and musicians they see on you tube, playing with 20000 dollar violins, using 2000 dollar bows to teach and play. Considering most new students are starting out with instruments way under 1000 dollars and whatever free bow came with it, it’s an easy way to discouraged. I was told there must be something wrong with my technique because all violins are basically the same. This is a schools music teacher, that eventually got extremely nasty, after I declined a music “battle”, her words, for saying that there is nothing wrong with my technique, I own more than several violins, and no 2 violins are the same, which means no 2 violins are equal, and many are vastly different, some unplayable.
I have a violin to fit whatever mood I’m in, to fit whatever music I want to play. I have a ming 905 that arrived today that I am super stoked to get home and pick up.
Violin is a means of expression, each person must find the best way to express themselves. I reccomend fiddlershop for the easiest transition into the perfect violin for the player.
Please post more G, your insights are fascinating.


My piano teacher once told me that Mr. Pythagoras believed that mathematics could explain music as well. While Pythagoras’s belief does not seem sensible – in terms of describing the quality of music, his mathematics does have tangible values in determining the quantity of music pitches. In other words, his math still guides the way we tune most of our instruments. Therefore, I’d be inclined to believe that maybe there exist certain links between mathematics and music, which we – human beings – have not yet fully comprehended. I also specifically like the thought that Pythagoras believed planets also make celestial music which could be calculated by math but which is not (yet) perceivable by us, the Earth-dwellers! How else can we explain symbolic images of Angels playing harps, violins, or psalteries? Perhaps everything – even the quality of music – could be explained by mathematics, but we – the mundane beings who eat too much tacos or whatever dishes – are not sufficiently conditioned to cogitate those highest mathematical levels!
I could go on, but now my lunch break is done, and I need to get back to being a mundane being…so my philosophical thoughts must stop here! :)

Tom Bolt

Sigh! Elegant essay. I have a knock-off Steiner I am desperately attempting to bring back to life. Most all my concerns have been addressed but for the life of me I cannot access information regarding string height from the fingerboard so I may make the proper bridge adjustment.

Ken Porter



Nice little piece. Thanks for sharing your thoughts. I agree completely about both extremes of music, and have the same hard time with reading (or hearing) people speak in either way entirely. The truth about hearing and playing music is somewhere between the two. Thanks for the welcome moment of distraction and contemplation!

Mac McCord

Thank you for this! I generally work from the woohoo side but realize the synthesis of music and math is what makes music so meaningful.

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