WO1984003165A1 - Method for the musical modelling of elemental particles and applications - Google Patents

Abstract

The method for the acoustic modelling of elemental particles comprises the representation of vibrations associated to particles according to the formula mc2 = hnu, by acoustic vibrations, by digitally transposing their frequency, measured in Hertz, of 68 octaves downwardly, the frequency obtained being taken as the fundamental of a periodic acoustic vibration including a small number of harmonics, the transposition being practically carried out by dividing the masses of particles expressed in MeV by 1.22066 and eventually by 2n, wherein n is a small relative integer so as to obtain an audible frequency. Application to industrial nuclear fusion.

Description

 Method of musical modeling of elementary particles and applications.

The present invention relates to musical, scientific and industrial applications of a discovery and a work carried out by the Inventor concerning the "musical" properties that elementary particles exhibit, and in particular to a method of modeling particles, based on these properties and which consists in representing particles and their properties by musical sounds and an organization of these sounds. This process includes the development of a range corresponding to the fine distribution of the natural frequencies of all the elementary particles, and also carrying out a synthesis of the musical ranges in use in the various countries of Occident and Orient; the development of a mode of representation of the particles in number, corresponding to the global distribution of the natural frequencies of these particles and making it possible in particular to characterize a balanced "orchestration", also usable as a mode of representation of musical works highlighting their overall characteristics; and various means related to the properties of fusion, composition and disintegration gration of particles, also transposable in musical form. This particle modeling method can be implemented, in accordance with the present invention, using musical instruments and acoustic instruments based on these ranges, mode of representation and means, and applies in particular to the teaching the properties of particles, researching them and developing processes in which the musical properties of particles play a role; and in particular to the development of a nuclear fusion process using particles in temperate agreement, based on the property which such particles, suitably orchestrated, of forming relatively stable compounds, this making it possible to solve the problems of scale ( and entropy balance) posed by the merger, and thus achieve it at relatively economical conditions for the industrial production of energy. Of course, the instruments, range, mode of representation and means developed in accordance with the present invention also have simply musical applications, both in terms of composition (making it possible to develop "tonal music of micro intervals", including chords rich in harmonics; to modulate the timbre according to the melody; and to balance orchestrations) only at the instrumental level (like the determination of the timbre of an instrument having to interpret a given melody).

The current theories aiming to describe the elementary particles, of which our universe and ourselves are constituted at the finest level, are indeed very incomplete. As the American physicist Richard FEYNMAN points out ("The nature of physics", p. 289, Le Seuil 1980):

"first, there are the masses of the particles. The gauge theories ... provide us with very nice models for the interactions, but not for the corresponding masses r we absolutely need to understand this complete set of numbers irregularly ". A certain number of empirical relations had however been noted between the masses of the particles (in particular by T. TAKABAYASI in Japan and RM STERNHEIMER, as well as J. SCHWINGER, in the USA), although not entering within the framework of These models, including D. BOHM in England, M. FLATO and D. STERNHEIMER in France in particular, had highlighted theoretical shortcomings, and developed some elements of a mathematical framework in order to address them. well summarized 'at a recent symposium on particles, where the Austrian physicist

PIETSCHMANN expressed in conclusion (Acta Physica Austriaca, Suppl. XXI, p. 716, Springer-Verlag 1979) his feeling that these models are "analogously to the BOHR model for the atom, a first compromise ... Before 1990 or well there will be an extraordinary novelty, or else physics will become very boring ".

The scientific discovery of which the Inventor is the Author, and which is at the basis of the present invention, can be summarized as establishing that the particles have musical properties because of their vibratory aspect. This aspect, which had been theoretically suggested by Louis de Broglie in 1923 precisely to explain the atomic model of Bohr, then highlighted a few years later, leads to attribute to each particle a natural frequency of vibration proportional to its mass at rest. Louis of

Broglie had been brought to this notion while trying to describe the quanta in a relativistic way, bringing him to bring together the quantum relation between energy and frequency, and the relativistic relation between mass and energy. However, the causality implying, in addition to the relativistic invariance, the invariance of scale, the consideration of this invariance leads, as developed by the Inventor, to additional consequences, and to relationships between the masses of the different existing particles, such as their distribution on the same exponential sequence. On the other hand, causality implies still non-separability, a property that a sound vibration, for example, can suggestively model.

These two properties are thus jointly realized by the distribution of the masses or natural frequencies of the particles according to a temperate musical range.

The new fact brought by the Inventor is the observation, that precisely, the masses of particles stable vis-à-vis strong and electromagnetic interactions are distributed along a range in use in Western music, the temperate chromatic range, consisting of divide the octave (i.e. the interval between two vibration frequencies, or two masses, one of which is double the other) into 12 equal parts, in other words such that the ratio between two successive frequencies is constant = 2 ^1/12 ; the masses of all the particles, including the very unstable "resonances", are distributed according to a finer "range", consisting of a subdivision of the previous range into unequal "micro-intervals", which is in fact found to respond , as will be highlighted in what follows, to the problem of designing a musical range adapted to both eastern and western music. In addition, there is a link between musical consonance and stability of the particles, which is reflected in the distribution described above (cf. figure la of the attached drawings), and which manifests itself on several levels; on the one hand the stability of the particles is correlated with their consonance relative to the proton and to the most stable particles (the music of the particles is essentially tonal, this being manifested in particular by the statistical presence on all the particles of a range with base 2); the frequencies of the particles form with those of their successive modes of disintegration, chords (octaves, fifth, fourth, major third or minor ...), whose consonance is correlated with their stability; finally there are experimental indications pillowcases and theories according to which the global stability of dynamic associations of particles in "nuclei" is correlated with their belonging to the same temperate range: thus, protons and neutrons, in constant interaction in ordinary nuclei by exchanging pions (meso π) form with them a temperate minor third, and the invariance of this property by scaling suggests that it is generally true.

If a histogram of the particles is produced by plotting their reduced masses modulo 2 ^1/12 multiplicatively (ie 1/2 tone) around the mass of one of them (the pawn for example) and on the ordinate the number of particles within a range of 1 / 80th of a tone (2 ^1/480 ), weighted taking into account their stability, that is to say represented either by a square of width

2 ^1/480 , either by a rectangle of the same surface and half width (for the most stable) or double (for the least stable or known with insufficient precision), we obtain the diagram represented in figure la, consisting of a very significant distribution, in six groups of particles harmoniously arranged.

A comparative study, carried out on a computer, confirms that this distribution (of probability ~ 10 ^-12 ) is the best possible (by far, others constituting "echoes", while in general, by varying the base , i.e. taking it other than 2 ^{1/1 2} , we get a chaotic distribution); this study gives the best basis as being 1.05946 ± 0.00001 (2 ^1/12 = 1.059463 ...), showing the correspondence between the particles and the temperate chromatic range; which must itself be subdivided into six unequal intervals, this subdivision including in fact the unstable particles: the particles stable with respect to strong and electromagnetic interactions are grouped on the three lines d, e and f, the constituents of the ordinary matter on the two preponderant lines d and e (yes are Droches of about sixteenth of a tone), and those of the nucleus are on line e, that is to say in precise agreement according to the temperate range. (It is by taking into account these groupings according to the stability, that one calculates the probability of 10 ^-12 ). In addition, the particles located in the same disintegration chain of a given particle form a chord whose consonance is correlated with the stability of this particle.

The different lines observed correspond roughly to the harmonics of order 5, 7 and 11 (and their inverses) which deviate somewhat from the temperate range, and which can be approached by a range 2 ^1/72 (the deviations from the temperate range of the chords constructed on the first twelve harmonics are shown in Figure 1b); with however a slight deviation from these harmonics involving higher order harmonics (which can be described by a range 2 ^1/288 ): the correlation between figures la (experimental particles) and 1b (first twelve harmonics) is 0.79 ± 0.12, the difference in unity coming in particular from the difference between line b and harmonic 11. These phenomena notably arise from the presence of the base 2 range, which has with the effect of accentuating, relative to the others, the harmonics neighboring the successive octaves of the base frequency, and thus in particular the harmonics 4, 15 and (29 to) 31 respectively with respect to the harmonics 3, 5 and 11 which are close in Figure 1b; hence a narrowing of the line e, a displacement of the line d to the right and of the line b to the left (at the same time as a rise in the line a), as can be seen on the figure it. This base 2 range - whose effect on the harmonics is that of a "forming" corresponding to the "aum" sound sung on the bass - acoustically corresponds to "the absolute ear" (cf. GR LOCKHEAD and R. BYRD, "Practically perfect pitch", J. ACOUST Soc. Am. 70 (2), p. 387, 1981). And in fact, the distribution of figure la corresponds to frequencies actually used by musicians from different countries. Figure 1 shows the correspondence between (a) the distribution of the natural frequencies of the particles, (b) the intervals of the harmonic range (of ZARLIN) used in the West, (c) the frequencies of the Persian "vosta" and "zaïd" such as reported by M. BARKECHLI ("Iranian music" in History of music. Encyclopédie de la Pléiade, Gallimard Paris 1960, pp. 460 et seq.), (d) the intervals of the Chinese range, attributed to King WEN of the Chou , (cf. M. GRANET, "The Chinese Thought". Ed. Albin Michel, the frequencies being related to the lowest note), all these frequencies and intervals being still related to the temperate range, that is to say say modulo 2 ^1/12 . The correspondence becomes remarkable. The use of some of these notes corresponds to the fact that, beyond the notes of the diatonic scale based on the first harmonics, and of the notes completing them (sharps and flats) in the chromatic scale, the musicians even want to involve for example intermediate notes between mi and fa or between si and do take the middle, on the instrument, of the positions of the corresponding fingers, locating them on line b (harmonic 31), rather than on harmonic 11 (which is around a quarter of a tone); thus proceed the Irish violinists interpreting melodies in unison, and the ligatures of the Iranian instruments, starting from the same principle but other notes (by taking for example the medium between the D and the Pythagoreans, then the middle between the C and this medium: "vosta" and "zaïd" V ₂ and Z ₂ ), ending in the same way a little below the quarter tone (modulo 2 ^1/12 ), thereby avoiding the maximum of dissonance (3/4 tone, i.e. a quarter of your modulo 2 ^1/12 , for the registers of the usual instruments).

This musical practice thus finds its justification in the "absolute ear" of many musicians.

In order to arrive then at determining for the particles the relative "weights" of the different exponen ranges The inventor was led to study a related problem where these different "weights" come into play, namely the overall distribution of particles in the mass scale. result, which is represented in FIG. 2a, corresponds to a sum of normal distributions multiplied by a periodic function of period α = Log2 / N (N = 1, 12 ...) in the scale (of the logarithms of the masses), the variance of the normal distribution corresponding to N being α, for which the inventor was able to provide evidence. the ratio of "weights" is then that of standard deviations

for N small. We observe the normal distribution corresponding to N = 12, centered on Ω-, with two "peaks" located roughly one tone above the lower octave (coming from the normal distribution multiplied by the basic periodic function 2, let N = 1, apparently centered on the proton) and higher, with the ratio

for their amplitudes. To do this, we made a histogram of all the particles with a "step of 2 ^1/4 (or a minor third). Very remarkably, the analogous study made on all the notes of a musical work gives results of the same type Figure 2 shows the correspondence between (a) the distribution of the natural frequencies of the particles, - compared to the theoretical distribution (in solid line, cf. b) as well as to the prediction of the "thermodynamics of strong interactions", in dotted lines -, (b) the equation curve:

whose envelope (term in square brackets) is given in (a), (c) and (d), - the periodic part (cos ² (12∏q / Log2) must be, in all accuracy, replaced by a function periodical whose figure represents a period if we want to include the higher order scales-, (c) the distribution of the notes of the first bars of the BACH Chaconne (whose "clear notes are like a tearing fresh wind the fog and revealing the clear structures that he hid behind him "according to HEISENBERG), and (d) the distribution of the notes of the first 128 bars of Symphony No. 40 by MOZART (about which EINSTEIN said that" it had not created his music, but that he had discovered it "). If the agreement is excellent between the envelope of (b) and the distribution (a), their similarity with the allure of the distributions (c ) and (d) is no less remarkable, while highlighting the differences specific to works and composers: thus (c) is fairly symmetrical, but centered on the relative of the tonic, (most melodies have their maximum simply on the tonic) while (d), slightly asymmetrical, is centered on the dominant (fifth of the tonic). Similarly the BEETHOVEN Hymn to Joy is centered on the third, the Third Gnossian of SATIE presents peaks on the relative (a tone above the dominant) as well as a hollow in s the distribution (half an octave without note - this piece is also annotated "so as to obtain a hollow" by its author); or again, the andante of HAYDN's Symphony No. 103 has its maximum on the dominant of this andante, offset relative to the whole, the center of the distribution being in the tone of the Symphony, different from that of the 'andante, thus making it appear that this piece was extracted from a work of a different tone.

This mode of representation (the comparison of the frequency distribution with the curve 2b) thus provides information on the harmonic and melodic allure of the music of the particles: most of the particles leaving a visible trace in a bubble chamber (living at least 10 ^-12 s) proceed from a minor tone (Λ is a ₇₂ ), of which Ω- is the dominant: if these particles follow the range introduced by BACH, the music they play (centered on the dominant) is closer to MOZART, somewhat mixed with SATIE (and not hesitating, if we include the unstable particles, to use intervals specific to oriental music). It is thus possible to determine if an "orchestration" of particles is balanced (note from Figure 2a that our universe does not seem to be extracted from a work of different tone) ...

By "music of particles" we mean the vibratory aspect of the composition of matter, which is not limited, moreover, to the concepts mentioned above. Thus the possibility of disintegrations followed by regenerations (which will be discussed later) implies a "rhythmic" aspect, that is to say the need for the lifetimes of the different particles to be commensurable. Reactions involving particles (which can be seen by making a histogram of "mass variations" for a sufficiently large number of reactions) have, like musical melodies, a property of scale invariance, namely a spectral density in reverse of the frequency, meaning that the notes are correlated to those which precede on all the time scales (aspect "history"). Note also that at the higher level, the hydrogen atom grants the wavelengths of the electron and the proton ...

On the other hand, musical sounds have other properties which relate them to the vibrations of particles. The temporal decrease in the amplitude of the sounds emitted by acoustic instruments is exponential like the disintegration of a set of identical particles (or the decrease in the probability of life of a particle over time); the sounds can "merge" with the ear (like the harmonics of a note with this one), and the recent verification by E. COHEN ("The influence of non-harmonic partials on tone perception", Ph. D. THESIS, Stanford 1980, chapter 3) of the fact that the (acoustic) fusion of electronic sounds whose time envelope can be modified is optimal for an exponential envelope, confirms that the acoustic "fusion" could model that of particles, like indi already had the consonance of the frequencies of the component particles as a criterion of the latter; the calculations and experiments of G. WEINREICH ("Coupled piano strings". Journal of the Acoustical Society of America, vol. 62, p. 1474 1977), showing the influence of chords close to unison (and therefore, for harmonic or compound sounds, the influence of consonance, corresponding to the presence of harmonics or components close to unison) over the duration as well as the amplitude of the vibrations of the strings coupled to a piano, and thus the link between consonance and stability of these vibrations, further confirm this point of view, which can only increase the interest of these experiences. On the other hand, an exponential decrease in the envelope of the amplitudes of the harmonics as a function of their rank, as observed approximately on a piano, improves the correlation between Figures la and 1b. It should also be stressed that the auditory frequency discrimination depends on the duration of the stimuli (acoustic "uncertainty relationships"); the extent of the spectrum of audible vibrations, comparable to that of particles today known; as well as the possibility for sound vibrations, whose character is to fill the space, to model the non-separability of the particles in space.

The demonstration of these properties has enabled the inventor to develop a certain number of applications which are the subject of the present invention, namely the production of acoustic models of particles in the form of musical sounds, these models being capable of making it possible to study and represent in a simple way many properties of particles and the matter which they compose; the implementation of these models using instruments, in accordance with the invention, in particular using a musical range developed from the distribution of FIG. the development of a new nuclear fusion process, resulting from these properties. Of course, the instruments used for the acoustic modeling of particles (including for the development of said method) can also receive simply musical applications, which also constitute an object of the present invention. The present invention therefore relates to a method of modeling elementary particles, which consists in representing the vibrations associated with particles according to the formula mc ² = hv, by acoustic vibrations, by digitally transposing their frequency measured in Herz of 68 octaves (more or less a small whole number, possibly) downwards, the frequency obtained being taken as fundamental of a periodic acoustic vibration including a small number of harmonics (whose amplitude decreases monotonously except for "peaks" in successive octaves of the fundamental), the transposition being able to be carried out practically by dividing the masses of the particles expressed in MeV (1 MeV = (1 / 1.22066) x 2 ⁶⁸ Hz) by 1.22066 (or about 11/9) and possibly by 2 ⁿ , where n is a small relative integer, so as to result in an audible frequency (expressed in Hz).

Thus, the proton (the most stable particle sensitive to strong nuclear force, with a mass of 938.28 MeV) corresponds (modulo 68 octaves) to a sol 768.67, octave of sol 384 (which was proposed in 1950 as "tone of base "to tune the instruments, to the Academy of Sciences); thus, if we take it as a flat floor, it is possible using an ordinary piano or any instrument tuned in temperate range, to model the stable particles and those which are in temperate agreement with them (lines d, e , f, of Figure la essentially) with the usual precision of the temperate scale with respect to the chords of the harmonic range.

As an example, the relatively stable particle Ω- forms with its successive decay products, ie Ω- → Ξ∏, Ξ → Λπ a minor, of which it is the dominant, and which que → N∏ completes in the sixth ; while for the party cule relatively unstable Σ °, Σ ° → Λγ followed by Λ → Nπ forms a dissonant chord. Ω- is located right in the middle of the piano (on 342 Hz), modulo 70 octaves. The best modeling of particles consists in fact in a rope or rather a vibrating plate of a few milligrams (or of the order of a centigram) including the harmonic ²⁷² , taken on a low frequency such that it would have both frequency, and approximately the mass (fraction 1/2 ⁷² of the initial mass) of a particle of the order of 2 GeV: that is to say in the vocal cords. The "aum" sound, the formants of which are close to the successive octaves of a bass (or between la and c approximately), is then the closest sound, sung by the human voice of the harmonic structure of a particle.

According to an embodiment capable of ensuring better precision, also allowing modeling of very unstable particles, the corresponding instruments must be tuned according to a finer range, capable of differentiating between them the different distribution lines of the particles according to their mass. . Consequently, the present invention has, for this purpose, also a new musical range, characterized by the subdivision of the temperate chromatic semitone into unequal micro-intervals of 1 / 12th, 1 / 12th, 1 / 24th, 1 / 8th, 5 / 48th, and 1 / 16th of a tone, connecting each note of the chromatic scale in this order to that located one semitone higher.

In addition, the mode of representation described above makes it possible to identify the characteristics of the "works" which it represents. Consequently, the present invention also relates to a method of representing particles in number, as well as musical works, consisting in comparing a histogram of these particles obtained by plotting on the ordinate the number of particles whose natural frequencies are included in a same interval of 2 ^1/4 (a minor tempered third) as a function of the logarithm of the natural frequencies of these particles plotted on the abscissa, at the equation curve where q denotes the scale of the logarithms of the masses (corresponding to a stable distribution), highlighting, as much by the location of the vertex of the curve, which provides the melodic dominant, as by the deviations from it, the characteristics of the "works" that these particles can compose, and allowing them to balance; and similarly for musical works by replacing in the preceding statement the frequencies (or masses) of the particles by those of the notes, which can for simplicity be counted by score line instead of by minor third.

The curve obtained by this means being linked to the harmonic structure, as measuring the relative importance of the third, the fifth ... it is possible, from its comparison with the equation curve above, to determine at least in part the harmonic structure, an element of the timbre, of an instrument intended to interpret a given work, which in a way constitutes a "development" of this timbre. Conversely, it is possible for a given instrument to "balance" an orchestration to make it conform to that corresponding to the timbre of the instrument.

Two types of instruments can be made to model the particles from this range and these different arrangements: electronic instruments and acoustic instruments.

An electronic instrument according to the present invention is characterized by a keyboard comprising, in combination, a series of piano keys and at least one series of calculator keys corresponding, on the one hand, to sounds different from those of the piano keys, including micro-intervals corresponding in particular to the different harmonics, thus making it possible to include in the sound harmonics of order 7 or more which can give rise to exact harmonic chords, and on the other hand and by switching, to the programming of the curve - time envelope of sound and programming of the harmonic envelope curve represented by the amplitude of the harmonics as a function of their rank.

In accordance with a particularly advantageous arrangement of this instrument, the keyboard includes five series or lines of keys, tuned like the piano keys following a temperate chromatic scale, but located 1 / 12th of a tone higher (corresponding to the inverse 5 harmonic ), 1 / 6th of a higher tone (corresponding to the inverse 7 harmonic), 7 / 24th of a lower tone (approximately corresponding to harmonic 11 and its inverse, and more exactly to harmonic 31), 1 / 6th in lower tone (corresponding to harmonic 5) respectively (hereinafter also called f, a, b, c, d). Naturally, each of these key lines can be programmed with an autonomous "timbre", the curve-envelope of the harmonics favoring the corresponding harmonic.

According to another advantageous arrangement, the harmonic structure of the sound (common to all the lines) is programmed using drawbars similar to those making it possible to choose the register of an organ, which makes it possible to view it. This electronic instrument makes it possible in particular to determine with precision the parameters of the two envelope curves (temporal - COHEN experiment - and harmonic) giving rise to the best degree of fusion, and to model all the particles, and thus to carry out numerous acoustic experiments. having relevance in particle physics.

According to a simplified variant of the electronic instrument according to the invention, it comprises a series of piano keys and only one (such an instrument can be designated by the name "quarter tone piano"), or two (" third tone piano ") series of calculator keys that can be programmed, as desired, on any of the" tuning forks "located higher or lower than that of the piano, previously described.

According to another simplified variant of this instrument, it comprises a unique series of six keys controlling a conventional piano keyboard so as to be able to modify the pitch (either permanently or only when pressed), respectively - 7 / 24th, - 1 / 6th, -1 / 16th, 0, + 1 / 12th and + 1 / 6th of a tone (lines b, c, d, e, f, a in this order), such a combination being sufficient for simply melodic use of micro-intervals. The two preceding variants can be combined, that is to say that the electronic instrument according to the invention can comprise 2 or 3 series of six keys respectively controlling a conventional piano keyboard and one or two series of keys tuned in temperate range, so that you can fix their height.

On the other hand, the electronic instrument can also be used in order to program melodies, either defined or accompanied by certain conditions which must be statistically fulfilled, such as the data of probabilities (connection ratios) of different modes of decay of a given particle. By way of example, the purely leptonic decays of the lepton form an un cadenced melody (fa, mi, la, flat), while the consideration of its hadronic decays restores the cadence (fa, la).

Likewise, the main decay mode of Ω-, or Ω- → ΛK- (with connection ratio 68.6%) is an incomplete seventh (the mid-ground), to which the third is missing (i.e. do for one the seventh minor), which is Ξ; it is in the Ω- → Ξ∏ mode (31.4%), which is a minor (completed in minor sixth with N); to re-establish the cadence a re-ninth is useful, which is in the Ω- → Ξ * π (0.2%) mode.

The instrument's calculator can still be used to determine characteristics of a "work" at starting from the data of the branching ratios determining a frequency distribution of a set of particles, by comparison with the theoretical curve, and to determine, either from a given melody, or from the distribution of the corresponding notes ( histogram of the notes by "third step"), the adequate harmonic structure (timbre of the corresponding sound) by comparison with this curve. For example, if the third "exceeds" while the fifth is back, the harmonic structure will accentuate the harmonic 5 and decrease the 3 accordingly.

Finally, the calculator keys of the electronic instrument can also be used to program the frequencies corresponding to the different keys, in particular on a simplified keyboard (quarter tone piano type), making it possible to model the frequencies of the different existing particles (the particles stable on the piano keys, unstable on the quarter tones), this modeling can also be performed on an acoustic instrument. If the electronic instrument according to the invention makes it possible to determine the parameters of the two envelope-curves - temporal and harmonic, as indicated above -, on the other hand it does not allow a study of the relationship between consonance and stability (such as WEINREICH experience, for example), which requires an acoustic instrument. For this purpose, one can use six pianos, or build an instrument comprising six superimposed piano keyboards, tuned according to determined tone frequencies (such as those shown in Figure 3 attached). Instruments based on such a principle but using a range other than the range according to the invention, were produced by MOURZINE at the Scriabin museum in Moscow (range in twelfths of equal tones), by Janko (piano with six rows of superimposed keys in range 2 ^1/41 ) and by FOKKER in Haarlem (organ with eleven keyboards in tricésimoprimal temperament). You can also use an ordinary guitar (or a ten-string guitar, which is even better) by playing "on harmonics", that is to say by touching the strings at a fraction 1 / n of their length for play the harmonic n; harmonic 5 is thus easily reached, harmonic 7 quite easily, harmonic 11 a little more difficult.

The registers of an organ (which, instrument with sound pipes, would otherwise only contain odd harmonics) allow for their part to accentuate the harmonics located in successive octaves of a fundamental. Such an instrument can thus be constructed, tuned to the frequencies of the particles.

Finally, the subject of the present invention is any fixed-sound instrument, in particular an instrument with vibrating plates or blades (the ratio 10 ²⁰ between the frequencies of the particles and the musical frequencies being close to the square of the ratio of the corresponding sizes, or in all case the scale dimension being of the order of 1.4 for an average instrument to 1.7 for the vocal cords) or with sound pipes constructed according to the range of the present invention. The keyboard described for the electronic instrument, in particular, can be used to control mechanically but by a set of electrical pulses, the acoustic vibration of very small vibrating blades or strings but placed in adjustable resonance boxes, amplifying the sound by modulating its harmonic structure.

The aim of the study on the relationship between consonance and stability carried out using the acoustic instrument according to the invention, and in particular for the temperate chords, which can be transposed in many ways to another scale, is - in addition to its strictly musical applications - its relevance for nuclear fusion.

The economic production of energy indeed appears as one of the problems of our civilization. Energy sources drawn from the earth's mineral resources are not only limited, but their yield is quite low and produces a lot of waste. This last point can be expressed by saying that their entropy balance - which roughly measures the change in order of the system - is not satisfactory: they make more noise than music. Thus nuclear fission adds to the increase in entropy due to the transformation of matter into energy, another increase in entropy due to the loss of organization produced by the fission of complex nuclei into smaller nuclei; while fusion, which is the principle of energy production in the sun, compensates for this increase by the reorganization of light nuclei fused into heavier nuclei. If we can say, fusion, unlike fission, "cleans up" behind it; but while fission starts from a relatively small mass of fissile product - a few kilograms of uranium or plutonium - the control of fusion comes up against a problem of scale which results, either in temperature too high for the usual thermonuclear fusion attempts, or by too short life times for the processes of the "cold fusion" type using particles as catalysts. Entropic balance problems also persist, resulting in the difficulty of achieving a "shield". To give an image, the sun is far too big for us to make one on earth.

The discovery of which the inventor is the author opens a possibility of solving this difficulty, by stating criteria, hitherto undetected, which allow the particles to merge into nuclei, and which consist in the need for the natural frequencies of vibration. of these particles to be in musical agreement. This property opens a way towards the realization of fusion processes on a smaller scale than that of stars, and accessible to current civilization. In addition, it leads to the possibility of carrying out development experiments in mod Acoustic analysis, at very moderate costs relative to those of the experiments, on particles using accelerators reaching a few tens of kilometers in diameter. The "confinement", which characterizes contemporary attempts to achieve fusion, aims to reproduce the extreme conditions of temperature and pressure achieved inside the stars due to gravitation, by artificially confining matter. But the gravitation which has this effect inside the stars, is, in these, a concrete manifestation of the causality, as one can deduce it from the invariance of the equations of EINSTEIN (gravitation) under the transformations causal group (WEYL group). We can conclude that its effect respects causality and concretely achieves scale invariance with a good approximation, that is to say that intervened in nuclear reactions at the heart of stars, transposed particles of scale of particles of ordinary matter, such as heavy particles appearing on line (e) of Figure la, further "orchestrated" in accordance with the distribution of Figure 2, which also follows from causality (invariant wave equation of ladder). The principle on which the nuclear fusion process according to the present invention is based therefore consists in directly reproducing the effect of causation.

Indeed, as a consequence of the relation between consonance and stability and of its invariance in a transposition of scale, the consonance of the particles located on the same line of figure 1 makes it possible to predict the existence of relatively stable nuclei formed from these particles, nuclei much more stable than their constituents themselves.

We can cite, as an example, the ordinary nucleus where nucleons and pions interact constantly (p

n + ∏ ⁺ , n

p + π- essentially) and form a temperate minor third, namely 8 ∏ ^± / N = 2 ^1/4 (to within 10 ^-5 , which is very different from a harmonic third), N denoting the average mass nucleon = 1/2 (p + n); thus the helium nucleus is stable, while some of its constituents (neutrons) are much less so. Similarly, preliminary calculations suggest that nuclei formed from Ξ ^º and K ^± , which form a very precise temperate fifth, namely 4 K ^± / Ξ = 2 ^7/12 (at the precision of the experiment , is better than 5.10 ^-4 , while the difference between 2 ^7/12 and 3/2 - fifth harmonic - is more than twice as large) could self-regenerate, the kaons can intervene here to compensate for the decays Ξ → Λ π by interactions for Λ + K → Ξ + ∏ regenerating the Ξ.

On the other hand, the properties (cited above) concerning the distribution of the natural frequencies of the particles in the scale, and which result from causality (invariant wave equation of scale), provide additional conditions: for example, the curve of FIG. 2a being centered on Ω-, such a distribution can be approximated using an energy beam of kaons directed on nuclei of light atoms, which will form hypernuclei of which one can predict relative stability, the presence of charmed particles being useful to complete the "orchestration". The simplest mechanism thus conceivable is that of proton-omega minus pairs, which form a musically stable (Ω- / p ~ 2 ^10/12 ) and electrically neutral nucleus; such nuclei can be obtained by directing negative kaons on deuterium. Other slightly more complex mechanisms can then "orchestrate" it.

The present invention therefore also relates to a nuclear fusion process, consisting in carrying out fusion reactions from particles in temperate agreement, either added to or substituted for the nuclei of ordinary matter, so as to form compound nuclei whose distribution natural frequencies of the components in the scale conforms to the equation curve (2)

X cos ² (12∏q / Log2 + Φ) cos (72∏q / Log2) where Φ is the phase defining the choice of the line comprising the particles (either Φ = 0, -∏ / 8, -π / 3, + 7∏ / 12, + ∏ / 3, + ∏ / 6), Φ = 0 corresponding to the nucleon; combining stability with the possibility of carrying out scale transpositions of the nuclear matter which constitutes the heart of the stars.

The equipment necessary for implementing the nuclear fusion process according to the invention comprises the coupling of an accelerator, responsible for producing the particles intended to participate in the fusion, such as kaons, and a reactor proper fusion, where the compound nuclei are formed.

From the point of view of the entropic balance, the use of consonant and well-orchestrated particles effectively optimizes this balance.

From the point of view of the energy balance, Lawson's criterion (which conditions the energy balance of the fusion reaction of particles in nuclei) and here satisfied by the conjunction of the effect of consonance on stability and the transposition of ladder. It is however necessary to produce the particles in fairly large numbers; however, this process responds to the obvious objection that attempts can be made to recreate, in order to elicit fusion reactions, the temperature and pressure conditions present in the heart of the sun, namely the problems of ladder they pose. Rather than recreating these conditions, the process builds its effects, which achieves significant savings: either we produce the particles intended to merge, or we produce particles which we add to nuclei, allowing the completed nuclei to merge .

Note the simplicity of the solution suggested by acoustic modeling: if a music is too high, the temperate range allows it to be transposed lower (or to enrich it with other notes so as to form a balanced distribution). And the fact that the two conditions necessary for the possibility of such a transposition - existence of particles transposed and stability of their compounds - are precisely those expressed by the distribution of the masses of the particles according to a temperate musical range.

The present invention also relates to purely musical applications of the methods, models and instruments described above. Besides the fact that physical reactions involving particles become, or can form the basis, once modeled, of musical works in themselves, and the fact that conversely, the existing rules in music can have a counterpart in particles - for example the successions, consonance, dissonance and resolution of the dissonance, give in themselves a "raison d'être" to the unstable particles -, the range followed by the particles and the instruments developed for its implementation have in in addition to the musical implications, some of which have already been pointed out in passing. Thus, many contemporary musicians use microintervals, and the need to "go beyond" the temperate range is felt in the West, especially under the influence of oriental music. In fact, "particle music" is a tonal music of micro-intervals, as in the East, although based essentially, as in the West, on the chromatic scale. Among the many attempts to micro-intervals ranges (quarter tones, Huygens ranges 2 ^1/31 Janko 2 ^1/41 and ^1/53 Holder 2, Alain Daniélou range based on reports 2 ^p 3 ^q 5 ^r where p , q, r are integers relative, and dividing the octave into 53 unequal intervals), two approach by certain aspects of the "range" of the present invention: thus, M. Barkechli divides the Pythagorean tone 9/8 into intervals unequal, either two limmas and a Pythagorean comma combining to divide the tone into five intervals; the attached FIG. 3b represents the values of the limma and the comma pythagoricians, as well as of the "comma magne" and of the "syntonic comma" sometimes used, approximated respectively by the deviations ed, bc, eb and cd, less than half a savart (~ 2 ^1/600 ) approximately. Mr. Barkechli had tried with this range, to represent the intervals of the Iranian range, except for a few "vosta" and "zaïd", however, which were represented in "rationalized" (simplified) form. The great interest of this range was, undoubtedly because of its empirical basis, to propose an unmodified division of the tone, as is the case for the particles (for the semitone), which corresponds to a "microtonality "(as a diatonic range of seven notes corresponds to a tone). On the other hand, Yankovski in the Soviet Union, suggested a scale 2 ^1/72 , according to which the apparatus of Mourzine is built, thus dividing the semitone into six intervals, like the scale according to the present invention, but equal , giving (cf. Figure 1b) a good representation of the transpositions of harmonic chords, although slightly different from the intervals used in oriental music. These two ranges, one empirical, the other theoretical, therefore constitute two different approximations to the range of the present invention, which in a way constitutes a synthesis.

The respectively fine and overall frequency distributions described above and represented in FIGS. 1 and 2 constitute, one might say, two "universals" of music; that is to say that it is a characteristic of well balanced musical works that the distribution of their frequencies

(including the harmonics, plotted with an ordinate proportional to their amplitude) modulo 2 ^1/12 multiplicatively follows a distribution similar to that of figure la, and that the distribution of their natural frequencies in steps of 2 ^1/4 follows a distribution similar to that of Figure 2a. By comparison, the major diatonic range do-re-mi-fasol-la-si is cultural, many modes being possible (and for example, metastable particles heavier than the proton follow an Andalusian mode); however it is very "stable" (its natural frequencies - in the Zarlin range modulo 21/12 are distributed over the lines. e and f of Figure 1, corresponding to the constituents of the atoms). Consequently, it is possible to determine with the aid of these two distributions the harmonic envelope of an instrument sound intended to interpret a given work, the comparison with the distribution of FIG. 2 making it possible to evaluate the amplitudes of the harmonics of low order (first six harmonics), and that with the distribution of figure 1, the amplitudes of the harmonics of higher order (mainly between 5 and 12); conversely, it is possible to "orchestrate" a work for a given instrument.

A musical work cannot in fact be played on any instrument, and such a piano work "calls" a sound that such a piano does not necessarily have. In fact, a given sound implies a type of work corresponding to it. In addition, the orchestration of a singer's voice depends on the timbre of the latter, and it is generally difficult to find the "timbre" of an instrument that completes the voice well, so as to form a well-balanced sound, all the more so since this varies for each work (even when translating the lyrics, the "formants" of the different sounds varying from one language to another).

Now (and in addition to its obvious utility for composition and computer orchestration tests) the theoretical frequency distribution curve, which characterizes a well balanced composition and orchestration (as is necessary for fusion applications , as regards the frequencies of the particles) finds an application here: the comparison with the distribution of figure 2 makes it possible to evaluate the relative amplitude of the third, the fifth, the sixth and the octave (or even more by making a distribution with a finer step), and thus harmonics 2, 3,

4, 5 (see more, - for a major work) or 2, 3,

5, 6 (idem, - for a work in minor); the "extension" of these amplitudes to the others, harmonics can then be compared, wearing them modulo 2 ^1/12 as in the figure

1b, with the distribution of figure 1a, to determine the amplitudes of the harmonics essentially until the 12th. Similarly, for the voice of a singer, the timbre of an accompanying instrument will be the complement (for what concretizes the amplitudes of the harmonics), compared to the timbre thus calculated, of that determined by Fourier analysis (which can, modulo 2 ^1/12 , be compared directly to figure 1a).

Conversely, given the instrument, the comparison with the equation curve (1) of the frequency distribution of a work performed with this instrument makes it possible to determine "what is missing" to complete it, and thus to orchestrate the 'work for this instrument (or in any case to guide this orchestration); and the same for the orchestration of a singer's voice. An instrument timbre can also be "developed", that is to say translated into the distribution of frequencies of a work suitable for it, thus giving criteria for the musical composition for this timbre (accentuation of the harmonic 5 for example involving a higher frequency of the major third); it will be noted that this is what particles do, in which the accentuation of harmonics of order 2, 4, 8 ... results in the statistical presence of a range with base 2.

These processes can be carried out in the form of a system which can be fitted to any music synthesizer or electronic organ with multiple sounds, automatically carrying out the necessary calculations and thus automatically determining the timbre on which a melody can be played. Such a system associated with a synthesizer or an electronic organ successively determines the histogram of the frequencies of the melody played on the instrument, using a calculator which stores each note and calculates this distribution by score line , then compare this histogram with the theoretical curve described above and deduce the amplitude of the first harmonics, hence a first determi nation of the harmonic envelope, then refined by comparison with the frequency distribution modulo 2 ^1/12 , finally giving the desired timbre which is then either synthesized or chosen as the closest from a range of given tones (by a method of least squares).

In addition to the foregoing provisions, the invention also comprises other provisions, which will emerge from the description which follows. The present invention relates more particularly to the method for modeling elementary particles, the models obtained with this method, the musical range, the electronic and acoustic instruments for modeling particles from said range, the nuclear fusion process and the apparatus for its implementation, in accordance with the above provisions, as well as the applications of these methods, models and instruments and in particular their musical applications.

The invention will be better understood with the aid of the additional description which follows, which refers to the appended drawings in which: FIG. 1 is a graphic representation:

(a) the histogram of the masses of the elementary particles modulo 2 ^1/12 multiplicatively, the corresponding particles being indicated below, opposite;

(b) the histogram of the intervals of the western harmonic range extended up to the 12th harmonic, - modulo 2 ^1/12 multiplically;

(c) frequencies of the Persian "vosta" and "zaïd", modulo 2 ^1/12 multiplically;

(d) intervals of the Chinese range, modulo 2 ^1/12 multiplically; which shows the correspondence between the natural frequencies of particles and those used by musicians from different countries. - Figure 2 is a graphic representation of the histogram of the masses of elementary particles between 0.6 and 5 GeV, with a step of 2 1/4, which shows the correspondence between the overall distribution of the frequencies of the particles and that of notes from an orchestral work of music;

- Figure 3 shows a semitone of the range according to the invention

(a) centered as in FIG. 1, (b) centered on the quarter tone, so as to show the division of the tempered semitone in accordance with the range according to the invention;

- Figure 4 shows the keyboard of an octave of an electronic instrument according to the invention, keyboard (micro-interval piano) allowing the modeling of all the particles in accordance with the present invention, the frequencies rising from low to top and from left to right, the touch lines can be distinguished by colors whose frequencies follow a progression in the same direction as the frequencies, and

- Figure 5 is a block diagram of the device for determining the timbre of an instrument to interpret a given work, according to the invention.

It should be understood, however, that these drawings and the corresponding descriptive parts, are given solely by way of illustration of the subject of the invention of which they do not in any way constitute a limitation.

Figure la represents the histogram of the masses of reduced elementary particles, modulo 2 ^1/12 multiplicatively (tempered chromatic range), at a value close to that of the pawn (ie between 133.4 and 141.3 MeV), plotted on the abscissa , with an ordinate proportional to their number, weighted taking into account their precision (taking beyond K the average mass of an isomultiplet) and their stability: represented either by a rectangle of width 2 ^1/960 (0.1 MeV) and quadruple in height (e ^± , μ ^± , ∏ ^± , ∏º,

K ^± , K °, N), or by a square with a width of 2 ^{1/4 80} (0.2 MeV)

[Λ, Σ, ≡, Ω-, ≡ * (1530), ω, Φ, K ^* (892), η ', D, D *, J / ψ, ψ], or by a rectangle of width 2 ^{1 / 2 40} quadruple of its height [Δ, Y * (1385), resonances Λ, Σ (1915), η, D (1286), f, f ',

T (slightly narrower), T 'verifying δm ≤ 0.36 MeV. (m / m _∏ ), plus τ and p "recovered" with a width 2 ^1/160 ].

FIG. 1b represents the histogram of the harmonic intervals related to the temperate range, that is to say whole fractions p / q for q <p ≤ 12, modulo 2 ^1/12 multiplically, carried with a height proportional to a (p) .a (q), (a (p) = 1 for p ≤ 6 and 0.5 for 7 ≤ p ≤ 12) and a "step" of 2 ^1/480 . Lines (a) to (f) correspond respectively to the first harmonics 7 ^-1 , 11 and 11 ^-1 , 7, 5, 2 and 3 and their inverses, and 5 ^-1.

As indicated above, FIGS. 1c and 1d respectively represent the frequencies of the Persian "vosta" and "zaïd" and the intervals of the Chinese range, showing the correspondence with the histograms relating, respectively, to the distribution of the natural frequencies of the particles. and the distribution of the range based on the first twelve harmonics, shown in Figures 1a and 1b. FIG. 2a represents the histogram of the masses of elementary particles between 0.6 and 5 GeV, with a "pitch" of 2 ^1/4 , where the curve in solid line corresponds to equation (1) given above and the dotted curve represents the curve deduced from the thermodynamics of strong interactions.

FIG. 2b represents the curve of equation (1) multiplied by cos ² (12 πq / log2). Figure 2c shows the distribution curve of the notes of the first bars of the Chaconne by Bach, where r is the relative (F major) of the tonic (D minor).

Figure 2d represents the distribution curve of the first 128 measures of Mozart's Symphony No. 40 where d denotes the dominant (d), d - 1 and d + 1 mean d - 1 octave and d + 1 octave, respectively, and t denotes the tonic (sol).

The last two curves are given as examples of the similarity of their distributions with the distribution curves of Figures 2a and 2b.

The new musical range according to the invention, which is characterized by the subdivision of the temperate chromatic semitone into unequal micro-intervals of 1 / 12th, 1 / 12th, l / 24th, 1 / 8th, 5 / 48th and 1 / 16th of ton, is shown in Figure 3a, where the microintervals correspond respectively to the intervals ef, fa, ab, bc, cd and de. The notes a, b, c, d, e and f then correspond, modulo 66 octaves (below) of the mass of the pawn, to "la" 440, 442.3, 448.6, 454, 457.36 and 461 , 8 respectively (Figure 3a being centered, like Figure la, on the average mass of the pawn). FIG. 3b represents, starting from the line e of FIG. 3a, the subdivision of the chromatic semitone in accordance with the present invention, the interval between e ₁ and b ₂ approaching the comma-magne, the interval between b ₂ and c ₂ approaching the Pythagorean comma, the interval between c ₂ and d ₂ approaching the svntonic coma, and the interval between e ₁ and d ₂ approaching the Pythagorean limma. The instrument according to the invention, the keyboard of which has been represented in FIG. 4, makes it possible to achieve exact harmonic chords, the d keys being suitable for thirds and sixtes major and the f keys for thirds and minor sixes: thus, the is major perfect chord e ₁ - d ₅ - e ₈ and minor perfect chord e ₁ - f ₄ - e ₈ instead of e ₁ - e ₅ - e ₈ and e ₁ - e ₄ - e ₈ respectively. Chords (with four sounds) can be made involving the harmonic 7 and its inverse (keys c and a corresponding to thirds or sixths of a tone), and the b keys (close to quarter-tones) are frequently used for melodies Eastern or even Irish; the instrument can thus accompany violins for "reels" or other traditional music for which a piano turns out to be quite insufficient. Many melodies actually "call" such notes, for which an F for example will be banal and an E too low, as can be found for the Hebrew melody "David yefe einayim" comprising a mixture of oriental influences and Central Europe, and where the b ₆ key will find an application. On the whole, the a, b and c, d, e, f keys are suitable for Chinese, Oriental, Church, Contemporary, Temperate and Slavic music, respectively; strikingly, moreover, the lines of figure 1 evoke architectural structures of these same respective countries, giving the feeling of a harmonious order of the universe contained in power in the particles which compose it. Which leads us to hope that the range in accordance with the present invention, constituting a synthesis of ranges in use in many countries of East and West, and meeting the conditions expressed by Mr. Barkechli at the 84th CNRS International Symposium held in May 1958 in Marseilles on musical acoustics (Ed. of the CNRS, 1959, p. 45), also responded to his wish: "I think that if we manage to have a simple scale divided into intervals as in Western music, we could have a universal range that could play a big role in international understanding. " FIG. 5 represents a block diagram of a device for determining the timbre of an instrument intended to interpret a given work, according to the invention, which comprises a calculator which stores in memory each note of a melody played by an instrument A, calculates the distribution of frequencies by partition line and thus determines the histogram of the frequencies of a given melody, in B, then compares the histogram obtained in B with the theoretical curve shown in dotted lines in FIG. 2a, and in deduces, in C, the amplitude of the first harmonics, hence a first determination of the harmonic envelope, which is then refined, in D, by comparison with the modulo 2 ^1/12 frequency distribution shown in FIG. 1a, the curve obtained being either translated into sounds by a synthesizer, or compared to the timbre of the pre-recorded sounds of an electronic organ. If a large number of notes (several hundred) makes it possible to precisely determine the harmonic envelope, a small number (a few tens) already makes it possible to obtain, from one passage to another, the first order of the difference between two curves-envelope: this device therefore makes it possible to simply modulate the timbre of an instrument whose essential characteristics are given ("piano" type for example) according to the different passages of a work, thus realizing the hope formulated at the beginning of the century by Schônberg to compose in the different dimensions of the "timbre", of which he considered the pitch of a note as only one of the dimensions. Table I below gives the list of some elementary particles (essentially those which are represented in histogram in figure la) with their modes of disintegration and connection ratios, translated into musical notes with indication of the corresponding lines in figure 1a .

To properly use this table for particle modeling, it will be noted that the "influence" reported above of the statistical presence of the base 2 range on the harmonic envelope indicates that the harmonics of a particle are not fixed but depend on the distribution of a set of particles, which can be modeled using the process described above for musical works.

As is apparent from the above, the invention is in no way limited to those of its modes of implementation, embodiment and application which have just been described more explicitly; on the contrary, it embraces all the variants which may come to the mind of the technician in the matter, without departing from the framework, or the scope, of the present invention.

Claims

CLAIMS 1 °) Process for obtaining selected quantum, acoustic or electronic vibrations, tuned between them, distributed according to a frequency association and a succession in time governed by determined laws, to catalyze the production of energy in the case of quantum vibrations, producing musical works in the case of acoustic or electronic vibrations or for acoustically modeling the vibrations of elementary particles, in particular for educational purposes or for checking the fusion of particle vibrations, which method is characterized in that said vibrations are obtained by producing, using an appropriate device such as a particle accelerator or an acoustic or electronic instrument capable of producing said vibrations, which is suitably adjusted for this purpose, vibrations whose fundamental frequencies are equal, at an integer number of octaves near eventual In addition, to those of existing particles, whose temporal envelope is negative exponential, and which include a small number of harmonics whose envelope of amplitudes as a function of their rank also decreases in negative exponential, except for "peaks" in octaves. successive of the fundamental frequency (these envelopes then being able to depend, for each vibration, on the presence of the other vibrations produced), of. so as to form with these vibrations

"chords" and "melodies" respecting both the laws of conservation such as those governing the reactions of fusion and disintegration of the corresponding particles, and the "musical" laws of consonance and global balanced distribution such as the chord of fundamental frequencies, following the same chromatic or diatonic range and their global distribution according to an equation I curve:

P (q) ~ exp (-6q ² / Log2) + (12) ^-1/2 exp (-q ² /2Log2).cos ² (∏q / Log2), (I) where q is the logarithm scale frequencies, said vibrations being produced, producing, during a first step, repeatedly, by implementing the vibration selection process which has just been defined, a reference vibration, which is completed, during a second step, also using the method defined above, by vibrations located in the octaves, and possibly by vibrations in musical agreement with them, said vibrations being supplemented by a third series of vibrations in the production of which they serve as origin, during a step subsequent, this third series of vibrations being obtained either by fusion and disintegration of the particles produced in the aforementioned particle accelerator, or by programmed selection of vibrations produced using the above method, in particular by respecting the laws of symmetry of the corresponding particles , and more specifically the branching laws of the latter, this third series of vibrations being itself complete ted during another step, by a fourth series of vibrations selected by implementing the above method, to complete the first three series of vibrations by forming with them chords, the proportion of vibrations of all of the four aforementioned series progressively obeying, as a function of their vibrational frequency, the proportions deduced from equation (I) above, each step of the process, and in particular the third, being able to be reproduced several times concomitantly with the fourth step.

2 °) Method according to Claim 1, characterized in that the adjustment of the means of production of said vibrations is obtained, in the case where the latter are produced by a particle accelerator, by first submitting nuclei of light atoms , such as deuterium in particular, to the action of a beam of particles identical to each other and which are chosen to be in temperate agreement (in the same reference system) with the nucleons of said nuclei, which beam is emitted by said accelerator with a energy which is a function of the mass of the particles, capable of allowing said beams to be captured by said nuclei, the nuclei thus treated then being supplemented by the implementation of the method according to Claim 1. 3 °) Method according to Claim 1, characterized in that the adjustment of the means for producing said vibrations is obtained, in the case where the latter are produced by an acoustic or electronic instrument, by appropriately modulating the amplitude of the harmonics of the vibrations produced by the process according to Claim 1 , the tuning of the instrument being consistent with the frequency spectrum defined in Claim 1, then transposing the fundamental frequencies of the vibrations produced from those of the particles at rest, from 68 plus or minus a small whole number of octaves towards the low, to give an audible frequency, and by adjusting the lifetimes (half decay time) of the vibrations produced es, by a commensurable transposition of those of the particles, to obtain, likewise, an audible vibration. 4 °) Method according to Claim 3, characterized in that the agreement of the instrument suitable for transposing the fundamental frequencies of the vibrations produced compared to those of the particles is obtained, in the case of an instrument with fixed sounds , by tuning said instrument in a first step by following the tempered chromatic scale, then by subdividing each tempered chromatic semitone, in successive unequal micro-intervals of 1 / 12th, 1 / 12th, 1 / 24th, 1 / 8th, 5 / 48th and 1 / 16th of a tone, the order of succession being that of the ascending frequencies, this subdivision being obtained by completing, by all appropriate means, the spectrum of fixed frequencies which can be produced by the instrument.

5 °) Method according to any one of Claims 1 and 3, characterized in that the spectral envelope of the periodic vibrations, ie the amplitude of the harmonics, is determined with respect to the defined spectral envelope in Claim 1, by establishing a histogram of all the vibrations produced in a given time interval, by comparing this histogram with the equation curve (I) according to Claim 1, and by deducing from this comparison the amplitude of the first harmonics, which makes it possible to carry out a first determination of the envelope. harmonic, which is obtained by comparison of the distribution of modulo 2 ^1/2 frequencies which is deduced therefrom, with the distribution of the masses of elementary particles modulo 2 ^1/2 , to obtain the spectral envelope representing the desired timbre .

6 °) Method according to claim 5, characterized in that said spectral envelope is detcrminόe, by establishing a histogram of the logarithms of the frequencies of the vibrations of the set E of vibrations produced during a given time interval, T, (counted by " not "such as 2 ^1/4 or more fine), comparing according to the

Claim 5 (the intervals being, for the individual notes, determined with respect to the tonic) this histogram with the equation curve (I) according to Claim 1 and deducing from this comparison the amplitude of the first harmonics, which makes it possible to performing a first determination of the harmonic envelope, that is refined by comparing the frequency distribution modulo 2 ^1/12 that is deduced with the weight distribution of the elementary particles modulo 2 ^1/12, for obtain the spectral envelope representing 1c desired stamp.

7 °) Method according to Claim 3, characterized in that the modulation of the amplitude of the harmonics is obtained in that the timbre represented by the spectral envelope determined as in any one of Claims 5 and 6 is then either synthesized , either chosen as the closest from a range of sounds given by a method of least squares, or still cut off from the timbre of the voice of a singer who is accompanied, recorded and determined by a Fourier analyzer, to also be synthesized or chosen as the closest from a range of given tones.

8 °) Device for modulating the amplitude of the harmonics according to Claim 7, characterized in that it comprises a calculator which stores the frequencies of the vibrations and performs the calculations and comparisons according to Claim 7, and which is transmitted the timbre searched for in a synthesizer or in an instrument with which it cooperates, either subtract from this timbre that determined by a harmonic analyzer depending on a microphone, with which it cooperates.

9 °) electronic instrument for implementing the method according to any one of Claims 1, 3 to 7, characterized in that it comprises a device according to Claim 8, including a calculator coupled with a sound synthesizer, of which the keys appear on the same keyboard, which comprises, in combination, a series of piano keys which delivers the temperate range and at least one series of calculator keys corresponding on the one hand to the programming of the temporal and spectral envelopes, and possibly the programming of frequencies associated with said keys, and on the other hand, and by switching, to sounds different from those of the piano, the frequencies of which are transposed from those of the particles, and capable of giving rise to substantially exact harmonic chords, the sounds delivered by the instrument resulting from the integration in the calculator of the characteristics of the sound which are either those of Claim 1, s or programmed by the user, or even determined by the calculator itself, and in particular the spectral envelope from the frequencies programmed or played by the user according to the method of Claim 7 using the device according to the Claim 8 included in the instrument.

10 °) Electronic instrument according to Claim 9, granted according to Claim 4, characterized in that that said keyboard includes five series or lines of keys, tuned like piano keys following a temperate chromatic scale, but located 1 / 12th of a tone higher (thus being able to substantially equal the inverse harmonic 5 of piano keys), 1 / 6th of a higher tone (which can be approximately equal to the inverse 7 harmonic), 7 / 24th of a lower tone (which can approach approximately 1 / 24th of a harmonic 11 and its inverse, and more exactly 31 ), 1 / 6th of a lower tone (which can substantially match harmonic 7) and 1 / 16th of a lower tone (which can substantially match harmonic 5) respectively (hereinafter also referred to as f, a, b, c, d), the timbre of each of these key lines can be programmed and modulated separately so as to increase the corresponding harmonics. 11 °) Electronic instrument according to Claim 10, characterized in that the harmonic structure of the sound common to all the lines is programmed using drawbars similar to those making it possible to choose the register of an organ, which allows the view. 12 °) Electronic instrument according to Claim 9 or Claim 10, characterized in that it comprises a series of piano keys and only one (such an instrument can be designated by the name "quarter tone piano"), or two ("third tone piano") series of calculator keys that can be programmed, as desired, on any of the "tuning forks" located higher or lower than that of the piano.

13 °) Electronic instrument according to Claim 9 or Claim 10, characterized in that it comprises a single series of six keys controlling a usual piano keyboard so as to be able to modify its pitch (either permanently or only when press it), respectively -7 / 24th, -1 / 6th, -1 / 16th, 0, + 1 / 12th and + 1 / 6th of a tone (lines b, c, d, e, f, a, in this order), such a combination being sufficient for simple use melodic micro-intervals.

14 °) Electronic instrument according to Claims 12 and 13, characterized in that it comprises 2 or 3 series of six keys according to Claim 14, respectively controlling a usual piano keyboard and one or two series of keys tuned in temperate range, so that you can fix their height.

15 °) Electronic instrument according to any one of Claims 9 to 14, characterized in that said keys carry out the programming of melodies and chords accompanied by certain conditions which must be statistically fulfilled, such as the probability data (connection ratios) of the different modes of disintegration of a given particle. 16 °) Electronic instrument according to any one of Claims 9 to 15, characterized in that the calculator keys carry out the determination of the characteristics of a "work" from the data of the connection ratios determining a frequency distribution d '' a set of particles, by comparison with the theoretical curve, and to determine, from the distribution of the corresponding notes (histogram of the notes by "step" of third), the adequate harmonic structure (timbre of the corresponding sound) by comparison with this curve.

17 °) Acoustic instrument with fixed sounds for the implementation of the method according to Claim 4, characterized in that it is an instrument with vibrating plates or blades or with sound pipes constructed according to the range defined in the Claim 4.

18 °) Instrument according to Claim 17, characterized in that the keyboard according to any one of Claims 9 to 14 controls mechanically but by a set of electric pulses, the acoustic vibration of very small vibrating blades or strings but placed in crates adjustable resonance, amplifying the sound while modulating its harmonic structure.

19 °) Process using the musical properties of the elementary particles according to Claims 1 and 2 to catalyze the production of nuclear fusion energy, characterized in that it consists in carrying out fusion reactions from particles in chromatic agreement temperate, either added or substituted for particles of ordinary matter nuclei, these particles being selected so as to form compound nuclei whose distribution of the natural frequencies of the components in the scale conforms to the curve of equation (2) ci -after:

where Φ is the phase defining the choice of the line comprising the particles (either Φ = 0, -∏ / 8, -∏ / 3, + 7∏ / l2, + ∏ / 3 or + ∏ / 6, Φ = 0 corresponding to the nucleon), an acoustic modeling according to Claims 1, 3 to 8 using a device according to any one of Claims 8 to 18 making it possible to verify in particular the fusion of their vibrations.

20 °) Apparatus for the implementation of the nuclear fusion process according to Claim 19, characterized in that it comprises the coupling of an accelerator, responsible for producing the particles intended to merge, and of a fusion reactor proper tells where the compound nuclei are formed.