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.