Western music in dialogue with the arts.


WESTERN MUSIC V
July - August 2015
THE HUMAN VOICE
THE EXPRESSION OF A ANTHROPOLOGICAL TRUTH.
“Theoretical and practical experience of the evolution of vocal music”
In search of the essence of vocal music III

Link to class material: 
https://www.wetransfer.com/downloads/2528101de3b667540b6d8070f359852620150820092004/5fa5f84bf347e1fd39aa91a5149ceab920150820092004/459f8b

 

 

 

Western Music IV

http://es.scribd.com/doc/236682668/In-Search-of-the-Essence-of-Vocal-Music-Goa-University 

 

Western Music I - Chowgule College

 

 

Western Music in dialogue with Philosophy, History and Arts- Part II by Professor Santiago Lusard Girelli

    ONB 116        
Western Music in dialogue with Philosophy, History and Arts.     Part II

Course Instructor:  
Professor Santiago Lusard Girelli
Anthony Gonsalves Visiting Professor at Goa University


Topics for the examination

Saturday 08/02/14 - 10.00 University of Goa.
 
1)  Philosophical foundations of Western musical tradition
2)  History of Western Music
3)  Theory of Western Music
4)  Music Appreciation
5)  Music in Dialogue with Arts, History and Philosophy



EXAMINATION OUTLINE


Philosophical foundations of Western musical tradition
1.     Philosophical Ideas of Western Music I: Introduction: The Ancient Western Music
·       Anciet GREEK MUSIC
·       Pithagoras
·       Harmony of the Spheres
·       Liberal Arts
·       Art definition
·       J. Cage and the noise.
2.  Philosophical Ideas of Western Music II: Goodness, Beauty & Truth.

History of Western Music.
1.     Origins of the Western Music - Ancient Greek Music  to XX Century
·       Medieval period (characteristics, composers and Works)
·       Baroque period (characteristics, composers and Works)
·       Classical period (characteristics, composers and Works)
·       Romantic period (characteristics, composers and Works)
·       Post romantic and XX century (Impressionism – Nationalism – Concrete Music)
2.  Vocal Music – The Human Expression.
·       Human voice
·       Classification of singing voices
·       Health benefits
·       Choir
·       Historical overview of choral music
·       Gregorian Chant
·       Origins of polyphony
·       Medieval Vocal Music
·       Perspective and Poliphony
·       Cantata Structure (Aria, Choral, Choro, Recitative)
·       Requiem
·       Vocal Music Composers
·        
2.     Instrumental Music - Music beyond words
·       String Quartet
·       Orchestra

3.     Choral Symphonic Music - The greatness of the human spirit
·       Requiem: Mozart – Faure – Britten – Ligeti.

Theory of Western Music.
1.     Writing and Reading music
·       Basic elements of Western Music: Pitch - Rythym – Dynamic - Timbre – Texture
·       Note duration
2.  Harmony, Melody and Rhythm 
3.  Dynamics and emotions (Relative loudness, Gradual changes "Crescendo & Diminuendo”, Sudden changes and accented notes)
4. Musical Instruments:  CLASIFICATION
 
Music Appreciation.
1.     Introduction – Music as language.
·       Definitions and debate.
2.  The limits of the sound. – The border between sound and noise.
·       Noise
·       Futurism
·       Musical noise, RUSSOLO
·       Parade Ballet
·       Stockhausen – Cage and Ligeti
·       Noise as music


Western Music II
Goa University
Prof. Santiago Lusardi girelli
Anthony Gonzalves cHAIR


 
"Music expresses that which cannot be said and on which it is impossible to be silent."
 
Victor Hugo, French writer
 
 
What do you think art is?
Write down a definition of art?

Art is a diverse range of human activities and the products of those activities looking for beauty.
Art…
the expression or application of human creative skill and imagination, typically in a visual form such as painting or sculpture, producing works to be appreciated primarily for their beauty or emotional power.


Subjects of study primarily concerned with human creativity and social life, such as languages, literature, and history (as contrasted with scientific or technical subjects).
Example:
The belief that the arts and sciences were incompatible
The Faculty of Arts

A skill at doing a specified thing, typically one acquired through practice: the art of conversation





Liberal arts

Modern Liberal Arts

What is to be an artist?


Write a definition using 3 to 4 words.
To be an Artist
The artist is the person who makes or produces artwork. What is meant by artist comes from the lexical family of the word art.

Given the changing meaning of the concept art, the term artist can only be defined or studied from a historical point of view. It depends on the aesthetic ideas of the time.
To be an artist
In the artist almost assumed a particularly sensitive disposition toward the world around him, leading him to produce works of art. The artist is an individual who has developed both its creativity and the ability to communicate, through good use of the talent and the technical (the word derives from τέχνη Greek art (techne).
Am I?
I´m free?


MUSIC -
All the universe is an immense symphony.




  Musica universalis or "music of the spheres" is an ancient philosophical concept that regards proportions in the movements of celestial bodies: the Sun, Moon, and planets - as a form of music.


Harmony
In music, harmony is the use of simultaneous pitches (tones, notes), or chords.[1 The study of harmony involves chords and their construction and chord progressions and the principles of connection that govern them.
Harmony is often said to refer to the "vertical" aspect of music, as distinguished from melodic line, or the "horizontal" aspect.
Counterpoint, which refers to the interweaving of melodic lines, and polyphony, which refers to the relationship of separate independent voices, are thus sometimes distinguished from harmony.



Harmony
In music, harmony is the use of simultaneous pitches (tones, notes), or chords.[1 The study of harmony involves chords and their construction and chord progressions and the principles of connection that govern them.
Harmony is often said to refer to the "vertical" aspect of music, as distinguished from melodic line, or the "horizontal" aspect.
Counterpoint, which refers to the interweaving of melodic lines, and polyphony, which refers to the relationship of separate independent voices, are thus sometimes distinguished from harmony.
Origins of polyphony 

Perotin
Pérotin (1200), also called Perotin the Great, was a European composer, believed to be French, who lived around the end of the 12th and beginning of the 13th century. He was the most famous member of the Notre Dame school of polyphony and the ars antiqua style. He was one of very few composers of his day whose name has been preserved, and can be reliably attached to individual compositions; this is due to the testimony of an anonymous English student at Notre Dame known as Anonymous IV, who wrote about him and his predecessor Léonin.



Medieval Music
Medieval music was both sacred and secular.  During the earlier medieval period the liturgical genre, predominantly Gregorian chant, was monophonic.

Polyphonic genres began to develop during the high medieval era, becoming prevalent by the later 13th and early 14th century.
Gregorian Chant
Gregorian chant, monophonic, or unison, liturgical music of the ROMAN Catholic Church, used to accompany the text of the mass and the canonical hours, or divine office. Gregorian chant is named after St. Gregory I, during whose papacy (590–604) it was collected and codified.
Perspective and Poliphony


The perspective In the year 1000 an excentric mathematician, Alhazán, was the first to recognize that we see an object because each point of it directs and reflects a ray into the eye, so that the cone of rays that come from the outline and shape of my hand grows smaller as I move my hand away. And if I move my hand towards you the cone of rays that enter your eye becomes larger and subtends a larger angle and that and only that acounts for the difference in size. It´s a simple notion that it is astoshing that the scientists didn´t notice it for 600 years, but artists did it almost at once: the concept of the cone of rays of the object to the eye becomes the foundation of perspective. And perspective is the new idea which now vivifies mathematics. The perspective passed into arts in North Italy, in Florence and Venice in the XV century.












Schoenberg's approach, both in terms of harmony and development, is among the major landmarks of 20th-century musical thought; at least three generations of composers in the European and American traditions have consciously extended his thinking or, in some cases, passionately reacted against it. During the rise of the Nazi Party in Austria, his music was labeled as degenerate art.

Schoenberg was widely known early in his career for his success in simultaneously extending the traditionally opposed German Romantic styles of Brahms and Wagner. Later, his name would come to personify pioneering innovations in atonality (although Schoenberg himself detested the term "atonality" as inaccurate in describing his intentions) that would become the most polemical feature of 20th-century art music. In the 1920s, Schoenberg developed the twelve-tone technique, a widely influential compositional method of manipulating an ordered series of all twelve notes in the chromatic scale.
Musique concrète
 is a form of electroacoustic music that is made in part from acousmatic sound. In addition to sounds derived from musical instruments or voices, it may use other sources of sound such as electronic synthesizers or sounds recorded from nature. Also, compositions in this idiom are not restricted to the normal musical rules of melody, harmony, rhythm, metre and so on. Originally contrasted with "pure" elektronische Musik (based solely on the production and manipulation of electronically produced sounds rather than recorded sounds), the theoretical basis of musique concrète as a compositional practice was developed by Pierre Schaeffer, beginning in the early 1940s.


 Technological advances led to the birth of electronic music. Experimentation with tape loops and repetitive textures contributed to the advent of minimalism. Still other composers started exploring the theatrical potential of the musical performance (performance art, mixed media, fluxus).




Eric Withacre
Is an American Grammy Award-winning composer and conductor. In 2008, the all-Whitacre choral CD Cloudburst (released by the British ensemble Polyphony on Hyperion Records) became an international best-seller, topping the classical charts and earning a Grammy nomination. In addition to Whitacre's litany of choral and wind ensemble compositions, he is also known for his "Virtual Choir" projects, bringing individual voices from around the globe together into an online choir.

Western Music II
Goa University
Prof. Santiago Lusardi girelli
Anthony Gonzalves cHAIR
Round Table
Social Musical Projects.




Western Music II
Goa University
Prof. Santiago Lusardi girelli
Anthony Gonzalves cHAIR


Western Music II
Goa University
Prof. Santiago Lusardi girelli
Anthony Gonzalves cHAIR


 
"Music expresses that which cannot be said and on which it is impossible to be silent."
 
Victor Hugo, French writer
 
 
What do you think art is?
Write down a definition of art?

Art is a diverse range of human activities and the products of those activities looking for beauty.
Art…
the expression or application of human creative skill and imagination, typically in a visual form such as painting or sculpture, producing works to be appreciated primarily for their beauty or emotional power.


Subjects of study primarily concerned with human creativity and social life, such as languages, literature, and history (as contrasted with scientific or technical subjects).
Example:
The belief that the arts and sciences were incompatible
The Faculty of Arts

A skill at doing a specified thing, typically one acquired through practice: the art of conversation





Liberal arts

Modern Liberal Arts
Modern Liberal Arts

What is to be an artist?


Write a definition using 3 to 4 words.
To be an Artist
The artist is the person who makes or produces artwork. What is meant by artist comes from the lexical family of the word art.

Given the changing meaning of the concept art, the term artist can only be defined or studied from a historical point of view. It depends on the aesthetic ideas of the time.
To be an artist
In the artist almost assumed a particularly sensitive disposition toward the world around him, leading him to produce works of art. The artist is an individual who has developed both its creativity and the ability to communicate, through good use of the talent and the technical (the word derives from τέχνη Greek art (techne).
Am I?
I´m free?


MUSIC -
All the universe is an immense symphony.










  Musica universalis or "music of the spheres" is an ancient philosophical concept that regards proportions in the movements of celestial bodies: the Sun, Moon, and planets - as a form of music.








Harmony
In music, harmony is the use of simultaneous pitches (tones, notes), or chords.[1 The study of harmony involves chords and their construction and chord progressions and the principles of connection that govern them.
Harmony is often said to refer to the "vertical" aspect of music, as distinguished from melodic line, or the "horizontal" aspect.
Counterpoint, which refers to the interweaving of melodic lines, and polyphony, which refers to the relationship of separate independent voices, are thus sometimes distinguished from harmony.






Western Music II
Goa University
Prof. Santiago Lusardi girelli
Anthony Gonzalves cHAIR






Harmony
In music, harmony is the use of simultaneous pitches (tones, notes), or chords.[1 The study of harmony involves chords and their construction and chord progressions and the principles of connection that govern them.
Harmony is often said to refer to the "vertical" aspect of music, as distinguished from melodic line, or the "horizontal" aspect.
Counterpoint, which refers to the interweaving of melodic lines, and polyphony, which refers to the relationship of separate independent voices, are thus sometimes distinguished from harmony.
Origins of polyphony 

Perotin
Pérotin (1200), also called Perotin the Great, was a European composer, believed to be French, who lived around the end of the 12th and beginning of the 13th century. He was the most famous member of the Notre Dame school of polyphony and the ars antiqua style. He was one of very few composers of his day whose name has been preserved, and can be reliably attached to individual compositions; this is due to the testimony of an anonymous English student at Notre Dame known as Anonymous IV, who wrote about him and his predecessor Léonin.



Medieval Music
Medieval music was both sacred and secular.  During the earlier medieval period the liturgical genre, predominantly Gregorian chant, was monophonic.

Polyphonic genres began to develop during the high medieval era, becoming prevalent by the later 13th and early 14th century.
Gregorian Chant
Gregorian chant, monophonic, or unison, liturgical music of the ROMAN Catholic Church, used to accompany the text of the mass and the canonical hours, or divine office. Gregorian chant is named after St. Gregory I, during whose papacy (590–604) it was collected and codified.
Perspective and Poliphony


The perspective In the year 1000 an excentric mathematician, Alhazán, was the first to recognize that we see an object because each point of it directs and reflects a ray into the eye, so that the cone of rays that come from the outline and shape of my hand grows smaller as I move my hand away. And if I move my hand towards you the cone of rays that enter your eye becomes larger and subtends a larger angle and that and only that acounts for the difference in size. It´s a simple notion that it is astoshing that the scientists didn´t notice it for 600 years, but artists did it almost at once: the concept of the cone of rays of the object to the eye becomes the foundation of perspective. And perspective is the new idea which now vivifies mathematics. The perspective passed into arts in North Italy, in Florence and Venice in the XV century.



 

Schoenberg's approach, both in terms of harmony and development, is among the major landmarks of 20th-century musical thought; at least three generations of composers in the European and American traditions have consciously extended his thinking or, in some cases, passionately reacted against it. During the rise of the Nazi Party in Austria, his music was labeled as degenerate art.

Schoenberg was widely known early in his career for his success in simultaneously extending the traditionally opposed German Romantic styles of Brahms and Wagner. Later, his name would come to personify pioneering innovations in atonality (although Schoenberg himself detested the term "atonality" as inaccurate in describing his intentions) that would become the most polemical feature of 20th-century art music. In the 1920s, Schoenberg developed the twelve-tone technique, a widely influential compositional method of manipulating an ordered series of all twelve notes in the chromatic scale.
Musique concrète
 is a form of electroacoustic music that is made in part from acousmatic sound. In addition to sounds derived from musical instruments or voices, it may use other sources of sound such as electronic synthesizers or sounds recorded from nature. Also, compositions in this idiom are not restricted to the normal musical rules of melody, harmony, rhythm, metre and so on. Originally contrasted with "pure" elektronische Musik (based solely on the production and manipulation of electronically produced sounds rather than recorded sounds), the theoretical basis of musique concrète as a compositional practice was developed by Pierre Schaeffer, beginning in the early 1940s.



 

 Technological advances led to the birth of electronic music. Experimentation with tape loops and repetitive textures contributed to the advent of minimalism. Still other composers started exploring the theatrical potential of the musical performance (performance art, mixed media, fluxus).




Eric Withacre
Is an American Grammy Award-winning composer and conductor. In 2008, the all-Whitacre choral CD Cloudburst (released by the British ensemble Polyphony on Hyperion Records) became an international best-seller, topping the classical charts and earning a Grammy nomination. In addition to Whitacre's litany of choral and wind ensemble compositions, he is also known for his "Virtual Choir" projects, bringing individual voices from around the globe together into an online choir.

Western Music II
Goa University
Prof. Santiago Lusardi girelli
Anthony Gonzalves cHAIR
Round Table
Social Musical Projects.







ARTISTIC MANIFESTO

“A manifesto is a communication made to the whole world, whose only pretension is to the discovery of an instant cure for political, astronomical, artistic, parliamentary, agronomical and literary syphilis.
It may be pleasant, and good-natured, it's always right, it's strong, vigorous and logical.

Tristan Tzara's explanation of the manifesto 
Write down your oun Artistic Manifiesto in 5 points commenting which should be the limits or beauty and Sound for you.

Aesthetics / Limits of the creativity / Own definition of Art and Beauty / Philosophical ideas that would inspire you /

Steps

Give some thought to what you want your manifiset to be like.
Write a list of statements - This is often called a laundry list because it's not in any particular order and includes everything you can think of.
Think of a way to reduce these statements to a few words that applies to all of them. You can think of this as a sort of motto. Some examples are "Live in the moment," "Have courage" or "Go boldly into the future.”Use your motto as the title of your manifesto, and arrange your laundry list into a few well-crafted paragraphs.

FUTURIST MANIFESTO

Conclusions

•Futurist composers should use their creativity and innovation to "enlarge and enrich the field of sound”by approaching the "noise-sound.”

Futurist musicians should strive to replicate the infinite timbres in noises.

Futurist musicians should free themselves from the traditional and seek to explore the diverse rhythms of noise.

The creation of instruments that replicate noise should not be a difficult task, since the manipulation of pitch will be simple once the mechanical principles that create the noise have been recreated. Pitch can be manipulated through simples changes in speed or tension. Strive for simplicity and clarity rather than trying to be artistic or poetic.

•The new orchestra will not evoke new and novel emotions by imitating the noises of life, but by finding new and unique combinations of timbres and rhythms in noise, to find a way to fully express the rhythm and sound that stretches beyond normal un-inebriated comprehension.

•The variety of noise is infinite, and as man creates new machines the number of noises he can differentiate between continues to grow.

•Therefore, he invites all talented musicians to pay attention to noises and their complexity, and once 
 They discover the broadness of noise's palette of timbres, they will develop a passion for noise.
Roussolo predicts that our "multiplied sensibility, having been conquered by futurist eyes, will finally have some futurist ears, and . . . every workshop will become an intoxicating orchestra of noise.”





Borders between sound and noise -  Class 3






COURSE OUTLINE

OPENING CONFERENCES.

1.  Philosophical Ideas of Western Music I: Introduction: The Ancient Western Music
2.  Philosophical Ideas of Western Music II: Goodness, Beauty & Truth.
3.  Philosophical Ideas of Western Music V: Goodness – Music Therapy and Sacred Music.
4.  Philosophical Ideas of Western Music III: Beauty  - Looking for the perfect proportion in Arts.
5.  Philosophical Ideas of Western Music IV: Truth – Sciences and music.
LECTURES.
1.  Origins of the Western Music - Ancient Greek Music
2.  Vocal Music – The Human Expression.
3.  Instrumental Music - Music beyond words
4.  Choral Symphonic Music - The greatness of the human spirit
5.  Contemporary Music and New Music - Creativity of the human spirit always makes its way
MUSIC ELEMENTS.
1.  Writing and Reading music
2.  Harmony, Melody and Rhythm
3.   Dynamics and emotions
4.   The tonal system of Western Music
MUSIC APPRECIATION.
1.  Introduction – Music as language.
2.  The limits of the sound. – The border between sound and noise.
3.  The Social Psychology of Music - The social role of music.
4.  Basic elements for understanding and critique of a concert.
5.  New avenues of research in Western music.
ROUND TABLES
1.   Western Music and Social Musical Projects. Experiences.
2.   Western Music in dialogue with Painting and Music Composition: The will to create.
3.   Western Music in Dialogue with Eastern Philosophy.
4.   Western Music in Dialogue with Indian Music.
5.   Western Music in Dialogue with Cinema and Contemporary Arts - The limits of Beauty.
Revision, Lecture, Auditions, Round Table (Western Music in Dialogue with Arts). Videos and auditions, Activity. Closing words and homework.

Music expresses that which cannot be said and on which it is impossible to be silent. 
-Victor Hugo­-






GOA UNIVERSITY
DEPARTMENT OF MANAGEMENT
Course ONB-101

WESTERN MUSIC IN DIALOGUE WITH THE ARTS, HISTORY AND PHILOSOPHY
Professor Santiago Lusardi Girelli
Anthony Gonsalves Chair - GOA UNIVERSITY



Music expresses that which cannot be said and on which it is impossible to be silent. 
-Victor Hugo­-



Class 1 –  Saturday 11/01/14

Readings for Class 2   18/01/14  - Western Music II 


Philosophy and Science of Music in Ancient Greece:
The Predecessors of Pythagoras and their Contribution

http://www.emis.de/journals/NNJ/Pont-v6n1.html#anchor153629



INTRODUCTION
One of the ironies of twentieth-century thought is that the final dethronement of Pythagoras as a 'father' of western science and philosophy and the 'inventor' of music and mathematics should be accompanied by a world-wide revival of Pythagorean research and speculation. During the seventeenth century, the 'harmony of the spheres', which had remained an article of faith until the age of Shakespeare and even Louis XIV [Isherwood 1973, Ch. 1], was suddenly overwhelmed by the mighty discoveries of Kepler and Newton; but this traumatic 'Untuning of the Sky' [Hollander 1970] did not entirely obliterate the Pythagorean tradition (to which both Kepler and Newton were sympathetic).
Since the pioneering studies of Thomas Taylor (1758-1835), Antoine Fabre d'Olivet (1767-1825) and Albert von Thimus (1806-1878), there has been a steady renewal of interest in the old science of harmonics, culminating in the work of Hans Kayser (1891-1964) and his two most influential successors, Rudolf Haase and Ernest G. McClain (both of whom are living in retirement). Neo-pythagoreanism is now a conspicuous feature of post-modern philosophy and science: the revival of musica speculativa, part of a larger resurgence of neo-classicism, is well represented in the writings of Joscelyn Godwin [Godwin 1987, 1993, etc.]. To his extensive bibliographies could be added not only impressive results of recent mainstream research into Pythagoras and the Pythagoreans, e.g., Huffman [1993], but also the publications of several 'alternative' thinkers, including the French-American composer, music theorist, and astrologer, Dane Rudhyar, the French 'neo-astrologer' Michel Gauquelin, the English numerologist John Michell, and the English geneticist Rupert Sheldrake. Sheldrake's notion of 'morphic resonance' -- forms resonating in Nature's memory -- is a very Pythagorean-Platonic alternative to mechanistic causality. His wife, Jill Purce, is a music therapist [Purce 1974]; so both sides of the Pythagorean tradition -- the 'hard' and the 'soft' sciences -- are here reunited in the work of one family.
Though hardly any of these writers would describe themselves as Pythagoreans, their ideas have important connections with the old tradition and all are symptomatic of a new era in the history of thought when mechanistic and reductionist paradigms are giving way to a holistic and organic world-view. This emergent rationality is fundamentally ecological and its impact is being felt from metaphysics to everyday manners. The new paradigms of the Age of Ecology are already transforming the professions, sciences, arts, academic disciplines, and human enterprises generally -- from the minute study of bird-song and insect music to the utopian vision of planet Earth designed and managed as a single, organic Gesamtkunstwerk [Pont 1997].
Central to this new understanding of the world is the concept of the 'Biosphere', which is the very antithesis of Newton's mechanistic universe [Teilhard de Chardin 1955]. Thus the Pythagorean vision of the living cosmos -- or Plato's 'World Soul' -- has reappeared in new vitalist theories, including the Gaia hypothesis of James E. Lovelock [1979]. The modern world-view and its vast astronomical time-frame have changed our conception of humanity itself, if only in recognising our evolutionary affiliations with, and biological dependence on, other species in the terrestrial ecosystem. And it has also transformed the idea of the 'humanities': never again can they be taught as just a narrow study of the 'classical' texts or litterae humaniores of Greece, Rome, and the Renaissance. No longer can the ancient Greeks be contemplated, in museum-like isolation, as perfect models of everything European.
With the growth of modern archaeology, prehistory, anthropology, linguistics, and other comparative studies, the marmoreal idols of Eurocentric scholarship are now revealed in something like their original gaudy splendour -- a Joseph's coat of distinctly oriental hues. Most of the discoveries traditionally ascribed to Pythagoras were Asiatic in origin; and, in a recent survey, Music and Musicians in Ancient Greece [Anderson 1994], the Pythagoreans have been reduced to four passing references and Pythagoras himself is omitted altogether!
The innovations still plausibly credited to the historical Pythagoras include the coining of the terms 'philosophy' and 'theory' which, in his case, must have referred to the dogmatic teachings and pre-scientific wisdom of a guru rather than genuinely theoretical inquiries like those of Heraclitus and the Eleatics. Pythagoras was also credited with inventing the term Kosmos, but the idea of the beautiful world-order (above and below) must surely have been Egyptian in origin [Cf. Plato, Laws II, 656a-657b]. Our admiration of the Greeks is now tempered by a better understanding of their true historical circumstance and actual indebtedness to other civilisations [Cf. Bernal 1987].
Just as Whitehead saw western philosophy as 'a series of footnotes to Plato', so modern scholarship has established that most of the doctrines traditionally ascribed to Pythagoras were really the contributions of the older high civilisations, particularly of Mespotamia and Egypt.[1] The rise and dissemination of these perennially influential doctrines remains one of the most formidable problems for the historian of ideas.
Many of these ideas had already been explored in my General Studies courses at the University of New South Wales, particularly in 'The Philosophy of Music' (Australia's first academic course on the subject, 1974-1988) and, more recently, in shorter courses on 'Ancient Rationality' and 'Modern Rationality' (1988-1995). It was with their arguments and conclusions in mind that I undertook during 1997 my last course at the University, entitled 'The Predecessors of Pythagoras'. This aimed to examine the origins and analogies of Pythagorean traditions in Mesopotamia, Egypt, China, and India. The lectures contained little that was new and the literature survey was, unavoidably, far from exhaustive; but, even so, the course had the unintended effect of changing the lecturer's point of view -- and, indeed, his whole approach to Greek philosophy and science of music.
Instead of burdening the class with the meagre texts of the early Pythagorean school and the interminable difficulties of their interpretation, lectures took a broad view of ancient history and prehistory, in an attempt to answer two very large and necessarily speculative questions: first, what might have been the origins of the famous 'analogy of the macrocosm and the microcosm'? And, second, how and when was this world-view 'mathematised'? -- that is, when was it precisely articulated with a system of musical numbers or harmonic ratios that eventually constituted the 'harmony of the spheres'? Most of the fifteen students had some background in history and philosophy of science but no prior musical knowledge was required for the course and readings had to be confined to material available in English. The only set text was The Pythagorean Sourcebook and Library [Guthrie 1987].

AS ABOVE SO BELOW
The division of the world into different levels (upper, middle, lower or Heaven, Earth and Hell) goes back to the prehistoric shamans who practised their magic for thousands of years before the appearance of organised religion. As F.M. Cornford [1952] and Mircea Eliade [1964] have made clear, the magical powers ascribed to Orpheus, Pythagoras, and other pre-Socratic sages (even Socrates himself) were recognisably shamanic [Cornford 1952, 107ff].[2] These included the art of healing through music; of communicating with and taking the form of other animals, especially birds [Guthrie 1987, 71, 127]; the ability to fly and to appear in two places at once;[3] and the Orphic control of human passions, brute animals and nature itself. Early biographers repeated stories of how Pythagoras 'chased away a pestilence, suppressed violent winds and hail, calmed storms both on rivers and on seas…' [Guthrie 1987, 70ff., 128-9].

Thus we arrived at a tentative answer to our first grand question: the 'analogy of the macrocosm and the microcosm' was the classical Greek formulation of a world-view that was prehistoric in origin. The late classical image of Urania dancing in the chorus of the Muses surely recalls the archaic astral dance which finally became the annual liturgy or song and dance of the Church, while achieving concrete form in the ziggurats of Mesopotamia and the pyramids of Egypt.

THE HARMONY OF THE SPHERES
The mathematisation of this primitive world-view obviously came much later, probably after the 'neolithic revolution' and the emergence of the first villages and towns was made possible by herding and agriculture. It was sometime during the era of civilisation -- the culture of cities -- that the old mimetic relationship between the larger universal system and the local human order was transformed into a precise mathematical analogy; that is, the heavenly order came to be seen as a harmony or attunement controlled by number and the earthly order was accordingly formed on, adjusted to, or interpreted in accordance with the same number system, which was duodecimal, not decimal. This, the oldest known mathematical cosmology, may have been suggested by the use of simple numbers in choreography, primarily the first few integers which are still used to measure rhythm today (1, 2, 3, 4, 6, 8, 9, 12). Thus the 'analogy of the macrocosm and microcosm' became the 'harmony of the spheres' when the earthly imitation of the heavenly dance was finally reinterpreted as a system of harmonic proportions shared by macrocosm and microcosm (both of which were still conceived as vital organisms).
The bold and ingenious hypothesis that the world was a harmony, a cosmos ordered on the proportions of the musical scale,[9] must have been invented by someone -- a very sophisticated thinker, indeed; but the identity and whereabouts of that Asiatic Pythagoras are also lost in time. The evidence points first to Babylon and then, second, to Egypt [10] -- to the very countries where the historical Pythagoras is said to have studied and where, presumably, he acquired the science of the monochord.
Descripción: he monochordIt has long been understood that the monochord, or kanon, played a central role in the philosophy of Pythagoras and Plato, but the early history of the instrument and its use in scientific theory and philosophical speculation are very poorly documented. Pythagoras, on his death-bed, is said to have recommended the study of the monochord to his disciples; and Plato in effect did the same -- if he really was responsible for the argument of the Epinomis, a kind of appendix or key to his last dialogue, the Laws (the imperfect text is thought to have been penned by his secretary, Philippus of Opus). The Epinomis is the only writing in the entire Platonic corpus that specifically alludes to the harmonic analogia or tuning module of 6:8::9:12 [Epinomis 991a-b], but at this very point, unfortunately, the text is obscure or corrupt!

MONOCHORD MATHEMATICS
Analogia means 'equality of ratios' or 'proportion' but the analogia is the module or system of whole-number ratios that gives the 'divisions of the monochord', the precise points at which the vibrating string can be stopped, with a movable bridge, to sound the 'fixed' or fundamental intervals of the musical scale, the octave (2:1); the fifth (3:2); the fourth (3:4); and the major tone (8:9). The integers 6, 8, 9 and 12 are the smallest whole numbers with which the symmetrical system of interlocking ratios -- the natural framework of the ancient and modern diatonic scales -- can be expressed. Just as the Greeks admitted that their lyre was a foreign invention (brought to their land by the winged messenger Mercury or, some say, by Pythagoras), so they knew that the tuning system of Mercury's lyre, 6:8::9:12, was also imported -- presumably from Babylon, where the precise relationship between pitch, string -- length and numerical proportion could have been discovered a thousand or even two thousand years before Pythagoras (indeed almost any time during the first three or four millennia of the harp's development).
The oldest surviving book on the monochord and its divisions was written by Euclid (c.300 BC) but the instrument itself was obviously much older. Its early use and significance have been greatly illuminated by Ernest G. McClain, first with The Myth of Invariance [1976] and then with The Pythagorean Plato [1978]. Neither a classical scholar nor a mathematician, in the ordinary sense, McClain was a professor of the clarinet at Brooklyn College, New York. Endowed with a rare combination of musical and philosophical intelligence -- and a virtuoso's grasp of tuning theory and practice -- he went in search of the ancient wisdom, inspired by like-minded colleagues including Ernst Levy and Antonio T. de Nicolas. Developing insights of Robert S. Brumbaugh as well, McClain made an 'intellectual breakthrough of the utmost significance' by offering a simple musical explanation of 'crucial passages in texts of world literature -- the Rg Veda, the Egyptian Book of the Dead, the Bible, Plato -- that have defied critics of the separate concerned disciplines' [Levarie 1976, xi ff.]. McClain's method was not new in principle but his development and application of it has produced amazing results.
Taking the numbers used in or derived from monochord tuning, McClain identified their widespread employment in numerical allegories, myths, and metaphors found in some of the oldest books in the world. For example, when Plato characterised the good man as 'living 729 times more pleasantly, and the tyrant more painfully by this same interval' (Republic 587e), he used the number which defines the tritone (the sixth power of three; that is, 6/5 above the fundamental tone). Thus the tension between the good man and the tyrant is compared to the worst possible dissonance in the western musical system (Plato's model here, incidentally, is both musical and geometrical). Similarly, McClain decoded many other musical allegories and discovered the meaning of some incredibly large numbers in Babylonian, Egyptian, Hindu, Greek, and Hebrew texts. In The Pythagorean Plato, he applied the same method to Plato's numerology and produced a simple, consistent and comprehensive explanation of allegorical texts that had defeated five hundred years of classical scholarship.
Though in fact a corollary to his first book, The Pythagorean Plato [1978] is much more approachable for the general reader. The introduction explains the basics of tuning theory and the graphic use of the monochord string turned into a tonal circle on which any scale can be represented geometrically. Seven of Plato's numerical allegories are then analysed in detail showing, for example, how his political theory was modeled on musical theory, with the constitutions of Callipolis, Athens, Atlantis and Magnesia corresponding to four different 'temperaments' or tuning systems (including the equally tempered scale, long considered to be a modern invention).
The key to Plato's musico-political analogies is here revealed for the first time, and they were by no means an idiosyncratic jest: the Greek word syntagma can refer to either a political or a musical system, just as the Sanskrit grama can denote a village or a scale [Rudhyar 1982, 14]. In Classical and Christian Ideas of World Harmony, written during the 1940s, Leo Spitzer set out to explain the compound meanings of the German Stimmung and discovered its relations with a whole gamut of harmonic terms resonating through the European languages [Spitzer 1963]. On purely philological grounds, Spitzer divided these terms into two groups: first, those related to 'chord' -- 'concord', 'accord', etc. -- and, second, those related to 'temperance' -- 'tempo', 'temperament', etc. The two groups correspond fairly well to the distinction between tuning by whole numbers and tempering by small adjustments (involving irrational proportions).
Spitzer was puzzled by the root-meaning of the second group, 'a section cut off' [Spitzer 1963, 82].[11] Of uncertain origin, the variety of the 'tem-' words and their wide distribution throughout the Indo-European languages testify to the existence of a very ancient harmonic world-view or musical cosmology: words like temenos (sacred place), 'temple', 'time', 'template', and 'terminus' all refer to divisions of space and time based, presumably, on a common mathematics -- which must have been musical in origin. Thus comparative philology might yet enable the reconstruction of a 'Pythagorean' cosmology and harmonic technology much older than Pythagoras himself.
The close association of the musical and spatial sciences was independently confirmed by Árpád Szabó in The Beginnings of Greek Mathematics [Szabó 1978, 99ff.], which argues that all the extant terms of pre-Euclidean Greek geometry were derived from music theory or harmonics. For example, 'diastema' means an interval, spatial or musical, just as 'chord' still has a geometrical as well as a musical meaning. The geometrical representation of an interval as a line terminated by vertical strokes could equally be a picture of the monochord string.

TEMPLE HARMONIES
The Predecessors of Pythagoras' now lead us into a brief survey of temple art and architecture and their connections with the science of music. Temples have always been the grandest monuments that man has built in imitation of the heavenly order. Reviewing a continuous tradition of five millennia, Joseph Campbell showed how the form of the temple has remained faithful to the old mandala of circle and square, symbols of Heaven and Earth. The Egyptian hieroglyph for a town is a circle enclosing a St Andrew's cross, with its arms pointing to the minor directions -- a perfect representation of the consecrated enclosure that was subdivided to make the four quarters of the town. Campbell pointed out that the with the rise of the hieratic city-state (c.3500-2500 BC):
…The whole city now (not simply the temple area) is conceived as an imitation on earth of the celestial order -- a sociological middle cosmos, or mesocosm, between the macrocosm of the universe and the microcosm of the individual, making visible their essential form: with the king in the center (either as sun or as mooon, according to the local cult) and an organization of the walled city, in the manner of a mandala, about the central sanctum of the palace and the ziggurat; and with a mathematically structured calendar, furthermore, to regulate the seasons of the city's life according to the passages of the sun and moon among the stars; as well as a highly developed system of ritual arts, including an art of rendering audible to human ears the harmony of the visible celestial spheres. It is at this moment that the art of writing first appears in the world...[ Campbell 1990, 151-2].

The mathematics of temple design fall outside the mainstream of Pythagorean studies but is directly relevant to the harmony of the spheres. If the ancient priests, sages and philosophers were able to discern musical proportions in the heavenly system, would they not have naturally encoded them in their earthly imitations -- just as their predecessors imitated the dance of the stars? A discordance between the macrocosm and the microcosm seems unthinkable but there is as yet no consensus on the ancient use of musical proportions in sacred architecture.

The relationship of dance geometry and the mathematical arts is a living reality in India: in The Square and the Circle of the Indian Arts [1983], dance authority Kapila Vatsyayan explored the connections between sacred dance, geometric mandalas, and temple architecture, illustrating her argument with photographs of ritual dances, some possibly as old as the Rg Veda. All of this confirms Lewis Mumford's great historical insight: his vision of the crucial role in human evolution of 'biotechnics', the arts of brain and body that preceded and made possible the mastery of tools [Mumford 1967, 6ff., 60ff]. Mumford argued that these biotechnics were a critical, though largely overlooked, factor in the prehistoric development of tool technology and the constructive arts. For the early Greeks, and all other preliterate cultures, the most important 'biotechnics' were the musical arts (the arts of the Muses); and this fact alone might be sufficient to explain the extraordinary value placed on musical numbers in the ancient arts and sciences. So, if architecture was indeed 'frozen music' -- the art of building regulated by cosmic measures and musical canons -- then one would expect to find the harmony of the spheres reflected in the temples of that era. Accordingly, John Michell has found cosmic numbers in the dimensions of the pyramids but they do not seem to match McClain's musical numbers! The secrets of the old temple builders remain a fascinating puzzle.
These grander issues, of course, are hardly ever addressed in ordinary musical theory, ancient or modern. The early treatises on Greek music are full of the forbidding technicalities of scales and tuning; and the modern literature is likewise replete with agonising discussions of textual problems and terminological difficulties which intimidate the general reader, repel the practical musician, and frustrate even the most determined scholar. In pursuing the predecessors of Pythagoras we avoided those complications by looking at the Greeks from the other end, so to speak: by viewing them, not as the founding fathers of western art and science but as the heirs of their predecessors in the older civilisations. This longer and larger perspective throws the Greek achievements into sharper focus -- however hazy the details might be. Looking to the West we can immediately discern the distant figure of Pythagoras -- or is it a chorus of Pythagoreans? -- standing at the gateway through which eastern ideas and inventions passed into Europe.
The long shadow of the Master has unjustly obscured other pioneers of Greek musical thought, such as Lasus of Hermione (late sixth century B.C.), who is traditionally credited with writing the first book On Music; a fragment preserves the earliest known musical use of the term 'harmonia'. [Comotti 1989, 25ff.] And, well before Pythagoras, there was another legendary citharode, Terpander, who established an influential school of music at Sparta early in the seventh century. In his final essay, "Pythagoras, Egypt, Sparta", the Dux of the 1997 class, Chad Bochan, identified the Spartans as the immediate predecessors of Pythagoras [12]: the Spartans were geographically the closest of the mainland Greeks to the Egyptians and perhaps the first to imitate their musical system.
This reversing of the temporal perspective also reveals that, for all the effort expended by the Greeks on rhythm and tuning theory, very little of their musical system could have been entirely original.[13] Scholars have long suspected that the diatonic scale had been imported from Asia and superimposed on the native tetrachordal system (another innovation ascribed to Pythagoras) but there was little hard evidence to go on. After centuries of literary exegesis and scholarly debate, new illumination was suddenly obtained from two highly important archeological discoveries.

ARCHAEOLOGY AND ANTHROPOLOGY OF HARMONICS

The first was the unearthing and decoding of the world's earliest known tuning manual, preserved in cuneiform writing on an Old-Babylonian (Akkadian) clay tablet from Ur, dating from the early to middle second millennium B.C. Reading this in the light of other tablets with mathematical and musical texts, an interdisciplinary group of scholars made a conjectural interpretation of the tuning instructions, which they demonstrated on a reproduction lyre (modeled on a genuine instrument of a later period). Assuming that the strings were meant to be tuned in a diatonic system, they found that the instructions made musical sense and yielded 'specific intervals of the diatonic scale familiar to us as traditional western intervals' [Kilmer, et al. 1976]. Their brilliant demonstration of 'Sounds from Silence' is not, of course, a conclusive proof, but it is a profoundly moving experience to hear our ordinary major scale among those performed on the disc recording. If these scholars are right in surmising that the Babylonians knew the modern diatonic system, then the contribution of the Greeks to tuning theory might have been little more than lexicographical![14] This important discovery serves only to reinforce the tradition that it was the Babylonian priests who invented the harmony of the spheres.
The second discovery is the most important ever made in the archeology of music. In 1977, 124 musical instruments were found among some 7,000 burial objects in the tomb of the obscure Marquis Yi, who was buried c. 433 in Zeng, now Hubei Province, west of Nanjing, in the People's Republic of China. The instruments included 65 bronze bells, forming a well-tuned carillon of five octaves, still in playing order. To everybody's astonishment, the bells produced a very accurate, mostly chromatic scale. Cast by a technique unknown to the West, each bell can sound two clear and distinct musical notes which are much purer than those of western bells, and the sound is obtained from a resonator that is a hundred times lighter than its western equivalent! Each bell is inscribed with instructions in gold, explaining the name and function of each note in the scale: a musical Rosetta Stone, no less.
Among those who were most surprised by this find were the Chinese themselves, who were totally unprepared for the discovery of the chromatic scale in their early history, and very slow to make the bells accessible to the wider scholarly world. Almost all memory of a Chinese chromatic scale had been lost, possibly through the burning of musical books and instruments by the Emperor Qin Shiuangdi (She Huang-Ti) who reigned from 221-210 B.C. [McClain 1985, 165]. On one of the first compact disc recordings, the bells perform 'Unique Music of Great Antiquity', which is arbitrarily restricted to the traditional pentatonic scale (China Record Corporation, CCD-89/26, 1989). But the bells are capable of performing tunes in the full diatonic scale, as is shown by later recordings which feature arrangements of western classical music. How long the chromatic scale had been known in ancient China is anybody's guess, but the existence of Marquis Yi's carillon now suggests that there may have been some truth in the legend of the twelve bamboo s (pitch-pipes sounding a twelve-note division of the octave) traditionally ascribed to the mythical 'Yellow Emperor' Huang Di. An elaborate description and analysis of these bells is to be found in Chén Cheng Yih (c.1994).
In a preliminary assessment of Marquis Yi's carillon, Ernest McClain pointed out that 'contemporary fifth century classical Greece, which we are in the habit of venerating, left no artifacts of comparable musical value' [McClain 1985, 171]. The bells confirm that 'the prevailing diatonic pattern in China as well as India, Greece, and Babylon is that of the C major scale or its inverse (Greek Dorian)', as argued by McClain in his book published the year before the discovery of these bells [McClain 1976]. Thus the bells point to a 'tonal cosmology' which anticipates that of Plato and was possibly inherited from Babylon; but, as McClain wisely counsels, the whole subject needs to be re-examined by an 'anthropology educated in the harmonical sciences of the ancient world', before any firm conclusions can be drawn on the early history of tuning theory and the dissemination of harmonic cosmology. Nonetheless, these astounding discoveries have already transformed our understanding of the ancient musical world and our appreciation of its vital continuity with, and enduring contribution to, the arts and sciences of modern civilisation.[15]
The writings of the classical Greeks and their Roman and Arabic successors remain the foundation of western philosophy and science of music, as well as their sometimes problematic applications to architecture and other constructive arts. Much of the Greek theory and practice of harmonics was unquestionably derived from earlier cultures, the still shadowy predecessors of Pythagoras. But, as we come to understand more about the achievements of those predecessors, the actual Greek contribution to musical philosophy and science will seem even more characteristically Hellenic: for here, as in most of the arts and sciences they cultivated, the Greeks created a rational theory, invented a systematic vocabulary, ordered the subject with a logical classification and infused the whole with a spirit of inquiry that still inspires us today.

NOTES

[1] An erudite and forthright critic of the Greeks was William Chappell (1809-1888): "There is no longer room to doubt that the entire Greek system was mainly derived from Egypt, Phoenicia, Babylon, or other countries of more ancient civilization than Greece" [Chappell 1874, 1].

[2] [Cornford 1952, 107ff]. Europe's last distinguished representative of this ancient tradition was probably St Francis of Assisi, whose fits of ecstasy and sermon to the birds (c.1220) are unmistakably shamanic. So are Socrates' 'daemon' (or 'inner voice') and his trances.

[3] From Abaris, his 'Hyperborean' (British?) disciple, Pythagoras obtained a golden arrow that, like the witch's broom, enabled him to fly and appear the same day in two towns separated by 'a journey of many days'. See Guthrie 1987, 90-91, 128.

[4] The story of Pythagoras meditating 'the greater part of day and night' in a cave outside the city of Samos [Guthrie 1987, 62] recalls another familiar practice of the shamans.

[5] Cf. Lawlor 1991, 48. It should be kept in mind that Chatwin's influential book, though based on personal experience of Aboriginal Australia , is a work of literary rather than strictly scientific anthropology.

[6] Some years ago I applied for a major research grant to conduct a comparative and historical study of the Aboriginal Corroboree as the 'indigenous Australian opera'. The application was referred to the two most eminent female anthropologists in the country, one of whom gave the project a top rating for its originality and national significance; the other (who happened to have been trained by the same philosophers who taught me) utterly damned the whole idea, especially with the revelation that I had never attended a corroboree (except, that is, of the imported kind).

[7] They also report a perfect example of 'As above so below': 'Central Australian tribes believed that the Milky Way divided the sky people into two tribes and hence served as a perpetual reminder that a similar division of lands should be observed by local neighbouring tribes' (loc. cit.).

[8] See [Miller 1986], especially Foreword and Chapter 1. Cf. [Doczi 1994, Chapter 4].

[9] For a concise summary of the Pythagorean doctrine and the ancient literary evidence, see [Michaelides 1978,129-30].

[10] Gadalla 2002, 22-3 claims the harmony of the spheres (that is, the 'planetary scale',the melodious movement of the classical 'planets', from Earth to Saturn, and including the Sun and Moon, in the proportions of a diatonic scale) as a purely Egpytian discovery. Fabre d'Olivet had long ago reached a similar conclusion. See Godwin 1993, 347ff.

[11] I once speculated that the root meaning of 'section cut off' referred to the sectio canonis or division of the monochord but this hypothesis over-simplifies what must have been a very protracted history of human invention and social development. Following Abraham Seidenberg, I now think it more likely that the 'tem-' words originally referred to ritual or liturgical procedures of 'cutting off' or delineating sections of space and time as, for example, in the timing of festivals or the reservation of sacred enclosures. Much later the 'tem-' vocabulary was extended to musical theory, as in the terms 'temper' and 'temperament'.

[12] 'In the seventh century… Sparta was the most important musical center of Greece' (Comotti 1989, 17).

[13] The classical Greek music theorists concentrated their efforts on the measurement of melody and rhythm and the development of a fairly precise notation for both (see [Comotti 1989, 110-20]). Their greatest achievement (the significance of which has often been overlooked) was probably the quantitative analysis of the various tribal or regional 'modes' and the codification of their distinctive rhythms and accents. While the Greeks relied heavily on their predecessors in speculative music and tuning systems, their empirical and mathematical studies of contemporary song and dance were the beginning of comparative musicology in the West.

[14] John Curtis Franklin has recently thrown new light on the influence of 'Mesopotamian diatony' on Greek music during the 'orientalising period' (c.750-650 BC). See [Franklin 2002a, 2002b]. r

[15] Even so, one might wonder how long it will take the recent progress in harmonic studies to affect the structure and content of academic courses in music, architecture, mathematics, aesthetics, cultural history, etc.
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v  Bernal, Martin. 1987. Black Athena: the Afroasiatic Roots of Classical Civilization. Vol. I of The Fabrication of Ancient Greece 1785-1985. London: Free Association Books.
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v  Elkin, Adolphus P. 1946. Aboriginal Men of High Degree. Sydney: Australasian Publishing Co.
v  Franklin, John Curtis. 2002a. Terpander: The Invention of Music in the Orientalising Period. Ph.D dissertation. London: University College.
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v  Godwin, Joscelyn. 1987. Harmonies of Heaven and Earth: The Spiritual Dimensions of Music from Antiquity to the Avant-Garde. London: Thames and Hudson.
v  ______. 1993. The Harmony of the Spheres; A Sourcebook of the Pythagorean Tradition in Music. Rochester,VT: Inner Traditions International.
v  Guthrie, Kenneth S., ed. 1987. The Pythagorean Sourcebook and Library; An Anthology of Ancient Writings Which Relate to Pythagoras and Pythagorean Philosophy. Grand Rapids MI: Phanes Press.
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v  Haynes, Raymond, et al. 1996. Explorers of the Southern Sky: A History of Australian Astronomy. Cambridge: Cambridge University Press.
v  Hollander, John, 1970. The Untuning of the Sky: Ideas of music in English poetry, 1500-1700. New York: Norton.
v  Huffman, Carl A. 1993. Philolaus of Croton: Pythagorean and Presocratic. Cambridge: Cambridge University Press.
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Autor. Graham Pont
Newtown, NSW 2042 AUSTRALIA


Lecture 2.

II LECTURE – MIDDLE AGE AND RENAISSANCE MUSIC

IN SEARCH OF GENUINE BEAUTY




Art & Society Should Art Reflect Society?
The Global Crisis, The Role and Meaning of Art in Society



Themes of the Carmina Burana: Medieval and Modern

An Analysis of the Work’s Performance, Practice on Commercial Recordings, Carmina Burana.

Perceptions of beauty in Renaissance art

Lecture 1.

 

The Pythagorean Theory of Music and Color

HARMONY is a state recognized by great philosophers as the immediate prerequisite of beauty. A compound is termed beautiful only when its parts are in harmonious combination. The world is called beautiful and its Creator is designated the Good because good perforce must act in conformity with its own nature; and good acting according to its own nature is harmony, because the good which it accomplishes is harmonious with the good which it is. Beauty, therefore, is harmony manifesting its own intrinsic nature in the world of form.
The universe is made up of successive gradations of good, these gradations ascending from matter (which is the least degree of good) to spirit (which is the greatest degree of good). In man, his superior nature is the summum bonum. It therefore follows that his highest nature most readily cognizes good because the good external to him in the world is in harmonic ratio with the good present in his soul. What man terms evil is therefore, in common with matter, merely the least degree of its own opposite. The least degree of good presupposes likewise the least degree of harmony and beauty. Thus deformity (evil) is really the least harmonious combination of elements naturally harmonic as individual units. Deformity is unnatural, for, the sum of all things being the Good, it is natural that all things should partake of the Good and be arranged in combinations that are harmonious. Harmony is the manifesting expression of the Will of the eternal Good.

THE PHILOSOPHY OF MUSIC

It is highly probable that the Greek initiates gained their knowledge of the philosophic and therapeutic aspects of music from the Egyptians, who, in turn, considered Hermes the founder of the art. According to one legend, this god constructed the first lyre by stretching strings across the concavity of a turtle shell. Both Isis and Osiris were patrons of music and poetry. Plato, in describing the antiquity of these arts among the Egyptians, declared that songs and poetry had existed in Egypt for at least ten thousand years, and that these were of such an exalted and inspiring nature that only gods or godlike men could have composed them. In the Mysteries the lyre was regarded as the secret symbol of the human constitution, the body of the instrument representing the physical form, the strings the nerves, and the musician the spirit. Playing upon the nerves, the spirit thus created the harmonies of normal functioning, which, however, became discords if the nature of man were defiled.
While the early Chinese, Hindus, Persians, Egyptians, Israelites, and Greeks employed both vocal and instrumental music in their religious ceremonials, also to complement their poetry and drama, it remained for Pythagoras to raise the art to its true dignity by demonstrating its mathematical foundation. Although it is said that he himself was not a musician, Pythagoras is now generally credited with the discovery of the diatonic scale. Having first learned the divine theory of music from the priests of the various Mysteries into which he had been accepted, Pythagoras pondered for several years upon the laws governing consonance and dissonance. How he actually solved the problem is unknown, but the following explanation has been invented.
One day while meditating upon the problem of harmony, Pythagoras chanced to pass a brazier's shop where workmen were pounding out a piece of metal upon an anvil. By noting the variances in pitch between the sounds made by large hammers and those made by smaller implements, and carefully estimating the harmonies and discords resulting from combinations of these sounds, he gained his first clue to the musical intervals of the diatonic scale. He entered the shop, and after carefully examining the tools and making mental note of their weights, returned to his own house and constructed an arm of wood so that it: extended out from the wall of his room. At regular intervals along this arm he attached four cords, all of like composition, size, and weight. To the first of these he attached a twelve-pound weight, to the second a nine-pound weight, to the third an eight-pound weight, and to the fourth a six-pound weight. These different weights corresponded to the sizes of the braziers' hammers.
Pythagoras thereupon discovered that the first and fourth strings when sounded together produced the harmonic interval of the octave, for doubling the weight had the same effect as halving the string. The tension of the first string being twice that of the fourth string, their ratio was said to be 2:1, or duple. By similar experimentation he ascertained that the first and third string produced the harmony of the diapente, or the interval of the fifth. The tension of the first string being half again as much as that of the third string, their ratio was said to be 3:2, or sesquialter. Likewise the second and fourth strings, having the same ratio as the first and third strings, yielded a diapente harmony. Continuing his investigation, Pythagoras discovered that the first and second strings produced the harmony of the diatessaron, or the interval of the third; and the tension of the first string being a third greater than that of the second string, their ratio was said to be 4:3, or sesquitercian. The third and fourth strings, having the same ratio as the first and second strings, produced another harmony of the diatessaron. According to Iamblichus, the second and third strings had the ratio of 8:9, or epogdoan.
The key to harmonic ratios is hidden in the famous Pythagorean tetractys, or pyramid of dots. The tetractys is made up of the first four numbers--1, 2, 3, and 4--which in their proportions reveal the intervals of the octave, the diapente, and the diatessaron. While the law of harmonic intervals as set forth above is true, it has been subsequently proved that hammers striking metal in the manner

THE INTERVALS AND HARMONIES OF THE SPHERES.
THE INTERVALS AND HARMONIES OF THE SPHERES.

From Stanley's The History of Philosophy.

In the Pythagorean concept of the music of the spheres, the interval between the earth and the sphere of the fixed stars was considered to be a diapason--the most perfect harmonic interval. The allowing arrangement is most generally accepted for the musical intervals of the planets between the earth and the sphere of the fixed stars: From the sphere of the earth to the sphere of the moon; one tone; from the sphere of the moon to that of Mercury, one half-tone; from Mercury to Venus, one-half; from Venus to the sun, one and one-half tones; from the sun to Mars, one tone; from Mars to Jupiter, one-half tone; from Jupiter to Saturn, one-half tone; from Saturn to the fixed stars, one-half tone. The sum of these intervals equals the six whole tones of the octave.

THE CONSONANCES OF THE MUNDANE MONOCHORD.
THE CONSONANCES OF THE MUNDANE MONOCHORD.

From Fludd's De Musica Mundana.

This diagrammatic sector represents the major gradations of energy and substance between elemental earth and absolute unconditioned force. Beginning with the superior, the fifteen graduated spheres descend in the following order: Limitless and Eternal Life; the superior, the middle, and the inferior Empyrean; the seven planets; and the four elements. Energy is symbolized by Fludd as a pyramid with its base upon the concave surface of the superior Empyrean, and substance as another Pyramid with its base upon the convex surface of the sphere (not planet) of earth. These pyramids demonstrate the relative proportions of energy and substance entering into the composition of the fifteen planes of being. It will be noted that the ascending pyramid of substance touches but does not pierce the fifteenth sphere--that of Limitless and Eternal Life. Likewise, the descending pyramid of energy touches but does not pierce the first sphere--the grossest condition of substance. The plane of the sun is denominated the sphere of equality, for here neither energy nor substance predominate. The mundane monochord consists of a hypothetical string stretched from the base of the pyramid of energy to the base of the pyramid of substance.
described will not produce the various tones ascribed to them. In all probability, therefore, Pythagoras actually worked out his theory of harmony from the monochord--a contrivance consisting of a single string stretched between two pegs and supplied with movable frets.
To Pythagoras music was one of the dependencies of the divine science of mathematics, and its harmonies were inflexibly controlled by mathematical proportions. The Pythagoreans averred that mathematics demonstrated the exact method by which the good established and maintained its universe. Number therefore preceded harmony, since it was the immutable law that governs all harmonic proportions. After discovering these harmonic ratios, Pythagoras gradually initiated his disciples into this, the supreme arcanum of his Mysteries. He divided the multitudinous parts of creation into a vast number of planes or spheres, to each of which he assigned a tone, a harmonic interval, a number, a name, a color, and a form. He then proceeded to prove the accuracy of his deductions by demonstrating them upon the different planes of intelligence and substance ranging from the most abstract logical premise to the most concrete geometrical solid. From the common agreement of these diversified methods of proof he established the indisputable existence of certain natural laws.
Having once established music as an exact science, Pythagoras applied his newly found law of harmonic intervals to all the phenomena of Nature, even going so far as to demonstrate the harmonic relationship of the planets, constellations, and elements to each other. A notable example of modern corroboration of ancient philosophical reaching is that of the progression of the elements according to harmonic ratios. While making a list of the elements in the ascending order of their atomic weights, John A. Newlands discovered at every eighth element a distinct repetition of properties. This discovery is known as the law of octaves in modern chemistry.
Since they held that harmony must be determined not by the sense perceptions but by reason and mathematics, the Pythagoreans called themselves Canonics, as distinguished from musicians of the Harmonic School, who asserted taste and instinct to be the true normative principles of harmony. Recognizing, however, the profound effect: of music upon the senses and emotions, Pythagoras did not hesitate to influence the mind and body with what he termed "musical medicine."
Pythagoras evinced such a marked preference for stringed instruments that he even went so far as to warn his disciples against allowing their ears to be defiled by the sounds of flutes or cymbals. He further declared that the soul could be purified from its irrational influences by solemn songs sung to the accompaniment of the lyre. In his investigation of the therapeutic value of harmonics, Pythagoras discovered that the seven modes--or keys--of the Greek system of music had the power to incite or allay the various emotions. It is related that while observing the stars one night he encountered a young man befuddled with strong drink and mad with jealousy who was piling faggots about his mistress' door with the intention of burning the house. The frenzy of the youth was accentuated by a flutist a short distance away who was playing a tune in the stirring Phrygian mode. Pythagoras induced the musician to change his air to the slow, and rhythmic Spondaic mode, whereupon the intoxicated youth immediately became composed and, gathering up his bundles of wood, returned quietly to his own home.
There is also an account of how Empedocles, a disciple of Pythagoras, by quickly changing the mode of a musical composition he was playing, saved the life of his host, Anchitus, when the latter was threatened with death by the sword of one whose father he had condemned to public execution. It is also known that Esculapius, the Greek physician, cured sciatica and other diseases of the nerves by blowing a loud trumpet in the presence of the patient.
Pythagoras cured many ailments of the spirit, soul, and body by having certain specially prepared musical compositions played in the presence of the sufferer or by personally reciting short selections from such early poets as Hesiod and Homer. In his university at Crotona it was customary for the Pythagoreans to open and to close each day with songs--those in the morning calculated to clear the mind from sleep and inspire it to the activities of the coming day; those in the evening of a mode soothing, relaxing, and conducive to rest. At the vernal equinox, Pythagoras caused his disciples to gather in a circle around one of their number who led them in song and played their accompaniment upon a lyre.
The therapeutic music of Pythagoras is described by Iamblichus thus: "And there are certain melodies devised as remedies against the passions of the soul, and also against despondency and lamentation, which Pythagoras invented as things that afford the greatest assistance in these maladies. And again, he employed other melodies against rage and anger, and against every aberration of the soul. There is also another kind of modulation invented as a remedy against desires." (See The Life of Pythagoras.)
It is probable that the Pythagoreans recognized a connection between the seven Greek modes and the planets. As an example, Pliny declares that Saturn moves in the Dorian mode and Jupiter in the Phrygian mode. It is also apparent that the temperaments are keyed to the various modes, and the passions likewise. Thus, anger--which is a fiery passion--may be accentuated by a fiery mode or its power neutralized by a watery mode.
The far-reaching effect exercised by music upon the culture of the Greeks is thus summed up by Emil Nauman: "Plato depreciated the notion that music was intended solely to create cheerful and agreeable emotions, maintaining rather that it should inculcate a love of all that is noble, and hatred of all that is mean, and that nothing could more strongly influence man's innermost feelings than melody and rhythm. Firmly convinced of this, he agreed with Damon of Athens, the musical instructor of Socrates, that the introduction of a new and presumably enervating scale would endanger the future of a whole nation, and that it was not possible to alter a key without shaking the very foundations of the State. Plato affirmed that music which ennobled the mind was of a far higher kind than that which merely appealed to the senses, and he strongly insisted that it was the paramount duty of the Legislature to suppress all music of an effeminate and lascivious character, and to encourage only s that which was pure and dignified; that bold and stirring melodies were for men, gentle and soothing ones for women. From this it is evident that music played a considerable part in the education of the Greek youth. The greatest care was also to be taken in the selection of instrumental music, because the absence of words rendered its signification doubtful, and it was difficult to foresee whether it would exercise upon the people a benign or baneful influence. Popular taste, being always tickled by sensuous and meretricious effects, was to be treated with deserved contempt. (See The History of Music.)
Even today martial music is used with telling effect in times of war, and religious music, while no longer developed in accordance with the ancient theory, still profoundly influences the emotions of the laity.

THE MUSIC OF THE SPHERES

The most sublime but least known of all the Pythagorean speculations was that of sidereal harmonics. It was said that of all men only Pythagoras heard the music of the spheres. Apparently the Chaldeans were the first people to conceive of the heavenly bodies joining in a cosmic chant as they moved in stately manner across the sky. Job describes a time "when the stars of the morning sang together," and in The Merchant of Venice the author of the Shakesperian plays

THE MUNDANE MONOCHORD WITH ITS PROPORTIONS AND INTERVALS.
THE MUNDANE MONOCHORD WITH ITS PROPORTIONS AND INTERVALS.

From Fludd's De Musica Mundana.

In this chart is set forth a summary of Fludd's theory of universal music. The interval between the element of earth and the highest heaven is considered as a double octave, thus showing the two extremes of existence to be in disdiapason harmony. It is signifies that the highest heaven, the sun, and the earth have the same time, the difference being in pitch. The sun is the lower octave of the highest heaven and the earth the lower octave of the sun. The lower octave (Γ to G) comprises that part of the universe in which substance predominate over energy. Its harmonies, therefore, are more gross than those of the higher octave (G to g) wherein energy predominates over substance. "If struck in the more spiritual part," writes Fludd, "the monochord will give eternal life; if in the more material part, transitory life." It will be noted that certain elements, planets, and celestial spheres sustain a harmonic ratio to each other, Fludd advanced this as a key to the sympathies and antipathies existing between the various departments of Nature.
writes: "There's not the smallest orb which thou behold'st but in his motion like an angel sings." So little remains, however, of the Pythagorean system of celestial music that it is only possible to approximate his actual theory.
Pythagoras conceived the universe to be an immense monochord, with its single string connected at its upper end to absolute spirit and at its lower end to absolute matter--in other words, a cord stretched between heaven and earth. Counting inward from the circumference of the heavens, Pythagoras, according to some authorities, divided the universe into nine parts; according to others, into twelve parts. The twelvefold system was as follows: The first division was called the empyrean, or the sphere of the fixed stars, and was the dwelling place of the immortals. The second to twelfth divisions were (in order) the spheres of Saturn, Jupiter, Mars, the sun, Venus, Mercury, and the moon, and fire, air, water, and earth. This arrangement of the seven planets (the sun and moon being regarded as planets in the old astronomy) is identical with the candlestick symbolism of the Jews--the sun in the center as the main stem with three planets on either side of it.
The names given by the Pythagoreans to the various notes of the diatonic scale were, according to Macrobius, derived from an estimation of the velocity and magnitude of the planetary bodies. Each of these gigantic spheres as it rushed endlessly through space was believed to sound a certain tone caused by its continuous displacement of the æthereal diffusion. As these tones were a manifestation of divine order and motion, it must necessarily follow that they partook of the harmony of their own source. "The assertion that the planets in their revolutions round the earth uttered certain sounds differing according to their respective 'magnitude, celerity and local distance,' was commonly made by the Greeks. Thus Saturn, the farthest planet, was said to give the gravest note, while the Moon, which is the nearest, gave the sharpest. 'These sounds of the seven planets, and the sphere of the fixed stars, together with that above us [Antichthon], are the nine Muses, and their joint symphony is called Mnemosyne.'" (See The Canon.)This quotation contains an obscure reference to the ninefold division of the universe previously mentioned.
The Greek initiates also recognized a fundamental relationship between the individual heavens or spheres of the seven planets, and the seven sacred vowels. The first heaven uttered the sound of the sacred vowel Α (Alpha); the second heaven, the sacred vowel Ε (Epsilon); the third, Η (Eta); the fourth, Ι (Iota); the fifth, Ο (Omicron); the sixth, Υ (Upsilon); and the seventh heaven, the sacred vowel Ω (Omega). When these seven heavens sing together they produce a perfect harmony which ascends as an everlasting praise to the throne of the Creator. (See Irenæus' Against Heresies.) Although not so stated, it is probable that the planetary heavens are to be considered as ascending in the Pythagorean order, beginning with the sphere of the moon, which would be the first heaven.
Many early instruments had seven Strings, and it is generally conceded that Pythagoras was the one who added the eighth string to the lyre of Terpander. The seven strings were always related both to their correspondences in the human body and to the planets. The names of God were also conceived to be formed from combinations of the seven planetary harmonies. The Egyptians confined their sacred songs to the seven primary sounds, forbidding any others to be uttered in their temples. One of their hymns contained the following invocation: "The seven sounding tones praise Thee, the Great God, the ceaseless working Father of the whole universe." In another the Deity describes Himself thus: "I am the great indestructible lyre of the whole world, attuning the songs of the heavens. (See Nauman's History of Music.)
The Pythagoreans believed that everything which existed had a voice and that all creatures were eternally singing the praise of the Creator. Man fails to hear these divine melodies because his soul is enmeshed in the illusion of material existence. When he liberates himself from the bondage of the lower world with its sense limitations, the music of the spheres will again be audible as it was in the Golden Age. Harmony recognizes harmony, and when the human soul regains its true estate it will not only hear the celestial choir but also join with it in an everlasting anthem of praise to that Eternal Good controlling the infinite number of parts and conditions of Being.
The Greek Mysteries included in their doctrines a magnificent concept of the relationship existing between music and form. The elements of architecture, for example, were considered as comparable to musical modes and notes, or as having a musical counterpart. Consequently when a building was erected in which a number of these elements were combined, the structure was then likened to a musical chord, which was harmonic only when it fully satisfied the mathematical requirements of harmonic intervals. The realization of this analogy between sound and form led Goethe to declare that "architecture is crystallized music."
In constructing their temples of initiation, the early priests frequently demonstrated their superior knowledge of the principles underlying the phenomena known as vibration. A considerable part of the Mystery rituals consisted of invocations and intonements, for which purpose special sound chambers were constructed. A word whispered in one of these apartments was so intensified that the reverberations made the entire building sway and be filled with a deafening roar. The very wood and stone used in the erection of these sacred buildings eventually became so thoroughly permeated with the sound vibrations of the religious ceremonies that when struck they would reproduce the same tones thus repeatedly impressed into their substances by the rituals.
Every element in Nature has its individual keynote. If these elements are combined in a composite structure the result is a chord that, if sounded, will disintegrate the compound into its integral parts. Likewise each individual has a keynote that, if sounded, will destroy him. The allegory of the walls of Jericho falling when the trumpets of Israel were sounded is undoubtedly intended to set forth the arcane significance of individual keynote or vibration.

THE PHILOSOPHY OF COLOR

"Light," writes Edwin D. Babbitt, "reveals the glories of the external world and yet is the most glorious of them all. It gives beauty, reveals beauty and is itself most beautiful. It is the analyzer, the truth-teller and the exposer of shams, for it shows things as they are. Its infinite streams measure off the universe and flow into our telescopes from stars which are quintillions of miles distant. On the other hand it descends to objects inconceivably small, and reveals through the microscope objects fifty millions of times less than can be seen by the naked eye. Like all other fine forces, its movement is wonderfully soft, yet penetrating and powerful. Without its vivifying influence, vegetable, animal, and human life must immediately perish from the earth, and general ruin take place. We shall do well, then, to consider this potential and beautiful principle of light and its component colors, for the more deeply we penetrate into its inner laws, the more will it present itself as a marvelous storehouse of power to vitalize, heal, refine, and delight mankind." (See The Principles of Light and Color.)
Since light is the basic physical manifestation of life, bathing all creation in its radiance, it is highly important to realize, in part at least, the subtle nature of this divine substance. That which is called light is actually a rate of vibration causing certain reactions upon the optic nerve. Few realize how they are walled in by the limitations

THE THEORY OF ELEMENTAL MUSIC.
THE THEORY OF ELEMENTAL MUSIC.

From Fludd's De Musica Mundana.

In this diagram two interpenetrating pyramids are again employed, one of which represents fire and the other earth. It is demonstrated according to the law of elemental harmony that fire does not enter into the composition of earth nor earth into the composition of fire. The figures on the chart disclose the harmonic relationships existing between the four primary elements according to both Fludd and the Pythagoreans. Earth consists of four parts of its own nature; water of three parts of earth and one part of fire. The sphere of equality is a hypothetical point where there is an equilibrium of two parts of earth and two parts of fire. Air is composed of three parts of fire and one part of earth; fire, of four parts of its own nature. Thus earth and water bear to each other the ratio of 4 to 3, or the diatessaron harmony, and water and the sphere of equality the ratio of 3 to 2, or the diapente harmony. Fire and air also bear to each other the ratio of 4 to 3, or the diatessaron harmony, and air and the sphere of equality the ratio of 3 to 2, or the diapente harmony. As the sum of a diatessaron and a diapente equals a diapason, or octave, it is evident that both the sphere of fire and the sphere of earth are in diapason harmony with the sphere of equality, and also that fire and earth are in disdiapason harmony with each other.
of the sense perceptions. Not only is there a great deal more to light than anyone has ever seen but there are also unknown forms of light which no optical equipment will ever register. There are unnumbered colors which cannot be seen, as well as sounds which cannot be heard, odors which cannot be smelt, flavors which cannot be tasted, and substances which cannot be felt. Man is thus surrounded by a supersensible universe of which he knows nothing because the centers of sense perception within himself have not been developed sufficiently to respond to the subtler rates of vibration of which that universe is composed.
Among both civilized and savage peoples color has been accepted as a natural language in which to couch their religious and philosophical doctrines. The ancient city of Ecbatana as described by Herodotus, its seven walls colored according to the seven planets, revealed the knowledge of this subject possessed by the Persian Magi. The famous zikkurat or astronomical tower of the god Nebo at Borsippa ascended in seven great steps or stages, each step being painted in the key color of one of the planetary bodies. (See Lenormant's Chaldean Magic.) It is thus evident that the Babylonians were familiar with the concept of the spectrum in its relation to the seven Creative Gods or Powers. In India, one of the Mogul emperors caused a fountain to be made with seven levels. The water pouring down the sides through specially arranged channels changed color as it descended, passing sequentially through all shades of the spectrum. In Tibet, color is employed by the native artists to express various moods. L. Austine Waddell, writing of Northern Buddhist art, notes that in Tibetan mythology "White and yellow complexions usually typify mild moods, while the red, blue, and black belong to fierce forms, though sometimes light blue, as indicating the sky, means merely celestial. Generally the gods are pictured white, goblins red, and devils black, like their European relative." (See The Buddhism of Tibet.)
In Meno, Plato, speaking through Socrates, describes color as "an effluence of form, commensurate with sight, and sensible." In Theætetus he discourses more at length on the subject thus: "Let us carry out the principle which has just been affirmed, that nothing is self-existent, and then we shall see that every color, white, black, and every other color, arises out of the eye meeting the appropriate motion, and that what we term the substance of each color is neither the active nor the passive element, but something which passes between them, and is peculiar to each percipient; are you certain that the several colors appear to every animal--say a dog--as they appear to you?"
In the Pythagorean tetractys--the supreme symbol of universal forces and processes--are set forth the theories of the Greeks concerning color and music. The first three dots represent the threefold White Light, which is the Godhead containing potentially all sound and color. The remaining seven dots are the colors of the spectrum and the notes of the musical scale. The colors and tones are the active creative powers which, emanating from the First Cause, establish the universe. The seven are divided into two groups, one containing three powers and the other four a relationship also shown in the tetractys. The higher group--that of three--becomes the spiritual nature of the created universe; the lower group--that of four--manifests as the irrational sphere, or inferior world.
In the Mysteries the seven Logi, or Creative Lords, are shown as streams of force issuing from the mouth of the Eternal One. This signifies the spectrum being extracted from the white light of the Supreme Deity. The seven Creators, or Fabricators, of the inferior spheres were called by the Jews the Elohim. By the Egyptians they were referred to as the Builders (sometimes as the Governors) and are depicted with great knives in their hands with which they carved the universe from its primordial substance. Worship of the planets is based upon their acceptation as the cosmic embodiments of the seven creative attributes of God. The Lords of the planets were described as dwelling within the body of the sun, for the true nature of the sun, being analogous to the white light, contains the seeds of all the tone and color potencies which it manifests.
There are numerous arbitrary arrangements setting forth the mutual relationships of the planets, the colors, and the musical notes. The most satisfactory system is that based upon the law of the octave. The sense of hearing has a much wider scope than that of sight, for whereas the ear can register from nine to eleven octaves of sound the eye is restricted to the cognition of but seven fundamental color tones, or one tone short of the octave. Red, when posited as the lowest color tone in the scale of chromatics, thus corresponds to do, the first note of the musical scale. Continuing the analogy, orange corresponds to re, yellow to mi, green to fa, blue to sol, indigo to la, and violet to si (ti). The eighth color tone necessary to complete the scale should be the higher octave of red, the first color tone. The accuracy of the above arrangement is attested by two striking facts: (1) the three fundamental notes of the musical scale--the first, the third, and the fifth--correspond with the three primary colors--red, yellow, and blue; (2) the seventh, and least perfect, note of the musical scale corresponds with purple, the least perfect tone of the color scale.
In The Principles of Light and Color, Edwin D. Babbitt confirms the correspondence of the color and musical scales: "As C is at the bottom of the musical scale and made with the coarsest waves of air, so is red at the bottom of the chromatic scale and made with the coarsest waves of luminous ether. As the musical note B [the seventh note of the scale] requires 45 vibrations of air every time the note C at the lower end of the scale requires 24, or but little over half as many, so does extreme violet require about 300 trillions of vibrations of ether in a second, while extreme red requires only about 450 trillions, which also are but little more than half as many. When one musical octave is finished another one commences and progresses with just twice as many vibrations as were used in the first octave, and so the same notes are repeated on a finer scale. In the same way when the scale of colors visible to the ordinary eye is completed in the violet, another octave of finer invisible colors, with just twice as many vibrations, will commence and progress on precisely the same law."
When the colors are related to the twelve signs of the zodiac, they are arranged as the spokes of a wheel. To Aries is assigned pure red; to Taurus, red-orange; to Gemini, pure orange; to Cancer, orange-yellow; to Leo, pure yellow; to Virgo, yellow-green; to Libra, pure green; to Scorpio, green-blue; to Sagittarius, pure blue; to Capricorn, blue-violet; to Aquarius, pure violet; and to Pisces, violet-red.
In expounding the Eastern system of esoteric philosophy, H. P, Blavatsky relates the colors to the septenary constitution of man and the seven states of matter as follows:
COLORPRINCIPLES OF MANSTATES OF MATTER
VioletChaya, or Etheric DoubleEther
IndigoHigher Manas, or Spiritual IntelligenceCritical State called Air
BlueAuric EnvelopeSteam or Vapor
GreenLower Manas, or Animal SoulCritical State
YellowBuddhi, or Spiritual SoulWater
OrangePrana, or Life PrincipleCritical State
RedKama Rupa, or Seat of Animal LifeIce
This arrangement of the colors of the spectrum and the musical notes of the octave necessitates a different grouping of the planets in order to preserve their proper tone and color analogies. Thus do becomes Mars; re, the sun; mi, Mercury; fa, Saturn; sol, Jupiter; la, Venus; si (ti) the moon. (See The E. S. Instructions.)

THE FOUR ELEMENTS AND THEIR CONSONANTAL INTERVALS.
THE FOUR ELEMENTS AND THEIR CONSONANTAL INTERVALS.

From Fludd's De Musica Mundana.

In this diagram Fludd has divided each of the four Primary elements into three subdivisions. The first division of each element is the grossest, partaking somewhat of the substance directly inferior to itself (except in the case of the earth, which has no state inferior to itself). The second division consists of the element in its relatively pure state, while the third division is that condition wherein the element partakes somewhat of the substance immediately superior to itself. For example the lowest division of the element of water is sedimentary, as it contains earth substance in solution; the second division represents water in its most common state--salty--as in the case of the ocean; and the third division is water in its purest state--free from salt. The harmonic interval assigned to the lowest division of each element is one tone, to the central division also a tone, but to the higher division a half-tone because it partakes of the division immediately above it. Fludd emphasizes the fact that as the elements ascend in series of two and a half tones, the diatessaron is the dominating harmonic interval of the elements.

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