Geometric theory of bioharmony
For some years ago I developed a model of music harmony. As a surprising side product a model of genetic code predicting correctly the number of codons coding given aminoacid emerged. Since music expresses and creates emotions, one can ask whether genes could have "moods" characterized by these bioharmonies. The fundamental realization could be in terms of dark photon triplets replacing phonon triplets for ordinary music.
 The model relies on the geometries of icosahedron and tetrahedron and representation of 12note scale as so called Hamiltonian cycle at icosahedron going through all 12 vertices of icosahedron. The 20 faces correspond to allowed 3chords for harmony defined by given Hamiltonian cycle. This brings in mind 20 aminoacids (AAs).
 One has three basic types of harmonies depending on whether the symmetries of icosahedron leaving the shape of the Hamiltonian cycle is Z_{6}, Z_{4} or Z_{2}. For Z_{2} there are two options: Z_{2,rot} is generated by rotation of π and Z_{2,refl} by reflection with respect to a median of equilateral triangle.
 Combining together one harmony from each type one obtains union of 3 harmonies and if there are no common chords between the harmonies, one has 20+20+20 3chords and a strong resemblance with the code table. To given AA one assigns the orbit of given face under icosahedral isometries so that codons correspond to the points of the orbit and orbit to the corresponding AA. 4 chords are however missing from 64. These one obtains by adding tetrahedron. One can glue it to icosahedron along chosen face or keep is disjoint.
 The model in its original form predicts 256 different harmonies with 64 3chords defining the harmony. DNA codon sequences would be analogous to sequences of chords, pieces of music. Same applies to mRNA. Music expresses and creates emotions and the natural proposal is that these bioharmonies correlate with moods that would appear already at molecular level. They could be realized in terms of dark photon triplets realized in terms of light and perhaps even music (living matter is full of piezoelectrets). In fact, also the emotions generated by other art forms could be realized using music of dark light.
The model of music harmony is separate from the model of genetic code based on dark proton triplets and one of the challenges has been to demonstrate that they are equivalent. This inspires several questions.
 Could the number of harmonies be actually larger than 256 as the original model predicts? One could rotate the 3 fused Hamilton's cycles with respect to each by icosahedral rotations other leaving the face shared by icosahedron and tetrahedron invariant. There are however conditions to be satisfied.
 There is a purely mathematical restriction. If the fused 3 harmonies have no common 3chords the number of coded AAs is 20. Can one give up the condition of having no common 3chords and only require that the number of coded AAs is 20?
 There is also the question about the chemical realizability of the harmony. Is it possible to have DNA and RNA molecules to which the 3chords of several harmonies couple resonantly? This could leave only very few realizable harmonies.
 The model predicts the representation of DNA and RNA codons as 3chords. Melody is also an important aspect of music. Could AAs couple resonantly to the sums of the frequencies (modulo octave equivalence) of the 3chords for codons coding for given AA? Could coding by the sum of frequencies appear in the coupling of tRNA with mRNA by codewords and coding by separate frequencies to the letterwise coupling of DNA and RNA nucleotides to DNA during replication and transcription?
 What about tRNA. Could tRNA correspond to pairs of harmonies with 20+20+444 codons? What about single 20+4=24 codon representation as kind of pretRNA?
 What is the origin of 12note scale? Does genetic code force it? The affirmative answer to this question relies on the observation that 11 correspondence between codons and triplets of photons requires that the frequency assignable to the letter must depend on its position. This gives just 12 notes altogether. Simple symmetry arguments fix the correspondence between codons and 3chords highly uniquely: only 4 alternatives are possible so that it would be possible to listen what DNA sequences sounds in given mood characterized by the harmony.
 What disharmony could mean? A possible answer comes from 6 Hamiltonian cycles having no symmetries. These disharmonies could express "negative" emotions.
See the new chapter Geometric theory of bioharmony or the article New results in the model of bioharmony .
