Constant major thirds scale

First I put m and p semitone factor variables alternatively :
C x m = C#
C# x p = D
D x m = Eb
Eb x p = E .... etc.

(m^6)(p^6)= 2

I assumed that G = 1.5 = (3/2)

Valid equations:
A)(m^4)(p^3) = 1.5 = (3/2)

B)(m^2)(p^3)= 4/3

(A)/(B) = m^2 = 9/8

m = (9/8)^(1/2)
-------
p = [(32/27)^(1/3)]= 1.05826736798

By assuming that octave 2 = X^3, we get the following tone frequencies

E = (2)^(1/3)= 1.25992104989

Ab = (E)^2 = (2)^(2/3)= 1.58740105197

2C = 2
----------
Since (3/2)= (m^4)(p^3)= (X^2)(p^5), we can use the second function.
X = [(3/2)(27/32)^(5/3)]^(1/2)= 1.06305838585.

Semitone factor arrangement:
X p p p X p p p X p p p

A new scale having equal major thirds follows:
C = 1
C# = 105.865 cents
D = 203.91
Eb = 301.955
E = 400
F = 505.865
F# = 603.91
G = 701.955
Ab = 800
A = 905.865
Bb = 1003.91
B = 1101.955
2C = 2
The chords of this scale sufficiently differt from those of 12 TET.
A pamphlet regarding this entonation has been written and registered.

Mario Pizarro
piagui@...

Lima, February 19, 2010