Does the model of bioharmony explain the major and minor scales?

The details of the bioharmony model have remained unclear. Bioharmony model (see this and this) predicts that 64 genetic codons can be identified as 64 3-chords as faces of 3 copies of icosahedron and one tetrahedron. This structure emerges from icosa tetrahedral tessellation (ITT) (see this this). There is an intriguing correspondence with the TGD based model for the icosahedral supercluster of water molecules and the supercluster is proposed to be in 1-1 correspondence with the realization of ITT at the field body of the system in terms of dark DNA (see this). The recent finding that animals communicated in frequency range peaked around 2 Hz gives additional support for the model (see this).

There are however long standing objections against the bioharmony model. In particular, the model predicts 12-note scale and complex bio-harmonies with 64 3-chords but does it allow us to understand the simplest major and minor scales and corresponding 3-chords?

1. Quint cycle modulo octave equivalence gives the notes of 12-note scale. This scale can be deformed to well-tempered scales in which notes correspond to powers of 2^1/12 modulo octave equivalence. The cycle FCGDAEH gives the notes of the major scale. 3 + 1/2 octaves are involved. Note that the quint cycle spans the note-scale of classical guitar. Also the minor scale is obtained. What remains missing are the altered notes F_# and G_#.

Interestingly, the recent findings about animal communications containing frequency range .5 Hz -4 Hz and also higher frequencies are consistent with the range of 3 and 1/2 octaves (see this).

If the quint cycle is continued, notes which do not belong to the basic scale appear and eventually give the 12-note scale. One can say that the standard scale emerges naturally.

The problem is that the icosahedral part of the bioharmony does not contain in a natural way major and minor chords containing minor third (e.g. CEG and ACE). Could the tetrahedral part of the bioharmony come to rescue? One can consider several options for tetrahedral harmony. The basic condition is that one obtains the major and minor chords. This is true if the tetrahedral scale contains edges defining minor third, major third and quint.

1. For the first option the tetrahedron does not share faces with the icosahedron and the tetrahedral Hamilton cycle is closed and corresponds to an octave. The simplest assumption is that the edges of the cycle correspond to minor thirds but one can also consider other options. 2 edges do not belong to the cycle. The notes of the 4-note cycle starting from A correspond to ACE_bF_#A. This does not allow chords containing minor third and major third.

It seems that one must give up the ACE_bF_#A scale. The tetrahedral cycle CGEAC however satisfies the constraints: the faces contain quint CG, major third CE, and minor thirds AC and EG. The 4 tetrahedral chords are CEG(major), ACE (minor), and AGC and EAG.

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.