Chemistry, physics, metaphysics, and mathematics. According to Lucas (1854), musicians, too ignorant to go beyond convention, have tied themselves hand and foot to mathematics. If today it is normal for us to depend on the dictatorship of calculation and analysis, it was misleading for the ancients.
Louis Lucas begins his journey into the forgotten rules of music. In the mid-nineteenth century, Lucas was not exempt from the fascination exercised by the disclosure of Indian culture in Europe, to the point of considering it the source of the culture of the ancient Egyptians.
My translation of l’Acoustic Nouvelle by Louis Lucas.
Introduction
After a patient and laborious study of the phenomena which take place in music, I have assured myself that the absence of genuinely rational principles, and the introduction of three significant errors, have particularly impeded the progress of pure science.
These unknown or ill-defined principles are the consequence of the general laws of attraction, which give rise to particular laws of succession, consonance, and comparison.
Errors respond to these principles, whose place they have usurped. They consist of the following:
- The exclusive division attributed to dissonances;
- The acceptance – by imitation – of absolute formulas of dissonance;
- The belief in an equally absolute tonality in the successive order.
This is why music, which, by its elements, could walk almost on a par with geometry and arithmetic, still finds itself, at the present time, completely outside the universal progress of knowledge.
Geometry is based on space and its combinations from the point of view of directions.
Music has the same conditions of existence, only relevant to another sense, hearing.
Geometry was founded by establishing simple figures in which all we can conceive comes to be identified; everything else is secondary and modifiable.
Music has such solid, invariable foundations.
The sound body, in essence, presents a constant phenomenon of resonance, of which we can accept the series as the absolute in music.
Apart from that, there are multiple, infinite combinations that all relate to this elementary principle, and this is by virtue of laws as exact as they are immutable.
What is needed, then, to find science, in music, on rational bases?…
Two things:
- Having the absolute type;
- Know the laws that govern contingent combinations.
We also know the law of contingency: it is the attraction of the non-absolute vibratory series by the portions of the absolute type, and that is in inverse proportion to the distance and direct proportion to the force acquired.
Taking hold of these first facts, so simple, so natural, we must take up all the musical phenomena by subjecting them to the analysis of these eternal laws.
We will then see, without a doubt, the inadequacy and limited scope of the rules still dividing the treaties’ exclusive domain.
Others will do better than I, no doubt, with time and more extensive instruction; I shall be only too happy to have been the first to show the proper path.
I will therefore develop without further preliminaries the principles that I have indicated, except to return to them later, when the role that each of them must occupy in this work will call on our part for a new examination.
I. On Attraction
Attraction is a phenomenon that governs all musical facts, both to constitute the fixed series of the sound body and to ensure the artificial hierarchy and the successive emission.
As we shall soon see, nature gives attractions in simultaneous resonance only in a latent state. It was, therefore, beneficial in the interest of musical progress that observation or instinct should produce more energetic and more varied artificial attractions to help us out of this elementary state when we had to use the successive emission.
This is what led to consider each isolated sound as part of a hierarchy constructed by imitation, according to principles that merge with the major divisions of the sound body and link the movement of each towards a common attractive center ( 1) determined by appellations placed according to the whim or skill of the musician.
In this way, the regulated melody or scale presents the double aspect of a multiple individual attraction, drawn into a collective and central movement called tonality, which seems to be an image of the universal attraction of the world.
This tonality, as well as the movement of certain spheres towards an established, actual center, like the sun, I suppose, has, like this movement, only a contingent existence, which can change at the slightest pretext, while the attraction itself is eternal, and never varies except in its modes of application.
In the following emission, as I said, the vibratory series was divided into its simplest parts, following the example of those furnished by the sonorous body; on this, we have not varied, but it was not the same when it was necessary to push this division to the parts which contain only appellatives.
Everyone has seen it, according to their habits and different reactions.
This question is undoubtedly the most important and the most curious that can be raised in music; it is she who, well resolved, must explain the multiple systems of all nationalities and find a communion of principles.
I will probably develop in more detail the reasons on which I rely to support my explanation; however, it is helpful to admit the following temporarily:
There is nothing absolutely necessary except the consonant formula given by the sound body, that is to say, the term 1, 3, 5.
Everything outside this series is without forced limitation, and left to the caprice of the musician, who can, like the Indians, divide his intervals, whatever they may be, by quarter tones; like the Arabs, by thirds; like the Europeans, halftones, or any other reaction if the ear can catch it.
Complete music, that is to say, the reunion of melody with harmony, offers the periodic succession of pure consonances, rest, and dissonances, or transitory resonances.
I claim that these dissonances are not, as it is believed, sounds produced by nature in a fixed and immutable way, like consonances, but capricious divisions, bearing, by virtue of specific laws, on centers of attraction, which are absolute consonances.
Now, these appellations or dissonances are subject only to the general law of attraction; this attraction can be excited or diminished by voluntary combinations of distancing or bringing together equilibrium or predominance.
So there is as much reason to be in an appellative by quarter as by third or halftone because wisely governed elements can bring about happy dispositions.
Because of this, it is a severe error to believe that one can unite to consonances only appellatives by half of the tone, by virtue of a principle of filiation by thirds, of which we will see later the austerity. Dissonances are appellatives and are just that, and these appellatives have no natural definition except their supporting note, their absorption.
So much for the individual, detached composition of the appellative formula, it now remains to know what will be its relative position in the hierarchical series.
If we construct these equal intervals, whatever division we adopt, the attraction disappears instantly under the influence of a similar movement. Indeed, whether we hear a series of octaves, fifths, fourths, thirds, major or minor seconds, we will obtain the same result, a vague emission, without any determination. This must make a similar movement in music look like a very important phenomenon, which destroys the attraction by modifying it sensibly, according to its intensity.
But if breaking this similar movement, one establishes between the sounds a sufficient inequality of interval, the attraction, the movement, is immediately reborn; so that it suffices to attach a single name to a sequence of equal intervals, so that, under certain conditions, it leads to the determination of the whole series on a single point of arrival.
Our range is made up of two series of tetrachords, each of which has one of these designations.
Also, two distinct naming points can break up the over-composed tonality that we call the major or minor scale.
According to us, any simple series is a tonality; our usual range is the union of two different tonalities reconciled by specific procedures that we will explain in their place.
We have varied a lot and still vary on the typical construction of these composite series. The ancients, as well as the moderns, have tried many forms. The Europeans are perhaps the only ones who use the closed circle that constitutes our ranges.
Whatever system is adopted, it consists essentially in establishing a sequence of sounds that are unequal in their proximity.
We have given the name of sensitive, sometimes of dissonance, to the sound which, by relative and actual weakness, leans towards another preponderant sound.
This denomination is incomplete and inconsistent. It was necessary to determine the two opposite terms of this movement: the attractive note, the attracted note, the first keeping its name, the second taking that of appellative, I suppose, already admitted by several authors.
Finally, by designating only sensitivity, we have attributed to this term, action received, a specific activity that has given the passive an importance that belongs only to the active.
We will soon see why it was not necessary to fall into this lack of observation; for it is this two-term phenomenon that, reversed by a changed preponderance, furnishes the variety of melodic successions and combinations.
Before explaining this important fact, I must finish what I have to say about the attraction.
The ancients and some modern peoples, with ancient habits, understood the principles of sensibility better than one might think.
Their successions contain such changes of attraction that they have obtained a great wealth of combinations in their modes.
For a long time, we have confined ourselves, from the melodic point of view to two series, which have been called major and minor modes.
Without discussing the beauty of this formula and the usefulness of its exclusive maintenance, I will point out that, by this only knowledge, we break with all originality, all foreign resources.
Just as by not understanding the free division of names, we have put an impassable barrier between us and all the East and many other peoples of which I cannot enumerate.
It is, however, probable, I would like to be able to say certainly that it is not impossible to make with these melodic nationalities an exchange that would benefit everyone.
It would be enough for that to give them the key of our harmonic processes, whose application would be made identically only on the consonances which are common between each one, by the necessary force of the law of absolute consonance, and by tolerating for them the assembly of dissonances divided according to their education (2).
People will say, as has happened so many times: How do you expect us to be able to grasp intervals divided by quarter tones, and which only produce to any European ear a dreadful cacophony?
I’m not saying that this can be done immediately, but I think it’s a mutual education to be exchanged; they will understand our harmony in the same space of time we take to appropriate what is useful or interesting in their melodies. It is enough that the thing be possible so that we must not reject it forever.
Isn’t simultaneous resonance immutable?… It will always serve as a point of contact between any series whatsoever.
In the musical system of the Orientals, it is not only the division of the attractants which differs from ours; it is also necessary to add to it the mechanism of the modulations.
It’s been a short time since we know the modulation and have determined modes.
The Indians have been in possession of these two processes for an unknown time. There is more; by a single formula, they give rise to these two orders of facts.
When we modulate, we go either into minor mode if we are in major, or into major mode if we are in minor, or different scales.
But, whatever the transition from one of these ranges to another, apart from the two modes above, we will never oppose only one definite type to another definite type whose elements are proportional. It is not the same in India. By means of a simple formula but ingeniously combined, extremely numerous modes are established which vary at will the register of the scales and the relative position of the sensible ones; That is to say, change key and mode, either dividedly or simultaneously.
Let’s take the Sriraga mode as an example:
Sol, la, si, do, re, mi, fa (A = la, B= si, C = do, D = re, E = mi, F = fa, G = sol).
Four mobile notes, sol, si, do, and fa, can vary according to the artist by a quarter tone on each side.
Now, considering their way of establishing and dividing the attractions, we notice that the above formula can give at-will scales analogous to those we call sol, re, ut, majors or minors, ut only major, and varieties of modes quite unknown to us.
All the notions we have about this oriental music are so incomplete, not to say so jumpy, that we cannot know exactly what we should gain from the borrowings that could be known from it. We must therefore stick to the simplest hypotheses, not disdainfully rejecting riches whose value we do not yet know.