My Math Forum  

Go Back   My Math Forum > College Math Forum > Number Theory

Number Theory Number Theory Math Forum


Reply
 
LinkBack Thread Tools Display Modes
July 24th, 2009, 01:12 AM   #1
Newbie
 
Joined: Jul 2009

Posts: 1
Thanks: 0

Proportion in music...

Hi there!

This right here is something, I posted in the Ableton forum ( Ableton is the company, manufacturing the music-software Live...) ...


http://forum.ableton.com/viewtopic.php?f=3&t=120125



I was wondering weather you guys could maybe tell me something about it? I find the idea fascinating, but maybe I'm totally wrong...

I'm not even sure weather I choosed the right topic, so...


All thoughts on this are aprechiated very much, especially here



all the best to you,

Felix
Aeroplay is offline  
 
July 24th, 2009, 11:45 PM   #2
Newbie
 
Joined: Jul 2009

Posts: 21
Thanks: 0

Re: Proportion in music...

It's all about the kind of music.

Dance is generally 54 bpm(vol)
Hip Hop is 45 bpm(vol)
And rap is 20 bpm(vol)

Hope that helped <3
Bon Qui Qui is offline  
July 26th, 2009, 10:02 PM   #3
Senior Member
 
Joined: Apr 2007

Posts: 2,140
Thanks: 0

Re: Proportion in music...

It's possible that one can use some mathematics for timing, etc. in music, but why does the musicians really need mathematics...? Even with no mathematical background, one can still make a genius musical composition. If you ask Beethoven to prove all of the theorems in advanced complex analysis, then do you honestly think he will have the ability to do so? Probably not, but at least he can compose some hot stuff!
johnny is offline  
July 27th, 2009, 03:24 AM   #4
Member
 
Joined: Jul 2009

Posts: 55
Thanks: 0

Re: Proportion in music...

Hi,

Of course anybody can do a genius musical composition even if he doesn't know anything in theory of music, but that would be rare as everybody could find a very hard theorem in theory of numbers with basic tools, why not ?

The knowledge in music implies you have heard a lot of compositions and even if it is not such "well explained" as in mathematics you can mix theory and practice for a better understanding.

Anyway, music was considered as a part of mathematics a long time ago, and the equal temperament and chromatic scale are also the result of all that. You can also look the indians shrutis and the mathematical link with Zarlino ratio (and Pythogorician ratios are a part of these ZR of course) : two D as 9:8 and also 10/9 quite different from the equal D which is 6th root of 2.

Of course hearing is not so precise, and with tonal music, your brain can change the frequency into another (it is why the equal temperament can work).

As there is a lot of good mathematicians on this forum, what do you think of using microtone which is the 45420th root of 2 ? You get the chromatic scale inside, and you can approach a lot of ZR (all of them with quite low exponents for 2,3, and 5), because 32805/32768 is very closed from ^74 with sometime correcting with ^11(that means ^85 is a break between two chromatic tracks). I call that the ultrachromatic system...


Euzenius
Euzenius is offline  
July 27th, 2009, 06:16 AM   #5
Member
 
Joined: Jul 2009

Posts: 55
Thanks: 0

Re: Proportion in music...

I forgot to say that is very closed from 65535/65536 or 65537/65536 and everybody on this forum knows that

65535 = 3 x 5 x 17 x 257 a product of prime Fermat numbers as 65537 is also a prime Fermat number.

Isn't it funny ?


Euzenius
Euzenius is offline  
July 27th, 2009, 07:30 AM   #6
Global Moderator
 
CRGreathouse's Avatar
 
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 938

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
Re: Proportion in music...

Quote:
Originally Posted by Euzenius
As there is a lot of good mathematicians on this forum, what do you think of using microtone which is the 45420th root of 2 ?
I'd think that would be too small to be perceived. Even at 10,000 Hz that's only a difference of 0.15 Hz, something like 1% of the perceptible limit -- right?
CRGreathouse is offline  
July 27th, 2009, 10:00 AM   #7
Member
 
Joined: Jul 2009

Posts: 55
Thanks: 0

Re: Proportion in music...

Yes, of course, CRGreathouse... all that is on paper.

Ultrachromatic system is in fact an "advanced" system of Zarlino (around 1200 ratios, not only the usual ones as 81/64, 5/4, 25/24... but the most with the lowest exponents) which can be dispatched through equivalent root system. Each chromatic track contains 51 possible values (as 10/9, equal D and 9/8...). So it includes equal temperament and indian shrutis system !

^74 = 1,001 129 940... > 32805/32768 = 1,001 129 150 > ^73 = 1,001 114 662...

so k = ^74 is very closed from 32805/32768 = 5 x 3^8 / 2^15 which is the interval between 81/80 and 3^12/2^19 (these are very wellknown intervals).
We know that k^11 is very closed from 81/80 and k^12 from 3^12 / 2^19. The fact " is quite equal to 65535/65536" is also something curious, but it is impossible to get any "advanced system of Fermat" with only 17 in addition to 2,3 and 5 or even 2, 3, 5, 17, 257. Euler tried to test a system with 2,3,5 and 7 but said it was only an exercise... (for mathematicians ?)


Euzenius
Euzenius is offline  
July 27th, 2009, 05:53 PM   #8
Senior Member
 
Joined: Apr 2007

Posts: 2,140
Thanks: 0

Re: Proportion in music...

Music theory is not about mathematical concepts, it's musical theory itself.
johnny is offline  
July 27th, 2009, 11:44 PM   #9
Member
 
Joined: Jul 2009

Posts: 55
Thanks: 0

Re: Proportion in music...

But what is music theory ?

Euzenius
Euzenius is offline  
July 27th, 2009, 11:58 PM   #10
Senior Member
 
Joined: Apr 2007

Posts: 2,140
Thanks: 0

Re: Proportion in music...

It's where it teaches a music student the small details behind the sound of music and the sight-reading of musical notes. For example, how one can explain the C minor scale, with complex details? Can we apply this to Beethoven's musical pieces (especially considering that C minor was one of Beethoven's favorite key)?
johnny is offline  
Reply

  My Math Forum > College Math Forum > Number Theory

Tags
music, proportion



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Math and Music mathemusician Art 16 April 24th, 2014 03:21 PM
Let's talk music. Dandaman0 New Users 0 October 21st, 2011 03:32 PM
Music and mathematics edu Art 16 June 23rd, 2011 12:04 PM
Physics of music johnny Physics 3 June 9th, 2010 02:44 PM
Math and Music mathemusician Abstract Algebra 2 December 31st, 1969 04:00 PM





Copyright © 2018 My Math Forum. All rights reserved.