Harmonics overview.
Consider the harmonic series: 1, 1/2, 1/3, 1/4, 1/5, 1/6......
Consider the counting numbers: 2, 3, 4, 5, 6, 7
The harmonic series represents the reciprocals of the counting numbers.
Consider the counting numbers: 2, 3, 4, 5, 6, 7
The harmonic series represents the reciprocals of the counting numbers.
Deriving the omnits from logical steps.
"Omnits" are numbers that are omnidivisible by consecutive factors starting from 2. They are highly composite numbers and do not represent the entire set of highly composite numbers. Starting from 2 to derive the next omnit we multiply by 3 to obtain six. Six is the "omnit of 3". The next omnit is also divisible by 4 and since six is already divisible by 2 we need only multiply 6 by another factor of 2 to obtain twelve. Twelve is the "omnit of 4". To obtain the next omnit we multiply 12 by 5 to obtain 60 which also is divisible by 6. 60 is the "omnit of 5 and 6". To obtain the next onmit we multiply 60 by 7 to obtain 420. To obtain the next omnit which captures 8 we know that the previous omnit is divisible by 4 so we need only multiply 420 by 2 to obtain 840. 840 is the "omnit of 8". Since this omnit is divisible by 3 to obtain the "omnit of 9" we need only multiply 840 by 3 to obtain 2520 which is also divisible by 10. Thus 2520 is the "omnit of 9 and 10.
Thus far we can state the steps that has just been completed mathematically as:
2 x 3 = 6
6 x 2 = 12
12 x 5 = 60
60 x 7 = 420
420 x 2 = 840
840 x 3 = 2520
Thus far we can state the steps that has just been completed mathematically as:
2 x 3 = 6
6 x 2 = 12
12 x 5 = 60
60 x 7 = 420
420 x 2 = 840
840 x 3 = 2520
Harmonic Triangles
Harmonic Triangles are derived from Omnits. Omnits in turn
were defined earlier as highly composite numbers with consecutive divisors starting from 2 which are the culmination of a cyclical reflective pattern revealed in certain "synchrographs". Diagram 6 described in detail later shows a harmonic triangle at level 2520 where 2520 is the omnit evenly divisible by the consecutive numbers 2-10. Because of the special property on omnits they can be used to describe the harmonic series using whole numbers.
were defined earlier as highly composite numbers with consecutive divisors starting from 2 which are the culmination of a cyclical reflective pattern revealed in certain "synchrographs". Diagram 6 described in detail later shows a harmonic triangle at level 2520 where 2520 is the omnit evenly divisible by the consecutive numbers 2-10. Because of the special property on omnits they can be used to describe the harmonic series using whole numbers.
The simplest harmonic triangle
From Diagram 1 we have A3 = C1
From diagram 2 we have: A1 - A2 - A4 = D1
From diagram 3 we have: A6 = E1