Philosophers and musicians since the most remote times have wondered if 1) the music can express emotions, cause in the listener feelings and well defined states of mind or if 2) it consists in a practice which seeks only the pleasure and in a simple manipulation of sounds; the secular debate among the promoters of the first position (definable as “expressionists”) and the seconds (definable as “formalists”) seemed destined to be relegated within vain polemics; the development of the music-therapy, its need to find scientific bases to its practice and its evident curative effects induce nowadays to re-examine the two conflicting theories; in fact, if the theory of the “formalists” were accepted (the music as pure and simple manipulation of sounds that the musician composes according to his/her mere musical taste, excluding a priori the emotional effects on the listener) the practice of the music-therapy would not have sense; such practice, in fact, founds him upon the tacit presupposition that the sounds have the possibility to cause on the mind of the listener and therefore to communicate psychological states and emotions; the music-therapy would slant therefore to accept the theory of the “expressionists.”
The position of the “expressionists”, nevertheless arouses different questions:
· In which way does the music have effects on the mind of the listener?
· In which way does it communicate meanings and states of mind?
· Which through perceptive mechanisms does the listener attribute her meanings?
· What is the human audio-mental system through which musical experience is perceived?
· In which way does such system give sense to the musical phenomenon?
· Which aspects of the musical phenomenon (height, pitch, rhythm, intensity) are more important in to arouse emotions and states of mind?
· Does the context of the fruition condition the attribution of sense?
· Does the same musical phenomenon convey the same meanings to listeners educated in different civilization and musical cultures? Or completely different emotions?
Questions of great importance that, if resolved in a way or in another, bring the music-therapist to acquire a new method to work: for example the constitution of a musical repertoire endowed with well precise emotional meanings to be applied on particular patients; composed repertoire selecting determined intervals of which it is known a priori the emotional content working, therefore, with knowledge of cause and effect.
Such questions and matters of method are been faced by A. Danielou; in his stays of study in India where he remained for more than twenty years in intimate contact with Indian musicians and musicologists, he realized how musical intervals, denominated jati-s in the Indian language, were classified by the Sangita-Ratnakara (the most complete treated of Indian musical theory) according to their emotional content, contrarily to the western musicology, that considers the intervals simply as a pitch between two notes, without meaning. Subsequently to having assimilated the Indian musical culture, he seeks for a scientific and mathematical base resorting to the discoveries of the physiology, cybernetics, semiotic, psychology of the perception and other western sciences.
How the audio-mental system operates.
The mind, according to the theory shared by Danielou, works through symbols or figure-type, to which the data are brought back coming from the experience.
Nevertheless such data are not gathered in all of their wealth but only through that few elements that constitute that is a figure, a scheme that analytically represents them. In the musical field, the audio-mental system, according to the studies of Winckel (Vues nouvelles sur les mondes des sones), classifies only that data that allow him to differentiate the colours of voice and the intensity; only in a second time the pitch.
During the learning these figure-types are stored and memorized according to a certain order; these figure-types are involved in the listening of a musical piece since they are the points of reference and comparison for the inputs. If there is similarity between the figure-type and the sifted musical data the audio-mental system easily proceeds in the classification and in the attribution of sense; on the contrary the data are postponed back for operating a choice with that procedure denominated feed-back.
The musical semantic.
The human ear, as a microphone, detects indifferently all the sounds that belong to a certain range of frequencies, but not all the sounds are analyzed and classified by the mind; this, according to the theories of Mark (Elementary thinking and the classification of behaviour)
and of N. Wiener (Cibernetics), is a mechanism that tends to resolve problems to adapt to change and it works as an electronic calculator that uses besides the binary system, employed by these, the ternary one and quinternary; the human mind, in other words, classifies the sounds for multiples and submultiples of 2, 3 and 5.
The same mathematical laws also preside the visual perception: the human eye, in fact, easily gathers 2, 3 or 5 objects, while from 6 objects in then tend to gather them in binary groups, ternary or quinternary.
The factor “2” and the octaves.
Multiplying a frequency for 2 or for someone of her multiples to the numerator they will be got some sounds having a similar characteristic; the first one of these sounds are called “octave”: for historical reasons, because it is the eighth sound of a diatonic scale after a succession of seven notes; in fact it would be called in other way if the system adopted was pentatonic, esatonic or dodecaphonic.
The factor “2” determines a spatial factor because it articulates across through the octaves the sonorous field where musical phenomenons happen; also in the visual or tactile perception you can empirically be ascertained that having two eyes, two hands over that two ears gives us a well precise sense of the space and that the stereo and stereoscopic perception are directly connected with having the two organs of sense.
The factor “3”: the cycle of the “fifth” and the “fourth”.
Multiplying a frequency for 3 or for someone of her multiples to the numerator the cycle of the “fifth” is formed (such denomination has origin, as for the octave, from the diatonic scale of seven notes). The factor “3” produces intervals having characteristic of activity.
Given a frequency (C, for instance) and multiplying it for 3 or someone of his multiples to the numerator are formed:
G 3/2
D 9/8
A+ 27/16 (where the signs + or – indicate that the sounds are increasing or decreasing if comparated to the temperated system)
E+ 81/64
B+ 243/128.
All the on listed intervals have according the Sangita-Ratnakara the same emotional characteristic: they are active, cheerful, bright and vigorous.
The expressive characteristic is stronger with the G and weaker gradually proceeding in the cycle of the “fifth”; in fact the emotional effect is inversely proportional to the simplicity of the first numbers (G = 3/2) to reach the most distant interval (B + = 243/128).
Multiplying a frequency (C, for instance) for 3 or for someone of his multiples to the denominator the cycle of the “fourth” is formed:
F 4/3
Bb 16/9
Eb 32/27
Ab 128/8
Db 256/243;
All the on listed intervals, according to the classification of the Sangita-Ratnakara, are passive, affectionate and calm.
The factor “5.”
The factor 5 is the most important point because produces intervals of accentuated emotional content; 5 is a factor of life, of growth and of expansion; this is also shown in the visual circle: building some geometric figures on the sides of squares (factor 2) or of triangles (factor 3) regular figures are produced while the figures built on the sides of a pentagon will multiply itself. To it retries of this is proved in an experiment on the field of the psychology of perception: a surface can indefinitely be divided in squares and identical triangles while this is not also possible with any irregular pentagons.
Multiplying a frequency given (C, for instance) for 5 to the numerator the following intervals are formed:
D – 10/9 anxious, weak
E 5/4 sensitive, active
F – 320/243 uncertain, unstable
F #45/32 uncertain
A 5/3 sweet, pleasant
B 15/8 sweet, tender
Multiplying the C for 5 to the denominator these intervals are formed:
Db+ 16/15 erotic, affectionate
E+ 6/5 passionate
F+ 27/20 aggressive, dangerous
F#+ 64/45 active, vital
Ab+ 8/5 loving, resourceful
Bb+ 9/5 desirous, anxious
The intervals with 52 to the numerator have an intense emotional character:
Db – 25/24 sad, pathetic
Eb – 75/64 sad, desolate
F #- 25/18 intensely painful
Ab – 25/16 sad, desperate
Bb – 225/128 resigned, desperate
The intervals with 52 to the denominator have a hard character; therefore they are rarely used in music:
Db++ 27/25 resourceful, aggressive
E++ 32/25 hard, insensitive
F#++ 36/25 hard,
A++ 128/75 insensitive, cruel
B++ 48/25 selfish, aggressive.
Limits and zones of instability.
The intervals formed within the three numerical factors are limited for two reasons:
1. more we move away from the first number and more the semantic content weakens, as has been previously seen;
2. the development of every series brings even if for different ways to almost identical sounds to those of the series formed by another numerical factor.
The factor numerical 2 correspondent to figure-type spatial can indefinitely be multiplied because this alters neither the character nor the form; the numerical factor 3 correspondent to figure-type triangular and the numerical factor 5, that produces emotions, are the most limited in their employment, being used up to 52; 53 also being recognizable and classifiable is not used in music because it transmits hardness and cruelty. The combinations 2 x 3 are recognizable up to 22 x 32 and 23 x 3; the combinations 5 x 2 and 5 x 3 are usable up to 52 (Eb -) and 52 x 32
(Bb -).
In our mechanism of mental comparison the contour of the perceived figure overlaps to the figure-type stored in the memory; if such “input” perfectly coincides with the figure-type is recognized and a determined meaning is attributed him. It can happen that an interval perceived and overlapped to the figure-type stored in the memory can be classified and interpreted with difficulty because it resembles to an interval produced by a different numerical factor; therefore a doubt will subsist and the classification will always miss of steadiness; the sound will be unpleasant therefore since the musical pleasure is tied up to the possibility to resolve the problems set to the audio-mental mechanism.
This is the case of the two “fourth” augmented endowed with double sense being formed both from the cycle of the “fifths” and from that of the “fourths”: F#(32 x 5/25 = 45/32) and F #+ (26 / 32 x 5 = 64/45) that have a different semantic content because they are formed by different numerical factors; the indeterminacy of these intervals produces an uncertainty of the audio-mental mechanism giving to the “fourth” augmented the characteristic of hard interval, unpleasant and endowed with ambiguous sense; also the followings intervals introduce the same ambivalence of the two “fourths” augmented:
· the second minor Db formed by 28 / 35 (256 / 243) and from 33 x 5 / 27 (135/128) different of 1,9 cents; it seems that the interval 23 / 35 predominates, being formed without double mechanism, but such interval is ambiguous; therefore the ear prefers the step up Db+ (24 / 3 x 5 =16/15), a “comma” above, or the Db – (52 /2 x 3), a “comma” under.
· The third minor Eb has two forms (25 / 33 = 32/27) and (35 x 5 / 210 = 1215/1024) with the difference of 1,9 cents; here it dominates 32/27: but this involves an element of indecision that doesn’t exist in the Eb+ (6/5), a “comma” above, neither in the Eb – (75/64), a “comma” under.
· The third pitagoric E+ is formed in two circuits (34 /26 =81/64) and (29 /34 x 5 =512/405) with the difference of 1,9 cents; being a hard interval is preferred the third harmonic (5/4), a “comma” under.
· The F- is formed in two circuits: (26 x 5 / 35 = 320/243) and (34 x 52 / 29 = 625/512) with the difference of 1,9 cents; this interval is very rarely used.
· The F+: (33 /22 x 5 = 27/20) and (213 / 35 x 52 = 8192/6075) is rarely used in music.
· The G – (23 x 5 / 33 = 40 / 27) and (35 x 52 / 212 = 6075/4096) with the difference of 1,9 cents.
· The G+ (35 / 25 x 5 = 243/160) and (210 / 33 x 52 = 1024/675) with the difference of 1,9 cents; both these intervals are rarely used because of the proximity of the G that predominates.
· The Ab: (27 / 34 =128/81) and (34 x 5 / 28 = 405/256) with the difference of 1,9 cents; the Ab – (25/16) and the Ab + (8/5) are preferred to it.
· The A+: (33 /24 = 27/16) and (211 / 35 x 5 = 2048/1215), with the difference of 1, 9 cents; ambiguity results as soon as perceptible; as a result the A+ preserves a positive character.
· The B+: (35 /27 =243/128) and (28 / 33 x 5 = 256/135).
· The C -: (25 x 5 /34 =160/81) and (34 x 52 / 210 = 2025/1024), with the difference of 1,9 cents.
· The C+: (34 / 24 x 5 = 81/80) and (211 / 34 x 52 = 2048 / 2025); both the intervals are not used because of the proximity of the C.
The temperament equalities.
The temperament equalities, that is the division of the octave in twelve equal semitones, has destroyed the differences among an interval and the other one impoverishing the expressive possibilities of the western music. The listener of a piece for piano, organ, or another keyboard is forced to operate the mechanism of “feed-back” that allows him to correctly interpret the intervals of the temperate system.
The pianist who wants to express determined emotions having available only the twelve temperate semitones and the relations that spring out from them will apply out to other musical means out of the pitch: relation of volume, touch, acceleration of the time, various types of embellishment, etc. While for the strings, wind instruments, or human voice only the writing on the pentagram is temperate, since such instrumentalists and singers tune up the intervals produced by the numerical factors 2, 3 and 5 according to their expressive intents.
The gradual destruction of the relation that connects certain intervals to certain emotions, caused by the temperate system, has brought the western music toward abstract structures up to become a pure combination of sounds deprived of semantic content; cerebral techniques of composition that privileges the structural aspect that have lost the very possibility of the music to produce emotions and meanings through intervals; for this reason certain musical structures of the western music are understood by the eye, analyzing the score, and not from the ear as it would be natural for the music, art of the time.
Modification of the semantics of the intervals: ornaments and simultaneous sounds.
The goal of the attack and the ornament of the sounds (trills, mordant inferior and superior, etc.) is to bring on an interval with a well defined semantic content some shades that alter the sense of the principal sound as it happens for the words whose disposition within the discourse can alter the sense making it more vanished, marked, definite, peremptory,… resorting to precise rhetorical figures (litotes, euphemism, alliteration, rhyme, consonance, assonance, etc.); this because adorning a note, the intervals neighbouring, determined by different numerical factors, are involved; therefore different meanings are conveyed; their disappearance in the polyphonic forms has involved an impoverishment of the expressive possibilities of the intervals.
Also the rhythmic ornamentations have so more intense emotional effects as the rhythmic unity is inferred by the cardiac pulsation; such ornamentations have been encoded by the Indian classical theory where they have assumed a well precise denomination: anahata = light anticipation, atita = light delay.
In the western music the ornamentations play an important role in the keyboards whose temperate intervals offer more limited expressive resources; in the literature for piano to the ornamentations typical of the literature for clavichord and organ (trills, mordants, anticipations, delays on the main time, etc.) is added the possibility to alter the volume of the sound (touch).
Monophonic and polyphonic music.
It is easily inferred that Danielou has a preference for the monophonic music because of his intrinsic characteristics:
· It has a fixed keynote to which are referred the various intervals performed during the execution and this increases the ability of the listener in order to discern the pitch of intervals and their semantic content.
· In the Indian classical music the tanpura or, in his lack, the tablas constantly playing the keynote, creates a propitious sonorous field for the right interpretation of the intervals.
The tonal music, instead, since it implies the harmonic logic (simultaneity of two or more sounds), sets some semantic problems:
· How much does the simultaneous execution of two or more sounds, as in the case of the western music from the Flemish polyphony to the advent of the harmonic logic, involve the weakening or the strengthening of the meaning of certain intervals?
· Which should be, in a certain accord, the position of the interval of which he intends to alter the sense? Soprano’s position, contralto, tenor, bass…?
In virtue of which law of the physics (resonance, sequence of the harmonic, third sound of Tartini…) the effect of weakening or strengthening of certain intervals it is explainable?
Conclusions
From this excursus on the theories of A. Danielou, that doesn’t have the pretension to be exhaustive but to offer sprouts of reflection for the operators of music-therapy, different questions they are aroused:
· Is the audio-mental system the same in the subjects of different historical time?
· Do the same intervals have the same effect on subjects him in different musical cultures?
· And in subjects of different musical competence?
· How the temperated system has formed the audio-mental mechanism of the Westerners?
· Is the audio-mental system the same for males and females?
· Is it the same for subjects of different bands of age?
· What is the semantic potentiality of the rhythm?
· And that of the stamp?
To the first question it seems can affirmatively be answered; in fact in the preface of his Traitè de musicologie comparèe (Hermann; Paris 1959) it declares that: “les anciens croyaient-ils trouver dans the musique la clè de toutes les sciences and de tous les arts, le liens entre la mètaphysique et la physique…Dans le présent étude…nous nous sommes efforcés d’expliquer brievement les idées que les anciens avaient des lois cosmiques…(pag. 11).” The number and the music have therefore for Danielou a value that transcends the historical periods.
Also to the second question can affirmatively be answered;
the constant call to the Indian music, the Sangitana-Ratnakara, to classify the intervals and their emotional meaning proves it.
To the fourth question he answers clearly: “La musique occidentale se trouve aujourd’hui enfermée dans un système sonore artificiel. La nature meme du dodécaphone tempéré et la nécessité de l’utiliser comme moyen d’expression, ont profondément affecté nos perceptions.” (pag. 12 of the Traitè)
To the seventh one and eighth questions he answers, in various of his works, that the rhythm and the colour can arouse emotions but he doesn’t analyze deeply these two dimensions of the music, in fact he has lavished its energies in to examine the semantic content of the intervals.
He doesn’t answer to the third, fifth and sixth question.
