The Longchen Harmony

The mind is the basis, the light behind the projector. The basic potential of the mind provides the space in which subject and object manifest, in which perception, thinking, emotions, language and concepts come into existence. One way to express this creative space is through light, sound and movement. Both color and music contain harmonies, forms and qualities that reflect their structure and composition. These harmonies, forms and qualities correspond to particular qualified spatial units or harmony fields.

The Longchen Harmony approach offers a rough overview of the whole harmonic space as a mirror for the mind's potential. This approach helps one to understand the vast range of harmonies, independent of individual preferences and dislikes. Preferences or dislikes for certain harmonies should not lead to fixations. The reader is encouraged to explore the particular characters and effects of lesser-known harmonies in order to appreciate them fully and equally.

In comparison to traditional theories of musical harmony, the Longchen Harmony approach allows a greater tolerance towards the display of light, colors and their varying effects; it is more open and receptive to musical harmonies that may be unfamiliar to the ear. This parallels developments in twentieth century painting and a growing acceptance of visual harmonies on a larger daily scale. It also may be caused by previously more precise examinations and applications on the nature of colors and light.

In order to present the interaction of color and tonal spaces as a general tool, we use the intervals of the twelve-tone scale, which allows us to approximate objectivity and realize the inner logic of color and sound. These intervals and structures reveal the scales of music as color and degrees of light, respectively. This will be presented by first establishing the criteria by which the three basic colors are mapped onto a musical context and then explaining how these colors fuse within the vertical and horizontal modalities of the scales' structures and functions.

The final aim of this examination is to present a method that is a reliable bridge or a mirror between colors and music.

In this way one can explore capacious space as a harmony of color and sound.

Basic Ideas for the Approach

This examination has the following objectives:

To establish the basis for an objective alignment of musical and color harmonies
To create a vast space in which to harmonies and their modulations can be presented within their development on the vertical and the horizontal
To reflect on the qualities of particular colors so that they can be appreciated in a broader context than usual. Through this, strange-seeming or less common harmonies are understood as equal and thus become more brilliant.

The main idea behind this approach is to understand that a harmonic space is defined by the correlation of tone intervals, which also reflect the character, the quality and the effect of a color. The objectivity of this approach lies in the logic with which harmonies are defined.

Basic Terms

A few basic terms will help to develop a relatively objective alignment of musical harmonies and color.

a) Defining the Intervals as Notation in Numbers

An Octave has 12 intervals within its chromatic order

[Presentation of the 12 Intervals]

Expl. 1,0)]

The intervals are defined through positive and negative integers.

Octave	8/1	2,13)
Major Seventh	+7	2,12)
Minor Seventh	-7	2,119
Major Sixth	+6 oder 6	2,10)
Augmented Fifth / Minor Sixth	+5 oder -6	2,9)
Fifth	5	2,8)
Augmented Fourth / Minor Fifth	+4 oder -5	2,7)
Fourth	4	2,6)
Third	+3	2,5)
Minor Third	-3	2,4)
Second	+2 oder 2	2,3)
Minor Second	-2	2,2)
Prime, Basic Tone, Tonic	1	2,1)

Expl.: [Showing the intervals together 1:1, 1:-2, 1:2, etc. ]

b) The Designation of the Tones

Tones are designated according to their common use:

- The sign 'b' after a tone means that the tone is diminished. A sharp sign (#) after the note indicates that the tone is a half-tone higher.

- Expl.: Ab, Bb, Gb oder F#, C# etc.

- A scale can show possibly diminished and augmented tones, depending on what is most convenient.

(e.g. Bb, B, C#, Fis, Db, C#, Gb, ..)

c) The sign'v'

The sign 'v'before or after a tone shows a minor third interval after or before the tone within the scale.

Expl.: +4v means +4 v +6, like F# to A,

First Color-Sound-Effects: Eccentric and Concentric

One source of inspiration for Longchen Harmony is the way Kandinsky treats color in his book The Spiritual in the Arts (das Geistige in der Kunst). Kandinsky did not differentiate colors by 'warm' and 'cold' but by 'eccentric' and 'concentric.’ These terms offer a way to translate it as a music aspect:

The Eccentric Color Effect

Kandinsky designated yellow, a big yellow painted wall for example, as eccentric in its effect because the color effectively comes towards the viewer.

The Concentric Color Effect

Similarly, if one focuses on a large wall that has been painted dark blue, the viewer’s perception is 'drawn in’, and hence it has a concentric effect.

Natural Light, Degrees of Light and Complementary Tendencies

Colors can be distinguished in relation to their natural degree of light. Yellow has a high degree of light while dark blue has a very low degree of light. In the same way musical harmonies tend to operate eccentrically or concentrically.

In reflecting on yellow and dark blue here we also show general complementary tendencies related to colors. This applies to the effect of an interval in the same way.

First Adaptation to Musical Harmony

The discrimination of basic expressions, functions, influences and tendencies on the basis of colors applies also to musical harmonies. In this regard, it is important to examine the intervals in their individual significance and place within the scale.

The following sections show how the basic intervals. The major and minor third can be equated with the basic tendencies of colors.

Basically the third plays a central role in the development of a harmony. Together with the seventh, it builds the basic character of a harmony, to which further intervals are joined to define the character and quality of the harmony.

Thirds and Seventh - First Definitions and Designation for Tendencies

Definition of Thirds

The major third (+3) is defined as eccentric. A crucial aspect of the major third is that it can be understood as an eccentric or yellow expression, coming towards the listener. Its effect as sound shines outwardly towards the listener. Thus, the minor third can be designated as yellow.

3,1) ton. expl.

By contrast, the minor third (-3) is concentric; it turns inwardly, in its blue effect, it draws the listener in. Thus, the minor third can be designated as blue.

3,2) ton. expl

These are the first general discriminations that reveal musical and color tendencies.

(Refers to Wassily Kandinsky 'Das Geistige in der Kunst')

A Crucial Point

These basic aspects are vital:

The eccentric color effect equates to the major third.

The concentric color effect equates to the minor third.

To comprehend this, it must be experienced within a visual-acoustic context. If, to test these relationships, one designates the minor third as eccentric and the major third as concentric, one might notice that the designation one has given clashes with the visual-acoustic context one experiences. If one is in agreement with this fundamental point, one can progress with the approach.

Definition of the Seventh

Next we want to examine the Seventh.

This follows a process to define a color as well as a basic degree of light.

Major Seventh (+7)

The major seventh is mainly understood in its leading tonality, its 'inner wish' or 'inner necessity' (Kandinsky) to dissolve to the octave or prime.

In the same way the major seventh’s leading tonality is perceived in its eccentric or yellow expression.4,1)

The Minor Seventh (-7)

By contrast, the minor seventh has a restrained or controlled expression and thereby can be designated as concentric or blue in effect. 4,2)

Defining the Three Basic Colors

Determining the Basic Intervals as Basic Colors

Now it might be interesting to see the relation between the major third and the major seventh:

The expressions of the third and seventh are strengthened when they (and thus, their tendencies) are combined. They show the bright, eccentric expression or the dark, concentric expression and give criteria and guidelines for the basic colors.

The general expression of the tonal relation of 1 +3 +7 is eccentric or yellow. These eccentric intervals lay the ground for a major scale

A major structure defines 1+3 +7 tonality as yellow.

The general expression of the tonal relation of 1 -3 -7 is concentric. The basic structure of these concentric intervals creates a minor scale.

The minor structure defines the 1 -3 -7 tonality as blue.

Musically the major third (+3) combined with the minor seventh (-7) reflects the character of dominant scales, like the mixolydian.

Here it shows the controlled eccentric expression of red. The basic structure is also a representative of the middle degree of light.

The 'Dominant’ structure defines the 1 +3 -7 tonality as red.

General Definitions of the Basic Colors

a) 1	+3	+7	= Yellow	5,1)
b) 1	+3	-7	= Red	5,2)
c) 1	-3	-7	= Blue	5,3)

Temporary Designation of the First Scales as Colors

The designation of the basic colors so far are giving temporal directions. Later the colors will be further defined with names and their mixture ratio. So the definitions are provisional and will assume more content and weight as the degrees of light and the complementary aspect are developed.

Definitions of Basic Colors in the Context of the Church Tone scales

Up to now we have been describing tendencies that are valid for the perception of color in music.

In the following, we progress to scales, first the church tone scales, to define modulations of a basic scale with one tritone (like F:B in C Major).

The definitions are provisional and will provide more content and weight as the degrees of light and the complementary are included.

Yellow

The color yellow expresses itself through the major third (+3) and the major seventh; these intervals create the perception of openness, which is enhanced by the leading tonality of the major seventh. The simple Ionic scale, presents yellow in its fullest saturation according to the degree of light. 6,1)

Interval	Tonal Example
8	G
+7	F#
6	E
5	D	= Basic Yellow
4	C
+3	B
+2	A
1	G

We designate the square as the general symbol for yellow

Yellow = ☐

Red

Basically, red expresses itself through the major third (+3) and the minor seventh (-7); the +3 creates an openness yet it does not aspire to dissolution through the leading tonality. Through the -7 it gets more strength, intensity and stability, a 'being-settled-within-itself'. The Mixolydian scale presents red in the optimal saturation as a primary color and declares it to be the general middle degree of light.

Interval	Tonal Example
8	D
-7	C
+6	B
5	A	= Basic Red
4	G
+3	F#
2	E
1	D

The circle has been chosen as the symbol for red (+3,-7) .

So red is designated as O 6,2)

Blue

Blue is characterized by the minor third and also through the minor seventh as a 'turning-inward' and unfolds in a multitude of ways. This happens through the addition of intervals like the +6, -6, 2, -2, 5, -5 and also through the major seventh (+7).

The Aeolic scale presents blue, in its optimal saturation and degree of light, as the basic blue.

Interval	Tonal Example
7	E
-7	D
-6	C
5	H	= Basic Blue
4	A
-3	G
2	F#
1	E

The triangle ∆ is chosen as symbol for blue (-3,-7).

Blue is ∆. 6,3)

The Further Church Tone Scales

Now we continue with the definition of further modal scales and harmonies within the church tone scales. Here each one is transposed onto a color in accordance with the criteria mentioned above.

Dorian 1 +2 -3 4 5 +6 -7 = ∆+6

In comparison to the Aeolic scale of middle blue, the Dorian includes the major sixth (+6). This makes the effect of the harmony lighter, more expressive. So we define this blue as light blue.

Light Blue = ∆+6 6,4)

Phrygian 1 -2 -3 4 5 -6 -7 = ∆-6-2

In comparison to the Aeolic Blue, the Phrygian includes the minor second (-2), whose concentric effect makes the blue darker, so that we provisionally call it a dark blue.

Dark Blue = ∆-6-2 6,5)

Locrian 1 -2 -3 4 -5 -6 -7 = ∆-5

In comparison to the Phrygian Blue, the Locrian scale additionally offers the tritone (-5). The -5 with its crucial energy brings the color to its darkest degrees, 'to the edge' of light. As a strengthener of blue, the tritone uses red to overcome and push the blue concentric character in order to reach the darkest color (of a primary-complementary relation), violet.

Violet= ∆-5 6,6)

The tritone’s presence is a 'musical spine' and a major tool to direct and define the harmony within music and in color.

Lydian 1 +2 +3 +4 5 +6 +7 = ☐+4

Coming to the Lydian scale again, we have the augmented fourth on the tritone. Here it heightens the eccentric character of the Ionic Major Yellow so that the yellow becomes brighter.

Bright Yellow = ☐+4 6,7)

Circle of Fourths in the Context of Degrees of Light

When we order the defined scales along the circle of fourths we come to this version:

Symbol	Expl. Basic Tone	Color	Structure
☐+4	F	Light Yellow	1 2 +3 +4 5 6 +7	7,7)
☐	C	Yellow	1 2 +3 4 5 6 +7	7,6)
O	G	Red	1 2 +3 4 5 +6 -7	7,5)
∆+6	D	Light Blue	1 2 -3 4 5 +6 -7	7,4)
∆-6	A	Middle Blue	1 2 -3 4 5 -6 -7	7,3)
∆-6-2	E	Dark Blue	1 -2 -3 4 5 -6 -7	7,2)
∆-5	B	Violet	1 -2 -3 4 -5 -6 -7	7,1)

4th upward^

This reveals the fourth to be an indicator of progressing degrees of light.

Here the development from the darkest to the lightest color is shown in the modulation of the 4th. It shows how colors in their particular position are representatives for a certain degree of light. From their position each of them represents a criterion to define later similar colors with similar structures:

Beginning from downward ^:

4th step downwards: 4th step upwards

symbol.,ton.expl.,color

∆-5	B	Violet	☐	+4	Light Yellow
∆-6-2	E	Dark Blue	☐	C	Yellow
∆-6	A	Middle Blue	O	G	Red
∆+6	D	Light Blue	∆+6	D	Light Blue
O	G	Red	∆-6	A	Middle Blue
☐	C	Yellow	∆-6-2	E	Dark Blue
☐+4	F	Light Yellow	∆-5	B	Violet
4^th	^			^

Structural Complimentary as Evidence

The crucial energy of the tritone becomes evident when it is seen through colors in this basic vertical modulation.

Now used as the basic tone, the tritone builds the two scales ☐+4 and ∆ -5, which are sources of a structural polarity. They reflect the basic lightest and darkest colors, light yellow and violet.

This supports the objectivity of this approach.

Position of the Triton

As already shown, a crucial criterion to determine the color in music is the position of the tritone (+4/-5). One or more tritones in a scale determine the structure, the particular expression, and the effect as a particular, more complex color.

Symbol	Color	Structure of Intervals	Position of Triton
☐+4	Light Yellow	1 2 +3 +4 5 6 +7 8	+4 8/1
☐	Yellow	1 2 +3 4 5 6 +7 8	4 +7
O	Red	1 2 +3 4 5 +6 -7 8	+3 -7
∆+6	Light Blue	1 2 -3 4 5 +6 -7 8	-3 +6
∆-6	Middle Blue	1 2 -3 4 5 -6 -7 8	2 -6
∆-6-2	Dark Blue	1 -2 -3 4 5 -6 -7 8	-2 5
∆-5	Violet	1 -2 -3 4 -5 -6 -7 8	1 -5

Labeling the Musical and Color Harmonies

Before we approach the horizontal and vertical spatial divisions, it is useful to designate the harmonies with names in order to discriminate them in sound and sight. These names are not irrevocable but rather provide a way for further discussions. Yet, since all the criteria mentioned are included, these names are meant to approximate a final definition.

Source of Names

The names for the colors are taken from the archive of 'Naomi Kuno and Forms Inc. Tokyo'. They include international designations used in design and painting.

Names for the previous mentioned colors

The exact compositions and mixtures come later:

∆-6-2	Dark Blue	as	Magellan Blue ∆-6-2
∆+6	Light Blue	as	Cosmic Blue ∆+6
☐	Yellow	as	Yellow Cap ☐
∆-5	Violet	as	Magic Violet or Violet ∆-5
∆-6	Middle Blue	as	Cote d'Azur ∆-6
O	Red	as	Fresque O
☐+4	Light Yellow	as	Lemon ☐+4

Harmonic Space in the Course towards Vertical and Horizontal Modulations

In order to come to a describable harmonic space and to present an approximate wholeness of musical and color possibilities, one has to approach possible modulations on the horizontal and vertical level. Each modulation is a spatial unity of a particular color with its criteria of different colors by saturation, mixture and as a particular degree of light.

The vertical view is for example the view of the church tone modulation as we have started. That means that the basic tones are changing in a vertical order.

Beginning with ☐+4, O, ∆-6….^ or ∆-5, ☐, ∆+6…

The Tritone Parallel for Demonstrating the Vertical

We are going to use the tritone parallel to describe the vertical view of harmonics. It is the easiest and most efficient way to bring all twelve tones into a harmonic context.

For example, by connecting F Major to B Major, you can define the functionality of all twelve tones with the same tritone (E-Bb).

Hereby we start with the ☐+4 or ∆-5 as the basic tone 1.

(this also refers to George Russell's 'Lydian Harmonic Concept')

First Presentation of Vertical Chromatic Modulation through the Tritone Parallel

Emphasizing the tritone parallel helps to present chromatic and complementarity. Here, the two scales E☐+4 and Bb☐+4 with the tritone F-B fit into each other.

Example: Parallel E-Bb

example: Tritone E - Bb

funct.	tone/ scale	color	parallel to
+7	D# ∆-6-2	Magellan Blue	4 A ∆-6-2
+6	C# ∆+6	Cosmic Blue	-3 G ∆+6
5	B ☐	Yellow	-2 F ☐
+4	Bb ∆-5	Violet	1 E ∆-5
+3	G# ∆-6	Cote A'zur	-7 D ∆-6
2	F# O	Fresque	-6 C O
1	E ☐+4	Lemon	-5 Bb ☐+4

As Chromatic Vertical

Function.	Ton.Expl.	Scale	Color
8/1	E	☐ +4	Lemon
+7	D#/Eb	∆-6-2	Magellan Blue
-7	D	∆-6
6	C#/Db	∆+6	Cosmic Blue
-6	C	O	Fresque
5	B	☐	Yellow Cab
+4/-5	Bb	☐+4	Lemon
+4/-5	Bb	∆-5	Violet
4	A	∆-6-2	Magellan Blue
+3	G#/Ab	∆-6	Cote A’zur
-3	G	∆+6	Cosmic Blue
2	F#/Gb	O	Fresque
-2	F	☐	Yellow Cab
1	E	∆-5	Violet

The Tritone 1 : +4 / -5 as Basis or Function 1

Function 1

As a point for further visual perception and illustration the light yellow ☐+4 and violet ∆-5 are established as Function 1.

Lemon 1 = ☐+4 1 2 3 +4 5 6 +7

Magic Violet/Violet 1= ∆-5 1 -2 -3 4 -5 -6 -7

(Again, refer to George Russell's 'Lydian Harmonic Concept')

Establishing the Tritone Scale +4 as Base 1

Again: The tritone determines the tension and strain of the scales inner proportion and its outer relationship. Scales with 2 or 3 tritones give rise to more variations and other spatial functions as degrees of light characterized as color.

And: The ☐+4 and the ∆-5 are the basic scales for discovering the poles between the lightest and darkest color and degree of light.

Horizontal

Horizontal modulations deal with possible parallel harmonies in a single function. In creating variations, they provide further qualities as light and color by incorporating an augmented or diminished note in their structure.

For example: F ☐+4 / F ☐ +4+5/ O +4+5 (wholetone scale) 8,1)

Tendencies to present parallel scales on the horizontal:

We have chosen the tendencies of the following augmented and diminished scales in order to present different tendencies towards brighter and darker colors and arrive at a representatively vast view on harmonic space,

Augmented: ☐+4 ☐+4+5 Butterfly Yellow (also contains melodic minor)

☐v -3+3 Nankeen Yellow(also containing harmonic minor)

O+4+5 Soleil

Diminished: ☐+4 ∆-3v +4 + 7 called `Hauch Grün

Φ Peter Pan

Ө Mosque

Modulations of Further Scales and Colors to Broaden the Spatial View

☐ +4+5 and its Modulations

For 1 ☐+4 the increase towards lighter colors starts with the scale: ☐+4+5

☐+4+5 and its modulations

Indication: Starting from the basic scale 1: Look at function 1, first the basic function is shown, then come further horizontal scales with their modulations of the augmented or diminished tendencies:

+7 ∆-6-2 => ∆-2+6 1 -2 -3 4 5 +6 -7

The +6 gives dark blue a fresh and unexpected lighter note (it puts the concentric leading tonality into a new light) and brings in a slight greenish-blue note.

The scale is called Cleopatra ∆-2+6

6 ∆+6 => ∆ +6+7 1 2 -3 4 5 +6 +7

The light Blue Cosmique to Trade Wind. With the +7 the Dorian scale has the leading tonality’s ability to dissolve into the octave. This is understood as an increase of blue without an alteration of the basic character.

The scale is called Trade Wind ∆ +6+7

+5 ☐ => +1/2 O=> O-3+3 1 -2 -3 +3 +4 +5 -7

Through the augmented +5 from☐+4+5, an 'alternating harmony' appears on the +5 function. As an alternating scale it has the character of major and minor. Here we combine the basic colors and the scale ends with four whole-tone steps, which is also a decisive factor for red-orange. Since it also has a twist to the halftone-wholetone scale, it is valued as an ocher brown.

The scale is called Knossos O-3+3

+4 ∆-5=> ∆-5+2 1 +2 -3 4 -5 -6 -7

Violet to Kai Murasaki . The particular +2 sharpens the violet, giving it a reddish note while the broad meaning of+2 gives a glow.

The scale is called Kai Murasaki ∆-5+2

+3 ∆-6 => O-6 1 2 +3 4 5 -6 -7

Middle Blue Cote Azur to Autumn Glory. The Minor Cote Azur becomes a dark red through the major third. That means it fulfills the criteria for a red +3 -7 with a diminished 6, -6.

The scale is called Autumn Glory O-6

2 O => O+4 1 2 +3 +4 5 6 -7

Red to the lighter Phoenix Red. Through the +4 the Red O becomes sharper and more luminous.

The scale is called Phoenix Red O+4.

1 ☐+4 = > ☐+4+5 1 2 +3 +4 +5 6 +7

Light Yellow Lemon to the lighter Yellow Butterfly. Lemon ☐+4 is enhanced by the +5 in its eccentric light effect whereby the leading tonality remains crucial.

The scale is called Yellow Butterfly ☐+4+5.

☐v-3+3 and its Modulations

(like harmonic minor ∆-6v+7 )

+7 ∆-6-2=> O-2v-6 1 -2v +3 4 5 -6 -7

Magellan Blue to Baghdad Rose.

The +3 changes the concentric character. It makes it a red; the degree of light does not change because of the -6 and the-2 of the Magellan.

The scale is called Baghdad Rose O-2v-6

6 ∆+6=> ∆+6v+4 1 2 -3v +4 5 +6 -7

Cosmique Blue to Bright Sea.

The +4 Tritone changes the blue while the whole-half-diminished connotes a yellow-green influence.

The scale is called Bright Sea ∆+6v+4

5 ☐ => ☐4v+5 1 2 +3 4v +5 6 +7

Yellow Cab to Mahatma Gandhi.

The basic Yellow receives an unexpected fresh note within this common scale. It enhances the effect like the meaning of +5 for Soleil orange.

This scale is called Mahatma Gandhi ☐ 4v+5

+4 ∆-5 => ∆-5v+6 1 -2 -3 4 -5v +6 -7

Magic Violet/Violet to Iris Blue.

The -3 step between the +4 and the 6 makes the blue in the violet brighter. This gives the violet a lighter blue notion.

This scale is called Iris Blue ∆-5v+6

+3 ∆-6 => ∆-6v+7 1 2 -3 4 5 -6v +7

Cote A'zur to Bright Sky Blue.

The middle blue gets a leading tonality from the major seven.

So here, through the half-tone step to the leading tonality, a bit of yellow gives the blue a stronger spacious harmony without losing the concentric blue character.

This scale is called Bright Sky Blue or Sky Blue ∆-6v+7

-3 O=> +½vert.step: ∆+6=> Φ 1-2-3+3+4+5 6v

The O Red changes to the half-tone upper function ∆+6 as a kind of half-diminished half-whole-tone diminished scale. 1 -2-3+3+4 +5+6 v.

Thus, concentric and eccentric characters come together, finishing with the -3 step to 8. Overall, this harmony has a preference for green and is seen as an Olive Green.

This scale is called Ganges Φ -2-3+3+4+5 6v

1 ☐+4 => ☐v -3+3 1 -3 +3 +4 5 6 +7

The major second (+2) is augmented to become a minor third (-3)., by which the influence of the concentric blue becomes obvious. It gives the harmony a slight ocher and green-yellowish character.

This scale is called Nankeen Yellow ☐v -3+3

∆-5-6+6v and its Modulations

+6 ∆-6=> - ½ to ∆+6 +4v-3 1-3 +3 +4 5 6 +7

Cote A'zur to Jena.

On the diminished tone +6, the new scale has the effect of diminished scales, with more green due to +6+7.

The scale is called Jena ∆+6 +4v-3

-6 O => O-2v 1 -2 +3 4 5 6 -7

Fresque to Granat.

The Fresque Red becomes darker through the -2, like the Magellan Blue. It does not change its color, but through the -2 it assumes a further connotation that can be called a 'concentric leading tonality'.

The scale is called Granat O-2v

-5 ☐+4 =>∆ v+4 +7 1 2 -3v +4 5 +6 +7

Lemon to Hauch Grün.

The Lemon Yellow changes concentric effects through the -3 without fundamentally changing its degree of light or its luminosity. Yet the influence of the blue makes it a very light greenish yellow.

The scale is called Hauch Grün ∆ v+4 +7

4 ∆-6-2 => O-3+3v-6 1 -2 -3 +3v 5 -6 -7

The diminished 4 becoming an alternating +3 changes the scale to a kind of half-wholetone diminished scale. So it becomes a reddish Brown.

This scale is called Maya O-3+3v-6

-3 ∆+6 => ∆ +6 -5v 1 2 -3 4 -5 +6 -7

Cosmique zu Verona.

Here the 5 is diminished to become a -5, like in the whole-half scale Ө.

So there is a stronger influence of the green according to its degree of light as Cosmique Blue.

This scale is called Verona ∆ +6 -5v

-2 ☐ => ☐-6v 1 2 +3 4 5 -6 +7

Yellow Cab to Breath of Spring.

Within the simple Yellow Cab comes a diminished -6, which changes the color to a yellowish Green.

This scale is called Breath of Spring ☐-6v

1 ∆-5 => ∆-5-6+6v 1 -2 -3 4 -5 -6 +6v

Magic Violet/ Violet to Parfait Grape.

In order to become the +6, the diminished minor seventh gives the harmony an enhancing effect, like the +6 in the Cosmique Blue. Yet it has a further concentric twist in the effect of the -3 step to the octave 8.

This scale is called Parfait Grape ∆-5-6+6v

Brown, Green and Orange the outer Rim of the Horizontal

As we mentioned above, there are still further colors and harmonies like brown, green and orange to include. They are multi-layered because they have a greater number of tritones to be understood and included according to context. These are scales with 8 tone or with 6 tone scales.

Since they can connect to the most functions, they are at the outer rim of the horizontal modulation. Since they are very symmetric in their structure, their modulation repeats itself either continuously or alternately (a b a b)

Green

1 2 -3 4 +4 +5 6 +7

The criteria for this color are the four minor thirds on top of each other. The scale also ends with a leading tonality (the +7). This symmetric order of a whole step following a half step can be understood as a series of tones with a leading tonality towards the minor third.

The scale as color is designated as Peter Pan Φ

Brown

1 -2 -3 +3 +4 5 6 -7

The alternating character of -3+3 is obvious.

It has a strong influence of red due to the -7. Also here the halftone-wholetone order can be understood as an indicator of its inner strength, similar to Knossos. The -2 is an indication of its darker degree of light.

The scale is designated as Mosque Ө

Orange

1 2 +3 +4 +5 -7

The scale has six wholetone steps or three major thirds, which continuously carry their own eccentricity. The scale keeps its structure without leading tonality and dissolution and expresses a tremendous luminosity.

This orange is designated as Soleil O+4+5

Space and Simultaneity- Harmonies based on the Tritone Parallel

Next we connect the scales, the colors in their modulation ,with the tritone parallel. The objective is, as before, to present spatial possibilities on the vertical and the horizontal.

Again: the tritone parallel has one tritone in common. We are adding two augmented and one diminished scale in Modulation to its functionality on the vertical.

This takes place in three steps:

1.Presentation of the tritone parallel

2.Connecting the further modulated scales and colors examined before.

Adding the half-and whole diminished scales and the whole tone scale.

1. The Tritone Parallel

8/1 C ☐ +4	8/1 C ∆ -5
+7 B ∆ -6 -2
	-7 Bb ∆ -6
+6 A ∆+6
	-6 Ab O
5 G ☐
+4 F# ∆ -5	-5Gb ☐+4
	4F ∆ -6 -2
+3 E ∆ -6
	-3 Eb∆ +6
2 D O
	-2 Db ☐
1 C ☐+4 Lemon	1 C ∆ -5 Violette

Starting on the tritone we can see that ☐+4 and ∆-5 are together on function 1 and +4/-5.

Here we can also see how the chromatic from 1 ☐+4 ,

to -2 ☐ to +2 O, to -3 ∆+6 indicates diminishing degrees of light.

2. Connecting the further Modulated Scales and Colors

The augmented scales are adjoined to each other:

1+ ☐ +4 => ☐+4+5 => ☐v-3+3 => O+4+5

Lemon Butterfly Yellow Nankeen Yellow Soleil

3. Adding the half-and whole diminished scales and the whole tone scale.

1- ∆-5 =>∆-5-6+6v =>dark Grey => Φ 1 2 -3 4 => Ө1-2-3+3

(undefined value)

Violet Parfait Grape Peter Pan Mosque

Complete Presentation of the Colors and Scales on the Horizontal and Vertical

see and hear the examples above !

Function

+7	Δ -6 -2 Magellan Blue	Δ -2+6 Cleopatra	O-2v+3 Bagdad Rose	lighter grey	Φ 1 2 -3 4 Peter Pan
-7	Δ-6Cote d’Azur	helles Grau	darker grey	Ө1-2-3+3 Mosque	O+4+5 Soleil
6	Δ+6 Cosmic Blue	Δ +6 +7 Trade Wind	Δ-3v+4 Bright Sea	Δ-3+3+4+56+7 Jena	Ө1-2-3+3 Mosque
-6	O Fresque	O -2v Granat	O-3+4+5 Knossos	lighter grey	O+4+5 Soleil
5	☐ Yellow Cab	☐4v+5 Mahatma Gandhi	etwas dunkles Grau	darker grey	Ө1-2-3+3 Mosque
+4/-5	☐+4 Lemon	Δ-3v +4 + 7 Hauch Grün	helles Grau	Φ 1 2 -3 4 Peter Pan	Ө1-2-3+3 Mosque
+4/-5	Δ -5 Magic Violet	Δ -5+2 Kai Murasaki	Δ-5v+6 Iris Blue	light grey	O+4+5 Soleil
4	Δ -6 -2 Magellan Blue	O-3 +3v 5 Maya	darker Grey	Φ 1 2 -3 4 Peter Pan	Ө1-2-3+3 Mosque
3	Δ -6 Cote d’Azur	O -6 Autumn Glory	Δ-6v+7 Sky Blue	lighter grey	O+4+5 Soleil
-3	Δ+6Cosmic Blue	Δ-5v+6 Verona	Φ-2-3+3+4+5 6v Ganges	Φ 1 2 -3 4 Peter Pan	Ө1-2-3+3 Mosque
2	O Fresque	O+4Phoenix Red	middle degree of grey	lighter grey	O+4+5 Soleil
-2	☐ Yellow Cab	☐-6 Breath of Spring	lighter grey	Φ 1 2 -3 4 Peter Pan	Ө1-2-3+3 Mosque
1	☐ +4 Lemon	☐+4+5 Butterfly Yellow	☐v -3+3 Nankeen Yellow	light grey	O+4+5 Soleil
1	Δ -5 Magic Violet	Δ-5-6+6v Parfait Grape	darker grey	Φ 1 2 -3 4 Peter Pan	Ө1-2-3+3 Mosque

[Excluded: For the Table of Colours and Music above there is a table of colors and music where one can see the particular color and hear a musical composition for this color as music. The effect of both can be perceived simultaneously.

As above, one can locate the chromatic development of horizontal and vertical harmonies; see and follow them as particular colors and listen to their effect as music.]

Origin of the Names and List of Colors and Scales

According to the names given to harmonies, here you can find the complete list of names with their composition and mixture.

The colors are given in the digital mode of CMYK.

This list is the closest approximation to the colors and their sound at the present time.

The names of the colors are taken from the 'Archive Naomi Kuno and Forms Incorporation Tokyo'.

List of Scales and Colors

Symbol Color	Function /Degree	Digital Composition
☐ Yellow Cap	-2/5 A	C0/ M10/ Y100/ K0
☐4v+5 Mahatma Gandhi	5B	C0/ M35/ Y100/ K0
☐+4 Lemon	1/-5A	C0/ M5/ Y100/ K0
☐+4+5 Butterfly Yellow	1B	C0/ M0/ Y50/ K0
☐–6v Breath of Spring	-2B	C25/ M0/ Y60/ K0
☐v -3+3 Nankeen Yellow	1C	C20/ M35/ Y100/ K30
∆v +4 + 7 Hauch Grün	-5b	C20/ M0/ Y50 / K0
∆-6 Cote d'Azur	+3/-7 A	C95 / M50/ Y0 / K 0
∆ -6-2 Magellan Blue	4/+7A	C100/ M70 / Y0 / K 50
∆-3v+4 Bright Sea	+6 D	C80 / M0 /Y20 / K0
∆ +6+7 Verona	-3B	C65/ M10/Y30/ K0
∆-6v+7 Bright Sky Blue	+3 C	C100/ M22/ Y14 /K0
∆ –2+6 Cleopatra	+7B	C100/ M0/ Y25/ K0
∆ +6+7 Trade Wind	+6B	C80/ M20/ Y0/ K0
∆-5-6+6v Parfait Grape	1 B	C65 / M50/ Y0 / K0
∆-5v+6 Iris Blue	+4 C	C75 /M60 / Y0 / K0
∆ –5+2 Kai Murasaki	+4B	C68/ M100/ Y0/ K0
∆ -5 Magic Violet	1/+4A	C90/ M100 / Y15/ K0
O Fresque	2/-6A	C0 / M100 /Y100 /K15
O-2v+3 Baghdad Rose	+7 C	C0/M100/ Y90/ K45
O +4 Phoenix Red	2B	C0 / M98/ Y90 / K0
O -6 Autumn Glory	+3B	C30 / M98 / Y80/ K0
O -6-2v Granat	-6B	C30 / M100 / Y80/ K0
O +4+5 Soleil	1/2/+3/+4/+5/-7 E	C0/ M65/ Y95 / K0
Ө -2-3+3+4+5 6v Ganges	-3 C	C60/ M30/Y95/K62
Ө v-3+3+4+5 6+7 Jena	+6D	C35/ M35/Y100/ K0
Φ Peter Pan	1/-2/-3/4/-5/+6/+7/ D	C85/ M0/Y85/ K0
Ө Mosque	1/-2-/3/+3/ +6/ -7/E	C20/ M75/ Y95/ K45
Ө –3+3v5-6 Maya	4B	C30/ M60/ Y75/ K0
Ө –3+3 +5 Knossos	-6 C	C20/ M93/ Y100/ K5

☐	Yellows
∆	Blues and Violets
O	Reds
Φ	whole-half Diminished Basic Greens
Ө	Half-Whole Diminished Basic Browns

Discourse on Tritone Relations

Tritone Relations as Bridges

Tritones and tritone relations significantly influence the character of a scale vis-a-vis the color. You can say that the tritone relation makes the harmonic space accessible so that it is possible to define the space.

Also one must consider their potential presence as an 'inductive presence.'

The tritone relations (TR) in the context of their particular relations to each other and as a way to progress in the potential of color-sound can be called ' bridges'.

We will talk about Red Bridge, Blue Bridge or Yellow Bridge.

The Tritone within the Octave

+4	8/1
4	+7
+3	-7
-3	+6
2	+5/-6
-2	5
1	+4

Bridges

Yellow Tritone Relation (TR) or Yellow Bridge

Relating 1 +4 to 4 +7

1 : +4 with 4 : +7

In relating these intervals to each other, they also can be seen in their tonal order:

1 4 +4 +7

Again we can see the eccentric effect. The fourth connects to the leading tonality on +7.

Supplementing Tritone: Which tritone supplements the effect?

The tritone -2: 5 offers itself.

Both intervals should be seen in the same light of tritone light progression. Thereby the 5 strengthens the 4 and is an indicator for the simplest progression of tritone steps. The -2 can be understood as a 'concentric leading tonality' with the particular tension ("inner wish"-Kandinsky) to dissolve from -2 into 1.

That means 1 +4 : -2 : 5 : +3 -7 are within the same character of relation.

Connecting the Tritone relation 1 +4 : -2 : 5 : +3 -7

is called a Yellow Bridge ☐

Red TR or Red Bridge

1 : +4 with +3 : -7

1 +3 +4 -7 is in accordance with Red.

Supplementing Tritone: Which tritone is supplementing the effect?

The Tritone +2 +5/-6 offers itself.

It contains a kind of enhancer for the red like in orange.

That means 1 +4 : 2 +5 : +3 -7 are within the same relation.

Connecting the tritone relation 1 +4 : 2 +5 : +3 -7

is called a Red Bridge O

Blue TR or Blue Bridge

1 +4/-5 with -3 +6

1 -3 -5 +6 Here the -5 is understood as an enhancer of the concentric or the depth of blue.

There are four minor thirds on top of each other. They 'cut' or divide the octave into four parts in a very geometric manner. Each time they express and confirm the concentric.

That means 1 +4 : -3 +6 are within the same character of relation.

Connecting the Tritone relation 1+4 : -3 +6

is called a Blue Bridge ∆

Table of Tritone Relations on 12 Tones

+7	☐
-7	O
6	∆
-6	O
5	☐
+4/ -5	∆ O ☐
4	☐
3	O
-3	∆
2	O
-2	☐
1 /1	☐ O ∆

This concludes the Tritone-Relations (TR) on 12 tones.

Miscellaneous: Points of Discussion

The presented space of music harmonies and colors presents a vastness of possible harmonies. It is obvious that there are many more colors to be added and more spatial units to be defined.

To the given criteria to define a color and a scale, like eccentric, concentric, degree of light, leading tonality there are more ways to create colors and present subtle differences, for example in the way of playing the luminosity of a color on the instrument.

Black and White

Black is seen as an expression of the density of following tones, therefore it is presenting the totality of possible notes, the chromatic scale and sounds or noises.

White is understood as the absence of presented notes, that means the pause. It is therefore also a mean to lighten a color in leaving pauses and gaps.

On Leading Tonality

Leading tonalities can be differentiated in eccentric leading tonalities (+7:8/1 and concentric leading tonalities (-2:1/8).

As follows, it also can be understood as a general dynamic of the next halftone function of the TR, which harmonically means the next degree of light, lighter or darker - or as an 'inner wish'[Kandinsky] to proceed or to dissolve.

Bspl. B-F : C-F# B-F from C-Dur/ B∆-5 : C-F# from G-Dur/ F# ∆-5

Practical Use of the Longchen Harmony

This approach to music and to color is intended for both musicians and artists, for musicologists and scientists of applied art. (It also might offer materials for new neuro-psychology, i.e. aspects to stimulate the brain). I regard this subject as an interdisciplinary field of its own, from which very particular insights and views can evolve. Further research is needed to explore the vast field of harmonic spaces and the use of harmony colors as a luminous mirror of the mind and its intelligent potential.

Work with the Sounds and Colors

0: In order to visualize a harmony as color it is helpful to encounter the training in a fresh and impartial state of mind.

Bring to mind the basic tones, understand their concentric or eccentric effect.

Carefully mingle the structure and the imagination of the color from the context of sound into their luminous context .

Ponder the particular character of the 'sound-color-harmony so that the unique dynamic of color and tune are increasing as luminosity within your experience of playing.

Maintain a contemplative attitude towards the color and the sound in order to deepen the simultaneous 'hearable luminous effect'.

Approach the next related harmony in the same way, noticing the difference and pondering on this.

Epilogue: Purpose and Request

The harmonic spaces presented above are intended to be exemplary, not exhaustive. They provide basic guidelines for the interdependence of color and sound. It also hints at further research and presentations of harmonic space along similar lines. The scales and colors can be applied to bring further, as-yet-undefined color-sound-spaces into existence.

The Longchen Harmony has the purpose of broadening ones’ tolerance towards and knowledge of less familiar effects and qualities.

It is a good way to train the pliability of the mind so that one can enjoy all experienceable harmonies and energies in context of their dynamic components.

From this point of view, it can serve as programmatic directions for the enrichment of music and art education.

The knowledge of harmonic space can also be understood in a wider sense, in which case it might also be of interest to other fields like neuroscience and areas that work with structural systems.

Final Remark

I would like everyone to reflect upon the Longchen Harmony with pleasure and to apply it with ease. At the same time, I would ask you to use the name Longchen Harmony out of respect for its source and in order to have a common ground for communication and inspiration.

I would be delighted to hear any ideas or commentary on this matter as well as offers to collaborate in the future.

It is worthwhile to state that 'Longchen' derives from 'Longchenpa', which in Tibetan means 'Knower of the Vast Space' and is the name of one of the most prominent Dzogpachenpo masters. He lived in the 15^th century, teaching on the 'Nature of Mind' and the mind's basic potential.

Markus Loebel / Jamyang Sangpo

the first version has been established in the digital net with the help of Niels Bogaards

Bamako/Paris on February, the 21st 2004/ Losar 2131.

this second version has been established in the net with the help of Niels Bogaards

Bamako/ Accra on March, the 1^st 2006/ Losar 2133.

written by Markus Loebel/ Jamyang Sangpo

Finished in Kassel/Germany at 'Fairytale Quarter', August, the 8^th 2015

Last edition: Vervier/ Belgium at Paws Palace 5^th Sept. 2017

A further work was finished on June , the 8^th 2020 at the Bohei Base.

Thanks to my old friend Robert Bobo Miller from Berkeley University for the English editing.