PDA

View Full Version : Mathematical Questions

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.

araucaria
15th October 2012, 16:57
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.

I think it may be a mistake using decimals here rather than vulgar fractions. Just as studying ancient monuments with a decimal value for pi will lead to a dead endbut 22/7 will not.

15th October 2012, 17:03
That's what I mean. I don't understand how to use fractions and ratio's.

I want to know what 2 1/12 mean's so I can use it practically...In layman's terms...

So 22/7 is pi then, interesting, 2 holy numbers. Thank's:)

lightpotential
15th October 2012, 18:42
Dear Awake,

I can indeed answer your question regarding the value 1.0594631, as you cite. This is a ratio that is found within the celestial realm, and is concerned with the transformation of the earth-moon system. The more accurate value you are looking for is 1.059531131.

Current Earth Tropical Year (days) = 365.242184. Ideal year = 360.

365.242184 / 360 = 1.014561622

1.014561622^4 (raised to the 4th power) = 1.059531131

If this value is then reduced to the 3rd root, one gets = 1.019462465 (1100/1079)

This is the ratio of change of increase for the mean distance between the moon and the earth (as accompanied the noted change of its year). Also, in units of 6000 feet - a special unit called an ideal geographical mile, the very mean distance between the moon and the earth is 210194.62465 IGM.

If you set aside the number 2, you will see the ratio of increase embedded within the distance itself.

If you go to my website Ancient World Mysteries, you can see the math in greater detail. The link is below.

araucaria
15th October 2012, 19:01
Dear Awake,

I can indeed answer your question regarding the value 1.0594631, as you cite. This is a ratio that is found within the celestial realm, and is concerned with the transformation of the earth-moon system. The more accurate value you are looking for is 1.059531131.

Current Earth Tropical Year (days) = 365.242184. Ideal year = 360.

365.242184 / 360 = 1.014561622

1.014561622^4 (raised to the 4th power) = 1.059531131

If this value is then reduced to the 3rd root, one gets = 1.019462465 (1100/1079)

This is the ratio of change of increase for the mean distance between the moon and the earth (as accompanied the noted change of its year). Also, in units of 6000 feet - a special unit called an ideal geographical mile, the very mean distance between the moon and the earth is 210194.62465 IGM.

If you set aside the number 2, you will see the ratio of increase embedded within the distance itself.

If you go to my website Ancient World Mysteries, you can see the math in greater detail. The link is below.

If Awake wasn't completely flummoxed already, he sure is now I reckon :)

Edit: what have the fluctuations of the Moon to do with music I wonder??

15th October 2012, 19:08
That's amazing Lightpotential!

The 12 note western system of music is related to the dance of the Earth and the Moon!

Pythagoras really did hear 'The Music of the Sphere's'!

EDIT: I still could do with someone to explain all these things in layman's terms though...

EDIT2: Great Website you've got BTW Lightpotential!:)

ghostrider
16th October 2012, 02:37
looks like it's just a version of yin/yang when you boil it all down. IMO

indigopete
16th October 2012, 03:07
QUESTION: The 12 note equal temperament system of western music is represented by 2 1/12.
What does this ratio mean? 2 1/12?

Hi Awake

If you can grasp the difference between a "linear" relationship (between 2 values) and a "logarithmic" one then you're in there.

A. BACKGROUND

To illustrate, a linear relationship is where one value changes in proportion to the other. For example:

BRICKS and HEIGHT
I have a brick that's 10 cm thick. If I build 2 bricks high, the wall will be 20cm. If I build 3 bricks high, it will be 30cm. i.e. if I double the number of bricks, the height also doubles. If I treble the number of bricks, the height also trebles.

TABLE A - LINEAR RELATIONSHIP
1st brick layer = bricks are 10cm thick
2nd brick layer = bricks are 10cm thick
3rd brick layer = bricks are 10cm thick

This is called a linear relationship because if you draw a graph of the wall height against the number of stacked bricks (brick count) it will be a straight line.

Now lets look at a LOGARITHMIC relationship. Do do that, you have to imagine a wall where, in each successive 10cm brick layer, the bricks are only a tenth of the thickness of those in the preceding one below it. So, each time I added another brick level, the height of the wall increases by a proportionately less amount. For example:

TABLE B - LOGARITHMIC RELATIONSHIP
1st brick layer = bricks are 10cm thick
2nd brick layer = bricks are 1 cm thick
3rd brick layer = bricks are 0.1 cm thick

... and so on. So by the time I'm at the 3rd layer of bricks, I need to add 100 more bricks just to get the 10cm increase I had with the first one. If we plot the number of bricks at each layer to get back to our 30 cm height of TABLE A, then it looks like this:

TABLE C - BRICK COUNT (LINEAR SCALE)
1st brick layer = 1 brick (We've reached 10cm height)
2nd brick layer = 10 bricks (We've reached 20cm height)
3rd brick layer = 100 bricks (We've reached 30cm height)

This is annoying, because the increment between the number of bricks at each layer is different (9 in the first, 90 in the second) so it's a headache to calculate things.

MATHEMATICAL TRICK !!!
Even mathematical boffins such as Einstein experience headaches with anything other than linear relationships, so they use a useful tool: We can get the graph back to a straight line if we plot the wall height against the LOGARITHM of the brick count instead of just the brick count itself. In this case TABLE C looks like this (try it yourself on your calculator. Use the Base 10 logs, not the natural (e) ones):

TABLE C - BRICK COUNT (LOGARITHMIC SCALE)
1st brick layer = log(1) = 0
2nd brick layer = log(10) = 1
3rd brick layer = log(100) = 2

Suddenly, were back in business ! We have the same increment between each brick layer (1) instead of a varying increment, which is easier on our tender brains.

To be specific, the Log is just the number of zeroes in each brick count. (So say the log of a million (in base 10 logs) would be 6, because it's got 6 zeroes after it).

B. HOW DOES THIS RELATE TO YOUR QUESTION

In your example, the pitch is the height of the wall (brick layer Nº) and the frequency is the number of bricks. Each time we go up 1 note, we need a much bigger increment in frequency (more bricks to achieve the same height increase). As with the example above, however, we can go up in equal increments if we use the logarithm of the frequency instead of the frequency itself.

The only difference, is that instead of Base 10 logarithms, we use base 2. That's where the 2 1/12 comes from. (It's actually 2 to the power 1/12, which is written as the digit 2 with 1/12 as a superscript. The superscript part is the LOGARITHM).

C. HOW DOES THIS NUMBER (1.0594631) RELATE TO THE RATIO 2 1/12

Try it for yourself ! On your calculator, type 2, then the power button (usually marked Y with an x superscript), then [open bracket] 1 / 12 [close bracket] [equals]. You should get the result 1.0594631. (That's just a decimal representation of 2 to the power of a twelfth). This can also be expressed as the twelfth root of 2.

Now lets continue to completion. If we plot each note against the base frequency expressed as powers of 2 (i.e. logarithms in base 2) we get this table:

TABLE D - PITCH and FREQUENCY

1st Note = Base Frequency x [2 to the power 0/12]
2nd Note = Base Frequency x [2 to the power 1/12]
3rd Note = Base Frequency x [2 to the power 2/12]
4th Note = Base Frequency x [2 to the power 3/12]
5th Note = Base Frequency x [2 to the power 4/12]

Do you see the numbers on the right hand side going up in equal increments ? 1/12, 2/12, 3/12 etc ? Those are the logarithms (in base 2) of the frequency instead of the frequency itself. Our ear agrees with the maths because our ear is listening to the logarithm of the frequency and hearing it go up in equal increments - not the frequency itself.

SUMMARY

[1] - The value 2 to the power one twelfth (2 1/12) is the ratio between each successive frequency in the western scale
[2] - This number can be represented as a decimal as approximately 1.0594631
[3] - If we represent each frequency as a ratio of the base frequency using powers of 2 (the logarithm of the frequency in base 2 instead of the frequency itself), then the increments are equal between each note

ONE FINAL THING

The number 2 to the power 1 twelfth is an IRRATIONAL NUMBER. These are quite fascinating phenomena in themselves because they represent a kind of "gap" or "black hole" in the number line. It is a number which does not exist and cannot ever be represented as a decimal. You can only represent exact numbers either side of it but not the number itself. You can, however, represent it with full precision as a ratio (i.e. an implied value which uses two other values to represent it, for example, the ratio of the circumference to the diameter of a circle (normally known as "Pi").

Hope that helps.

Pete

16th October 2012, 03:50
Wow! That was amazingly lucid, not only did I understand every word, but also I've just done logarithm's for the first time in my entire life, and understood them!

I did the calculations for 12ET using buttons on my calculator that I've never pressed before and it worked. I've also tested it for 2 1/22 and 2 1/14 and that worked too.
And just for fun 2 1/1200 = 1.00057779. That's amazing! Thank you so much for this, I was half expecting this thread to be buried before anyone super smart noticed.

Irrational numbers too, I've never been sure before, I guess the decimals just flow on till infinity, the mind of God. Cool.:cool:

:)Thank you so much Pete!:) I hope you'll pop back in to this thread from time to time, to help anyone else who might have questions.

Rocky_Shorz
16th October 2012, 05:08
25/12 is Christmas...

how does it relate to music?

let's go Caroling... ;)

16th October 2012, 05:22
25/12 is Christmas...

how does it relate to music?

let's go Caroling... ;)

I might just be crazy enough to test that musical scale out you know!

I once re-worked 'The Hymn to St. John the Baptist' using Solfeggio tones and it sounded awful!:)

Rocky_Shorz
16th October 2012, 06:07
your post is at 22:22 as in the day after the Mayan Calendar ends...

my birthday, I'm starting to think we were meant to bump into each other... ;)

16th October 2012, 06:20
I told you those numbers are everywhere lately!

The day after the Mayan calendar ends! Wow! That's really hopeful!

I guess the world won't end then after all...:clap2:

Rocky_Shorz
16th October 2012, 07:12
naaa just the grumpy old crusty dudes and dudettes currently running it...

the looking glass doesn't show what is beyond the 21st...

the ones who depended on knowing the future before it happens have been cut off...

but you're right, I never miss a Birthday... ;)

leavesoftrees
16th October 2012, 21:04
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.

See

this lists notes assigned to each Hebrew letter

Sammy
16th October 2012, 22:03
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.

If I recall correctly, the notes of the musical scale do not correspond in the way you mentioned as the scale is not based on a straight line (instead it is logarithmic). I hope that doesn't throw too much of a monkey wrench into your idea.

I also have heard that musical note correspondences have already been established (though I know not the authority nor the credibility of said authority) in relation to some alphabets and I seem to recall the Hebrew alphabet being one of them.

I am fascinated by your idea and I hope it leads you to some wonderful self discoveries... can't wait to hear about your adventures in this regard, Chester

EDIT: I broke one of my rules... read all the prior posts before posting as you may be unnecessarily redundant and I was! haha

Sammy
16th October 2012, 22:06
Dear Awake,

I can indeed answer your question regarding the value 1.0594631, as you cite. This is a ratio that is found within the celestial realm, and is concerned with the transformation of the earth-moon system. The more accurate value you are looking for is 1.059531131.

Current Earth Tropical Year (days) = 365.242184. Ideal year = 360.

365.242184 / 360 = 1.014561622

1.014561622^4 (raised to the 4th power) = 1.059531131

If this value is then reduced to the 3rd root, one gets = 1.019462465 (1100/1079)

This is the ratio of change of increase for the mean distance between the moon and the earth (as accompanied the noted change of its year). Also, in units of 6000 feet - a special unit called an ideal geographical mile, the very mean distance between the moon and the earth is 210194.62465 IGM.

If you set aside the number 2, you will see the ratio of increase embedded within the distance itself.

If you go to my website Ancient World Mysteries, you can see the math in greater detail. The link is below.

WoW! Are you friends with Christopher Knight and Alan Butler?

http://www.amazon.com/Built-Moon-Christopher-Knight-Butler/dp/190585711X

fascinating info - thanks, lightpotential

17th October 2012, 04:10
I've got a question I think might be easier for someone to answer.

If 22/7 represents Pi (thank's Araucaria!).

What fraction represents the golden ratio Phi?

Sammy
17th October 2012, 04:41
I've got a question I think might be easier for someone to answer.

If 22/7 represents Pi (thank's Araucaria!).

What fraction represents the golden ratio Phi?

http://www.jcu.edu/math/vignettes/continued.htm

17th October 2012, 05:13
I've got a question I think might be easier for someone to answer.

If 22/7 represents Pi (thank's Araucaria!).

What fraction represents the golden ratio Phi?

http://www.jcu.edu/math/vignettes/continued.htm

OK! You're right, the answer is there, but all that stuff just looks like a foreign language to me.

It's more complicated than I thought it would be. Quadratic equations?:confused:

Thank's JustOneMan!:)

Can you explain this?http://www.jcu.edu/math/vignettes/v18im15.gif

EDIT: I've got it now, I was just scared by the language. The square route of 5 plus 1 then divided by 2 is 1.618033989 the Golden Ratio. Cheers!

Michelle Marie
17th October 2012, 05:43
When I first saw the question, what does 2 1/12, I saw 13 over 12. Think of the implication of this in a base 12 system. The 13th iteration is the same fraction 1/12 that has just surpassed the whole.

Going from 12 to 13 is significant. In fact, I just documented this week all the 12s in my life this year, and all the 13s next year. (It has taken me 12 years to establish a body of literary work. I'm entering a new phase the 13th year when I leave my home and go on the road.)
I began a new era in my life in 2000 -moved to Oregon from Florida- and I've recently been guided to leave the area. This is the end of the 12th year in the NW and I'll begin my 13th year elsewhere.
My age adds up to 12, but having a birthday in early January, I my age numbers will add up to 13 right after the beginning of the year.

As far as calculation, it looks like you have it covered, but I used to teach fractions as a math teacher at the age level where they had to be able to do it by hand without a calculator.

Smiles,
Michelle Marie

I feel the shift. I'm getting lots of signs. I've always been intuitive, but now off the charts! This is a phenomenon. Many people are talking about the information they are receiving.

17th October 2012, 06:02
I've only just realized myself that I was asking what does 2 1/12 mean in relation to music, but symbolically, perhaps subconsciously
I was also asking what does 21/12 mean in terms of the consciousness shift that we are all feeling as the Mayan calendar draws to a new beginning.

Thank's Michelle Marie!:)

Michelle Marie
17th October 2012, 06:11
I'm seeing mirror image numbers a lot and have for awhile.

But, you were talking about two and a twelfth, right?

Anyway, I've been thinking about the reconciliation of opposites, or responding pairs. and in my mind I see like an accordion folding up. The octaves of music, sound. color, etc. folding into its complement. Oh, I'm getting it as I write...all back to zero, or zero point. Well, this is just perfect. I just realized I'll be sending this at 11:11.

Cheers!
Michelle

17th October 2012, 06:31
I like numbers that are symmetrical like 121 and 101, I don't know why. It's as if I can see a number and sense it's vibration on some level.

It's interesting that you mention octaves of sound and colour, I made a post on this last week here:http://projectavalon.net/forum4/showthread.php?42500-Frequencies-of-colours-and-shapes.&p=568115&viewfull=1#post568115

I'd like you to take a look at this since I'm not sure if my calculations are right, but I'm trying to figure out what the octaves of musical notes would be
if they were doubled up into the Theta Hertz range of colour. I'd rather find out myself, than simply trust blindly the generally accepted values.

Cheers!

EDIT: I've given 404 thank's! Nice symmetry and synchronicity!

Rantaak
17th October 2012, 14:06
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.

Well your values may be off.

Very interesting question, though - I am very excited to see where this leads. I have a background in mathematics as I studied all aspects of video game production while in college. Needless to say, we did a lot of math and from working with applying math for so long, it was very natural that I developed a particular intimacy with the relationships it seems to suggest.

I believe that the natural frequency of A4 is actually 432 hertz - one of those Nazi guys changed the standard during their reign to 440 for some unspeakably nefarious reason. If you multiply 432 hertz by your ratio of 1.0594631, you will instead arrive at 457.6880592, which should be the natural frequency of A4#. Anyway, I hope you find whatever you're looking for!

Michelle Marie
17th October 2012, 15:02
I'm getting this stuff come into my mind from inside. It is emerging. I do get information about sacred geometry, numbers, relationships, equations/balance. It's more like pieces of a puzzle that is just now coming into view and will be put together and clear as time goes on.

I like 404 and symmetry, too. It's good for mirror math! ...and mirror matter

Lots of love,
Michelle

17th October 2012, 17:45
I have a background in mathematics as I studied all aspects of video game production while in college. Needless to say, we did a lot of math and from working with applying math for so long, it was very natural that I developed a particular intimacy with the relationships it seems to suggest.

I believe that the natural frequency of A4 is actually 432 hertz - one of those Nazi guys changed the standard during their reign to 440 for some unspeakably nefarious reason. If you multiply 432 hertz by your ratio of 1.0594631, you will instead arrive at 457.6880592, which should be the natural frequency of A4#. Anyway, I hope you find whatever you're looking for!

Yes! I've already been sold on the virtues of the 432 tuning, I just used 440 here because that's the one most people recognize.

I'm also now considering making A 444Hz (888Hz) because that would make C 528Hz(the frequency of love and DNA repair), and 888 is the numerology of Jesus in Greek.

Video games production, fascinating! I wish I could have studied that. I program a little in C++, just simple things (numerology and music theory stuff), I don't know how to use sound and graphics yet (which I would love to do)...

I've been thinking of writing a program that would analyze any number I give it in the Pythagorean method (abundant/deficient/perfect numbers etc..), and other ways too.

Maybe you can help?

Do you know an easy way to find out if any number is a prime number?
(in a way that a computer can understand)

Cheers!:)

Michelle Marie
19th October 2012, 07:39
I have a background in mathematics as I studied all aspects of video game production while in college. Needless to say, we did a lot of math and from working with applying math for so long, it was very natural that I developed a particular intimacy with the relationships it seems to suggest.

I believe that the natural frequency of A4 is actually 432 hertz - one of those Nazi guys changed the standard during their reign to 440 for some unspeakably nefarious reason. If you multiply 432 hertz by your ratio of 1.0594631, you will instead arrive at 457.6880592, which should be the natural frequency of A4#. Anyway, I hope you find whatever you're looking for!

Yes! I've already been sold on the virtues of the 432 tuning, I just used 440 here because that's the one most people recognize.

I'm also now considering making A 444Hz (888Hz) because that would make C 528Hz(the frequency of love and DNA repair), and 888 is the numerology of Jesus in Greek.

Video games production, fascinating! I wish I could have studied that. I program a little in C++, just simple things (numerology and music theory stuff), I don't know how to use sound and graphics yet (which I would love to do)...

I've been thinking of writing a program that would analyze any number I give it in the Pythagorean method (abundant/deficient/perfect numbers etc..), and other ways too.

Maybe you can help?

Do you know an easy way to find out if any number is a prime number?
(in a way that a computer can understand)

Cheers!:)

Maybe this will help:
http://www.paulgriffiths.net/program/c/prime.php

19th October 2012, 08:02
Thank's Michelle!:)

by definition any number which is not prime can be divided by at least one other prime number
That's a useful rule!

Do you know anything interesting about Pythagorean Mathematics?

I'd love to hear from one that knows...

In fact tell me anything number related...
Sacred Geometry is just pretty pictures to most people,
but to a Maths Teacher!!! I can't imagine...

araucaria
19th October 2012, 08:07
I've got a question I think might be easier for someone to answer.

If 22/7 represents Pi (thank's Araucaria!).

What fraction represents the golden ratio Phi?

Answer: any number in the Fibonnaci sequence divided by the previous number: eg 8/5 (which incidentally is the ratio between kilometers and miles :))
These are approximations and if you move higher up the sequence they improve.
According to Maurice Chatelain the Phi value in ancient Egypt was 196/121, which equals 14 squared divided by 11 squared. Hence the square root of phi equals 14/11 = 4/Pi - 1.27272

The practical advantage of using fractions means that if you have a piece of string 7 units long, you can draw a circle 2 * 22/7 * 7 units (2 Pi x r) = 44 units in circumference. Or with 12 units of string, you can divide it into 3, 4 and 5, which will draw a Pythagorean triangle and give you a right angle without having to measure it :)

19th October 2012, 08:28
Thank's Araucaria! :)
So the further up the Fibonnaci sequence you get the closer to Phi you get.
Where do you stop? Infinity?
Ah! Then Phi must be an irrational number?
Like Pete said...:)

Did you know that the Greek word for 'Wisdom' is 'Sophia',
and the Greek letter that is in the center of that word is Phi.
So it seems that the Golden Ratio is 'central' to Greek Wisdom!;)

Cheers!:)

araucaria
19th October 2012, 08:53
Thank's Araucaria! :)
So the further up the Fibonnaci sequence you get the closer to Phi you get.
Where do you stop? Infinity?
Ah! Then Phi must be an irrational number?
Like Pete said...:)

Did you know that the Greek word for 'Wisdom' is 'Sophia',
and the Greek letter that is in the center of that word is Phi.
So it seems that the Golden Ratio is 'central' to Greek Wisdom!;)

Cheers!:)

You might also say the further down the sequence you go, the closer Phi approximates to 1 :)

I also hown that the Greek word for one kind of love is Philos -Phi again - hence philosophy is phi to the second power.

Violet
19th October 2012, 10:04
Oh, now this reminds me of Marty Leeds and the theory of Gematria:

TyjD2IWgD-A

I haven't yet properly thought it through, so I can't really say anything about it.

Michelle Marie
19th October 2012, 13:14
I've got a question I think might be easier for someone to answer.

If 22/7 represents Pi (thank's Araucaria!).

What fraction represents the golden ratio Phi?

Answer: any number in the Fibonnaci sequence divided by the previous number: eg 8/5 (which incidentally is the ratio between kilometers and miles :)

The crux of the matter is the debate over the base 10 vs. base 12 number systems. I looked into this awhile back...fascinating.
Another paradoxical reconciliation at hand???? Both/and??

Now, this is interesting...

Base 12 and Plastic Reality

Agreed upon reality-objective (similar experiences), and subjective reality.
REALITY: "Subjective stream of experience of data points."
Fascinating!

Oh, I see...
We create reality by causing through intention

Consecutive and linear is also in play, this guy says.

But, to ME it IS both/and.
Nonlinear reality is base 12. Linear reality is base 10.Different realms exist simultaneously.
Out of the subjective base 12 reality emerges the base 10 objective reality.

As the base 10 scientists discredit the base 12 reality (imagination, dreams, etc) to prove themselves right, they are compromising the integrity of Wholeness.

We are TRULY reconciling opposites at this time.

I have to say that looking at math and consciousness together is activating some remembrance. I often contemplate and use sacred geometry consciousness.
If I ever get enough people on board who can understand it enough to use its power, I intend to create a consciousness plan I wrote up several years ago.
YES! Group mind power. We don't use it enough. Why?

Thanks to all for sharing.

Blessings of peace and happiness,
Michelle Marie

araucaria
19th October 2012, 13:41
I've got a question I think might be easier for someone to answer.

If 22/7 represents Pi (thank's Araucaria!).

What fraction represents the golden ratio Phi?

Answer: any number in the Fibonnaci sequence divided by the previous number: eg 8/5 (which incidentally is the ratio between kilometers and miles :)

The crux of the matter is the debate over the base 10 vs. base 12 number systems. I looked into this awhile back...fascinating.
Another paradoxical reconciliation at hand???? Both/and??

Now, this is interesting...

Base 12 and Plastic Reality

Agreed upon reality-objective (similar experiences), and subjective reality.
REALITY: "Subjective stream of experience of data points."
Fascinating!

Oh, I see...
We create reality by causing through intention

Consecutive and linear is also in play, this guy says.

But, to ME it IS both/and.
Nonlinear reality is base 12. Linear reality is base 10.Different realms exist simultaneously.
Out of the subjective base 12 reality emerges the base 10 objective reality.

As the base 10 scientists discredit the base 12 reality (imagination, dreams, etc) to prove themselves right, they are compromising the integrity of Wholeness.

We are TRULY reconciling opposites at this time.

I have to say that looking at math and consciousness together is activating some remembrance. I often contemplate and use sacred geometry consciousness.
If I ever get enough people on board who can understand it enough to use its power, I intend to create a consciousness plan I wrote up several years ago.
YES! Group mind power. We don't use it enough. Why?

Thanks to all for sharing.

Blessings of peace and happiness,
Michelle Marie

Not watched the video, but to reconcile base 10 and base 12, try the Sumerian base 60 :)

19th October 2012, 14:31
Puzzle me this... according to Ed Leedskalnin THE SECRET TO THE UNIVERSE IS 7129 / 6105195.

<just bookmarking an interesting thread :p>

araucaria
19th October 2012, 19:46
Puzzle me this... according to Ed Leedskalnin THE SECRET TO THE UNIVERSE IS 7129 / 6105195.

<just bookmarking an interesting thread :p>

I doubt it somehow. The 'Niniveh constant' is probably a much more interesting number: 70 times 60 to the power six. This works out as 1955200000 which, according to Maurice Chatelain, corresponds to the time in seconds for the entire solar system to revert to a previous configuration! It comes to about 6.2 million years, and, for example, Comet Halley will complete exactly 81,000 orbits in that time. All the other known planetary orbits are multiples of this number. And it appeared on a Sumerian talbet from 6,000 years ago...

Paul
19th October 2012, 21:17
I doubt it somehow. The 'Niniveh constant' is probably a much more interesting number: 70 times 60 to the power six. This works out as 1955200000 which, according to Maurice Chatelain, corresponds to the time in seconds for the entire solar system to revert to a previous configuration! It comes to about 6.2 million years, and, ...
Those numbers aren't adding up for me.

1955200000 seconds is about 62 years, not 62 million years.

70 times (60 to the power of 6) is 3265920000000, which is not equal 1955200000, but rather about 1670 times larger.

3265920000000 seconds is about 100,000 years.

So ... searching around Google, according to CHAPTER 18: THE NINEVEH CONSTANT: CELESTIAL HARMONICS (Divine Cosmos, David Wilcock) (http://divinecosmos.com/index.php?option=com_content&task=view&id=74&Itemid=36"):

It's spelled the Nineveh Constant, not the Niniveh Constant.
It's 70 times (60 to the power of 7), not 70 times (60 to the power of 6)
It's 195,955,200,000, not 1,955,200,000

It is about 6.2 million years.

:)

20th October 2012, 01:27
Re: Wavelength !!

Is Hertz and Wavelength the same thing by a different name?

Posted by Paul

No - not the same.

Imagine yourself at the sea shore, with the waves coming in.

Stand where the waves lap up on the sand. Close your eyes and notice how rapidly (how many times per minute) the waves wash over your feet. That's frequency, which for sound waves is usually measured in waves per second (aka Hertz) not waves per minute, just because the waves of compression and decompression in air that we know as sound come faster.

Now take a major aircraft carrier (or other long ship) out into that water, and look along the side of the ship at the water line. You will perhaps see more than one wave top, and one wave bottom, all visible at once, along the length of the ship. Measure the distance from one wave top to the next; that's the wave length, which might be measured in feet or meters or whatever unit of length is familiar and of an appropriate magnitude.

The above is fairly straight forward, in my view at least.

Here's the weirder part. If you know the velocity at which that wave travels (the speed of light, the speed of sound, or the speed of waves across the ocean, say) then there is a well known relation between these properties:
https://www.k12.gov.sk.ca/docs/physics/images/u2b12_4.gif
where:
v = the velocity,
f = the frequency, and
= (the Greek letter lambda) wave length.
I usually read the above equation as "vee equals eff lambda". It says that the velocity is equal to the frequency times the wave length.

Since most waves of a given kind in a given medium have fairly constant velocity (v), this means that higher frequencies (f) have proportionally shorter wavelengths ().

I think I understand it. I've brought your answer over to this thread because I don't want to go too far off topic over there, also I'd like a little clarification of how to use the formula practically.

Can you give me an example of the formula's usage(to find wavelength), using say 432Hz so that I will understand it better?

I assume that V in the case of sound, would be the speed of sound, but I don't know what units of measurement to use in the calculation.

Oh! And a funny thought came into my head as I re-read your post. It starts off rather like a guided visualization CD for relaxation, only it also teaches you maths. It made me giggle...:)

P.S Thank's Michelle(The Blues, Maths and Londoners a surreal mix) and Violet(Pi and the alphabet-equally surreal) for the videos, I have downloaded them and will watch them soon. They look really good.:)

EDIT: I've just realized that Operator gave an example that answered this question on the Wavelength thread. I didn't understand it though so I still need some clarification:confused:.

Paul
20th October 2012, 05:59
Can you give me an example of the formula's usage(to find wavelength), using say 432Hz so that I will understand it better?

I assume that V in the case of sound, would be the speed of sound, but I don't know what units of measurement to use in the calculation.
Which units of measurement to use probably depends on where you live :).

If you're in the USA or England, you probably prefer feet. If you're in many other places, you probably prefer meters.

I'd avoid working with the speed of sound in miles per hour in these situations, because we usually think of the frequency of sound in cycles per second (Hz), not in cycles per hour. You want to have the time unit (seconds) used in your frequency numbers match the time unit used in your speed of sound numbers (meters or feet per second.)

From http://en.wikipedia.org/wiki/Speed_of_sound:

In dry air at 20 °C (68 °F), the speed of sound is 343.2 metres per second (1,126 ft/s).

So, dealing in feet per second, if you're in "dry air at 68 °F", where sound travels at 1126 feet per second, then a sound at 432 Hz will have a wave length (lambda) of f/v == 1126/432 == 2.6 feet.

These wavelengths matter in such things as designing organs. A typical closed end organ pipe will be 1/4 of the wave length of the sound it produces. So an organ pipe for 432 Hz would need to be 2.6/4 == 0.65 feet long. For a note an octave lower, 432/2 == 216 Hz, the pipe would have to be twice as long, or 1.3 feet long. (I'm no organ designer, so the above calculation might not be all that useful in "real organ design.")

Each octave you go up or down doubles or halves the frequency, so halves or doubles the length. Lower frequencies require longer lengths.

The speed of sound in air varies with temperature, air pressure and humidity, which is part of why wind instruments need to be tuned when playing them, if you want them to have the intended frequency, or to play in harmony with each other.

Some organs, such as the Atlantic City Auditorium organ, USA and Liverpool Cathedral Organ in the UK have 64-foot ranks giving the lowest note as 8.2 Hz.
Here's a link to a picture of the seriously big Grand Organ in Sydney’s Town Hall, Australia: http://www.australiaimg.com/wp-content/uploads/2012/09/sydney-town-hall-grand-organ.jpg

21st October 2012, 23:59
Thank's Paul!:)

I understand it now, and I've tested it out in trying to find out the wavelength 432Hz would get in space.

In space the speed of sound is 300 Kilometers/Sec which is 984251.9685 Feet/Sec.

984251.6985/432==2278.360413 Feet.

So the wavelength of 432Hz in space is 2278.36 Feet (is that right?).

A very long wavelength, and that's why in space "No One Can Hear You Scream!", because the wavelength is too long for the ear to detect.

So there is sound in space, we just can't hear it.

Could the orbits of the planets be seen as a wavelength?

And if so how could I turn that wavelength into a Hertz measurement so that I can find out the musical notes which correspond to each planet?

In order to find the 'Music of the Sphere's' that Pythagoras could apparently hear.

Or to look at it another way, if I imagined the planets to be hollow steel balls, how could I find out the frequency that would result from striking each one?

That was very interesting about the organs with their lowest note at 8.2Hz(close to the Schumann resonance ). That frequency can not be heard, but I wonder if the organ's were designed to have a psychological effect...

Paul
22nd October 2012, 00:21
In space the speed of sound is 300 Kilometers/Sec which is 984251.9685 Feet/Sec.

984251.6985/432==2278.360413 Feet.

So the wavelength of 432Hz in space is 2278.36 Feet (is that right?).

A very long wavelength, and that's why in space "No One Can Hear You Scream!", because the wavelength is too long for the ear to detect.

So there is sound in space, we just can't hear it.
Oops - a minor confusion here.

In space (the vacuum of "outer" space) the speed of light is about 300,000 Kilometers/Sec. There is no sound in the vacuum of outer space, hence no speed of sound to consider, because sound is the vibration of air, and there is rather a shortage of air in a vacuum.

Also there is an error in one of your numbers ... the speed of light is 983571056 ft/sec, not 984251 ft/sec. The decimal point was off by three places.

You are correct in calculating a wavelength by dividing the velocity by the frequency. So the wavelength of "light" in a vacuum that is 432 Hz would be 983571056/432 == 2276784 feet, or 431 miles.

The key lesson from the above is that frequencies and wavelengths are measures of the vibration of something ... don't lose track of what that something is ... sound vibrating air, light vibrating in the electromagnetic field (some would say of an ether), ...

22nd October 2012, 00:36
Oops - a minor confusion here.

Those are my middle names.:biggrin:

Cheers Paul!:)

22nd October 2012, 15:55
If I had some typical organ pipes that were the same length as the proportions on The Statue of Liberty, then I can use the wavelength formula to give me the frequency in Hertz that these pipes would produce.

http://statueofliberty.org/images/funfactsstatue.jpg
*Note also the face is 8 feet long*

Height in feet divided by 4 is the wavelength.

Speed of sound divided by the wavelength is the frequency in Hertz.

305/4=76.25 and then 1126/76.25=14.7 Hertz: In music roughly an A# note.

In the same way 151 becomes 29.8 Hertz: A# again so the proportion is in musical harmony.

111 becomes 40.59 Hertz: An E note, also 40Hz is reported to be the brains overall operating frequency. 111 is a very holy number too showing the unity of God.

The face at 8 feet would be 563 Hertz: A C# note.

The musical notes taken from these imagined organ pipes in proportion to the statue
can all be found in the A# Blues Scale, in fact E and C# are the flattened 5th and flattened 3rd respectively and are called the blue notes. The overall chord created would be A#m with a flattened 5th which sounds rather tense and dramatic.

It seems that The Statue of Liberty has got the blues!:cool:

I think I understand it now, as long as I don't go out into the vacuum of space.:)

I hope I got that right in theory, even if it is impractical in the real world. I just find it fun to think of everything in terms of music and frequency.:music:

araucaria
23rd October 2012, 16:17
I doubt it somehow. The 'Niniveh constant' is probably a much more interesting number: 70 times 60 to the power six. This works out as 1955200000 which, according to Maurice Chatelain, corresponds to the time in seconds for the entire solar system to revert to a previous configuration! It comes to about 6.2 million years, and, ...
Those numbers aren't adding up for me.

1955200000 seconds is about 62 years, not 62 million years.

70 times (60 to the power of 6) is 3265920000000, which is not equal 1955200000, but rather about 1670 times larger.

3265920000000 seconds is about 100,000 years.

So ... searching around Google, according to CHAPTER 18: THE NINEVEH CONSTANT: CELESTIAL HARMONICS (Divine Cosmos, David Wilcock) (http://divinecosmos.com/index.php?option=com_content&task=view&id=74&Itemid=36&quot;):

It's spelled the Nineveh Constant, not the Niniveh Constant.
It's 70 times (60 to the power of 7), not 70 times (60 to the power of 6)
It's 195,955,200,000, not 1,955,200,000

It is about 6.2 million years.

:)

Sorry Paul, thanks – too tired to remember straight and too tired to check.
The above years and seconds correspond to 2268 million days, equal to the following numbers of cycles:

18900

Paul
23rd October 2012, 16:58
...
So ... searching around Google, according to CHAPTER 18: THE NINEVEH CONSTANT: CELESTIAL HARMONICS (Divine Cosmos, David Wilcock) (http://divinecosmos.com/index.php?option=com_content&task=view&id=74&Itemid=36&quot;):

...
It's 70 times (60 to the power of 7), not 70 times (60 to the power of 6)
...

It is about 6.2 million years.

:)

Sorry Paul, thanks – too tired to remember straight and too tired to check.
The above years and seconds correspond to 2268 million days, equal to the following numbers of cycles:

Yes - 70 times (60 to the power of 7) seconds is the same as 2268 million days :).

24th October 2012, 03:02
...
So ... searching around Google, according to CHAPTER 18: THE NINEVEH CONSTANT: CELESTIAL HARMONICS (Divine Cosmos, David Wilcock) (http://divinecosmos.com/index.php?option=com_content&task=view&id=74&Itemid=36&quot;):

...
It's 70 times (60 to the power of 7), not 70 times (60 to the power of 6)
...

It is about 6.2 million years.

:)

Sorry Paul, thanks – too tired to remember straight and too tired to check.
The above years and seconds correspond to 2268 million days, equal to the following numbers of cycles:

Yes - 70 times (60 to the power of 7) seconds is the same as 2268 million days :).

That's fascinating stuff about The Niveveh constant, it's amazing how the ancient Sumerians knew about it, they must have been cleverer than the Mayans.

It makes me wonder what Pythagoras really learned from all those Mystery Schools he joined.

Thank's for bringing the subject up Araucaria!:) And thank's to Paul for that great link!:)

I've worked out that The Niveveh Constant is an octave of 729.99 (EDIT: 712.88 if the constant has 8 0's:confused: same note between F/F#)
so in Hertz this would make the fundamental tone of our solar system somewhere between an F and an F#.

Does anyone know how I can put "70 times (60 to the power of 7)" into a spreadsheet?
I use Open Office, but I think it would be the same in Excel. I don't know how to use the POWER function.

Also I wonder if The Niveveh Constant was encoded into the Bible, in the creation story 6 days and the 7th rest?
You know Issac Newton was always looking for hidden mathematical mysteries in the Bible.
He even worked out when the world would end, I can't remember the date he got, but I think we've got quite a long time left yet to go.

EDIT: Actually there is less time than I thought, it's 2060 AD!!
So that's the next end date to worry about. Lol:scared:.:biggrin:
http://en.wikipedia.org/wiki/Isaac_Newton's_religious_views

applecrusher1992
24th October 2012, 05:27
...
So ... searching around Google, according to CHAPTER 18: THE NINEVEH CONSTANT: CELESTIAL HARMONICS (Divine Cosmos, David Wilcock) (http://divinecosmos.com/index.php?option=com_content&task=view&id=74&Itemid=36&quot;):

...
It's 70 times (60 to the power of 7), not 70 times (60 to the power of 6)
...

It is about 6.2 million years.

:)

Sorry Paul, thanks – too tired to remember straight and too tired to check.
The above years and seconds correspond to 2268 million days, equal to the following numbers of cycles:

Yes - 70 times (60 to the power of 7) seconds is the same as 2268 million days :).

That's fascinating stuff about The Niveveh constant, it's amazing how the ancient Sumerians knew about it, they must have been cleverer than the Mayans.

It makes me wonder what Pythagoras really learned from all those Mystery Schools he joined.

Thank's for bringing the subject up Araucaria!:) And thank's to Paul for that great link!:)

I've worked out that The Niveveh Constant is an octave of 729.99
so in Hertz this would make the fundamental tone of our solar system somewhere between an F and an F#.

Does anyone know how I can put "70 times (60 to the power of 7)" into a spreadsheet?
I use Open Office, but I think it would be the same in Excel. I don't know how to use the POWER function.

Also I wonder if The Niveveh Constant was encoded into the Bible, in the creation story 6 days and the 7th rest?
You know Issac Newton was always looking for hidden mathematical mysteries in the Bible.
He even worked out when the world would end, I can't remember the date he got, but I think we've got quite a long time left yet to go.

EDIT: Actually there is less time than I thought, it's 2060 AD!!
So that's the next end date to worry about. Lol:scared:.:biggrin:
http://en.wikipedia.org/wiki/Isaac_Newton's_religious_views

60 to the power of 7 is the same as putting "=POWER(60,7)" in one cell(call it cell1), "70" in another cell (call it cell2), and then you call the "=MMULT(cell1, cell2)" in a third cell

24th October 2012, 06:17
Thank's AppleCrusher!:) That worked! I had to use ; instead of ,

It gave me 195,955,200,000,000. I think there are too many 0's:confused:

Paul
24th October 2012, 06:31
It gave me 195,955,200,000,000. I think there are too many 0's:confused:

That looks like the right number of zero's to me.

From http://web2.0calc.com/, after entering 70 * 60 ^ 7

http://thepythoniccow.us/70_times_60_pow_7.png

araucaria
24th October 2012, 11:41
There is one tiny discrepancy in these cycles due to the tropical year shortening by 16 millionths of a second per year. Chatelain uses this discrepancy to work out when the Nineveh number was first given: 64800 years ago.

24th October 2012, 21:15
Nonlinear reality is base 12. Linear reality is base 10.Different realms exist simultaneously.
Out of the subjective base 12 reality emerges the base 10 objective reality.

As the base 10 scientists discredit the base 12 reality (imagination, dreams, etc) to prove themselves right, they are compromising the integrity of Wholeness.

We are TRULY reconciling opposites at this time.

I have to say that looking at math and consciousness together is activating some remembrance. I often contemplate and use sacred geometry consciousness.
If I ever get enough people on board who can understand it enough to use its power, I intend to create a consciousness plan I wrote up several years ago.
YES! Group mind power. We don't use it enough. Why?

Thanks to all for sharing.

Blessings of peace and happiness,
Michelle Marie

Thank's Michelle Marie!:)
It's fascinating to think about different counting systems, and their effects on consciousness. I've thought of a few more questions to help me understand a little better.

1. In the base 12 system does 12+12=20?

2. When you count the hours on a clock are you using base 60?

3. When you count weeks are you using base 7?

4. When you count years are you using base 365?

5. Also, if all these units of time are measured using different base values,
does this affect our perception of time?

Paul
24th October 2012, 21:57
1. In the base 12 system does 12+12=20?

In any base 5 or higher (so long as 2 + 2 doesn't cause a carry), 12+12 = 24 :).

But I'm likely reading that differently than you were.

I am reading both the 12 and 24 in my equation "12+12=24" as being in base 12. I suspect you were reading the 12 in your equation "12+12=20" as being in 10, not base 12.

The number 12, when expressed in base 12, requires all my fingers plus four toes to express. It is two more than a dozen.

The number 24, when expressed in base 12, requires all my fingers, all my toes, four legs of my cat, and four more legs of the neighbor's cat to express. (Normal folks call that "28".)

But the 12 as it appears in the phrase "base 12" requires just all my fingers, plus just two toes to express. That is, I'm always stating the base using base 10.

===

Your other questions, involving 60 minutes in an hour, 7 days in a week, and 365 days in a year, were all expressed in ordinary base 10.

If expressed in base 60, there are 10 minutes in an hour.

If expressed in base 7, there are 10 days in a week.

If expressed in base 365, there are 10 days in a year.

24th October 2012, 23:49
Thank's Paul!:) I got confused.:confused:

I've just found this table, that helped me understand it better:

So 10 x 2 = 20 in duodecimal, but in decimal that means 12 x 2 = 24. How strange.

I was confused about time too, but this quote helped me to understand:

We use a duodecimal number system to measure time; although we annotate it in decimal.
http://ideonexus.com/2008/07/08/why-a-base-10-number-system/

So the answers are always the same no matter what base you use, just the terminology is different.

Are there any advantages to using base 12 over base 10?

I guess Mickey Mouse would use base 8.:biggrin:

http://www.mickey-mouse.com/clipart/m049.gif

29th October 2012, 02:11
I have another question.

Is there a formula to find out how the speed of sound is affected by temperature?

Like, how hot does it need to be, before the pitch is changed in a noticeable way?

Also, how can you find out what the speed of sound is, as it travels through different bodies, like water or brick?

An example would be if I were to get a loud speaker, and bypassing my ears, played a certain frequency directly into my brain,

how would the speed of the sound change as it passed through the skull, and then how would it change as it passed through the brain?

If sound can be used for healing, then these factors need to be taken into account.

Paul
29th October 2012, 03:04
Is there a formula to find out how the speed of sound is affected by temperature?
Perhaps someone else knows ... I've no idea about such things ... sorry.

Michelle Marie
29th October 2012, 19:07
I have another question.

Is there a formula to find out how the speed of sound is affected by temperature?

Like, how hot does it need to be, before the pitch is changed in a noticeable way?

Also, how can you find out what the speed of sound is, as it travels through different bodies, like water or brick?

An example would be if I were to get a loud speaker, and bypassing my ears, played a certain frequency directly into my brain,

how would the speed of the sound change as it passed through the skull, and then how would it change as it passed through the brain?

If sound can be used for healing, then these factors need to be taken into account.

Hi! math friends,

I haven't been able to keep up since I'm in the process of moving. I've been back and forth between states, and doing Lightwork on many realms. It's been INTENSE!

When I read this post, I pondered how wonderful it would be if I was settled enough to contemplate your questions. They are fascinating questions! To me they help to reconcile paradox, which means we bring things into union, balance, and harmony. These ARE auspicious times.

I'm moving fast...in fact, it feels more like I'm being moved. This rate of change is phenomenal.

In fact, "rate of change" comes to mind as a factor in this question about temperature. We need to not just look at quantity, but also qualities in the essence of the substance.

I'll get more caught up when I can, but I just wanted to check in and say why I disappeared.

Lots of love,
Michelle Marie

3rd November 2012, 05:11
A while back I tried to figure out which colours were octaves of which musical notes,
but I've just found out I made a huge mistake.

The colour green has a frequency between 530-580 Thz.

I ass-u-me-d that Thz meant Thetahertz, but it actually means Terahertz.

One Terahertz is One Trillion Hertz. I don't even know how many zero's are in that:confused:. Can anyone help me?

How do I work with such large numbers?

I want to divide 580 Terahertz by 2 enough times until it gets into the Hertz range.

Can a handheld calculator even handle such large numbers?

Also...Does anyone know how to find out the Terahertz values for a specific type of green?
(Like 'Sap Green' or 'Viridian'?)

Paul
3rd November 2012, 06:32
Also...Does anyone know how to find out the Terahertz values for a specific type of green?
(Like 'Sap Green' or 'Viridian'?)
From http://en.wikipedia.org/wiki/Visible_spectrum, here is a color spectrum of visible light, with the wavelength in nanometers (nm) indicated below the color:

Click the above image to see it full size.
The green colors have wavelengths of about 495–570 nm, which corresponds to frequencies of 526–606 terahertz (THz).

Recall that http://www.studyphysics.ca/newnotes/20/unit03_mechanicalwaves/chp141516_waves/images/v_f_lambda.png, which says velocity is equal to frequency times wavelength (I pronounce that equation as "vee equals eff lambda"). In this case, we're talking about light (electromagnetic waves), so the velocity is the speed of light, which is usually denoted as "c", and has the value of 299,792,458 meters per second in a vacuum, and slightly slower in air. Using "c" instead of "v" for light, this equation is written http://thepythoniccow.us/c_equals_freq_lambda.jpeg

So to to convert from wavelength (lambda http://www.rbjones.com/rbjgifs/lambda.gif) to frequency (f), divide the speed of light c by the wavelength http://www.rbjones.com/rbjgifs/lambda.gif.

For example, the frequency of that nice 520 nm green light in the middle of the green section in the above image has a frequency of 299792458/520 billion cycles per second. 299792458/520 is equal to 576524 GHz, or about 576 THz (there are 1000 terahertz THz in a gigahertz GHz).

I couldn't find a color spectrum marked in terahertz instead of nanometers, so you will have to convert between the two, as I describe above. But here (http://www.techexpo.com/WWW/opto-knowledge/images/Echelle_Solar_Spectra.jpg) is a color spectrum that shows the various colors of the rainbow (optical light) in more detail (still marked in nanometers - nm.)

Ah - here's an online calculator that will do this for you. See the second calculator on this page (http://www.optoplex.com/FiberOpticsCalculator.htm), which converts Wavelength (nm) to Frequency (THz). If you enter 520 for the Wavelength in nanometers (nm), it will tell you that the frequency is 576.524 THz, which is the same as the 576.524 I calculated above.

3rd November 2012, 06:59
Thank's Paul!:)

That's very useful! The visible spectrum chart in particular.

I've just found an online conversion tool for Terahertz to Hertz.

It said 1THz is 1e+12Hz.

What does 1e+12 mean?

That 'e' appears on my calculator sometime, but I don't understand it.:confused:

How many zero's in a Trillion?
And how many times do I have to divide it by 2 until it goes into the Hertz range?

P.S. I'm rather embarrassed by the fact that when I search Google for answers on this subject, one of my posts comes up from this forum, and I was wrong. :o

I'm getting back on track now, I really don't want to misinform anyone.

3rd November 2012, 07:47
Thank's Paul!:)
I've just found an online conversion tool for Terahertz to Hertz.

Paul
3rd November 2012, 08:39
It said 1THz is 1e+12Hz.

What does 1e+12 mean?
It means ten to the power of twelve.

A thousand (1000) is ten to the three or 1e+3.
A million (1000000) is ten to the six or 1e+6.
A billion (1000000000) is ten to the nine or 1e+9.
A trillion (1000000000000) is ten to the twelve or 1e+12.

The expression "1e+12" is shorthand for "one times ten to the twelve" ... the "e", standing for "exponent" is kinda of a shorthand for "ten to the power of ...".

For some simple examples, the following numbers are all equal to each other:

365.24
365.24e+0
365.24 * 1
36.524e+1
36.524 * 10
3.6524e+2
3.6524 * 100

All the above numbers are the number of days in a year - a little over 365. The strange looking "e+0" is ten to the power of zero; it's not obvious, but any positive number to the power of zero equals one. The '*' above is plain old ordinary multiplication (this stuff is not all weird.)

How many zero's in a Trillion?
12

And how many times do I have to divide it by 2 until it goes into the Hertz range?
39.86313713864835 times

To a rough approximation, 1000 (ten to the power of three) is equal to 1024 (two to the power of ten).

That is, each three zeros in a decimal number represents roughly ten doublings, or to remove three zeros one has to divide by two ten times.

To remove 12 zeros (to go from THz to Hz) one has to divide by two 12/3 == 4 times as much as to remove three (3) zeros. That is, to go from THz to Hz, one has to divide by two approximately 40 times (4 times the ten divisions needed to remove just three (3) zeros.) That approximate 40 is more exactly 39.86313713864835, the log base two of a trillion (which is what I know it as ... nevermind.)

P.S. I'm rather embarrassed by the fact that when I search Google for answers on this subject, one of my posts comes up from this forum, and I was wrong. :o
Sometimes the difference between fame and infamy is a fine line :).

3rd November 2012, 08:57
Thank's Paul!:)
I've just found an online conversion tool for Terahertz to Hertz.

Sorry, I forgot there were others who like to do this kind of thing.
Cheers!:)

Also Thank's Paul!:) 1e+12 just means add 12 zero's to it then? (1,000,000,000,000)

How do I put 1e+12 into my calculator? So I can divide it by 2^39.86313713864835.

Paul
3rd November 2012, 09:00
And how many times do I have to divide it by 2 until it goes into the Hertz range?

A more useful way to answer this would be for me to work backwards. If I use the term "octave" to mean a doubling of frequencies (as it is used with sound), then:
The wavelength 532.538 nm (a green color) is equal to the frequency of 562.950 THz, which is exactly 49 octaves above 1 Hz.
The wavelength 619.681 nm (a reddish orange) is equal to the frequency of 483.785, which is exactly 40 octaves above 440 Hz.
The wavelength of the oxygen (O2) spectral line is 627.661 nm, which is equal to the frequency of 477.634, which is exactly 40 octaves above 434.4 Hz. This is the red color marked with the lower case 'a' on the chart at http://www.techexpo.com/WWW/opto-knowledge/images/Echelle_Solar_Spectra.jpg.

Paul
3rd November 2012, 09:06
1e+12 just means add 12 zero's to it then? (1,000,000,000,000)
Yes.

How do I put 1e+12 into my calculator? So I can divide it by 2^39.86313713864835.
I'm not sure. What kind of calculator do you have?

(I suppose you could key in 1000000000000.)

If you do it right, then 1e+12 divided by 2^39.86313713864835 will equal exactly 1 (within the accuracy of your calculator.)

¤=[Post Update]=¤

Ah - if that '^' lets you do exponents on your calculator, then you can put 1e+12 into your calculator by entering "10^12".

3rd November 2012, 09:08
The wavelength of Oxygen!!!!! Wow! I've never heard of such a thing! That's great! Thanks!:)

I've just typed 434.4 * 2^40 into my calculator and got 4.776278511 (x10 14).
So I only have to move the decimal place two times to the right to get the Terahertz value (I assume).

EDIT: My calculator only has 10 digits. I think I've sorted it now. Cheers!:)

EDIT2: 39.86313713864835 won't fit in my calculator so I just put in as much as I could, and the answer was 1*10^12/2^39.86313713==1.000,000,006. Near enough.

Paul
3rd November 2012, 09:13
4.776278511 (x10 14)
10^14 Hz is the same as 100 * 10^12 Hz is the same as 100 THz.

So I only have to move the decimal place two times to the right to get the Terahertz value (I assume).
Yes.

4th November 2012, 12:31
An update on my progress. Here are the colour to note values I have figured out
from what I have learned here.
http://projectavalon.net/forum4/attachment.php?attachmentid=19083&thumb=1&d=1352025696
The circles of colour next to the notes and wavelengths are taken from this image:

It seems that the colours for the notes F,F# and G are either on the edge or outside
of our field of vision, and yellow doesn't have a note assigned to it
from the standard 12 note system tuned to 440Hz.
Tuning to 448 instead of 440 would fix this, and make the music a little brighter.

I don't know how accurate the 'Rendered Spectrum' image is in terms of colour,
so I placed a colour wheel in the centre of the image and rotated it into place,
as my best guess. The yellow is in the right place though for sure.

Thank's for your help Paul!:) I'm going to remedy my old post now with this more accurate image. I won't delete the post, I will just add this image to the end and admit that I was completely wrong first time around.

11th November 2012, 11:11
The wavelength of the oxygen (O2) spectral line is 627.661 nm, which is equal to the frequency of 477.634, which is exactly 40 octaves above 434.4 Hz. This is the red color marked with the lower case 'a' on the chart at http://www.techexpo.com/WWW/opto-knowledge/images/Echelle_Solar_Spectra.jpg.
[/LIST]

I've only just realized the significance of the Fraunhofer Lines in that link.
I can find out what the Sun is made of, and (what's more exciting to me) what it sounds like! Cool!:cool:

Is there anywhere I can find out the wavelengths for all of the chemical elements?

I've been reading about Balmer's Formula for Hydrogen emissions, which I don't
understand at all quite yet. I will probably ask about that sometime next week.
(It interests me greatly, but I need to get my head around it before I can even

It seems that I've placed my foot on the first rung on the ladder of Quantum Theory, without even noticing. And what a strange ladder that is....

Thank's Paul!:)

Paul
11th November 2012, 16:28
Is there anywhere I can find out the wavelengths for all of the chemical elements?
Try searching Google for something like "spectral lines of elements".

When I did that, one of the images I found looked useful: http://jersey.uoregon.edu/elements/Elements.html

But look around at other results from that search as well.

28th November 2012, 03:40
I've got another question to do with music.

To find out the effect of adding 100 Cents to 440 Hertz, you do this:

440Hz*1.0005777895^100 = 466.16Hz

My question is how do I change this formula around to give me the Cent value?

Say I know the end frequency is 466.16 Hertz and I know the start note is 440 Hertz.

How do I find out how many times 440 has been multiplied by 1.0005777895 to get to 466.16?

I don't know much about Algebra, and the rules for changing formulas...
I guess it would look like this: A*B^C=D.
So If I know A,B and D, how do I change the formula to give me C as the answer?
Does the ^ symbol have an opposite?:confused:

Paul
28th November 2012, 04:52
I guess it would look like this: A*B^C=D.
So If I know A,B and D, how do I change the formula to give me C as the answer?
Does the ^ symbol have an opposite?:confused:
The opposite of the exponential ^ is the logarithm (log). Using logarithms to base 10, for x any positive number, log(10^x) == x == 10^(log(x)).

The following steps show the conversions need to solve your original equation for the value of C, given the values of A, B and D.

A*B^C == D #########Original equation
B^C == D/A #########Divide by A
log(B^C) == log(D/A) ###log() both sides
C * log(B) == log(D/A) ###See below
C == log(D/A) / log(B) ###Divide by log(B)

Given that:

A == 440
B == 1.0005777895
D == 466.16

then:

C == log(466.16/440) / log(1.0005777895) == 99.986
The key conversion from step 3. to 4. above depends on knowing that "log(B^C) == C * log(B)"

6th December 2012, 06:39
I guess it would look like this: A*B^C=D.
So If I know A,B and D, how do I change the formula to give me C as the answer?
Does the ^ symbol have an opposite?:confused:
The opposite of the exponential ^ is the logarithm (log). Using logarithms to base 10, for x any positive number, log(10^x) == x == 10^(log(x)).

The following steps show the conversions need to solve your original equation for the value of C, given the values of A, B and D.

A*B^C == D #########Original equation
B^C == D/A #########Divide by A
log(B^C) == log(D/A) ###log() both sides
C * log(B) == log(D/A) ###See below
C == log(D/A) / log(B) ###Divide by log(B)

Given that:

A == 440
B == 1.0005777895
D == 466.16

then:

C == log(466.16/440) / log(1.0005777895) == 99.986
The key conversion from step 3. to 4. above depends on knowing that "log(B^C) == C * log(B)"

Thank's Paul!:)

That will come in useful. I've been able to follow the steps on my own without looking at the answers,
but I still don't know what's happening in steps 3 to 4. Why does log(B^C) == C * log(B)?

Also If I used the same formula A*B^C=D, and if I knew A,C and D, how would I find B?

I guess I would follow the same steps as before to get to here: log(B^C) == log(D/A),
but what would I do next?

>>>> Unrelated Question<<<<
Also, on a totally different topic. If I have a sound sample and I reduce the playing speed by 50%,
what I am really doing is doubling the wavelength and thus halving the frequency. Is that right?

Oh! Also, would it be possible to update the fonts in the forums text editor to
include a Greek font? That way it would be easier to include mathematical and scientific terms like Phi, Pi and Lambada without having to search for images. A Hebrew font would be nice too for more spiritual reasons. Others may also like an Arabic font, or any other holy Alphabets. Would this be an easy thing to do?

Paul
6th December 2012, 07:13
Why does log(B^C) == C * log(B)?
Try reading this explanation: http://oakroadsystems.com/math/loglaws.htm, under the sub-title "Exponent, Multiply the Logarithm"

Also If I used the same formula A*B^C=D, and if I knew A,C and D, how would I find B?

The following steps show the conversions need to solve your original equation for the value of B, given the values of A, C and D.

A*B^C == D ###########Original equation
B^C == D/A ###########Divide by A
log(B^C) == log(D/A) ######log() both sides
C * log(B) == log(D/A) #####As before
log(B) == log(D/A) / C #####Divide by C
B == 10 ^ ((log(D/A) / C) ###Raise both sides to power of 10

Paul
6th December 2012, 07:17
Also, on a totally different topic. If I have a sound sample and I reduce the playing speed by 50%,
what I am really doing is doubling the wavelength and thus halving the frequency. Is that right?
That sounds right.

Oh! Also, would it be possible to update the fonts in the forums text editor to
include a Greek font? That way it would be easier to include mathematical and scientific terms like Phi, Pi and Lambada without having to search for images. A Hebrew font would be nice too for more spiritual reasons. Others may also like an Arabic font, or any other holy Alphabets. Would this be an easy thing to do?
That would be nice, but so far as I am aware, that would not be easy :).