Gosport: Printed by E. Groves, 31, High Street.
By John Denis Macdonald, M.D., F. R. S.,
London:Longmans, Green, Reader, and Dyer.
Gosport:Groves, High Street 1869.
Agreement of the Musical and Colorific Scales.
Like the notes of the musical scale, the prismatic colours are seven, as shewn in the following diagram.
DIAGRAM I. (Compound Gamut.)
The staff, or stave of five lines, gives the musical notation of the natural scale;below this are the names and numbers of the notes, and next follow the corresponding colours as they occur in the iris. Now of the above series of colours, the red, yellow and blue are said to be primitives, as they are incapable of further analysis, whilst they themselves are variously combined, so as to produce all the remaining colours, which are therefore denominated compounds or derivatives.
The primitive colours, red, yellow and blue, occuring respectively upon the first, third and fifth intervals, in truthful analogy, independent of coincidence, or fortuity of any kind, may be said to compose the perfect chord of colour, answerable to that in music which all musicians admit to be the very ground work and basis of harmony. In favour of this combination, we have the most conclusive natural indications in the harmonics of strings and membranes, the open notes of musical instruments of inflation, and indeed under any circumstances in which the conditions for vibration exist.
The primitives, therefore, may be regarded as one family, in relation with the derivatives as in pedigree,
Here the derivatives are marshalled in line, in the respective order of their descent, and including them with the primitives, we have the whole prismatic scale as given in the proceeding diagram (I.)
In mechanical mixture, red and yellow make orange, yellow and blue make green, and bLue and red make pure purple;but, in the spectrum, arising from the diffiusibility of the yellow ray, (as indicated in the diagram) instead of simple purple, we find the two colours, indigo and violet, interposed between blue and the 8ve red, and so the number is made up.
Constitution of the Musical Scale.
The diatonic musical scale, consisting (with the octave) of eight notes, is divided into two lesser scales or tetrachords, each consisting of four notes, and terminating in a semitone, as shewn in the following stave.
Although the intervals between and D, and between D and E, are said to be whole tones. The first is a little larger than the second, as expressed by the fractions, but in the second tetrachord the relative size of the corresponding intervals is reversed;that between G and A being a little smaller than that between A and 13. On the other hand, the semitones between E and F, and between B and C, hold a corresponding relationship, or are, in other words, of equal value.
It may be fairly argued that tint or hue in colours determining their relations to each other, is equivalent to pitch in sounds, which is in like manner due to the rate or number of vibrations in a given time, as previously alluded to.
In this inquiry we shall confine our attention to the natural key of music, or that commencing with the note C, assuming red to be its analogue in the colorific scale, in favour of which position, several arguments may be adduced. Thus, red is by position the first of its own series;it is the least refrangible constituent, and the vibrations producing it occupy more time and space than those of the succeeding colours, as also may be affirmed of the musical tonic or key note, with reference to the other intervals of the scale.
The notes of the gamut, hi uninterrupted succession, do not appear to occur anywhere in nature, yet their relative pitch and order have been determined by natural indications, mathematical calculation and the test of the ear. On the other hand, the order of colours occuring in the rainbow and the prismatic spectrum, may be assumed to be the right one, from what has been already stated.
We are now prepared to enter upon the subject of musical harmony, with the view of tabulating the colorific agreements, so as on the one hand to submit the truth of the analogy to further test, and on the other, should the foregoing premises be correct, to afford useful examples and practical hints for the painter's guidance.
Practical music is of little use to painters, consisting chiefly of digital performance, which, like laying on colour, is simply mechanical or operative. They may, 'however, profit much by the study of musical principles, including a knowledge of the properties and relations of sounds, both in single sequence and in combination, governed by rhythm.
Rudiments of Harmony
1.- Sounds in unison are those whose respective undulation are of the same size and number, so that they occupy equal portions of time and space. Fig. 1, diagram IV.
2.- All other concords must hold a relation between the numbers of their vibrations as to render it possible for them to act freely together without interfering with one another;and while this is the case, any number of notes may be combined, and they will all be in harmony. Fig. 2, diagram IV.
3.- Should the vibrations of one note be in irregular proportion to those of another, a coincidence between them can only happen occasionally, and they will interfere with, and neutralize each other in the intervals. This is the true nature of dissonance and the element of discord. (Fig. 3, diagram IV.) Such is the law of "interference," and the lines of light and shade occurring where two sets of luminous undulations so interfere, are analogous to the alteration of sound and silence, taking place where two notes not perfectly in tune are sounding together.
From the study of their properties and offices, the different intervals of the musical scale have received appropriate names, thus:is denominated the tonic, 1) the super-tonic, E the mediant, F the sub-dominant, G the dominant, A the sub-mediant, and B the sub-tonic. The word tonic is always applied to the 1st or key note;the dominant to the 5th from its predominance in the harmony;and the mediant to the 3rd from the position it holds between the tonic and dominant;the 4th
or sub-dominant is next in precedence to the dominant, and the sub-mediant though above the mediant in position, is yet musically speaking subordinate to it, as its name implies.
The super and sub-tonic, or the 2nd and the 7th need no special remark at present, but that they are dissonant with the tonic.
The technical names of the notes here briefly alluded to, are given seriatim in the following diagram, which is also intended to show that every note in the gamut may be supported by a fundamental bass note with its third and fifth, forming what is denominated a common chord. The equivalent colours have also been supplied to the musical characters.
It will be observed that, only three common chords occur on the bass clef, and these are all that are required for common purposes without change of key. The first is founded on the tonic, C (red), E (yellow), andG (blue), the second on the sub-dominant, F (green), A (indigo), C (red), and the third on the dominant, G (blue), B (violet), & D (orange.) The first note of each is its fundamental bass, but this gives place to the others in the changes of position or inversions of the chords, as in the annexed diagrams.
That the three common chords as given, include all the intervals of the scale may be thus simply shown.
From this it will be apparent that any plain melody may be readily harmonised, with the proviso that each note must itself occur as a component of the particular chord selected to sustain it.
To the fore-going may be added the minor common chord of the super-tonic, the imperfect common chord of the sub-tonic, and the chord of the dominant seventh.
As B and D the first and third of the last chord form respectively the third and fifth of the common chord of the dominant, it is more usual to combine the two triads in the form, known as the chord of the seventh, consisting of the dominant with its third, fifth and seventh as follows :
As there arc four distinct notes in this chord it admits of four positions, moreover, the painter should observe the musical ride that it always requires preparation;(i.e.), a particular chord to precede it, and resolution, (i.e.), another to follow it, which must be that of the tonic as a close.
The common chord of A minor, which is the relative minor to C, having no signature at the commencement of the staff, stands thus :
The sub-dominant and dominant common chords of this key, correspond respectively with the chords of the tonic and super-tonic, already given in Diagrams VI and IX, and therefore need not be repeated here.
The great latitude exhibited in the foregoing examples for the selection of chords of colour, should not mislead the painter in their promiscuous use. He should first determine his key, and then translate some good harmonic phrases into colours most befitting the nature of his subject. The method to be followed in their distribution, and other readings of the rules of art, where they can be sustained by the musical analogy, will be found in a more advanced part of this essay. I shall now merely append some of the leading principles of counter point to assist the painter in harmonizing a theme, or phrase for pictorial purposes.
Euphony in music is analogous to euphony in language, and determines the most easy transition, or sequence of accordant intervals, consistently with the physiology of hearing. The following principles are involved in it.
1.- A clear perception of the fifth interval is essential to the determination of a key. Hence a sequence of octaves and fifths in similar motion, when the parts uniformly ascend or descend together, having a tendency to assimilate a change of key, is prohibited by the rules of harmony.
2.- Skips from a given note to any wide interval, and dispersed harmony, so called, for the reason already given in the preceding paragraph are also to be avoided. Hence compressed harmony, or the closest possible arrangement of the parts is to be studied in composition.
3.-In supplying harmonies to an air in C major, the chords in Diagrams V to X, inclusive, are available, and they will afford the composer sufficient materials to furnish parts with the double advantage of having a theme in themselves, without infringing rules. Those chords taken singly will support any of their own parts. Hence any note in the scale taken singly will agree, or harmonize with any chord, in which, it occurs as an ingredient. See annexed diagram.
In plain counter point, the notes of tbe parts added are of uniform length with those of the subject;but where it is "florid" the notes are of different lengths, and variously intermixed at least in one of the parts. In the latter case attention must be paid to the accented parts of each bar, so as to know where the harmonies should be supplied, without involving the passing notes and embelishments.
I have dwelt thus long on the subject of harmony, seeing that frequent allusion to its principles must be
made in the course of this essay, moreover, even a slight primary knowledge of music will greatly facilitate the comprehension of the views and arguments advanced;while the examples given in the diagrams will stand for reference.
I have reserved special notice of the complementary colours until something had been said with reference to harmony, so as to enable us the more correctly to form a judgment of the theory which connects them with the so called u physiological basis " of the harmony of colours.
In giving an account of the complementary colours, it is usual to adduce the series resulting from the binary mixture of the primitives, forming a sort of colorific hexachord, like the old musical one, in which the 7th interval equivalent to violet was wanting. Had Guido the monk taken the prismatic scale for his guide, instead of, in effect, making a mechanical mixture of the three major constituents of the diatonic scale, he would have transmitted a still greater name to posterity. The hexachord arranged in a circular manner, forms an instructive diagram, showing at a glance the colours that are complementary to each other.
The alternate colours compose two common chords, one on the first and the other on the second interval of the scale. The opposite colours are also concords, standing in the double relation of fourths and fifths to each other, one being primitive and the other compound. Now in all the relations just mentioned, namely, the alternate simple and alternate compound, or any two opposite colours, the components are complementary, (i.e.), in the proportions to neutralize each other, and produce white or colourless light. It being assumed that the latter is in all cases composed of the three primitive colours in achromatic combination. Thus, if we take one primitive, say red, the other two, yellow and blue must exist in its complementary green, or separately. Or taking a compound colour, say green, composed of yellow and blue, its complementary will be found either in the opposite colour, red, or in the alternate compounds, orange and purple taken together. The complementary colours therefore, may be divided into two groups, as under:
1. - Binary group Red/Green, Yellow/Purple, Blue/Orange
2.- Ternary group Red/Yellow/Blue, Green/Purple/Orange
Though the musical analogy declares all complementary colours to be accordances, I cannot think with Professor Muller, that all other combinations of colour are disharmonic, or where he says that "combinations of two of the simple colours, the third which would render them complementary being deficient, are the most offensive to the eye;for instance, combinations of yellow and red, blue and red, or yellow and blue." Instead of "complete disharmony," as components of the perfect chord of colour, the examples here given ought to produce rather an agreeable effect. He further states that "in the 14 association of two colours of which one forms a transition to the other, there is neither harmony nor disharmony "-such colours are indifferent to each other - as yellow to green, red to orange, or violet to blue" (probably indigo). So far as indifference goes, these intervals, musically speaking, being seconds are positive discliords. Finally lie writes "the disharmony between two colours "may, however, be removed by the interposition of a third colour, which is the harmonic of one of them, and is indifferent with relation to the other. We have examples of this in such combinations as red, green and yellow;yellow, violet and red;blue, orange and red;or red, green and blue, &c." But this doctrine, and the discordant colours suggested by it are quite opposed to the musical analogy, which teaches us to look for agreements in concordant or coincident vibrations without interference," rather than to submit to any arbitrary rule however plausible, that may be antagonistic to so philosophical a principle.
As before explained, musical strings have a physical tendency to divide in the production of harmonic sounds, into parts of 4, 5 and 9, so as to embrace all the intervals of the diatonic scale;and the complementary sounds so developed, when translated to colours, correspond in every instance with what the colorific analogy would demand of them.
If a string sounding 0, answerable to red, be divided into 4 parts, 1/4th and 2/4ths will also produce C, but the complement of 1/4th are 3/4ths yielding F, which is equivalent to green, the complementary colour to red. Diagram XV, Fig. 1.
Divide the string into five parts, and 1/5th, 2/5ths and 4/5ths will produce E, (yellow), but the complement of 2/5ths are 3/5ths, yielding A, the equivalent of indigo or purple, which is the colour required. Diagram XV, Fig. 2. Again, dividing the string into nine parts, 1/9th, 2/9ths, 4/9ths and 8/9ths produce D, (orange), but 3/9ths 6/9ths make G-, (blue), and the complements, whether single or double make only these two notes, whose equivalent colours, orange and blue, are complementarie3 (Fig. 3). These facts lead to the inference that complementary colours are, as it were, chromatic harmonics;and perhaps it is in this way that complementary sensations arise in the retina, whose surface being long excited by the influence of a particular colour would appear to be more susceptible of the vibrations of the complementary in white light, but, it is not at all improbable that these are actually included in the way of harmonic vibrations in general.