ALAIN DANIÉLOU’S MUSICAL DIALOGUE
In this essay, Celso Cintra, author of the book Alain Daniélou’s Musical Dialogue [Alain Daniélou e seu laberinto musical, 2020]presents four dialogues that can be extracted from Alain Daniélou’s musicological work: between the collective and the individual, between the West and the East, between civilizations beyond the India-Europe axis, and between knowledge disciplines. He also delves into the problem of the correspondence between sound combination and feelings, the metaphysical basis for the understanding of sound and psychological phenomena, and Daniélou’s critique of Western music, its distortion of sound and its theoretical simplification.
Many consider Alain Daniélou an ethnomusicologist, but while his studies can be useful for ethnomusicology – and in fact they are – his persistence seems to occur in a field in which his work is not so much a research object: that of musical theory and cognition, extending into the field of aesthetics and philosophy of music.
As Alan P. Merrian1 rightly points out, we can find in ethnomusicology many anthropological and musicological trends. Daniélou fits the latter if we understand him within ethnomusicology. Nevertheless, Joseph Kerman tells us: “musicology, theory and ethnomusicology should not be defined […]in terms of their object of study, but in terms of their philosophies and ideologies”2.
In The Way to the Labyrinth Daniélou comments on the publication of his works stating: “[Pierre] Bérès brought out some of my more difficult works, such as the Traité de musicologie comparée4 and especially Sémantique Musicale, which challenges the basic principles of all the musical systems”3. These two works are the basis of Daniélou’s understanding of music.
The following four dialogues can be extracted from the work of Alain Daniélou: 1) Dialogue between the collective and the individual (Musicology vs. Semantics); 2) Dialogue between West and East; 3) Dialogue Between Civilizations: China, India, Ancient Greece and Today’s West and 4) Interdisciplinary Dialogue: Philosophy of Music and Music Theory.
1. Dialogue between the collective and the individual (Musicology vs. Semantics)
It is no coincidence that the most recent version of Traité de Musicologie Comparée (eng. Music and the Power of Sound) bears the subtitle the influence of tuning and interval on consciousness5. Intervals and their numerical symbolism is a theme very dear to Alain Daniélou and it is from this focus that he initially discusses issues of musical language, such as the nature of musical sounds, harmonic series, construction of scales and musical relationships, the measurement of intervals and their notation.
Rather than understanding how human beings acquired knowledge of intervals, it is important to discover how the phenomenon occurs that allows certain sound combinations to evoke different feelings, emotions or images. According to Daniélou, it is by studying traditional metaphysics, with its internal logic and coherence, despite apparent external changes, that we can understand the possible links between sound phenomena and their psychological effects6.
Daniélou recalls that several elements of our musical system are symbolic, as are spatial and temporal measurement patterns, and that such elements are used and considered as natural only because of the correspondences between these symbols and the real world.
The Sanskrit word for universe is jagat (“that which moves”), and every movement generates a vibration, which in turn can be associated with a sound, which thus becomes a common principle throughout the universe. In this sense, this statement would be “in tune” with the descriptions of matter made after the advent of quantum mechanics. Since all matter can be understood in terms of vibration and consequently of sound, even if inaudible, the relationships between the various elements existing in the world can be understood as sound relationships. Consequently, music can be an audible manifestation of these relationships in the world, providing the power to recreate the things of the world themselves, as described in the Vedas and in Genesis.
However, if these relationships cannot be reproduced perfectly to provide the power of creation, they can at least evoke such creations, certain feelings, emotions or even realities of a spiritual nature7.
Evocation through sound, like creation itself, takes place not because of the material fact of physical vibration but on account of the existence of metaphysical correspondences. Therefore all psychological explanation of musical experience has to be discarded. In reality, the personality of the hearer counts for nothing in the phenomenon of musical evocation because evocation takes place even if there is no hearer, and if the existence of this evocation is ephemeral it is only because of the imperfection of the relation of sounds8.
As all matter can be understood in terms of vibration and consequently of sounds, even if inaudible, the relationship between the various elements existing in the world can be understood as sound relationships.
In turn, Sémantique Musicale9 was originally published in 1967. The second edition, which appeared in 1978, contained an introduction written by Françoise Escal, and an Annex of a project for the construction of a keyboard instrument. In this book, Daniélou also grounds the development of his theme on the question of intervals and their numerical symbolism. However, whereas in Music and the Power of Sound he uses intervals to deal with ethnic and historical issues, here he takes them as a basis for an analysis of how musical meaning arises in our audio-mental apparatus. Daniélou intends thereby to investigate the possibility of the occurrence of an objective musical phenomenon that would cause a certain effect or have the same meaning for all people, also analyzing the reason for the occurrence of different and even contradictory effects in listeners by the same song. His references here were the following: Elementary thinking and the classification of behavior10 by the pediatrician and otolaryngologist Henry J. Mark, Cybernetics11 by the American mathematician and founder of cybernetics Norbert Wiener, and Vues nouvelles sur le monde des sons12 by the Austro-German acoustic engineer and pioneer of electronic music Fritz Winckel.
2. Dialogue between West and East
For a time, Daniélou undertook the discipline of reading books, newspapers or magazines only in Hindi or Sanskrit, in order to learn both languages. In this way, he became fluent in Hindi and could study ancient Indian music treatises in Sanskrit. By studying these treatises, as well as playing the vīṇā instrument, he reached another conception of both Eastern and Western music. As he reports:
Little by little I was initiated into an astonishing new world – the music of India. But although it was very different from Western music, the two styles remained separate and distinct in my mind and I never tried to mingle them. Musical systems, like languages, do not mix; but one gradually becomes aware of the resemblances between them, not in form but in evocative power.13
Through his works, mostly published on his return to Europe, Daniélou seeks to show the Hindu world in its many different aspects – philosophical, religious, ethical and artistic – since he understands that this civilization has very little to do with the usual pseudo-mystical picture people have made of it. For him, Indian civilization is the only one of the ancient great civilizations still alive and a better acquaintance with their possible contributions could lead modern thought to a new Renaissance.
During his stay in Benares, Daniélou recorded both the best representatives of Indian classical music as well as Vedic chants and popular Indian songs. Thanks to the interest of Serge Moreux and his assistant Roland de Candé, of the French label Ducretet-Thomson, the first Anthologie de la musique classique de l’Inde was published, which includes recordings by the young Ravi Shankar.
Jack Bornoff, who was Executive Secretary of the International Music Council, persuaded UNESCO to launch a record series of great Eastern and African music and hired Alain Daniélou to be his consultant. He made recordings in several countries: Afghanistan, Cambodia, Laos, Iran, Japan, Tibet, Tunisia and Morocco.
With the release in the West of this record series of traditional music promoted by UNESCO, the musicians included in it became internationally prestigious. Owing to this prestige, they are no longer neglected, ignored and despised in their countries of origin; their music is broadcast, and their financial situation has improved. Daniélou claimed that he was “far less interested in attracting the attention of Westerners to Oriental music than in helping musicians maintain their traditions.”14
Unsurprisingly, we find statements by sitarist Ravi Shankar and violinist Yehudi Menuhin praising Alain Daniélou. Shankar claims that it was due to Alain Daniélou that Indian music is no longer considered mere folklore, but classical music, on an equal footing with the greatest Western music and composers. Menuhin also praises Daniélou’s work for having made this dialogue between Western and Eastern music possible.
3. Dialogue between civilizations: China, India, ancient Greece and today’s West
According to Daniélou, the Chinese, the Indians and the ancient Greeks all believed in the evocative power of music and regarded knowledge of the connections between sounds and other aspects of reality as a science, even if that is today deemed to be magic or superstition.
Numerical symbolisms linked to music are present in all three of these civilizations. Regarding China, Daniélou refers to René Guénon’s quotation from the Tao Te King: “One has given birth to two, two has given birth to three, three has given birth to all numbers.”15 In musical terms, this means from the first partials of a harmonic series, or the first divisions of a string. The one is the fundamental, the two its octave, and the three the fifth interval which, when repeated, would give rise to all other possible sounds. These sounds, selected in groups of 5 – forming a pentatonic scale – represented, for the Chinese, a correspondence with “the material world, the five directions (four cardinal points and center), the five elements and so on”.16
Adding two sounds to these 5, we reach the number 7, which in Plato’s Timaeus dialogue already represents the divisions of the world’s soul17, but which also represents the image of the celestial world and the seven visible planets. We find the number 7 in the number of strings of the lyre, in the seven pipes of Pan’s flute, in Dante’s seven steps to reach paradise and in the seven horses that pull the chariot of Sūrya, the Hindu god of the Sun18.
The number seven can also be understood as the sum of three plus four (3 + 4 = 7) which, when multiplied, generate the number twelve (3 × 4 = 12). For the Pythagorean tradition, the dodecahedron represents the symbol of the universe. The seven planets move in the twelve regions of the zodiac, just as the seven notes of our diatonic scale move in the 12 regions of the octave.19
The number 12, rather than a series or sequence within numerical symbolism, may be considered an area, a plane, by virtue of being the product of three and four. Thus, in relation to music, the twelve notes of our musical system relate to regions within which different pitches would be possible according to the tuning used, not to be confused with 12 notes of absolute pitch, as they came to be considered within of the Western Equal Temperament system20. In this way, music for the ancients was more than mere enjoyment for the ears; it represented a kind of “algebra of metaphysical abstractions”.21
The cycle of fifths, which in passing through twelve fifths does not take us back to the octave, is explained by Daniélou as one of the signs of the imperfection necessary for the world to avoid being reabsorbed by infinite perfection, just as the earth’s axis is tilted, the heart is not in the center of the chest and the solar cycle does not coincide with the lunar cycle.
This small difference that exists in the cycle of fifths is called a comma, the difference that the cultures with their diverse musical systems need to deal with: the difference between what is finite and what is infinite.
The fifths form a spiral whose sound coiled in itself, can never meet. For us, this limitless spiral can be the joint in the structure of the world, the narrow gate that will allow us to escape from the appearance of a closed universe, to travel in other worlds and explore their secrets.22
Daniélou considers that the difference existing between Eastern and Western musical systems is not fundamental but is established by virtue of a contradiction between practice and theory. The acoustic principles that govern music in the two systems are the same, it is only in their exteriorization, in their actualization as a sound event that such differences present themselves. He understands that, rather than different systems, they are complementary systems.23
In his investigation, Daniélou shows that intervals are presented in two aspects: in their mathematical and logical proportions and in their expressive, symbolic and psychological aspect, which arouses feelings, ideas and visions based on their harmony. These two aspects have nourished compilations on music theory according to various circumstances, such as time, people and place. Emphasis placed on the expressive aspect heralds the birth of modal music in its aspect of relating the various notes to a tonic, based on the octave interval. When emphasis is placed on the numerical aspect, the basis for the construction of such a theory is the cycle of fifths in its modulatory and harmonic aspect. However, in this apparent duality, the metaphysical aspects are still preserved.24
According to Daniélou, Western tonal music lacks a rational theory. It was developed using aspects of these two different theories. Although a combination of both harmonic and melodic expressions is considered possible, harmonic development makes melodic subtleties practically impossible.
The Western musical system is the result of a chaotic mixture of various theoretical definitions. While the system is cyclic, with constant changes of keynote resulting from modulatory processes, each keynote, and even each note of each scale, is accompanied by a chord that depends, for its formation, on characteristics of the modal system it is based on, on the relationships with a tonic provided by the phenomenon of resonance and by the harmonic series. The problem with this combination is that the notes needed for a consonant chord are different from those needed for modulation25.
In an attempt to solve this problem, the West gradually adopted equal temperament. Equal temperament, by distorting the intervals, makes their meaning vague and imprecise. Daniélou agrees with the claim that the ear recognizes the true range, which would temper the range’s auditory representation, but he notes that each listener makes individual adaptations according to personal tendencies. Each interval or chord would have different meanings, for different people, according to their mood. The result is that Westerners increasingly lose any conception of music capable of expressing emotions, feelings or the highest ideas26.
Daniélou considers that the difference existing between Eastern and Western musical systems is not a fundamental difference, but a difference established by virtue of a contradiction between practice and theory. The acoustic principles that govern music in the different systems are the same, it is only in their exteriorization, in their actualization as a sound event that such differences present themselves.
The progressive theoretical simplification adopted by the West to implement harmonic and polyphonic characteristics distances its music from acoustic principles and from the laws on which the metaphysical correspondences are based, thus losing its evocative appeal27.
According to Daniélou, Western music starts in a disorderly manner. Pope Gregory I, in bringing the eight modes of plainsong from the East, when he was ambassador at Constantinople, transcribed them from the eight Byzantine modes used by the Patriarch Severus of Antioch. However, what was lost proved to be fundamental for the definition of each tone and the expression of each note: the ison, the drone tone that serves as support for modal musical expression. This absence makes plainchant vague and ethereal, without any clarity of meaning28.
The Zarlino scale, also known as just intonation, has the problem of being a joining of two systems, an ascending, cyclical characteristic, responsible for the notes C, G, D and a descending, modal characteristic, responsible for the E, A, B and F notes. The problem with this scale arises when it is modulated because, according to the new tonic, several notes would need to have their pitch unevenly raised or lowered
By making all semitones equal, equal temperament makes the ratios between frequencies quite different from the simpler ratios that, according to Daniélou, are responsible for symbolic, emotional and idea evocations, possibly because of their metaphysical correspondences.
4. Interdisciplinary Dialogue: Philosophy of Music and Music Theory
With regard to the Philosophy of Music, let us take as a guiding principle the heteronomous aspect that Daniélou attributes to music. Not just because he considers music as a language, and as such a vehicle for transmitting information, but also because this transmitted information is something beyond music, be it feelings, ideas or emotions. Such conceptions are noted when he refers to Indian music, which he studied not only in theory but also in instrumental practice:
the purport of this music is not to sound beautiful, but rather to suggest beauty, to shape and to create it. It evokes the splendor [sic]of the seasons and of the hours of day and night, the depth of man’s feelings, and the power of his emotions. It opens for us the door to the heavenly worlds, but remains like truth, that is niranjana, ‘the unadorned’. It is not beautiful in itself. […]The harmonies of forms, colours, and sounds seem beautiful to us only because they call up a higher reality.29
Daniélou considers music from the Hindu point of view, that is, as a bridge between the physical and metaphysical aspects of reality. Therefore, not only music but the arts in general were “considered in ancient India as the vehicle or instrument of popular education” conveying “in the form of illustrations and parables, the principles of philosophy, ethics and religion, which dialectical exposition would have brought within the reach of only a cultural minority”.30
Although it may give the impression that, should the population have access to and an understanding of a dialectical exposition of the principles of philosophy, ethics and religion, art, and in this case music, would become useless, we can recall that Daniélou considers no language capable of transmitting the whole truth, and in this case there would always be something to be transmitted, whether for quantitative reasons, i.e. the lack of elements and or vocabulary of transmission, or for qualitative reasons, i.e. the impossibility of expressing an idea as a whole. Based on these observations, Daniélou’s work allows us to understand three musical approaches that we consider to be of a philosophical nature.
The first refers to the epistemological change in the conception of music in the West, in which music is no longer a Quadrivium discipline, together with Arithmetic, Geometry and Astrology/Astronomy, and has become an art supported by Rhetoric, which belonged to the Trivium with Grammar and Dialectics. We identify two terms for this change: Speculative Music in the first case, in which music serves to interpret and study the universe, and Musical Speculation, in which music becomes an object of study. This change took place with the Scientific Revolution in which physics became the most adopted and appropriate metaphor model for the interpretation of reality, to the point that M. H. Abrams creates a metaphor in which he states that “art [in our case, music]changed from mirror to lamp, no longer reflecting the external natural world, but shining inside the mind and heart of the creator”31.
The second approach refers to the differences between what we define as Sacred Music – based on the work Sacred Art in the East and the West by Titus Burckhardt, in which music is a means to an end, or a representation of a truth that originates outside it, in which “it is not enough that its themes derive from a spiritual truth. It is also necessary that its formal language bears witness to and manifests this origin”32 – and what we observe as the Sacralization of Music, a phenomenon that occurs mainly from Romanticism onwards, in which music itself becomes sacred and an object of worship, and which influences musical thinking to this day.
The third approach would be to identify the subtle differences between the Greek Doctrine of Ethos, the Theory of Affects in the Baroque period and the Expression of Feelings in Romanticism. These three conceptions of musical heteronomy are all of them in some way linked to the issue of feelings aroused, provoked or expressed by music. I feel that Daniélou’s work would relate his musical definition more closely to the Greek Doctrine of Ethos than to other formulations.
In turn, Music Theory is a very important field in Daniélou’s work, as he uses the musical theory of three great civilizations, and compares them on a common basis, thus managing to establish parallels to help us understand the path of Western music from this context.
We can understand Alain Daniélou’s meaning of Musical Theory as being closer to the Philosophy of Music than to musical practice, since, as shown by Hans-Georg Gadamer in his text Praise of Theory, the word theory, among other interpretative possibilities, has to do with observation, contemplation and speculation, which leads to its being the very definition of philosophy, and that this, in fact, would be “the old name for theory”33.
In turn, both Carl Dahlhaus and Joscelyn Godwin affirm the existence of what can be called the Speculative Theory of Music. Dahlhaus understands it as the “ontological contemplation of tone systems”34 while Godwin understands that “[t]he speculative musician discovers universal principles as the mathematician or the philosopher”35. We may say that these are the main characteristics present in the musical work of Alain Daniélou, who also considers that
[t]he connection between physical reality and metaphysical principles can be felt in music as nowhere else. Music was therefore justly considered by the ancients as the key to all sciences and arts – the link between metaphysics and physics through which the universal laws and their multiple applications could be understood36.
[t]herefore, in judging the possibilities and the value of musical systems, we should not trust the prejudiced judgement of our ears, but consider in their most abstract form their theoretical possibilities. We may then discover the equivalence of systems that at first seem to have nothing in common. We may also discover a profound difference between systems whose forms are outwardly very similar. By so doing we shall, in any case, judge the musical systems soundly and on safe grounds. To be able to realize their beauty or directly perceive their meaning is another matter and generally requires very long practice37.
Daniélou defines four methods of forming a scale: by proportional relations; by cycle (scale of fifths); by roots (tempered scale) and by multiples (scale by harmonics). From here, he interprets the musical systems mentioned as model cases, classifying Chinese music as a cyclical system and Indian music as a modal system tuned by harmonics. As for Greek music, he interprets it as a “confusion of systems”38, in which descriptions by various theorists such as Pythagoras, Aristotle, Boethius, Aristides Quintiliano, among others, make it difficult to generalize a single and homogeneous system.
Daniélou then created the Universal Sound Scale by cycles and multiples of 2, 3 and 5. He justifies the need for this scale by stating the following:
For the comparative study of different musical systems, as well as for correct execution of each one, it is necessary to establish a scale of sounds that will allow both a clear and accurate notation of all the usual intervals and an immediate appreciation of their nature and relative value39.
The philosopher Giovanni Piana suggests that this scale would serve as a kind of “graded ruler” – as it divides the octave into 53 parts, with natural and untempered intervals – so that “a scale will be considered ‘natural’ if all its intervals coincide with some of the 53 parts of the ‘harmonic scale’”40. Thus, Daniélou’s scale allows us to analyze the characteristics common to the scales of different musical cultures.
The scale of sounds elaborated by Daniélou addresses two aspects: theoretical and perceptive. He states more precisely:
For our investigation, musical intervals appear under two aspects: one mathematical, involving numbers and logical ratios; the other symbolic and psychological, in which the relations of sounds (their harmony) awaken in us feelings, ideas, and precise visions. Their two aspects obviously have their origin in the same principles, but this unity is beyond the scope of experiment and consequently beyond the understanding of modern Westerners. This deficiency naturally brings them to the illogical situation of leaving aside one aspect of experience whenever they study the other, as if the laws of acoustics and those of musical expression did not refer to the same sounds.41
Daniélou is an advocate not only of modal music, but also of natural tunings, considering that temperament, especially Equal Temperament, is not capable of providing all relevant and possible effects to the interval relations present in music, because
[i]t is generally said that the ear can recognize the true interval represented by the tempered interval. This is a fact; but each ear makes a different adaptation according to individual tendencies, and the same chord may have a different significance for different people according to their mood. The meaning of an accurate chord, on the other hand, is determined absolutely and perceived by all.42
Alain Daniélou also justifies the use of natural intervals. For him, just as the brain works like a kind of computer operating in three languages simultaneously, binary, ternary and quinary, any interval that does not correspond to one of these languages is as it were corrected by the brain so that it can interpret it, causing fatigue in our audio-mental apparatus. This is why his scale divides the octave into 53 parts and, even though there are other theories that work with this same division using the equal temperament, Daniélou’s option is for natural intervals derived from 2, 3 and 5, an option related to musical cognition.
Here we have seen four possible dialogues raised by Daniélou’s work, in the hope of contributing to a better understanding of his musical work as well as possible relationships that may be established between the latter and other areas of knowledge.
- MERRIAN, Alan P. Ethnomusicology Revisited. Ethnomusicology, University of Illinois Press on behalf of Society for Ethnomusicology, v.13, Nº 2 p. 213-29, 1969. Stable URL: www.jstor.org/stable/850146 Accessed: 02/06/2010 08:57
- KERMAN, Joseph. Musicologia. São Paulo: Martins Fontes, 1987, p. 7.
- DANIÉLOU, Alain. The Way to the Labyrinth. Trad. Marie-Claire Cournand. (French Original) New York: New Directions Book, 1987, pp. 235-236.
- DANIÉLOU, Alain. Traité de Musicologie Comparée. Paris: Hermann, 2004.
- DANIÉLOU, Alain. Music and the power of sound: the influence of tuning and interval on consciousness. Rochester, Vermont: Inner traditions International, 1995.
- Ibidem, p. 2.
- Ibidem, pp. 4-5.
- DANIÉLOU, Alain. Sémantique Musicale: essai de psycho-physiologie auditive. 2 ed. Paris: Hermann, 1993 (nouveau tirage).
- MARCK, Henry J. Elementary Thinking and the Classification of Behavior. Science, American Association for the Advancement of Science, v.135, Nº 3498 p. 75-87, 1962. Stable URL: http://www.jstor.org/stable/1707549. Accessed: 02/06/2013 00:39
- WIENER, Norbert. Cybernetics: or control and communication in the animal and the machine. 2ª
ed. Massachussets: M.I.T. Press, 1962.
- WINCKEL, Fritz. Vues nouvelles sur le monde des sons. Trad. A. Moles e J. Lequeux. Original German 1952. Paris: Dunod, 1960.
- DANIÉLOU, Alain. The Way to the Labyrinth. Trad. Marie-Claire Cournand. (French Original) New York: New Directions Book, 1987, pp. 235-236, p. 54.
- Ibidem, p. 239.
- Guénon apud Daniélou, Ibidem, p. 6
- PLATÃO. Timeu-Crítias. From Greek, introdução e notas Rodolfo Lopes. Coimbra: Centro de Estudos Clássicos e Humanísticos (CECH) / Classica Digitalia – Vniversitatis Conimbrigensis (Edição Digital), 2011.
- DANIÉLOU, Alain. Music and the power of sound: the influence of tuning and interval on consciousness. Rochester, Vermont: Inner traditions International, 1995, pp. 6-7
- Ibidem, p. 7.
- Ibidem, pp. 6-7
- Mengel apud Daniélou, Ibidem.
- Ibidem, p. 8.
- Ibidem, pp. 10-11
- Ibidem, p. 121.
- Ibidem, pp. 121-122.
- Ibidem, p. 124.
- Ibidem, p. 125.
- DANIÉLOU, Alain. Aesthetics and Indian Music. Sangeet Natak, New Delhi (India): Sangeet Natak Akademi – The National Academy of Music, Dance and Drama for India, v. XLII, n. 1, p. 86-90, 2008, here p. 86.
- DANIÉLOU, Alain. The traditional arts and their place in the culture of India. Sangeet Natak, New Delhi (India): Sangeet Natak Akademi – The National Academy of Music, Dance and Drama for India, v. XLII, n. 1, p. 91-103, 2008, here p. 91.
- MH Abrams apud Blanning in: BLANNING, Tim. O triunfo da música: a ascensão dos compositores, dos músicos e de sua arte. São Paulo: Companhia das letras, 2011, p. 109.
- BURCKHARDT, Titus. A arte sagrada no oriente e no ocidente: princípios e métodos. São Paulo: Attar, 2004, p. 117.
- GADAMER, Hans-Georg. Elogio da Teoria. Lisboa: Edições 70, 2001, p. 23 et seq.
- Dahlhaus apud Christensen in: CHRISTENSEN, Thomas. Introduction. In: _____ (Ed.). The Cambridge history of Western Music Theory. Cambridge (UK): Cambridge University Press, 2002 (reprinted 2004) p. 1-23, here p. 13.
- GODWIN, Joscelyn. Harmonies of Heaven and Earth: mysticism in music from antiquity to the avant-garde. 5ed. Rochester (Vermont): Inner Traditions International, 1995, p. 271.
- DANIÉLOU, Alain. Music and the power of sound: the influence of tuning and interval on consciousness. Rochester, Vermont: Inner traditions International, 1995, p. 1.
- Ibidem, p. 18.
- Ibidem, p. 135.
- regoli graduati […]Una scala sarà da considerarsi “naturale” se tutti i suoi intervalli coincidono con alcune delle 53 lineette della “scala armonica”. In: PIANA, Giovanni. La scala universale dei suoni di Daniélou. Pdf version 2003. Disponível em: http://filosofia.dipafilo.unimi.it/piana/index.php/filosofia-della-musica/106-la-scala-universale-dei-suoni-di-danielou. Acesso em: 25 mar. 2011. 51p, p. 23.
- DANIÉLOU, Alain. Music and the power of sound: the influence of tuning and interval on consciousness. Rochester, Vermont: Inner traditions International, 1995, p. 13.
- Idem, pp. 121-122.