Table 12.02  Length Area and Volume Math
Figure 12.09  Dimensions and Their Relationships
courtesy University of Science and Philosophy
In graphic Figure 12.09  Dimensions and Relationships it is clear:
Relative Volume
Accumulating Dispersing
4+ = 1/8 of 3+ or 3+ = 8 X 4+ or 8^{1}
3+ = 1/8 of 2+ or 2+ = 8 X 3+ or 8^{2}
2+ = 1/8 of 1+ or 1+ = 8 X 2+ or 8^{3}
Numeric Progressions (units)
1st Dimension = Linear = 1, 2, 4, 8.. (Doubling, nX2)
2nd Dimension = Area = 1, 4, 8, 64.. (Squaring, n^{2})
3rd Dimension = Volume = 1, 8, 64, 512.. (Cubing, n^{3})
Volumes
Cube volume = 1 = 1^{3}
Cube Volume = 2 = cube root of 2 = 1.259922 on side
Cube Volume = 4 = cube root of 4 = 1.587403 on side
Cube Volume = 8 = cube root of 8 = 2 on side
4+ = 1/8 of 3+ or 3+ = 8 X 4+ or 8^{1}
3+ = 1/8 of 2+ or 2+ = 8 X 3+ or 8^{2}
2+ = 1/8 of 1+ or 1+ = 8 X 2+ or 8^{3}
Numeric Progressions (units)
1st Dimension = Linear = 1, 2, 4, 8.. (Doubling, nX2)
2nd Dimension = Area = 1, 4, 8, 64.. (Squaring, n^{2})
3rd Dimension = Volume = 1, 8, 64, 512.. (Cubing, n^{3})
Volumes
Cube volume = 1 = 1^{3}
Cube Volume = 2 = cube root of 2 = 1.259922 on side
Cube Volume = 4 = cube root of 4 = 1.587403 on side
Cube Volume = 8 = cube root of 8 = 2 on side
therefore
Wavelengths and Frequencies  Octave Relations of Russell's Indig Number System
Indig  Vol. Units  Vol. Calc  Wavelength  Example  Octave  Note

4  1  1^{3}  1  1 cps  4  G as 4th octave

3  8  2^{3}  2  1/2 cps  3  F as 3rd octave

2  64  4^{3}  4  1/4 cps  2  E as 2nd octave

1  512  8^{3}  8  1/8 cps  1  D as 1st octave

0  C## nonoctave 
Table 12.02.01  Wavelengths and Frequencies
Showing linear versus geometric progressions as also other types of progressions (counting methods or scales).
See Also
12.00  Reciprocating Proportionality
Frequency
Ratio
Reciprocal
Reciprocating Proportionality
Square Law
Tone
Laws of Being
Volume
Wavelength
wave number
References
Calculate various Properties of a Cylinder
Page last modified on Sunday 11 of August, 2013 05:05:01 MDT