Imaginary music (PRELIMINARY ENGLISH VERSION)
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Figure 1 : forms and patterns (pier of Cap Breton)
We have achieved to investigatie the sound space in its three dimensions. We own now precise words to describe the properties of the sound material, as well as the limits and the constraints of the auditive perception. We are in an environment populated with sound objects created in this material by the nature or by the urban life, or then in an environment populated with sound objects created by musicians (instrument makers, interpreters, composers, singers) to communicate an emotion.
This chapter speaks now about the forms of these object, as well as the varied textures which the sound matter can take on.
Four basic types are going to interest us to generate forms: continuous, discrete, random, fractal. To help to understand the principles, let us imagine in a visual way. We shall transpose afterward into the musical domain.
Figure 2 : illustration of continuous forms : the beach of Hossegor in autumn
Continuous forms are straight, curved or broken lines: for the draftsman: the pencil links points by drawing all the intermediate positions.
We can notice it in the landscape: the horizon if it is visible, roads and paths, the undulations of the telephone lines who go from pole to pole, as well as their shadow on the road.
These continuous lines are rather rare in the nature, which is richer in forms less easily descriptibles. They are often the result of the hand of the man: roads, fences, architecture of buildings, dike on the seaside.
Let us transpose these ideas into the sound domain. We find examples as the playing of slide trombone, the portamento effect to pass from a note to the following one, the progressive noise of the passage of a plane.
Figure 3 : electric lines evoke the lines of a paper music
Figure 4 :
Many musical instruments, as the piano, allow to play only notes of fixed height, within the grid of a scale. It's as if our draftsman could put the points of the drawing only in pre-existent dots, tiles or boxes. It is the case also for the embroidery or the display by brilliant points (pixels).
As when we take a staircase, we set our steps strictly on stairs. The staves of printed music illustrate completely this quantization (or dithering) of the sound space: the pitches by the lines, the durations by bar-lines.
Figure 5 : pixels
Figure 6 : keyboard
Figure 7 : stairs
(Palais of Popes, Avignon)
Some phenomena seem to result from an unpredictable but not surprising fate. For example:
the precise place where every snowflake falls seems to have no link with the others, but the distribution of flakes results finally in an identical height of snow everywhere;
the density of a crowd is stronger near the point of interest of people, and weaker when we go away from it.
These random forms are very remarkable and also can be encountered in the sound universe, for example: noise of the rain, noise of crowd, disorder of the musicians who tune their instruments before the concert.
Every single object is uncertain, but the density of objects respects a law of probability.
Among the patterns which seem due to the fates of the nature, some are particularly beautiful or fascinating. For example, the branching of trees, this of the nervures of leaves, heaps of rocks, the contour of a rocky coast, crossing waves and wavelets.
These forms result from a well ordered hazard. They belong to the fractal geometry. They possess an interesting property: the smallest element contains the generic form of the whole. These shapes of so complex appearance are often elaborated from elementary shapes and according to a simple process.
The principle of the process consists in drawing a shape, then in splitting this starting shape in several elements, which are thus juxtaposed. Then, inside the borders of each of the elements, we draw a shape in reduction similar to the starting shape. We split then every element in a similar way in the splitting of the first shape to obtain smaller elements, and we perform this process again as desired.
Figure 12 : two examples of the fractal breakdown principle.
The nature creates new objects by division; either during the biological growth (a small seedling will become a big tree), or on the contrary during the breaks coming from the confrontation of elements: clouds, vortex, dust of stars, spark or flash of lighting, shaping of dunes, ragged rocky coast....
The sound universe also include fractal forms. Some are not easyly recognizable when directly listening, but we can reveal them by the analysis: it can be the distribution of the harmonics in the tone of an instrument, the noise of a waterfall. Forkings in the Art de la Fugue de Bach, or in the repetitive music join this geometry.
Figure 15 : oaks in Winter (Ile de France)
To combine two forms between them, we shall define two roles:
on one hand, the texture of the sound material (as a tissue, or pattern) ;
on the other hand, the shape of the drawing made (as a sculpture in a material of type wood or stone, or a drape in a tissue).
The following figures propose some examples of combinations of forms in the visual domain.
Figure 16 :
quantization on fractal natural wooden texture
(logs, Landes forest)
Figure 17 : continuous form on dithered texture
Figure 18 : fractal form on continuous texture
Figure 19 : fractal forms on continuous liquid texture (sequence of broken waves, Opale Coast)
Figure 20 : form of animal and coat... ...on a fur texture
Here are now three examples in the musical domain :
Example 1 : the recording of the noise of the rain :
At the beginning we hear the impact of some scattered drops, then the shower is more intense, and gradually the rhythm of drops becomes hastier, until become an almost continuous noise, and conversely, when the cloud goes away. We have here a sound material the consistency of which is random, but the drawing is a progressive then degressive line.
Example 2 : up and down chromatic swoop at the piano :
The pitches of notes are perfectly separated by the interval of a half-step, thus the sound material is tiled by half-steps, but the outline of the melodic line is continuous. (If it is the cat which walks on the piano, the melodic line is rather random).
Example 3 : performance of a classic melody at the violin :
The violin allows to slide on all the extent of the frequencies of its tessitura, but to interpret a classic melody, the instrumentalist may only use the pitches belonging to the key of the scale in which the score is written.
The sound material of the violin is continuous, but the drawing of the melody is quantized.
The typology and the examples which we have just discovered illustrate an only descriptive and factual approach of the morphology of the sound objects. Can we report now also the potential aesthetic interest for a listener?
Our ambient universe contains plenty of visual or sound objects, but only someones interest us. Why do those interest us, and not the others?
Let us discard at first what seems to us trivial. The originality gets our attention because it can have a semantic content. The semantic value or the originality is carried by an important characteristic related to any observable or perceptible form: its complexity.
The complexity of a form is independent from the size of the object which it models. It is both a function:
of the number of elementary points which determine the form: for example, the complexity of a melody is a function of the number of notes and their durations (minim, quarter ...). So the air of the toreador of Carmen of Bizet is more complex and rich than that of "Twinkle, twinkle littte star";
of the unpredictability of the successive points with regard to the points which precede them; so the rhythm of a military march, containing tens of measures, is incomparably less complex and less original than a single phrase of an African griot's drum.
In a similar way, in the written language or the spoken language, every word is linked to the precedent according to a probability, related to the grammatical structure of the sentence and from its meaning. So, deviating originally from the commonplace language, the poetic language plays with deviations and breaks with this expected probability.
The theory of the communication, developed by Shannon, demonstrates however that the understandability of a message is in inverse function of its originality: the message the most difficult to transmit is the one which carries most information.
The aesthetic interest of a shape is then situated between two reefs :
either the message is little complex, poor, semantically trivial, and thus arouses no reaction of the receiver;
either the message is very complex, very rich, very semantically original , but its unpredictability makes it unintelligible: the receiver finally gives up and loses interest.
A musically interesting form thus has to provide enough predictability between the successive points so that the receiver can about guess what is going to follow from what precedes, but however not certainly. This property is the redundancy of the message, which measures the part of repetition (or of re-use) of what precedes to form what is going to follow.
The redundancy of the communication (that can be mathematically calculated by the signal auto-correlation function), enables to report the subtle compromise between understandability and originality " to make pass " the complexity.
The continuity brings a strong predictability, because all the points are contiguous: the continuous forms are thus relatively simple: straight line, parabol, sine, saw-tooth. The elements of originality can be in breaking points, at the beginning (attack) or at the end (release) of a sound.
Whether in the duration dimension (rhythm), or in the color dimension (pitch), the complexity of quantized forms depends on several factors.
At first, the fact that notes always fall into boxes of a preexistent grid causes a good predictability: they will almost never fall otherwhere ; and should the opposite occur, the originality would appear very strongly.
For example, the blues in three chords and binary beat would leave in principle only little room for the originality; in fact, the black bluesman shifts his notes and his rhythms to drop them just next to the agreed "boxes", while often the pale imitator bores us in making efforts to respect the paper music.
The complexity increases with the fineness of grain of the adopted scale: number of steps of the scale, durations of notes (from the semibreve to the hemidemisemiquaver).
So, for example, the chromatic scale is richer than the diatonic scale (and what to say about micro-intervals of the Indian music!).
Other example, the uniformity of the duration of notes in the Gregorian chant leads to some dullness.
The music styles, the conventions, and finally all that we use to call the rules of musical language, act as understandability factors by redundancy; they are available as compulsory figures, melodic, harmonic and rhythmic forms, with which we can build sequences by respecting a syntax.
For example, the choice of a key, major or minor, leads to the selection of a limited number of possible chords,
Other examples, the musics of folk dances repeat the conventional schemes passed on by the previous generations.
Figure 21 :
An underlying grid
(Harbour of Gorey, Jersey)
These small boats seem distributed according to a charming fate in the grounding harbour. Really, each is moored to one buoy of a regular network of equidistant buoys, to avoid that they contact when they will float again with the high tide.
In principle, if the form is random, the unpredictability should be maximal, and, for the receiver, the comprehensibility should be null.
Nevertheless any listener has a little experience of the hazard; he is thus used to basic statistics and to the probability of drawing lots. So, by listening to a succession of notes of random pitch, he does not expect to hear the same note several times following (what would surprise him as much as with successive draws of the same number in a game of chance). Also, after a long time of silence, he expects rather a hasty suite. If the music breaks these rules of the nature, we can consider that this brings much originality. So, paradoxically, random forms can arouse a very attentive listening.
Another way of bringing some predictability is to apply a law of density the shape of which is understandable (as in our previous example of the rain which approaches and then goes away).
The chaotic natural phenomena which illustrate our presentation of the fractal forms (flashes of lighting, clouds, waterfall, etc.) seem to supply the example of the indescribable complexity, as much from a visual point of view as for sounds.
Nevertheless, the redundancy is at the origin of the generation of these forms: the smallest element contains the generic form of the whole. This generic form, which we can consider as a signature, carries the information enabling to identify without hesitation the fractal image: it is a flash of lighting, it is a cloud, it is a waterfall, it is a tree, it is the sound of a saxophone, an oboe...
Figure 22 : Some simple signatures of fractal forms of indescribable complexity
Figure 23 : the beach of Ault-Onival in August
The magnificent complexity of this image can be understandably analyzed according to a combination of continuous, quantized, fractal and random forms.
The area of sand at the right is lined by continuous lines of both the row of dunes and the limit of the water. It is crossed by a breakwater grid.
Fractal forms are outlined on the surface of the sea: waves at the left and sandbanks in the center.
The random distribution of the crowd of the swimmers respects a law of progressive density: numerous on the beach at the right of the photo, it clears up away to the left.
For an attentive listener walking on the beach, the combination of the noises of the long waves and the small wavelets is typically fractal, and the shouts of the children at random of the density of their crowd.
The descriptions which precede applies to the music a language often taken from the visual domain, what can seem unappropriate. Nevertheless this bridge is interesting.
Let us study a first point of view: that of an observer who contemplates the plain down from a mountain, and who can place in the panorama the meadows and the fields, the houses, the bushes, the rivers, and get a global idea of all these outlines.
Let us study now the second point of view: that, quite different, of the walker in the same plain: he discovers these same objects according to his route, and appreciates each one according to the field of vision at some point: big or small, to the left or to the right, partially hidden, etc...
Also let us compare the work of the topographer, which goes through all the surface to be mapped by recording his aiming reports, with the work realized by air photo or by satellite telemetry.
So the same objects, arranged in the same composition, can give place to two types of description, according to the position of the subject which observes :
global description : the observer has a total, simultaneous image, and independent from himself;
relative description : the observer benefits from a partial perception related to the moment: it is proper to the auditive perception.
The global or visual perception specifically concerns the composer or the musical analyst.
The relative or auditive perception concerns the listener.
We can so use two methods (topologies) to describe the same universe: an auditive topology and a visual topology.
Figure 24 : global topologiy and relative topology.
At left :
vision by helicopter of the crossing of the village by theTour of
At right : vision of the same location at the racing cyclists' level.
It is the listener who perceives the sound phenomena by centring everytime his marks with regard to himself.
Every new perception is thus put in perspective against the previous perception, or at least the perceptions still present in immediate memory.
Thus, to describe a sound object, he will estimate it: more intense, less intense, longer, shorter, more brilliant, higher, lower, etc. Any evaluation so integrates the previous evaluations.
It is the composer who elaborates the work in general, build it, gives it a movement, arrange sounds and noises in the simultaneity and in the time
The speech is the one that we used in our statement, with off-time landmarks and absolute evaluation scales. But it is necessary to be conscious that in priori the listener does not reach the music by this topology.
This duality of points of view is also observed in the cinema, between the spectator and the film-maker.
Imaginary music ISBN 978-2-9530118-0-7 copyright Charles-Edouard Platel
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