Compositional Techniques
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Those who perform improvisationally may not get further involved
in the complications rendered. You may work mainly from the mixed
symmetrical chords and alter them as felt mellifluous.
As with atonality where certain pitch class sets are arranged
to be specified in a section of a piece, here also it is necessary to
appoint a number of chord sets intended. The number of (mixed)
symmetrical chords allowable to inter-relate ranges from 2 to 6. Seven
chords do not always add up to equate out one particular mode or tone.
Here are the Formulas for Inter-relating chords.
So now if for example one was to use:
Extrovertions of Motivations
531-263-1 Interval ordered
051-2-436 Stringed-tone ordered
Impressions of Adaptations Expressions of Beliefs
444-564-1 555-354-1
041-5-326 053-1-426
then it becomes possible to inter-relate these chords thus:
531-263-1 531-263-1 555-354-1
& 555-354-1 & 444-564-1 & 444-564-1
--------- --------- ---------
543-620-1 106-060-1 111-424-1
531-263-1
555-354-1
(tri) 444-564-1
---------
041-116-1
(Mixed) Symmetrical chords are also called pure chords and chords
after inter-relating are called blended chords.
At this time it becomes proper to indicate that the remaining
modes can be assessed by using base 7 arithmetic.
543-620-1 The formula is, in using mode 1 a direct series
543-620-1 of the modes unveil, add mode 1's chord first to
--------- itself then to the results of each calculation.
316-540-2 When adding the two numbers arriving at an answer
larger or equal to 7, substract 7 from the value.
316-540-2 152-460-3 625-300-4
543-620-1 543-620-1 543-620-1
--------- --------- ---------
152-460-3 625-300-4 468-220-5
468-220-5 234-140-6
543-620-1 543-620-1
--------- ---------
234-140-6 000-000-0
It shows, interestingly, that by splitting a chord say 555-354-1
by two to 222-423-6 and 111-215-3, when inter-relating it to another chord
say 531-263-1, does maintain the same result as the unsplit version when
inter-relating the results together. With this it is understood that
inter-relating more than one split at a time is not allowed because they
are parts of the mode swing.
531-263-1 531-263-1
& 222-423-6 & 111-215-3
--------- ---------
065-343-0 321-204-2
\ /
531-263-1 065-343-0
& 555-354-1 & 321-204-2
--------- ---------
543-620-1 = 543-620-1
It is also possible with a three or more split:
531-263-1 531-263-1 531-263-1
& 333-631-2 & 111-215-3 & 444-146-5
--------- --------- ---------
432-412-5 321-204-2 106-551-3
432-412-5
321-204-2
(tri) 106-551-3
---------
543-620-1
These examples given are meant to display the manner in which
these chords function together. The exactness of the modes implying may
need to be adhered to since they are roll-around derivatives to one
another by mode swing. So when there is an interjection of a blended
chord with pure chords (or visa versa) it may by appropriated to the same
mode swing that is occurring at the moment.
Many blended chords can be fashioned from just these three
description of forces. A total of more than 2052 to less than 3744,
which is too much to list.
Inter-relations of example chords
It is also possible to work from the string-tone ordered tables.
The available combinations regulates to only one roll-around derivative
mode from each description of force is to be inter-related up to six other
description of forces. Blended chords may also have their roll-around
derivatives which may be substituted in the mode swing method.
These are the the string-tone orders of the chosen description of
forces:
E1: Extrovert H3: Impress O3: Express
051-2-436 041-5-326 053-1-426
032-4-165 012-3-645 036-2-145
013-6-524 053-1-254 012-3-564
064-1-253 024-6-513 065-4-213
045-3-612 065-4-132 041-5-632
026-5-341 036-2-451 024-6-351
And some selected inter-relations:
E1: Extrovert/M1 E1: Extrovert/M1 E1: Extrovert/M1
H3: Impress/M1 H3: Impress/M2 H3: Impress/M5
"and their roll-around
derivatives"
011-0-066 035-6-502 023-3-634
022-0-055 063-5-304 046-6-561
033-0-044 021-4-106 062-2-425
044-0-033 056-3-601 015-5-352
055-0-022 014-2-403 031-1-216
066-0-011 042-1-205 054-4-143
Again it can be proven the pertinence of inter-relations:
051-2-436 051-2-436
& 041-5-326 & 012-3-645
--------- ---------
011-0-066 035-6-502
\ /
051-2-436 011-0-066
& 065-4-132 & 035-6-502
--------- ---------
023-3-634 = 023-3-634
This is the farthest that inter-relationships expands to, but it
seem enough. Individual calculation may be done during composition
proving a very toilsome effort. It is probably best to have made a
programming that lists all relevant chords.