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:

1. The 7 notes, the 7 imaginaries.
2. The Tonika-sub-dominant-Dominant, quaternion triple.
3. 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.

52.2 The 12 Structure

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

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

1. The best harmony = c + C^2 (12 half-tones).

2. 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.

3. Inverting 7 + 5 = 5 + 7 = c, F, C^2 and F, as we recall, is the sub-dominant.

4. 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.

5. The 4 + 3 = The Major chord CEF, the most harmonic triad...

6. The inversion 3 + 4 = The minor chord, the second most harmonic triad.

(Note: What needs to be done here is to compare the 7 half-tone mirror image to Yang's statement, "If one performs a mirror reflection "and" converts all matter into antimatter"...the true mirror reflection process).

1. Electrons are antimatter. Scientific American Magazine.
2. Extreme negative soft electrons (are) antigravity. Robert L. (Clark9.asc, keelynet.com)
3. Frequency of Nitrogen- 23,870 Megacycles (10^6).
4. 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.

Impossible Correspondence Index