musings: ustring & harmonic surfaces PDF Print E-mail
Written by D. Bond   
Wednesday, 09 June 2010 00:00

Following the discovery of a harmonic cube containing the major scale, it is seen that the major scale can be thought of as the ordered result of the cross-multiplication of ustrings 3 and 6. I will tentatively refer to matrices created by two ustrings as 'harmonic surfaces'.

Using the '3' ustring and the '6' ustring, we arrive at this matrix:

       1/6  2/6  3/6 4/6  5/6  6/6  6/5  6/4  6/3  6/2  6/1

1/3   C    C    G     C     E      G     Bb  D    G     D    D

2/3   C    C    G     C     E      G     Bb  D    G     D    D

3/3   G    G    D     G      B     D    F    A    D     A     A

3/2   D    D    A     D     F#    A    C    E    A      E     E

3/1   D    D    A     D     F#    A    C    E    A      E     E

Here is u-surface 4x6:

       4/6  5/6  6/6  6/5  6/4

3/4   D     F#    A    C    E

4/4   G     B      D    F     A

4/3   C      E    G     Bb   D

And just for fun:

       4/6  5/6  6/6  6/5  6/4

4/6   C     E     G    Bb    D

5/6   E     G#   B    D     F#

6/6   G     B     D     F     A

6/5   Bb    D    F     A    C

6/4   D     F#   A    C#   E

You see where we're going with all this?

In other words, don't skip 5.

       4/6  5/6  6/6  6/5  6/4               [reduced, irrespective of octave]

3/5   Bb   D     F     Ab    C                 4/5   1/1     3/5  18/25  9/10 

4/5   Eb   G    Bb    Db    F                 8/15  2/3     4/5  24/25  6/5

5/5   G     B      D     F     A                2/3    5/6     1/1   6/5    3/2

5/4   B    D#    F#     A    C#             5/6    25/24  5/4   3/2    15/8

5/3   E     G#    B     D     F#             10/9   25/18  5/3   1/1    5/4

Amazing, eh? Name the notes what you will, the ustring 5 is simply sublime.              

Here is a just chromatic scale:

D    D#     Eb      E     F    F#  G   G#     Ab     A    Bb   B   C    C#   Db      D

1/1 25/24 16/15 10/9 6/5 5/4 4/3 25/18 36/25 3/2 4/5 5/3 9/5 15/8 48/25 2/1                                      

So then, write the equation for all regular harmonic surfaces made of ustrings of arbitrary magnitude [i,j].

 

    what?

    you expect me to do that for you too?

 

p.s. believe me when I say, I NEVER once mapped the wiimote to a chromatic scale or considered making a theramin out of it.

[People of the future simply can't believe how ugly our music got before these mappings were discovered.]

p.p.s. I never once thought this belonged to me. it's just too beautiful to hoard. there are some blisses that are simply much too fine to describe!

Last Updated on Wednesday, 09 June 2010 11:01