Uniform scales and group theory (mod 12) | Maths and Music | N J Wildberger

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
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[@brendawilliams8062]

Thankyou Dr. Wildberger

[@kendebusk2540]

I continue to enjoy your musical analysis, hope you continue!

[@njwildberger]

Hi Ken, Yes there is still lots more to be investigated

[@draconyster]

Thanks!

[@njwildberger]

@Dracony, You're welcome!

[@gilfelribeiro7212]

Thanks, Teacher. Blessings. ❤

[@blakemcalevey-scurr1454]

What would the Octatonic scale correspond to in group theory? I'm thinking of [C, C#, Eb, E, F#, G, A, Bb] i.e., [0,1,3,4,6,7,9,10]. It's kind of like if you combined the subgroup generated by 3, with one of its cosets - but I don't know the name for that in group theory!

[@whig01]

The math is nice if only 12-TET gave nice thirds and sevenths. You can MAP 12 tones to a 31-TET, to create an unequal scale as well, substituting 3 dieses for half step, and 5 dieses for whole step.

[@theoremus]

Many of these notes are sad sounding to me. Cinematography uses musical notes to create a mood, in the background.