Focal Mode Table
                       Modes                                Harmonies

+3      +2      +1       0      -1      -2      -3

M:3     M:2     M:1     M:7     M:6     M:5     M:4             3 (Quartral)
M:4     M:3     M:2     M:1     M:7     M:6     M:5             4 (Quintal)

M:2     M:1     M:7     M:6     M:5     M:4     M:3             2 (tertian)
M:5     M:4     M:3     M:2     M:1     M:7     M:6             5 (Sextal)

M:1     M:7     M:6     M:5     M:4     M:3     M:2             1 (Secondal)
M:6     M:5     M:4     M:3     M:2     M:1     M:7             6 (Septal)

                    Focal Modes                           Focal Harmony

M:7     M:6     M:5     M:4     M:3     M:2     M:1             0 (Octal)



                       Modes                                Harmonies

+3      +2      +1       0      -1      -2      -3

M:3     M:2     M:1     M:7     M:6     M:5     M:4             4 (Quintal)
M:4     M:3     M:2     M:1     M:7     M:6     M:5             3 (Quartral)

M:2     M:1     M:7     M:6     M:5     M:4     M:3             5 (Sextal)
M:5     M:4     M:3     M:2     M:1     M:7     M:6             2 (tertian)

M:1     M:7     M:6     M:5     M:4     M:3     M:2             6 (Septal)
M:6     M:5     M:4     M:3     M:2     M:1     M:7             1 (Secondal)

                    Focal Modes                           Focal Harmony

M:7     M:6     M:5     M:4     M:3     M:2     M:1             0 (Octal)


Poly-Modality Tables

Bi-Modality

                Chord Modes     Possibilities

                0               61      52      43
                1               02      63      54
                2               13      04      65
                3               24      15      06
                4               35      26      10
                5               46      30      21
                6               50      41      32

Tri-Modality

                Chord Modes     Possibilities

                0               016     025     034     124     356
                1               012     046     136     145     235
                2               015     024     123     256     346
                3               036     045     126     135     234
                4               014     023     156     246     345
                5               026     035     125     134     456
                6               013     056     146     236     245

Quad-Modality

                Chord Modes     Possibilities

                0               0124    0356    1256    1346    2345
                1               0146    0236    0245    1235    3456
                2               0125    0134    0456    1356    2346
                3               0156    0246    0345    1236    1245
                4               0126    0135    0234    1456    2356
                5               0123    0256    0346    1246    1345
                6               0136    0145    0235    1234    2456

Quint-Modality

                Chord Modes     Possibilities

                0               02345   01346   01256
                1               13456   01245   01236
                2               02456   12356   01234
                3               01356   02346   12345
                4               01246   01345   23456
                5               01235   12456   03456
                6               12346   02356   01456

Sext-Modality

        Use Mode not selected for Chord Modes

Bi-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

Tri-Formula

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

        Where cm7 = Closest multiple of 7.

Quad-Formula

Apply the Tri-Formula on the three numbers not used.

Quint-Formula

Apply the Bi-Formula on the two numbers not used.

Sext-Formula

Apply the number not used.

Sequence Splitting Tables

                                Two Split

        Category        Totals

        0               0, 7
        1               2, 9
        2               4, 11
        3               6
        4               1, 8
        5               3, 10
        6               5, 12


                                Three Split

        Category        Totals

        0               0, 7, 14
        1               3, 10 ,17
        2               6, 13
        3               2, 9, 16
        4               5, 12
        5               1, 8, 15
        6               4, 11, 18


                                Four Split

        Category        Totals

        0               0, 7, 14, 21
        1               4, 11, 18
        2               1, 8, 15, 22
        3               5, 12, 19
        4               2, 9, 16, 23
        5               6, 12, 20
        6               3, 10, 17, 24


                                Five Split

        Category        Totals

        0               0, 7, 14, 21, 28
        1               5, 12, 19, 26
        2               3, 10, 17, 24
        3               1, 8, 15, 22, 29
        4               6, 13, 20, 27
        5               4, 11, 18, 25
        6               2, 9, 16, 23, 30


                                Six Split

        Category        Totals

        0               0, 7, 14, 21, 28, 35
        1               6, 13, 20, 27, 34
        2               5, 12, 19, 26, 33
        3               4, 11, 18, 25, 32
        4               3, 10, 17, 24, 31
        5               2, 9, 16, 23, 30
        6               1, 8, 15, 22, 29, 36


Tonal Comparisions

Table of Concordance/Discordance values:

      Tonic                     +3
P 4th   | P 5th                 +2
maj 3rd | aug 5th               +1
min 3rd | 6th                    0
maj 2nd | min 7th               -1
min 2nd | maj 7th               -2
     dim 5th                    -3

Tables of Compared Tones

Compared                Related overtones
Tones                   by value

Tonic to:                               maj 3rd to:
--------                                -----------
Tonic                   +3      +3      maj 3rd                 +1      +3
min 2nd                 -2      -2      P 4th                    0      -2
maj 2nd                 -1      -1      dim 5th                 -1      -1
min 3rd                  0       0      P 5th                   -2       0
maj 3rd                 +1      +1      aug 5th                 +3      +1
P 4th                   +2      +2      6th                     -2      +2
dim 5th                 -3      -3      min 7th                 -1      -3
P 5th                   +2      +2      maj 7th                  0      +2
aug 5th                 +1      +1
6th                      0       0      P 4th to:
min 7th                 -1      -1      ---------
maj 7th                 -2      -2      P 4th                   -1      +3
                                        dim 5th                 -2      -2
min 2nd to:                             P 5th                   +3      -1
-----------                             aug 5th                 -2       0
min 2nd                 -1      +3      6th                     -1      +1
maj 2nd                  0      -2      min 7th                  0      +2
min 3rd                 +1      -1      maj 7th                 +1      -3
maj 3rd                 +2       0
P 4th                   -3      +1      dim 5th to:
dim 5th                 +2      +2      -----------
P 5th                   +1      -3      dim 5th                 +3      +3
aug 5th                  0      +2      P 5th                   -2      -2
6th                     -1      +1      aug 5th                 -1      -1
min 7th                 -2       0      6th                      0       0
maj 7th                 +3      -1      min 7th                 +1      +1
                                        maj 7th                 +2      +2
maj 2nd to:
-----------                             P 5th to:
maj 2nd                 +1      +3      ---------
min 3rd                 +2      -2      P 5th                   -1      +3
maj 3rd                 -3      -1      aug 5th                  0      -2
P 4th                   +2       0      6th                     +1      -1
dim 5th                 +1      +1      min 7th                 +2       0
p 5th                    0      +2      maj 7th                 -3      +1
aug 5th                 -1      -3
6th                     -2      +2      aug 5th to:
min 7th                 +3      +1      -----------
maj 7th                 -2       0      aug 5th                 +1      +3
                                        6th                     +2      -2
min 3rd to:                             min 7th                 -3      -1
-----------                             maj 7th                 +2       0
min 3rd                 -3      +3
maj 3rd                 +2      -2      6th to:
P 4th                   +1      -1      -------
dim 5th                  0       0      6th                     -3      +3
p 5th                   -1      +1      min 7th                 +2      -2
aug 5th                 -2      +2      maj 7th                 +1      -1
6th                     +3      -3
min 7th                 -2      +2      min 7th to:
maj 7th                 -1      +1      -----------
                                        min 7th                 +1      +3
                                        maj 7th                  0      -2

                                        maj 7th to:
                                        -----------
                                        maj 7th                 -1      +3


Inter-relation Formulas

Bi-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

Tri-Formula

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

                Where cm7 = Closest multiple of 7.

Quad-Formula

        Separate the four numbers into pairs and apply the bi-table to
each and once again the bi-table to their results.

Quint-Formula

        Separate the five into two groups, one having 3 and the other 2,
apply the tri-formula on the 3 and the bi-table on the 2.  The result of
the 3 group = A and the result of the pair = B, obtaining AAA|BB. Then
shuffle this and dividing the two groups apart, making BAA|AB.  Apply the
formula and the table again.  Take the original and the latter results and
use the bi-table to each, then once more to that result.

Sext-Formula

        Separate the six numbers into threes and apply the tri-formula to
each and then apply the bi-table to their results.