A standard standard Cartesian coordinate system sys tem
A phyllotaxis phyllotaxis spatiotemporal spatiotem poral coordinate coordinate system A section of the mod 9 daisy 9 daisy phyllotaxis integer matrix
Red 9 indicates a “[0,0 “[0,0 ]” ]” point of origin for a discrete, biological coordinate system.
Coordinate system I with Y-axis Y-axis (orange) and X-axis (blue). Axes are spirals on the surface of a cone.
Coordinate system II with Y-axis (green) and X-axis (yellow). Axes are spirals on the surface of a cone.
Formula used to transform daisy integer matrix into modulo 9 matrix. m atrix.
There are 9 “multiplication “multiplicat ion series”, denoted M1…M9. They are colored coded here to indicate the 4 “polar pairs” of multiplication multiplic ation series that are virtually identical, but in reverse order. “Go forth and multiply…”
Multiplication table (human origin)
Axes of the coordinate system are modulo 9 multiplication multiplic ation series.
M9 M9
9 multiplication multiplic ation series define the x, y, y, and z (M9) axes of life
M9
CARTESTIAN COORDINATE SYSTEM
PHYLLOTAXIS PHYLLOT AXIS COORDINATE SYSTEM
Continuous
Discrete
Axes arithmetic
Axes geometric
Axes inf inite
Axes perpetual
Pos. and neg. numbers and direction Axes are lines
Only pos. number and direction Axes are curves (spirals)
3-D
4-D
Not fractal
Fractal
Four multiplication series associated with four Fibonacci differences. M3 Fibonacci difference 21 M1 Fibonacci difference 55 M7 Fibonacci difference 34 M4 Fibonacci difference 13
Life is a magic square
Life is a fractal
A section of the the mod 9 congruent congruent phyllotaxis phyllotaxis integ integer er matrix. Small black black numbers represent represent the digital digital surface of an object. Red numbers in in squares indicate indicate the mod 9 sum of numbers numbers in the the square. The number sequences are self-replicating at different scales. Thus, the integer matrix is a type of discrete, numerical fractal.
Table 1. Musical overtone series based on C vibrating as the fundamental tone at 256 hertz (hz). A repeating, repeating, 9-digit cycle occurs occ urs for the overtones. Note
Interval
Solfege
Harmonic
Freqeuncy (hertz)
hz == m hz (mod 9)*
1. C
Unison
do (1)
1st partial
256 hz
4
2. C
Octave
do (2)
2nd partial
512 hz
8
3. G
Perfect fifth
sol (1)
2nd partial
768 hz
3
4. C
Octave
do (3)
4th partial
1,024 hz
7
5. E
Major third
mi (1)
5th partial
1,280 hz
2
6. G
Perfect fifth
sol (2)
6th partial
1,536 hz
6
7. B flat -
Minor seventh
si (1)
7th partial
1,792 hz
1
8. C
Octave
do (4)
8th partial
2,048 hz
5
9. D
Major second
re (1)
9th partial
2,304 hz
9
10. E
Major third
mi (2)
10th partial
2,560 hz
4
11. F sharp -
Augmented fourth
fa (1)
11th partial
2,816 hz
8
12. G
Perfect fifth
sol (3)
12th partial
3,072 hz
3
13. A-
Minor sixth
lab (1)
13th partial
3,328 hz
7
14. B flat-
Minor seventh
si (2)
14th partial
3,584 hz
2
15. B
Major seventh
si (1)
15th partial
3,840 hz
6
16. C
Octave
do (5)
16th partial
4,096 hz
1
*the (mod 9) equivalent of the numeric value for hertz (frequency)
Table 1. Musical overtone series based on C vibrating as the fundamental tone at 256 hertz (hz). A repeating, repeating, 9-digit cycle occurs occ urs for the overtones. Note
Interval
Solfege
Harmonic
Freqeuncy (hertz)
hz == m hz (mod 9)*
1. C
Unison
do (1)
1st partial
256 hz
4
2. C
Octave
do (2)
2nd partial
512 hz
8
3. G
Perfect fifth
sol (1)
2nd partial
768 hz
3
4. C
Octave
do (3)
4th partial
1,024 hz
7
5. E
Major third
mi (1)
5th partial
1,280 hz
2
6. G
Perfect fifth
sol (2)
6th partial
1,536 hz
6
7. B flat -
Minor seventh
si (1)
7th partial
1,792 hz
1
8. C
Octave
do (4)
8th partial
2,048 hz
5
9. D
Major second
re (1)
9th partial
2,304 hz
9
10. E
Major third
mi (2)
10th partial
2,560 hz
4
11. F sharp -
Augmented fourth
fa (1)
11th partial
2,816 hz
8
12. G
Perfect fifth
sol (3)
12th partial
3,072 hz
3
13. A-
Minor sixth
lab (1)
13th partial
3,328 hz
7
14. B flat-
Minor seventh
si (2)
14th partial
3,584 hz
2
15. B
Major seventh
si (1)
15th partial
3,840 hz
6
16. C
Octave
do (5)
16th partial
4,096 hz
1
*the (mod 9) equivalent of the numeric value for hertz (frequency)
Table 1. Musical overtone series based on C vibrating as the fundamental tone at 256 hertz (hz). A repeating, repeating, 9-digit cycle occurs occ urs for the overtones. Note
Interval
Solfege
Harmonic
Freqeuncy (hertz)
hz == m hz (mod 9)*
1. C
Unison
do (1)
1st partial
256 hz
4
2. C
Octave
do (2)
2nd partial
512 hz
8
3. G
Perfect fifth
sol (1)
2nd partial
768 hz
3
4. C
Octave
do (3)
4th partial
1,024 hz
7
5. E
Major third
mi (1)
5th partial
1,280 hz
2
6. G
Perfect fifth
sol (2)
6th partial
1,536 hz
6
7. B flat -
Minor seventh
si (1)
7th partial
1,792 hz
1
8. C
Octave
do (4)
8th partial
2,048 hz
5
9. D
Major second
re (1)
9th partial
2,304 hz
9
10. E
Major third
mi (2)
10th partial
2,560 hz
4
11. F sharp -
Augmented fourth
fa (1)
11th partial
2,816 hz
8
12. G
Perfect fifth
sol (3)
12th partial
3,072 hz
3
13. A-
Minor sixth
lab (1)
13th partial
3,328 hz
7
14. B flat-
Minor seventh
si (2)
14th partial
3,584 hz
2
15. B
Major seventh
si (1)
15th partial
3,840 hz
6
16. C
Octave
do (5)
16th partial
4,096 hz
1
*the (mod 9) equivalent of the numeric value for hertz (frequency)
Number=color=tone=polarity 9/0 = Red = C = (neutral) 1 = Yellow = D = (+) 2 = Orange = E = (-) 3 = shock = x = (neutral) 4 = Green = F = (+) 5 = Blue = G = (-) 6 = shock G-sharp = (neutral) 7 = Indigo I ndigo = A = (+) 8 = Violet = B = (-) = shock = y = (neutral)
The daisy as a musical composition
Electromagnetic daisy coil design, inspired by the daisy integer matrix and prime number sieve. Red & Blue wires: 2 prime number circuits
Daisy lattice with 2 prime number circuits or “growth circuits” (yellow and green)
Dotted line: Equipotential lines of force.
Toroidal thistle thistle flower flower
“The Dandelion Puff Principle” m 2
4
1
7
4
1
7
4
1
7
4
1
7
4
1
7
4
1
7
6
3
9
6
3
9
6
3
9
6
3
9
6
3
9
6
3
9
8
5
2
8
5
2
8
5
2
8
5
2
8
5
2
8
5
2
1
7
4
1
7
4
1
7
4
1
7
4
1
7
4
1
7
4
3
9
6
3
9
6
3
9
6
3
9
6
3
9
6
3
9
6
5
2
8
5
2
8
5
2
8
5
2
8
5
2
8
5
2
8
7
4
1
7
4
1
7
4
1
7
4
1
7
4
1
7
4
1
9
6
3
9
6
3
9
6
3
9
6
3
9
6
3
9
6
3
2
8
5
2
8
5
2
8
5
2
8
5
2
8
5
2
8
5
m 8
m 3
m 4
4 6 8 1
1 3 5 7
7 9 2 4
4 6 8 1
1 3 5 7
7 9 2 4
4 6 8 1
1 3 5 7
7 9 2 4
3 5 7 9
9 2 4 6
6 8 1 3
3 5 7 9
9
6 8 1 3
3 5 7 9
9 2 4 6
6 8 1 3
2
8
5
2
5
2
8
5
2 4 6 8 m 7
m 5
m 6
m 1
