The theory behind the waves based on the golden number

The golden number comes from the divine proportion that divides The whole into parts by an ideal ratio, so that every part will reflect the whole. The principle which is at the base of the universe in creates and sustains it.    

Mathematically the entire reported by a part must be equal to the ratio of the two divisions.    

1/a = a/b    

1/a = a/(1-a) 

1=a*a+a 

a=0,618033988....
(phi)=1/a=1,618033988....    

Divine ratio is a perfect ratio which creates everything

Thus we have obtained an ideal primary division. To keep this perfection we must continue in the same way, the obtained divisions we divide them by the golden ratio. This way you can get a perfect growth and division that maintains the holistic principle: the part in everything and everything in the part. This principle is also used in fractals.     

Mathematically we can write:

It is a growing and an indefinitely dividing formula that can grow infinite keeping the original harmony.      

Non-linear time concept

The symmetrical sinusoid (classic sinusoid) is based on a linear time but the time is non-linear! Golden sinusoid is based on a non-linear time, cyclical with a waveform variations too. So this is the way how we generate the Golden Sinusoid in our generators. Below are the graphical results.

Golden  waveforms 

Golden Triangle Wave:

We start with the triangle golden wave because basis on its we generated the sine wave.   

Golden Sinusoid:

Using the non-linear time concept, we apply a triangle wave on the time axis and then generate a classical sinusoid. So we got  a divided wave cycle in two perfect divisions through the golden ratio as follows:   

Golden Sine Half: 

Golden Square Wave:

In this way we obtained pure, ideal waveforms, with a specific timbre, excellent for binaural beats. You can make a lot of music applications or pure sounds in the therapeutic, psychological or spiritual domain and in electronic music.    

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This waveforms were discovered by EmRysRa, all rights regarding such wave shapes and concepts by: golden waveforms, golden sinusoid, golden triangle wave and golden square wave are exclusively reserved by © EmRysRa.

If you wish to use these waveforms for publication or post material that contains notions mentioned above it is absolutely necessary to specify the author's name and if the Internet is a medium for publication must add the website address  http://www.emrys.ro/en or http://vst.saschart.com