All the parts in each of these scales, from the first tonic to the second, relate to the same parts of the scale below them in the simple ratio of 2:1; and serially to the first tonic in the following ratios:—
8:9, 4:5, 3:4, 2:3, 3:5, 4:7, 8:15, 1:2.
First Series of Scales.
| Tonic. | Supertonic. | Mediant. | Subdominant. | Dominant. | Submediant. | Subtonic. | Semi-Subtonic. | Tonic. | |
|---|---|---|---|---|---|---|---|---|---|
| I. | (¹⁄₂) | (⁴⁄₉) | (²⁄₅) | (³⁄₈) | (¹⁄₃) | (³⁄₁₀) | (²⁄₇) | (⁴⁄₁₅) | (¹⁄₄) |
| Red. | Red-orange. | Orange. | Yellow-orange. | Yellow. | Yellow-green. | Green. | Blue-green. | Blue. | |
| II. | (¹⁄₄) | (²⁄₉) | (¹⁄₅) | (³⁄₁₆) | (¹⁄₆) | (³⁄₂₀) | (¹⁄₇) | (²⁄₁₅) | (¹⁄₈) |
| Green. | Blue-green hue. | Blue hue. | Blue-purple hue. | Purple hue. | Red-purple hue. | Red hue. | Red-orange hue. | Orange. | |
| III. | (¹⁄₈) | (¹⁄₉) | (¹⁄₁₀) | (³⁄₃₂) | (¹⁄₁₂) | (³⁄₄₀) | (¹⁄₁₄) | (¹⁄₁₅) | (¹⁄₁₆) |
| Red hue. | Red-orange hue. | Orange hue. | Yellow-orange hue. | Yellow hue. | Yellow-green hue. | Green hue. | Blue-green hue. | Blue hue. | |
| IV. | (¹⁄₁₆) | (¹⁄₁₈) | (¹⁄₂₀) | (³⁄₆₄) | (¹⁄₂₄) | (³⁄₈₀) | (¹⁄₂₈) | (¹⁄₃₀) | (¹⁄₃₂) |
| Green hue. | Blue-green-toned gray. | Blue-toned gray. | Blue-purple-toned gray. | Purple hue. | Red-purple-toned gray. | Red-toned gray. | Red-orange-toned gray. | Orange hue. | |
| V. | (¹⁄₃₂) | (¹⁄₃₆) | (¹⁄₄₀) | (³⁄₁₂₈) | (¹⁄₄₈) | (³⁄₁₆₀) | (¹⁄₅₆) | (¹⁄₆₀) | (¹⁄₆₄) |
| Red-toned gray. | Red-orange-toned gray. | Orange-toned gray. | Yellow-orange-toned gray. | Yellow-toned gray. | Yellow-green-toned gray. | Green-toned gray. | Blue-green-toned gray. | Blue-toned gray. |
To the scales of chromatic power I add another series of scales, in which yellow, being the first tonic, and blue the second, the numerical divisions express the ratios which the colours in each scale bear to one another in respect to light and shade. Thus red is to yellow, in respect to light, as 2:3; blue to red, as 3:4; green to orange, as 5:6, and purple to green, as 6:7.
These scales may therefore be termed scales for the colour-blind, because, in comparing colours, those whose sight is thus defective, naturally compare the ratios of the light and shade of which different colours are primarily constituted.
The following is a series of five complete scales of the harmonic parts into which the light and shade in colours may be divided in each scale according to the above arrangement:—