reply to post by truthseeker10
write down your theory in mathmatical terms
I am sure that you wouldn't understand but I will give you a clue and that's all because I presented to much proof and that was to much
contested.
ext text
"
A "Harmonic Tree" is a series of intervals that branch off from one another relative to the harmonic series. It is a structure based on simplicity,
requiring only multiplication and division.
A "Harmonic Tree" is created through the process of repeatedly choosing a harmonic interval while feeding back the previous value. Each new interval
can be chosen either explicitly, at random or using any other process.
The "destination" refers to the harmonic to which the new frequency is relative. The "relative" is the relative harmonic to which the new
destination harmonic is relative. Combined, they create the interval destination/relative. For each branch created, the previous destination harmonic
becomes a new relative harmonic. See figure 1.
r = relative harmonic
d = destination harmonic
r1:d1
|
r2:d2
|
r3:d3
|
r4:d4
|
...
|
rn:dn
Figure 1 - Harmonic Tree Diagram
1:2
|
2:3
|
3:4
|
4:5
|
5:6
|
6:7
|
7:8
Figure 2 - Harmonic Tree of the Harmonic Series up to the 8th Harmonic
Mathematically, each new value is derived by multiplying the previous value with an integer 1 or greater (destination) divided by an integer 1 or
greater (relative).
x = value
d = destination harmonic
r = relative harmonic
f(xn+1) = f(xn) * d / r
Figure 3 - Basic Harmonic Tree Equation
If you wanted to use the "Harmonic Tree" for getting pitches, assign x a starting value. In this next example, x is assigned 100. The relative and
destination harmonics are assigned random harmonic integers between 1 and 5.
f(xn+1) = f(xn) * int(rand(5) + 1) / int(rand(5) + 1)
1:5
|
3:2
|
4:2
|
3:4
|
1:3
f1 = 100
f2 = 100 * 5 / 1 = 500
f3 = 500 * 2 / 3 = 333.333
f4 = 333.333 * 2 / 4 = 166.666
f5 = 166.666 * 4 / 3 = 222.222
f6 = 222.222 * 3 / 1 = 666.6"source(
csounds.com...
What is the harmonic tree of our planet?
