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#1 2006-07-31 02:17:59

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,562

6th root of 2 (whole tone scale)

I came across this approximation for the 6th root of 2.

55/49

It has some interest in the physics of music.
If 440Hz (Hertz) is a concert A, then 440 * 55/49 Hz is close to a "B concert".

Note that 55 - 49 is 6 and 36/6 = 6, hence near 6th root of 2, I noticed.

So following that idea.

56/48 should be the 4.5th root of 2 because 56-48 = 8 and 36/8 = 4.5, and it is pretty close!

And 54/50 should be close to the 9th root of 2. 

I haven't graphed this relationship, just playing on a calculator.


igloo myrtilles fourmis

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#2 2006-07-31 05:28:37

Ricky
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Registered: 2005-12-04
Posts: 3,791

Re: 6th root of 2 (whole tone scale)

Where does the 36 come from?


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#3 2006-07-31 06:04:40

Kurre
Member
Registered: 2006-07-18
Posts: 280

Re: 6th root of 2 (whole tone scale)

was gonna test it but...doh my calculator died sad

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#4 2006-07-31 10:19:03

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,562

Re: 6th root of 2 (whole tone scale)

I don't know where the 36 comes from, I just made it up out of nowhere!


igloo myrtilles fourmis

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#5 2006-07-31 12:55:01

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: 6th root of 2 (whole tone scale)

Holds pretty well till x is about 20, where it is 0.2 off.  Then it gets exponetially worse.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#6 2006-07-31 13:14:25

mikau
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Registered: 2005-08-22
Posts: 1,504

Re: 6th root of 2 (whole tone scale)

you know there are certain mathematical patterns to music, if thats true, there must be a way to randomly generate a song through math. Kind of creepy to think about.


A logarithm is just a misspelled algorithm.

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#7 2006-07-31 13:52:16

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,562

Re: 6th root of 2 (whole tone scale)

Nice equation, Ricky.  mikau, what is creepy to you is magical to me!


igloo myrtilles fourmis

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#8 2006-07-31 14:02:22

George,Y
Member
Registered: 2006-03-12
Posts: 1,306

Re: 6th root of 2 (whole tone scale)

I still wonder how and why...


X'(y-Xβ)=0

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