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Message: Re: Base 12 - the octave as foundation for the study of prime numbers

Changed By: fluo2005
Change Date: June 26, 2021 05:44PM

Re: Base 12 - the octave as foundation for the study of prime numbers
Hi Treblebypass,

You can email me at fluo2005@gmail.com. Or we can post on this forum or the one below so all can see.

Using base 12, I discovered a way to produce the list of all the prime numbers, and posted it on mathforums.com recently. Not on this site, because base 12 work had no followers.

The posters on mathforums.com basically state that all I've done was repeat the sieve of Eratosthenes, which uses the addition of primes to remove their composites from the list of whole numbers, conceived 2,300 years ago I am told.

They also claim that base 12 is no way better than base 10, or any other base. I disagree, because base 12 can create two musical staffs which show all the notes of the octave, removing the need for sharps and flats. This provides for immediate musical literacy. These two patterns can also be applied to the piano keyboard, modifying its appearance substantially, and improving both note and chord recognition.

Have a look at my latest post on mathforums.com which is a verbal rendition of the algorithm I used. It uses multiplication rather than addition, because using factors rather than the difference with previous values makes it easier to understand what is going on.

Here is the link: mathforums.com/threads/how-to-remove-prime-composites-and-reveal-the-primes-in-base-12.358553/

It will take me a while to answer the last post because it covers so many topics and will require research on my part.

The one important discovery I made with base 12 concerning prime numbers is that base 12 creates the list of all the prime numbers starting with 5 on up, and of all the composites of prime numbers starting with 5 and up. They are all found when you add 12 in layers to intervals 1 5 7 11 in order to create columns of indefinite size.

I call this list the 'list of possible primes', because you don't know just by looking at large numbers which are prime and which are composite, except for those that end with 5.

Prime numbers 2 and 3, and all the composite numbers they create, are all found in intervals 0 2 4 6 8 9 10.

Base 12 in music uses the semitone as the basic interval, and not the tone, which is a variable containing either two semitones or one only (algebra). So it provides a proper name to the five black keys. It also breaks the scales into two half-units containing four notes, but covering 7 note spaces. And it breaks the 12 semitones into two families, the whole tone scales, coloring one family of six tones white, and the other family black.

I am wondering what other discoveries if any can be made in the world of prime numbers using base 12 as a foundation.

Original Message

Author: fluo2005
Date: June 26, 2021 05:19PM

Re: Base 12 - the octave as foundation for the study of prime numbers
Hi Treblebypass,

You can email me at fluo2005@gmail.com. Or we can post on this forum or the one below so all can see.

Using base 12, I discovered a way to produce the list of all the prime numbers, and posted it on mathforums.com recently. Not on this site, because base 12 work had no followers.

The posters on mathforums.com basically state that all I've done was repeat the sieve of Eratosthenes, which uses the addition of primes to remove their composites from the list of whole numbers, conceived 2,300 years ago I am told.

They also claim that base 12 is no way better than base 10, or any other base. I disagree, because base 12 can create two musical staffs which show all the notes of the octave, removing the need for sharps and flats. This provides for immediate musical literacy. These two patterns can also be applied to the piano keyboard, modifying its appearance substantially, and improving both note and chord recognition.

Have a look at my latest post on mathforums.com which is a verbal rendition of the algorithm I used. It uses multiplication rather than addition, because using factors rather than the difference with previous values makes it easier to understand what is going on.

Here is the link: mathforums.com/threads/how-to-remove-prime-composites-and-reveal-the-primes-in-base-12.358553/

It will take me a while to answer the last post because it covers so many topics and will require research on my part.

The one important discovery I made with base 12 concerning prime numbers is that base 12 creates the list of all the prime numbers starting with 5 on up, and of all the composites of prime numbers starting with 5 and up. They are all found when you add 12 in layers to intervals 1 5 7 11 in order to create columns of indefinite size.

I call this list the 'list of possible primes', because you don't know just by looking at large numbers which are prime and which are composite, except for those that end with 5.

Prime numbers 2 and 3, and all the composite numbers they create, are all found in intervals 0 2 4 6 8 9 10.

Base 12 in music uses the semitone as the basic interval, and not the tone, which is a variable containing either two semitones or one only (algebra). So it provides a proper name to the five black keys. It also breaks the scales into two half-units containing four notes, but covering 7 note spaces. And it breaks the 12 semitones into two families, the whole tone scales, coloring one family of six tones white, and the other family black.

I am wondering what other discoveries can be made in the world of prime numbers using base 12 as a foundation.