Poly-Modality

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Epicurus 342 B.C. - 270 B.C.  Greek. Philosopher

	I can find no meaning which I can attach to that is termed good,
if I take away from it the pleasures obtained by taste, the pleasures
which come from listening to music, the charm derived by the eyes from the
sight of figures in movement, or other pleasures produced by any of the
senses in the whole man. 

	- - Athens, vii, 280


        Two or more melodies coexisting at any one segment is not required
to be harmonious by counterpoint.  They can be also handled as melodies
only.

        So now on to poly-modality.  More than one mode brings up the
question as to what harmony is to be placed.  As mentioned earlier, at any
one given time, there are 7 established diatonic tones.  Therefore, the
melodies, at any one particular mode, usually are to lie within that
scheme.  Multiple harmonies would sound too confusing and have to many
notes sounding.  To levee this, one must find a common ground mode for the
chords.

        To take an example, one might want to use modes 2 and 3.  These
two modes are a roll-around figure for mode 6.  That is to say, if we were
to increment and decrement 6, we would have 5 & 7.  Keep in mind, there
are seven modes, so we are working in base seven.  Hence, 7 could also be
written as 0.  If this is done two more time, we have then Modes 4 & 1 and
3 & 2.  These relations are listed below in the table.  The & symbol means
to refer to the rotation table.
Rotation Table

        0)      6|1     5|2     4|3
        1)      0|2     6|3     5|4
        2)      1|3     0|4     6|5
        3)      2|4     1|5     0|6
        4)      3|5     2|6     1|0
        5)      4|6     3|0     2|1
        6)      5|0     4|1     3|2

With this, it is understood that Mode 6 is to be used, as the common chord
ground.

        However, when one wants to try three modes a different formula
needs to be introduced.  For example, the Modes 2, 3, and 5 are entertained,
what would prove that they are actually common to Mode 1?  One may
roll-around the numbers till they show up all ones, but that would take
some time.  Instead, take each mode, call them a, b, and c, add these
modes together.  This would render w=10 then subtract the closest multiple
of 7 [cm7] (if the number is greater than 7), making x=3 double it y=6
then subtract again [cm7] is still z=6.  Then just subtract that from 7
leaving Mode 1.

235

2 +3 +5 =10 -7     =3 *2 =6  -0     =6       7 -6 =1

a +b +c =w  -[cm7] =x *2 =y  -[cm7] =z  then 7 -z =Mode

        As to four modes, this simply reverts back to the rotation table
by doing it two times.  Using, example 2, 3, 1, and 6, just split them any
way causing possibly 2&3 =6 and 1&6 =0.  Now, apply the table once more by
6&0 effecting Mode 3.

2316    Mode 3

        2&3 = 6         1&6 =0  then    0&6 =Mode 3

        Now on to five modes, we need to break this up to two groups.  A
combination may not have repeated melody modes.  Therefore, a possible
choice could by 1, 3, 4, 2, and 5.  We separate this by a group of two and
three: 134 and 25.  Working the formula for tri-modality to 134 renders 5
and the table to 25 renders 0.  Now it is ascertained that it is the same
as 55500.

13452   Mode 7

        134|25
         5 | 0

        555|00

Then we mix this up dividing the two groups apart, obtains 05550.  Apply
the formula and the table again:

        055|50
         1 | 6

Take the original and the latter results and use the table again: 5&1 =3
and 0&6 =3.  Then, once more to that result: 3&3 availing mode 3.

         5       0
        &1      &6
        __      __
         3  &    3      =Mode 3

Or much easier, take the two modes not used and apply to the Rotation
Table. Here
are the complete tables.

        Music has evolved to point where it is rarely at rest in any one
setting; there are always changes taking place, be it that it is the
loudness, pitch setting, keys, meter, measure, modes, etc.  In this
system also modes behave in a continual changing manner, where it is a
requirement to change modes within 1 to 6 bars.  Having achieved the
basis for poly-modality, it is now important to realize that in itself
there will not appear any effect since a melody can be placed anywhere and
that will be the melody.  So, then what will show the difference?  In the
example where Modes 2, 3, and 5 were used and the common chord mode is 1:
The mode swing for the chord will be to 6, but the melodies' mode swing
will be 5, 4, and 2, which does assume to the common chord Mode 6.  Now,
for the implication of moving to the chord Mode 3, the melodic modes will
shift to 2, 1, and 6 respectively.  Which are the numbers in the Mode
Swing Variant Tables's vertical observations.  And for Chord Mode 2 the
melodic modes will be 1, 0, and 5 in that order.  


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