**52.1 Inversion of Music Symmetry**

Omar Aam, in addition to linking music with real, complex and quaternion numbers, also illustrates the 12 rhombic faces (the collapsed octahedron of the 24-cell) inside a rhombic dodecahedron...

(Note: The accounting can be related to Einstein's 24 tensor vector calculus).

Omar Aam further postulates that the mathematical structure of music may be related to octonians:

- The 7 notes, the 7 imaginaries.
- The Tonika-sub-dominant-Dominant, quaternion triple.
- The octave repeats itself. It is fundamentally
cyclic.
The 7 keys do not add up trivially into the octonian rules...another problem...the octave is just a subset of the 12-tone scale. The octonian being embedded in a larger geometrical structure, (a) structure related to the 24-cell. The 12 structure is just the background fundament from which the harmonic balance of the octonian stands out.

... The octonian has a 3 + 4, or a 3 + 1 + 3 structure. We should expect to pop up a lot. The first appearance is the white keys (piano)- C, D, E + F, G, A, B. From the 7 imaginaries...we see the 3 + 1 + 3 structure- GAB mirrors CDE and F is an extraordinary number. The keys corresponding to CFG are considered base harmonics, G is called Dominant because it "dominates over F". The reason: Harmonically, GAB...looks and sounds...like CDE.

Finally we see a 3 + 1 + 3 structure if we play triad chords...throughout the octave:

CEG, DFA, EGB, FAC, GBD, ACE and BDF. (See Rameau, the French musician).

These make up the 3 Major, 3 minor chords and 1 diminished.

7 white keys + 5 black keys can be called the 7 + 5 structure.

(Note: Is this the 7/5 ratio found elsewhere?).

- The best harmony = c + C^2 (12 half-tones).
- The next best = Dominant G. Guess what. This is 7 half-tones from c. So the chord c + G + C^2 makes a 7 + 5 structure.
- Inverting 7 + 5 = 5 + 7 = c, F, C^2 and F, as we recall, is the sub-dominant.
- Lets stick with the 7-chord (C+G). Suppose these 7 half-tones are a mirror of the 7 imaginaries. We should then expect there to be a 3 +4 structure in it. Is there? Yes.
- The 4 + 3 = The Major chord CEF, the most harmonic triad...
- The inversion 3 + 4 = The minor chord, the second most harmonic triad.

**52.3 Collected Frequencies of Atoms**

- Electrons are antimatter. Scientific American Magazine.
- Extreme negative soft electrons (are) antigravity. Robert L. (Clark9.asc, keelynet.com)
- Frequency of Nitrogen- 23,870 Megacycles (10^6).
- Frequency of a Neutron Beam- v = 743 KHz (10^30). To spin-flip a Neutron, tune the current and guide field for 100% flip. Dewey Decimal Number: QC 793.5 N4624, p. 101.

© Copyright. Robert Grace. 1999