The Pure Natural Tuning is based on the natural overtone series.

A tuning system consists of the reference frequencies and intervals based on these reference frequencies .

Music consists of frequencies (vibrations). A piece of music usually has a reference frequency, for example „Bach Johann Sebastian – Prelude No. 1 in C major“.
However, this does not make any statement about the pitch.
How should the piano be tuned? You need an indication of the physical frequency, e.g. 440 Hz for the A4 tone. There are quite a few opinions as to which is the correct reference pitch for the tuning of instruments, which is the right concert pitch ?
The answers are diverse and interspersed with ideological trench wars.

The natural ordering system of reference frequencies, which is derived from the frequency of 1 Hz, solves the contradictions of the 432 Hz – 128 Hz discussion in a simple, natural way. First of all, it is based on the natural overtone series or on the tuning .

The base frequency of this tuning system is 1 Hz ( 1 oscillation per second ).
The eighth octave of 1 Hz is 256 Hz.
An octave means doubling a frequency.
If the reference frequency = 1 Hz = one oscillation per second, then the first octave has 2 x 1 = 2 Hz,
the second 2 x 2 = 4 Hz,
the third 2 x 4 = 8 Hz, the fourth 2 x 8 = 16 Hz, the fifth 2 x 16 Hz = 32 Hz, the sixth 2 x 32 = 64 Hz, the seventh 2 x 64 = 128 Hz and the eighth octave 2 x 128 = 256 Hz.
Octave row :
0-1-2-4- 8-16-32-64-128-256-512-1024-2048-4096-8192-16384-32768 ………

The naturally pure tuning system means on the one hand the definition of 1 Hz as the base reference frequency and on the other hand the successive processing of the following higher reference frequencies. In this way we also get to the frequency of a ‚= 432 Hz.
However, this can only be achieved by including the pure tuning .

The reference frequencies are always odd, whole, natural numbers and can be assigned to the traditional fundamental tones of the major scale.

The system consists of the reference frequency and other intervals related to the fundamental tone , the frequency ratios of which are the quotients of small whole numbers. This is the case with the
pure mood.

The pure tuning system is based on the natural overtone series and can therefore also be called a natural system.

The tuning system also refers to Pythagoras.
Since number and its qualities such as polarity, harmony and proportion are archetypal principles underlying the physical manifestation, Pythagoras‘ mathematics is discovered rather than invented and has the ability to reflect the essential nature of reality rather than just modeling it or to describe. In addition, in the Pythagorean view, because the number is universal, it is also divine. While modern science is understood experimentally, ancient Greek science was mathematical.

All frequencies with the intervals at a glance and in detail.