Math and Music (metal, rock, d12, tune, bands)

Mathemusician7 · 10-16-2008, 07:19 PM

Have you ever wondered where the rules of music theory come from? Musical structure, i.e. songs, scales, chords, etc. are some of the most beautiful mathematical structures one can see. In fact on of the most interesting groups to look at in math is the dihedral groups. Dihedrals are the most symmetrical shapes in the world (triangle, square, pentagon, and so forth). Well there is actually an isomorphism between the set of all the major and minor triad chords and the D12 dihedral group, the group generated by the translations and inversions of the 12 sided dihedral. This is such an amazing outcome, these are both very complicated unrelated objects, but written as a mathematical structure, you cannot tell the difference between the two.

What other kinds of musical structures do you think could be represented using mathematical structures?

mr dave · 10-16-2008, 07:23 PM

free improv == chaos theory.

Mathemusician7 · 10-16-2008, 07:26 PM

Hahaha great!

WWWP · 10-16-2008, 07:27 PM

lol.

Double X · 10-16-2008, 07:42 PM

I am taking a Pre-Calc honors course but that made my head hurt...wtf are some of those words?

ProggyMan · 10-16-2008, 07:50 PM

My Dad's friend Gareth wrote a book on this called 'Musimathics' or something of that ilk.

Seltzer · 10-16-2008, 07:55 PM

I imagine the maths surrounding the timbre of different musical instruments would be quite interesting. I've been thinking about this lately because I've been working on coding an app which uses voice recognition.

Also, I've heard of Euclid's Algorithm being used to tune instruments.

Then there's Tool - Lateralus.

mr dave · 10-16-2008, 08:09 PM

i know there are a bunch of rock and metal bands that use math quite a bit when creating their rhythms, but autechre is the only group i can think of that creates their music as a result of mathematic formulas they create for their pieces.

Seltzer · 10-16-2008, 08:17 PM

I didn't know Autechre did that.

Chiastic Slide is a great album.

Mathemusician7 · 10-16-2008, 08:55 PM

Wow, theres so much I don't know. It would be great if you could let me know the names of some of the songs that Autechre uses math to create. Also, proggyman, if you could get me the name of that book, that would be awesome.
I love the Fibonacci sequence, it's another one of those things that is seen everywhere in the natural world and is an excellent example of how deeply everything is connected.
Physics is used widely with the timbre of instruments, there are many physics equations that deal with that, I however do not know much about the physical equations, I look more abstractly at the structures underneath.
And yes, Euclids algorithm to find the highest common factor of two numbers can also be used to find the largest measure of string segment that would fit into both. This is would have been extremely useful in tuning instruments in Euclids time since they talked about lengths of string rather then pitch and frequency.
This is awesome, keep throwing the ideas out there, what more does everyone know? Have you ever thought about what happens when you invert the notes of a chord mod 12? It's actually quite interesting. If you refer to the notes as numbers in the chromatic scale rather than by the note name, then all you have to do is negate each number of the chord and mod it by 12 and you will actually get the chord which is rooted on the minor third of the chord, and it will switch from major to minor, or vice versa.
E.g. Take C major (C,E,G) or in terms of the numbers on the scale (1,5,8). Now negate those (-1,-5,-8) and mod by 12 (11,7,4) This is an Eb minor chord. It works like this for any triad chord.

10-16-2008, 07:19 PM	#1 (permalink)
Mathemusician7 Groupie Join Date: Oct 2008 Location: Ventura, CA Posts: 4	Math and Music Have you ever wondered where the rules of music theory come from? Musical structure, i.e. songs, scales, chords, etc. are some of the most beautiful mathematical structures one can see. In fact on of the most interesting groups to look at in math is the dihedral groups. Dihedrals are the most symmetrical shapes in the world (triangle, square, pentagon, and so forth). Well there is actually an isomorphism between the set of all the major and minor triad chords and the D12 dihedral group, the group generated by the translations and inversions of the 12 sided dihedral. This is such an amazing outcome, these are both very complicated unrelated objects, but written as a mathematical structure, you cannot tell the difference between the two. What other kinds of musical structures do you think could be represented using mathematical structures? __________________ Mathemusician Math and Music World

10-16-2008, 07:26 PM	#3 (permalink)
Mathemusician7 Groupie Join Date: Oct 2008 Location: Ventura, CA Posts: 4	Hahaha great! __________________ Mathemusician Math and Music World

10-16-2008, 07:55 PM	#7 (permalink)
Seltzer Fish in the percolator! Join Date: Dec 2005 Location: Hobbit Land NZ Posts: 2,870	I imagine the maths surrounding the timbre of different musical instruments would be quite interesting. I've been thinking about this lately because I've been working on coding an app which uses voice recognition. Also, I've heard of Euclid's Algorithm being used to tune instruments. Then there's Tool - Lateralus. __________________ In the Court of King Crimson \| Last.fm \| RYM

10-16-2008, 08:17 PM	#9 (permalink)
Seltzer Fish in the percolator! Join Date: Dec 2005 Location: Hobbit Land NZ Posts: 2,870	I didn't know Autechre did that. Chiastic Slide is a great album. __________________ In the Court of King Crimson \| Last.fm \| RYM

10-16-2008, 08:55 PM	#10 (permalink)
Mathemusician7 Groupie Join Date: Oct 2008 Location: Ventura, CA Posts: 4	Wow, theres so much I don't know. It would be great if you could let me know the names of some of the songs that Autechre uses math to create. Also, proggyman, if you could get me the name of that book, that would be awesome. I love the Fibonacci sequence, it's another one of those things that is seen everywhere in the natural world and is an excellent example of how deeply everything is connected. Physics is used widely with the timbre of instruments, there are many physics equations that deal with that, I however do not know much about the physical equations, I look more abstractly at the structures underneath. And yes, Euclids algorithm to find the highest common factor of two numbers can also be used to find the largest measure of string segment that would fit into both. This is would have been extremely useful in tuning instruments in Euclids time since they talked about lengths of string rather then pitch and frequency. This is awesome, keep throwing the ideas out there, what more does everyone know? Have you ever thought about what happens when you invert the notes of a chord mod 12? It's actually quite interesting. If you refer to the notes as numbers in the chromatic scale rather than by the note name, then all you have to do is negate each number of the chord and mod it by 12 and you will actually get the chord which is rooted on the minor third of the chord, and it will switch from major to minor, or vice versa. E.g. Take C major (C,E,G) or in terms of the numbers on the scale (1,5,8). Now negate those (-1,-5,-8) and mod by 12 (11,7,4) This is an Eb minor chord. It works like this for any triad chord. __________________ Mathemusician Math and Music World

10-16-2008, 07:42 PM	#5 (permalink)
Double X sleepe Join Date: Jun 2008 Location: boston Posts: 1,140	I am taking a Pre-Calc honors course but that made my head hurt...wtf are some of those words?

10-16-2008, 07:50 PM	#6 (permalink)
ProggyMan Reformed Jackass Join Date: Sep 2007 Posts: 3,964	My Dad's friend Gareth wrote a book on this called 'Musimathics' or something of that ilk.