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**A Magic Beyond**

January 19, 2017

"Ah, music, a magic beyond all we do here." - Albus Dumbledore

(Harry Potter & the Sorcerer's Stone)

Musicians and other artists are a bit like the wizards and witches in the Harry Potter series. We don't have "supernatural" powers so much as we have a special and sometimes eccentric way of experiencing and relating to the world around us. This space is where I will share a bit about how it works for me. It won't be just about Native Flutes or music or Native issues, although it sometimes might be. Other times, it might be about interesting things students say that I hadn't thought about before or some book I love or what's going at the nature center where I do volunteer work from time to time.

A Musician Listens to Harry Potter, Part 1

Since the name of this blog was inspired by the wisdom of Albus Dumbledore, the first entries will be

a series of articles that can be thought of collectively as, “A Musician Listens to Harry Potter”. To clarify, “A Musician Listens to the Harry Potter books, not the movies.” The movies are enjoyable and entertaining. The books are necessary. And, in some ways, the books are more musical than the movies. They are full of imaginative soundscapes and evocative descriptions of aural events. They are also full of the kinds of large scale rhythms and structural resonances that many musicians love.

More on that later.

Let’s start with number. Music can be thought of as beginning with rhythm and resonance, the proportions between durations and frequencies. Musicians use number to express these. “The 3rd beat of measure 49 should be a D7 chord”, for one example. “The pitch that is a perfect 12th above the fundamental is vibrating 3 times as fast”, for another. Don’t worry if these numbers mean nothing to you. They are here just to show that musicians find numbers to be very useful in communicating to each other and in trying to verbalize the musical experience. So, when I notice an author using numbers in consistent ways, my ears start to tickle.

Many people have offered interesting insights into significant numbers and number patterns in the Potter series, particularly the number 7 (7 Weasley children, 7 obstacles in the Chamber of Secrets, 7 horcruxes, etc). That digit is part of the number that was a rabbit-hole for me. Harry’s birthday falls on the 31st day of the 7th month. Whether you express it in the common European style, 31-7, or in the common American style, 7-31, it has some interesting properties that resonate throughout Harry’s journey. Since Harry is Brit, let’s use 317.

I am a musician, not a mathematician, so please excuse my clumsy definitions, but a Prime number is a whole number which can only be evenly divided by itself and the number 1. 1, 2 and 3 are all Prime numbers. 4 is the first digit that is not a Prime number. There are many Prime numbers - 317 is one of them. This is a curiosity, but not especially interesting in and of itself.

Musicians like taking a simple idea and messing with it. What does it sound like if I play this melody backwards? Musicians call that retrograde. How about upside down (inversion – of the melody, not the musician)? What if I change the order of things (permutations)? What if I break this melody into bits and make new melodies out of the bits?

If we do some of these things to 317, its special magic quickly becomes clear. Not only is the number itself a Prime, but each of its individual digits (1, 3 and 7) is also a Prime. The sum of its digits (1+3+7) is 11, also a Prime number. Any combination of two of the digits in any order creates a Prime, i.e., 13, 17, 31, 37, 71 and 73 are all Prime numbers. Three of the possible permutations of the three digit number generate Primes, the original 317, as well as 137 and 173. The other three possible permutations, 371, 713 and 731, are all Products of Primes, meaning they can be expressed by multiplying two Prime numbers together. They have other properties, too.

731 is the product of two Prime numbers (17 X 43). It is also the sum of three consecutive Primes (239 + 241 + 251 = 731).

713 is the product of two Prime numbers (23 X 31) and is also the sum of three consecutive Primes (233 + 239 + 241 = 713)

371 is also the product of two Primes (7 X 53), and is the sum of all Primes from 7 through 53. It is also the sum of the cubes of its own digits. (33 + 73 + 13 = 371).

How’s that for a magic number? And for some very musical style number play?

If this were an isolated thing, we still might ask, “so what”? But did any of the numbers that passed by seem familiar? Say 713? It is the retrograde of 317 and the number of the Gringotts vault where the Sorcerer’s Stone is hidden. 11, the sum of our magic digits, is Harry’s age when he enters Hogwarts. 17 is the age when Wizards become legal adults (not the mundane non-Prime 18 of the Muggle world). 17 is also the number of Harry’s hotel room during the Dursleys’ flight from the letters in “Sorcerer’s Stone”. In the rescue sequence at the end of “Prisoner of Azkaban”, we learn that Sirius is being held in an office which is on the 7th floor, 13th window from the right of the West Tower. I could go on, but you get the idea.

The use of the individual digits, especially 7 and 3, has been discussed in many places and doesn’t need to be repeated here, so let’s continue exploring other uses of Prime numbers.

There are 29 (Prime) Knuts to a Sickle and 17 (Prime) Sickles to a Galleon. So there are 493 Knuts to a Galleon (29 X 17, a product of Primes). At yet another level of resonance, does that last set of digits sound familiar, Hogwarts Express riders?

In the famous textbook, Quidditch Through the Ages, we are told that there are 700 ways to foul in a Quidditch match and they all happened in one match in the year 1473, which can be expressed as a product of Primes (3 X 491 = 1473). The number 491 itself has powerful magic. It is a Prime and its digits are the squares of the first three Primes (1 X 1 = 1; 2 X 2 = 4; 3 X 3 = 9). All possible three digit permutations are either Primes or can be expressed as the Product of Primes. All possible two digit permutations are also Primes or can be expressed as the Product of Primes. It’s almost as powerful as the 317 set.

Again, I could go on, but it might be more fun for you if you did. Taken as a whole, it’s difficult to dismiss this as a happy accident. It seems to be an elegant device that Prime numbers and variants derived from them provide a sense of unity and resonance in the Wizarding World. Is it any wonder that the Dursleys live at #4 Privet Drive – the first non-Prime digit?

It’s good fun to look for relationships like this and to label things. But as I always ask my students when we are listening to music and labeling things, why do this? Is it just playing games? Just “books and cleverness”? Or are there deeper resonances to consider? While it certainly seems that the use of numbers in the Potter books is intentional, I would not presume to speculate about why Ms. Rowling chose to do it so consistently and in so many imaginative ways. But here is a way of thinking about it that resonates for me.

The special quality of Prime numbers is that they can only be divided evenly by themselves and the number 1 (one). They are a beautiful metaphor for unity and love. Harry emerges at the end of Deathly Hallows healed and free because he keeps his soul intact and because he has the courage to love. He is an embodiment of his birthday number and the other magical Primes that are sprinkled throughout the books. Or perhaps we should say that the Prime Numbers are metaphors for Harry’s unity of soul. Voldemort, who is motivated by fear, cannot love and divides his soul in an ill-considered attempt to avoid his greatest fear, death. He has lost his center of gravity, his sense of the Prime. And, though he doesn’t realize it (nor do we), he is defeated before Harry’s story even begins.

For musicians, the center of gravity is the “one”, whether it be the last beat of a rhythmic cycle, the final of the mode or the one chord. Often, the music cannot seem to end until we return to the “one”. In the end, Harry Potter survives because he never loses track of the “one”. He is always able to return to his center of gravity, the Prime unity that is his undivided soul.

The use of Prime numbers is one of many interesting devices Rowling uses to weave her magic. Even if you are unaware of them, their use helps the story to make sense and helps the Magical World seem more real. They are like the devices musicians use to provide aural signposts for listeners even if the listeners can’t label them with musical jargon. They also reveal an author who cares deeply about every detail of the world they are creating, its inhabitants and their story, a story that is as meticulously crafted as a Haydn String Quartet or a song by Prince.