Vertical and Horizontal Modulation
Vertical Modulation
The vertical modulation emerges by changing the basic tone on the same
tones, how it is applied for the 'church mode'. [Further scales like
with two triton are modulating in the same way.]
In order to come to a graphic development, the basic Vertical can be shown as followed
| +7 | Δ | - | 6-2 | |
| 6 | Δ | + | 6 | |
| 5 |  |
|||
| +4 | Δ | - | 5 | |
| 3 | Δ | - | 6 | |
| 2 | O | |||
|
1 |
|
+ | 4 |
Horizontal Modulation
The horizontal modulation is the display of changing structures and scales on the basic tone 1.
Mainly through two ore more tritons the the structure unfolds in going into depth, defining further
degrees of light and effects as colours). Accordingly the colours are defined by their function,
development and degree of light.
| for example: | F +4 |
/ | F +4+5 |
O +4+4 | ( whole tone scale) |
More Colours
Further colours constitute as mélange of effects of two or three basic colors / scales and as an enrichment of tritons.
Orange
If Red is increased from O to a lighter Red O+4 (1 2 +3 4 +4 6 -7) the further step could
be 1 2 +3 +4 +5 6 -7 with 2 halftone steps, within the context of the effect of the color;
this is questionable and does not explain the one-pointed brightness of orange. Instead it
appears to be most appropriate to use the whole tone scale (6 tone scale) to present its
luminous character. This is supported by the strength of 3 following tritons as a scale,.not
giving up the meaning of -7.
| Orange: | 1 | 2 | +3 | +4 | +5 | -7 |
Green
Green is a mélange of Yellow and Blue. In this case it means a scale that includes a -3 and a +7,
the whole tone-halftone scale offers the effects of these colours simultaneously in 8 tones:
| Basic Green: | 1 | 2 | -3 | 4 | -5 | -6 | +6 | +7 |
Brown
Within its twofold modulation, the 8 tone scale is changing from whole tone- halftone as Green to
halftone-whole tone as an Alterating scale with a minor 7 and a minor 2 which darkens the character
and is valued as a dark Brown accordingly.
| Brown: | 1 | -2 | -3 | +3 | +4 | 5 | +6 | -7 |
Establishing the Triton Scale +4 as Base 1
The triton determines the tension and strain of the scales´ inner proportion and its outer relationship.
Scales with second or third tritons give rise to more variations and other spatial functions as degrees
of light characterized as colour.
The +4 and the Δ-5 are the basic scales from where to discover contents between the poles
of the lightest and darkest colour in evaluating degrees of light.
As a point of further visual perception and illustration the light Yellow
+4 are established as Base 1 horizontal.
| Light Yellow | 1 = +4 |
1 | 2 | 3 | +4 | 5 | 6 | +7 |
First Impressions of Vertical Chromatic Modulation
The Tritone Parallel
In order to find more chronology and complimentary, it is appropriate to establish the triton parallel.
This means to combine the 2 scales which have the same (prime-) triton. This is the simplest way to build
a vertical functionality with all 12 tones with one single triton in common.
For example Mayor E Lydian and Bflat Lydian have the same triton in common.
As follows:
example: Triton E - Bb
| funct. | tone/scale | colour | parallel | |
| +7 | D# Δ-6-2 | Dark Blue | 4 | A Δ-6-2 |
| +6 | C# Δ+6 | Light Blue | -3 | G Δ+6 |
| 5 | |
Yellow | -2 | F |
| +4 | Bb Δ-5 | Violet | 1 | E Δ-5 |
| +3 | G# Δ-6 | Middle Blue | -7 | D Δ-6 |
| 2 | F# O | Red | -6 | C O |
| 1 | E + |
Light Yellow | -5 | Bb +4 |
Combined as 'Vertical Chromatic':
| funct. | tone.expl | scale | colour |
| 1 | E | Δ-5 | Violet simultaneous to light Yellow as 1 |
| +7 | D#/Eb | Δ-6-2 | Dark Blue |
| -7 | D | Δ-6 | Middle Blue |
| 6 | C#/Db | Δ+6 | Light Blue |
| -6 | C | O | Red |
| 5 | B | |
Yellow (+4=-5 simultaneous) |
| Bb | Δ-5Bb/ +4 |
Violet / Light Yellow | |
| 4 | A | Δ-6-2 | Dark Blue |
| +3 | G#/Ab | Δ-6 | Middle Blue |
| -3 | G | Δ +6 | Light Blue |
| 2 | F# | Gb O | Red |
| -2 | F | |
Yellow |
| 1 | E | +4 / ( E Δ-5) |
Light Yellow (Violet) |
again: as seen in the vertical chromatic of the triton parallel, function 1
and +4/-5 are covering the 2 complimentary scales and colours +4
and Δ-5 simultaneously.
(Confirmation of the logic and `inner necessity´)
Horizontal Modulation
In order to present possible tendencies and developments of scales and colours on the horizontal level on both basic scales, 2 tendencies are established, whereby one tendency is contained within the modulations of an augmented scale and the other tendency within a diminished scale.
For +4 the increasing towards lighter colours is the scale: +4+5
+4+5 and its modulations:
| +7 | Δ-6-2 => Δ-2+ | 1 | -2 | -3 | 4 | 5 | +6 | -7 | Darker Blue |
| 6 | Δ+6 => Δ +6+7 | 1 | 2 | -3 | 4 | 5 | +6 | +7 | Lightest Blue |
| +5 | ≈O => O-3+3 | 1 | -2 | -3 | +3 | +4 | +5 | -7 | Sand Brown |
| +4 | Δ-5 => Δ-5+2 | 1 | +2 | -3 | 4 | -5 | -6 | -7 | Light Violet |
| +3 | Δ-6 => O-6 | 1 | 2 | +3 | 4 | 5 | -6 | -7 | Dark Red |
| 2 | O => O+4 | 1 | 2 | +3 | +4 | 5 | 6 | -7 | Bright Red |
| 1 | +4 => +4+5 |
1 | 2 | +3 | +4 | +5 | 6 | +7 | Lightest Yellow |
For Δ -5 the diminishing towards darker colours, the chosen scale for
proceeding modulations is: Δ-5-6+6v
Δ-5-6+6v and its Modulations
| +6 | ≈Δ+6 => +4v-3 |
1 | -3 | +3 | +4 | 5 | 6 | +7 | Light Green |
| -6 | O => O-2v | 1 | -2 | +3 | 4 | 5 | 6 | -7 | Dark Red |
| -5 | +4 => Δ v+4 +6+7 |
1 | 2 | -3v | +4 | 5 | +6 | +7 | Light Green |
| 4 | Δ-6-2 => O-3+3v -6 | 1 | -2 | -3 | +3v | 5 | -6 | -7 | Darker Sand |
| -3 | Δ+6 => D+6 -5v | 1 | 2 | -3 | 4 | -5 | +6 | -7 | Lighter Turquise |
| -2 | => -6v |
1 | 2 | +3 | 4 | 5 | -6 | +7 | Greenish Yellow |
| 1 | Δ-5 => Δ-5-6+6v | 1 | -2 | -3 | 4 | -5 | -6 | +6v | Darker Violet |