Philosophy Lecture

1. Themes and Motifs in Music and
Mathematics
Brendan Larvor
University of Hertfordshire

2. Symmetry
Bilateral Rotational

3. Self-Symmetry

4. Symmetry
x3
+px2
+qx+r = 0
(x-a)(x-b)(x-c) = 0

5. Duality

6. Duality

7. Duality

8. Duality
Vectors can be added And scaled

9. Duality
The set of functions from a vector space to its
scalar field is itself a vector space, called the
‘dual space’:
(x is a vector; Greek letters are
functions; a is a scalar)

10. Duality
This new vector space has a dual of its own.
If the original vector space is finite-
dimensional, then this second dual is a mirror
image of it.

11. Duality