The ratios $256/243, 25/24, 16/15$ are known as the minor
Pythagorean, chromatic, and diatonic semitone, respectively.
The main result of this paper is the following statement
which has a valuable consequence for the music acoustic
theory:

{\sl According to the symmetry, all rational triplets $(X_1,
 X_2, X_3)$ TDS-generating generalized geometrical
 progressions $$\left\langle\Gamma_i\right\rangle =
 \left\langle X_1^{\nu_{i, 1}} X_2^{\nu_{i, 2}} X_3^{\nu_{i,
 3}};   \nu_{i, 1} + \nu_{i, 2} + \nu_{i, 3} = i, 0 \leq
 \nu_{0, \cdot} \leq   \nu_{1, \cdot} \leq \dots \leq
 \nu_{i, \cdot} \leq \dots\right\rangle_{\nu_{i,\cdot} \in
 {\cal N}^3} $$ with the subsequences \begin{center}
 $\left\langle\Gamma_{12 l}\right\rangle = \left\langle
 2^l \right\rangle, \left\langle\Gamma_{12l +
 7}\right\rangle = \left\langle 3 \cdot 2^{l-1}
 \right\rangle, \left\langle\Gamma_{12l + 4}\right\rangle =
 \left\langle 5 \cdot 2^{l-2} \right\rangle$ \end{center}
 are exactly the following: $$ (25/24, 135/128, 16/15),
 (256/243, 135/128, 16/15), (25/24, 16/15, 27/25).$$}

Thus, not only the diatonic and chromatic but also the minor
Pythagorean semitone (together with the diatonic semitone
and its complement  to the major whole tone) can serve as a
basis for the construction of  12-degree diatonic scales.
