Group Theory And Music

>>8631100
Nice double dubs.
I play guitar and I dont have a sloghtest idea what the fuck are you talking about.

>>8631110
>I play guitar and I dont have a sloghtest idea what the fuck are you talking about.


https://en.wikipedia.org/wiki/Music_and_mathematics#Connections_to_Mathematics

>The 24 ‘Monsters’ posts are (mostly) about finite simple (sporadic) groups : we start with the Scottish solids (hoax?), move on to the 14-15 game groupoid and a new Conway M13-sliding game which uses the sporadic Mathieu group M12. This Mathieu group appears in musical compositions of Olivier Messiaen and it can be used also to get a winning strategy of ‘mathematical blackjack’.

>group theory is responsible for the musical mess that is messiaen

dropped harder than the piano in that one messiaen piece

>>8631139
alskdjflaksdjfaslkdjf

If I understood any of that, my mind would be blown.

>>8631100
Literally the only connection to group theory is that musical notes vaguely correspond to Z/12Z group. That's it. There's not really anything you can do with it. All the stuff that's interesting relies on what sound good and what sounds shit.

>>8631218
>Literally the only connection to group theory is that musical notes vaguely correspond to Z/12Z group. That's it. There's not really anything you can do with it. All the stuff that's interesting relies on what sound good and what sounds shit.

So far.

>>8631218
no the 12s thing is a relatively modern invention that has more to do with tuning a piano than anything else

I can see a connection to modular arithmetics, like congruence modulo 7 or something

>>8631315
I would think either mod8 or mod12.

Is there a way to account for all of the tones being 12 half steps, but any key only having 8 notes, with either a whole or half step between them?

>>8631235
It has to do with 12 evenly distributed notes on a logarithmic scale being pretty close to natural harmonics. The next number of notes that gets closer to natural harmonics is a 53 note system, but the notes there are so close together that we can barely keep them separate. So we settled with 12 notes. That's why it's everywhere.

And yes, music is built on that system. You can't look at music without choosing one tonal system.

>>8631393
Has anyone attempted to make music in the 53 note system?

>>8631218
Laughably not true, but I can see why you might think that given that the texts are pretty advanced from the math side.

Off the top of my head there's
>The Topos of Music: Geometric Logic of Concepts, Theory, and Performance
Note: This book uses legit topos theory which is grad level pure math.
>A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice
Totally different flavor from the last text. Uses geometry in the more traditional sense but still a non-trivial text to work thorough.
>Music a Mathematical Offering
Totally different flavor from the other two. Seems to be more interested in more conventional mathematics.
>Here's some more introductory material in the vein of the first book
http://www-personal.umd.umich.edu/~tmfiore/1/FioreTriadTalkStonyBrook.pdf

https://www.youtube.com/watch?v=krH0muWvQXY

Watched this series of videos not too long ago. It somewhat helped me see the mathematics involved in music. And then I stumbled upon this channel "Mathemusic4D." Utilized tonnetz and a hypersphere to relate notes.

>>8631393
There exist cultures who make music using different tonal systems from those. There's even microtonal music out there.

File: figure_just.png (32KB, 1119x819px) Image search: [Google]

32KB, 1119x819px

>>8631404
Don't think so. It wouldn't be feasible anyway. To neighboring notes would basically sound the same to most people. There are other systems that have been used because of the reasons I mentioned.

Pic related is a plot I made ages ago.

>>8631412
What a tone deaf post. Look up microtonal music, or regular diatonic tuning. Hell even in equal temperament there's a large variety.