https://m.soundcloud.com/lracd/finale-feat-fruityloops-rewire

My new piece of music. Learning how to compose music on Fl studio and then finish the touch ups on Finale. 

 

Solution of infinite procedures (without words, I apologize, just take it as art or ask me for an explanation and I would be happy to provide one)

A measure of consonance. I'll test it later. (Consonance is not a measurement of how good pitches sound, but instead how long two waves of different periods must be propagated in order to have them sync back up. Like setting two toy trains moving the same velocity on two circular tracks of differing circumferences and timing how long it takes the trains on the short track to catch up with the train on the longer track.)

Sounds that take longer are regarded as more distinct because they literally just don't pair up often.

Corrections to my neuron. Several aspects were wrong, upon cursory observation, but that's ok. No normalization of the sine product in this version because that makes problems for integer evaluations.

 

Doing the inverse of the first formula, get F(n-2)=F(n-1)/F(n). Should use modulus operators, but MEH. If want tangent, which is F(3), we know that this is F(2)/F(1) = F(3), and since F(2)=Sin and F(1)=cos, Sin/Cos = Tan. cos^2+sin^2=1, 1^2+tan^2 = sec^2, cot^2+1^2=csc^2

Calculator can't tell you how to use it or remember each one or all the formulas that relate them.

 Sine Function   

In that animation, the angle of that triangle in the circle and the height of the triangle are correlated by the sine function. Cosine is the base. But only when the radius of the circle is 1. Else it's r*cos(angle) or r*sin(angle)  

Sine and cosine look similar to each other. 

Now, looking at that triangle I showed you at first, it is clear that when the height is 1, the base is zero, and vice versa. When sin(0) = 0 since at zero degrees the height is zero. sin(90) = 1 since the height is of the triangle becomes equal to the radius at 90 degrees. cos(0) = 1, since cosine is just the base length and the triangle is all base at an angle of zero. Tan is the slope, because it is a ratio of y/x, which in this case is Sin/Cos or Height/Base

All of this can be used to do things like find out how tall something is without ever reaching it, based on angles a multiple positions. It is also how triangulation works, and this helps to locate where you are using only a few cell towers. 

    

  

 

Working on logic. I think understanding 'or' to mean 'union', 'and' to be 'intersection' and 'xor' as it is, this become a lot less confusing.

I wanted, basically, to give xor for two circle in three, so I had to admit c using the "implies" operator.

((A xor B ) and not C) or (B xor C and not A) = (A and B and C) xor A xor B xor C

or

((A xor B) and not C) or (B xor C and not A) = (A and B and C) xor A xor B xor C (Translated by Bing)   

Butterfly Curve

http://en.wikipedia.org/wiki/Butterfly_curve_%28transcendental%29