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

The derivative of f(x) is a transformation g on f(x), hence, you can find g(x) to be the same effect reinterpreted to 'x'. This reminds me of linear algebra for some reason.

Geometric construction of a beam sweeping around a room from a point, and another beam sweeping around the same room from a different point, where both beams remain to have the same destination.

Because the difference (x+1)^(1/2)-x^(1/2), as x approaches infinity, approaches zero, we are allowed to say that this approaches the derivative of the first term, with respect to x. That is, if the function is becoming more like a horizontal line as our position on the x-axis increases toward infinity, the better a line approximates the change over any sub-interval starting from your position to any position ahead.

A relation I will likely be using to do regression for non-linear plots.

If a teacher asks you to find out the coefficients on some specific polynomial that joins a list of points, they are asking you to do a job that a computer can do in seconds. You can learn to program in minutes, and by pen and paper takes hours.

Cos approximation on the interval of pi/2 to 2pi (tau/4 to tau) using interpolation and regression. Points chosen from the cos function where equally spaced apart, and there are 5 points in total it uses to come to this approximation. My program will be ready to learn soon enough.

The behavior of an algorithm.

Algorithm-Fitting a series of curves to a set of points without over-fitting.

A useful fact.

Useful, because the groups of length k-1 are used to form each group of length k, in the same that [1 2 3] becomes [0 1 2 3]+[1 1 1 1]

[1 2 3 4] 

A conjecture, related to the prime sieve list length.

function primes = Sieve(x)
primes = 2;
feature accel on
for i=1:x
vi = primes(end)+1:2*max(primes);

for j=1:i
vi = vi((vi/primes(j)-floor(vi/primes(j)))~=0);
end

primes = [primes vi];
end
feature accel off

end

Related to finding a good way to preallocate for the prime list. 

 

Probably will convert the values to strings and stick them in a cell array with an approximately appropriate reallocated length, and then just get rid of empty cells.

I would use it for x>6,
rather, x>=6

 

 

 

The top and bottom are of the same form, this reduces in all cases

 

 

 

 

The non-unique results seem very few and almost seem regular but I am not sure yet.

 

 

 

 

 

 

Because they could! Now to move on to a way of representing shapes by uniquely projecting points that construct them onto the real plane, given by the nature of the reals themselves.

Minor + (Major - Mixolydian) = Harmonic Minor

[0 2 3 5 7 8 10 12] + ([0 2 4 5 7 9 11 12] - [0 2 4 5 7 9 10 12]) =

[0 2 3 5 7 8 10 12] + [0 0 0 0 0 0 1 0] = [0 2 3 5 7 8 11 12]

Because Linear Algebra is legit

The only thing I don't get about the orbifold representation of chords is that chord inversions do actually effect the transition probabilities from chord to chord in most musical styles, because many musical pieces are composed voice by voice, and there is even correlation over time that gives rise to such techniques as suspensions and anticipations. (D-G-Bb) ---> (D-F#-A) are very near when inversion is taken into account, and it is easy to see that the pedal tone on D is justified by way of the progression G minor (2nd inversion) ---> D major (root)

"Observe what happens when sunbeams are admitted into a building and shed light on its shadowy places. You will see a multitude of tiny particles mingling in a multitude of ways... their dancing is an actual indication of underlying movements of matter that are hidden from our sight... It originates with the atoms which move of themselves [i.e., spontaneously]. Then those small compound bodies that are least removed from the impetus of the atoms are set in motion by the impact of their invisible blows and in turn cannon against slightly larger bodies. So the movement mounts up from the atoms and gradually emerges to the level of our senses, so that those bodies are in motion that we see in sunbeams, moved by blows that remain invisible."Lucretius

Math and Religion

Even if there are any infinite number of mutually exclusive religions each with a probability of some unique negative integer power of two, such that;
1/2,1/4,1/8,1/16...
 
And your religion is that which bears the probability 1/2, then the probability of your religion not being the right one is equivalently 1/2, since the limit of the series is 1. And even this is far too generous, since we assumed many things we were unaware of, such as
 
1.) There is a true religion
2.) The probability distribution for truth of all mutually exclusion religions may be given as the series 1/2+1/4+1/8...
3.) Supporting evidence that would allow partial construction of a probability distribution.
4.) The highly fortunate circumstance that the religion ascribed to by the believer is assigned the highest probability of truth of any single religion within the distribution.

Without these assumptions, however, the situation of choosing the correct religion is nearly impossible. And if faith is the only evidence one has for the correctness of their religion, anyone else's faith in any other belief is just as potent a demonstration of truth, which then lends equal probability to these contrasting assertions.