Topic 3 The coordinates

In music the coordinates are: 

1) time as regards the horizontal translation or the sequence of beats 

2) musical intervals (see lesson 2) which instead indicate the vertical translation along the staff 

From a practical point of view, this is not too complicated. Let’s go back to our C major scale and remember that: 

  • C-D = second (2 sT) 
  • C-E = third (4 sT) 
  • C-F = fourth (5 sT) 
  • C-G = fifth (7 sT) 
  • C-A = sixth (9 sT) 
  • C-B = seventh (11 sT) 
  • C-C (upper octave) = octave (12sT) 

For example, saying we transpose the notes of the first bar of Frère Jacques by a second means that the first note will no longer be C but its second, i.e. D. At that point the subsequent notes will follow the same logic of composition of the original melody. Let’s see the result: 

In the first bar the notes are C (1) D (2) E (3) C (1); in the second bar the original melody was raised by a second, i.e. starting from the second note with respect to C, but, having done this, the succession of intervals with respect to D will always be: D (1) E (2) F (3) D ( 1). 

Starting from the initial melody, a new melody was generated through a mathematical/geometric process.