MathNovatory/Applied Maths/Convergence/Brahma Triangle

The Jordan Triangle And The Brahma Board

We will be comparing the Jordan Triangle, part of the Structure of Musical Pitch, and the Triangular disposition of the pegs on the Brahma board.

The Sides
In the Jordan Triangle, the sides represent mathematical ratios of intervals,
     in two cases "3/2", the size of the perfct fifth,
          essentially a harmonic interval, the FRAME of each chord,
     and in one case "9/8", the size of the major second, sum of the 2 perfect fifths,
          essentially a melodic interval, the basic material of all scales.
In the Triangular disposition of the Brahma board, the sides represent the distance between the pegs,
     three equal sides of an equilateral triangle, which must accomodate the two largest disks.

The Points
In the Jordan Triangle, the points represent the notes at the extremities of the interval,
     chosen arbitrarily because everything in music is relative.
In the Brahma Triangle, the points represent the absolute position of the pegs themselves,
     2 in front and 1 in the back.

Despite the considerable differences observed in both the sides and points, we feel that these two triangles deserve to be related. Both the Jordan Triangle and the Brahma Triangle were originally straight lines, and the triangular interpretation was helpful in clarifying the process of music, as well as in simplifying the playing of the game.