We apply some elementary group theory to study the 12 tone chromatic scale and its subgroups, which correspond to uniform scales. The fact that the number 12 is so highly divisible strongly influences the musical possibilities here. Besides the notion of a subgroup, the related concept of a coset of a subgroup also plays an important role.

This is part of a Playlist where we look at the intimate relations between mathematics and music. This video is a very clear example of the power of some abstract mathematics to clarify what is going on with structures in music.

Video Contents:
00:00 Scales with a particularly uniform property
03:13 Corresponding subgroups and scales
03:40 The generating subgroup (chromatic scale)
04:14 The two-step uniform scale
05:12 The three-step uniform scale (diminished)
06:00 The four-step uniform scale (augmented)
06:46 The 6-step uniform scale
07:20 Uniform scale
08:00 Cosets of a group and translations