AwakeInADream

15th October 2012, 16:34

I thought it would be a good idea to start a thread about mathematical questions,

because whatever I happen to be researching, it always leads back to numbers.

And from numbers to infinity and ultimately back to the mind of God.

I am hoping this thread will attract any mathematician's out there with a desire to teach,

and also others like myself who desire to learn or re-learn a subject that was sadly

made so dull at school and yet remains so vitally important to every field of knowledge.

It is becoming increasingly obvious that the establishment cannot be trusted to teach us

anything of value, particularly when it comes to things like statistics.

This is why I seek to test things out for myself, in order to gain a practical understanding,

and this attitude applies just as much to spirituality as it does to the science's.

I feel it makes no sense at all to believe anything blindly.

I think this thread fit's in pretty well with Project Avalon's main theme, and I think there is a

real need for the spiritually minded to have a strong foundation in mathematics.

I will be eternally grateful to anyone who can help with this.

My first question is this and has to do with ratio's and music:

QUESTION: The 12 note equal temperament system of western music is represented by 2 1/12.

What does this ratio mean? 2 1/12?

(*Note ET stands for equal temperament throughout)

I was lucky enough to find a decimal value online in order to work out the frequencies for

a 12 note equal temperament scale which is 1.0594631.

You take the start note 440Hz(A) and times it by 1.0594631 to get the 2nd note 466.16Hz(A#) and so on until you reach the octave 880Hz(A).

How does this number (1.0594631) relate to the ratio 2 1/12?

The reason I needed to know was because I wanted to work out how to calculate other equal temperaments like 22ET and 14ET. 22 equal temperament is expressed as 2 1/22 and 14ET is 2 1/14.

I have now figured out all of the decimal values needed to get any equal temperament from 2-26, which I did

in a spreadsheet through trial and error, changing the values slightly until the octave was right. This process took many unnecessary hours.

This is what I got for 22ET: 1.03200827973421 but how does it relate to 2 1/22?

And 14ET: 1.05075663865322 to 2 1/14?

This process would have been much easier if I had known more about ratio's and math's.

I'm sure it could have been done in no time at all with a much more elegant solution.

Does this have something to do with logarithms(I don't understand them at all)?

The only relationship I have found between these decimal values is that

the square root of the 12 equal temperament number gives you the number needed for a 24ET. And if you square the 12ET number you get the 6ET number...

If you're wondering how all this relates to spirituality, it's because I wanted first to be able

to represent the 22 letters of the holy Hebrew alphabet by musical notes, and secondly I am interested in how music made with various different ET's might affect consciousness.

because whatever I happen to be researching, it always leads back to numbers.

And from numbers to infinity and ultimately back to the mind of God.

I am hoping this thread will attract any mathematician's out there with a desire to teach,

and also others like myself who desire to learn or re-learn a subject that was sadly

made so dull at school and yet remains so vitally important to every field of knowledge.

It is becoming increasingly obvious that the establishment cannot be trusted to teach us

anything of value, particularly when it comes to things like statistics.

This is why I seek to test things out for myself, in order to gain a practical understanding,

and this attitude applies just as much to spirituality as it does to the science's.

I feel it makes no sense at all to believe anything blindly.

I think this thread fit's in pretty well with Project Avalon's main theme, and I think there is a

real need for the spiritually minded to have a strong foundation in mathematics.

I will be eternally grateful to anyone who can help with this.

My first question is this and has to do with ratio's and music:

QUESTION: The 12 note equal temperament system of western music is represented by 2 1/12.

What does this ratio mean? 2 1/12?

(*Note ET stands for equal temperament throughout)

I was lucky enough to find a decimal value online in order to work out the frequencies for

a 12 note equal temperament scale which is 1.0594631.

You take the start note 440Hz(A) and times it by 1.0594631 to get the 2nd note 466.16Hz(A#) and so on until you reach the octave 880Hz(A).

How does this number (1.0594631) relate to the ratio 2 1/12?

The reason I needed to know was because I wanted to work out how to calculate other equal temperaments like 22ET and 14ET. 22 equal temperament is expressed as 2 1/22 and 14ET is 2 1/14.

I have now figured out all of the decimal values needed to get any equal temperament from 2-26, which I did

in a spreadsheet through trial and error, changing the values slightly until the octave was right. This process took many unnecessary hours.

This is what I got for 22ET: 1.03200827973421 but how does it relate to 2 1/22?

And 14ET: 1.05075663865322 to 2 1/14?

This process would have been much easier if I had known more about ratio's and math's.

I'm sure it could have been done in no time at all with a much more elegant solution.

Does this have something to do with logarithms(I don't understand them at all)?

The only relationship I have found between these decimal values is that

the square root of the 12 equal temperament number gives you the number needed for a 24ET. And if you square the 12ET number you get the 6ET number...

If you're wondering how all this relates to spirituality, it's because I wanted first to be able

to represent the 22 letters of the holy Hebrew alphabet by musical notes, and secondly I am interested in how music made with various different ET's might affect consciousness.