Sudoku: Explorations of Harmony and Scales through Numbers
Often we hear the thought expressed that if you are good at music you'll be good at maths. Expressed the other way round and it sounds peculiar. Do good mathematicians make good musicians? Where has this idea come from? I know from past experience that there were indeed students that I studied with who were gifted musicians and who also had an affinity for maths however there were also quite a few musicians who clearly were not gifted in maths or logic but were obviously gifted with musical ability. So is there anything to this notion?
A few years ago I decided after years of reflection to grapple with the Bach sinfonias and the frustrating inability I had in memorising music of a contrapuntal nature. In the years that followed my journey away from music I felt that discovering other possibilities in life would indirectly help me understand music and appreciate it in new ways. The idea that running a business or social networking or even composing photographs could further enhance abilities in another seemingly unrelated field like music has kept me firmly focused on my continuing advancement in music technique and expression. Although I would like to limit this article to Sudoku and music there are parallels between other disciplines and music and the necessity of learning new disciplines to enhance those already learned. So back to Soduko!
Intuitively I felt that in grappling with Soduko puzzles I would be training my mind to grapple more easily with the logic behind harmonic progression and counterpoint. My first encounter with Soduko was through a gift I received. A book: Sudoku for Dummies. I'm not sure if it was meant as a hint that perhaps intellectually I was a bit fuzzy, or if it was just one of those strange syncronicitous events that the universe sends our way. Whatever the case I became aware that the logic behind the squares and the placement of numbers was reminiscent of the logic behind harmony and melody. So to highlight this point think of a major scale. Any major scale. The first one that comes to mind visually is Dmajor. Two sharps: c and f sharp. Horizontally the scale is made up notes d,e,f#,g,a,b,c#,d. Sudoku puzzles the vertical line numbers 1,2,3,4,5,6,7,8,9...... Now mix these numbers and notes up on the vertical line without adding extras and you get the picture. Now in the Sudoku block you get the numbers grouped together 3x3. A little different to a triad or chord but you get the picure. A block of numbers or group of notes and these configurations dictated to by the layout of notes on the horizontal. Take away the predilection to project emotional meaning to groups of notes or sound clusters and viewing them in a a purely abstract tonal sense and suddenly the world of note relationships to each other and their limitations to certain sequences within a specific scale becomes self evident. My belief then is that in focusing the mind on sudoku puzzles, the mind becomes tuned into the logic behind the numbers just as in counterpoint the mind and ear become tuned into the logic behind the sequence of chords and notes in a fugue or sinfonia. The added dimension in music is that the body needs to replicate the framework of grids in the sudoku puzzle through playing or the manuscript paper does this in the music score. I think that there is a close enough corelation between the two disciplines for them to activate and train the same centres of the brain that are used to process and understand tonal and mathematical relationships.
