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Vibrating Numbers.Octave-like Scale of Calculation

Decimal calculation system is used in the world. It consists of 9 numbers. If to emagine, that these numbers are notes, we will get an octave of nine notes and if one writes the combination of numbers it will sound as though notes, and when zero will be written it will mean, that not any note sounds.

We can imagine the piano octave consisting from 9 notes and having a lot of octaves

 

Looking at this table we can see that after the reduction numbers of notes in all octaves are the same. So the number after reduction or vibrating number shows the note number in the first octave.
Vibrating numbers can also be found by other means.
For example:

Example 1
Int - the whole part of a number, that means the number without commas
FIRST STEP
Int (10 / 9) = 1
10 – the number which turns into vibration number
9 - the last digit in decimal notation
1 – the result of dividing without comma

SECOND STEP
10-9 * 1 = 1
1 - vibration number
Example 2
int (154 / 9) = 17
154-9 * 17 = 1
or 1 + 5 + 4 = 10 = 1 + 0 = 1
You can find vibrating numbers for different notation systems. For example, duodecimal

system: int (154/12) = 12 154-12 * 12 = 10, hence 10 is the vibrating number.

Number Harmonics.
 If to imagine that the number represents the number of string vibrations per second, we can find the number harmonics. When the string
vibrates except the main vibration other higher vibrations in 2,3,4,5,6 ... n times are produced, but with smaller amplitude. They are called harmonics. There are 9 notes in Decimal Scale of Calculation. Thus it is the same as 9 strings having 1,2,3,4,5,6,7,8,9 vibrations per second.
Let us find their harmonics:

 

 

 
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