a n a lo g o s
a s a b o v e, so b e lo w
a s b e lo w, so a b o v e
In ancient times it was believed
that all humans were connected
to the cosmos through vibrations.
Microcosm and macrocosm,
the inner and the outer.
The harmonies with which the universe operated,
the movements of the heavenly bodies
were reflected into music,
thus assigning the seven musical notes to planets:
The 7 step diatonic scale.
Known as Musica universalis,
the ratios of the space between planets
corresponded to those between note intervals.
Fourths, fifths, octaves, etc. (Kepler)
‘all is number’
Quadrivium, the teachings of
Pythagoras of arithmetic, geometry,
harmony and astronomy as one.
The study of the perfection of heavens
was a way of perfecting the
movements of one’s soul.
The Greek mathematical principle that
proportion is built ‘upon’ ana and ‘ratio’ logos.
In this project we revive ideas from ancient charts through performance, condensing the vastness of the universe into a limited space. Such ideas derive from astrological, astronomical, mathematical, and philosophical concepts that permeated human thought for many centuries, as well as spiritual rituals of the ancient Greeks and Indians.
Béla Bartók – Mikrokozmosz
1. Six unison melodies: 1, 3
14. Question and answer
17. Contrary motion
25. Imitation and inversion
34. In Phrygian mode
37. In Lydian mode
48. In Mixolydian mode
59. Major and minor
69. Chord study
73. Sixths and triads
76. Three parts
78. Five-tone scale
86. Two Major Pentachords
György Ligeti – Musica Ricercata:
Sostenuto – Misurato – Prestissimo
Mesto, rigido e cerimoniale
Allegro con spirito
Tempo di valse
Allegro molto capriccioso
Cantabile, molto legato
Olivier Messiaen - Vingt Regards sur l'enfant-Jésus:
VIII. Regard des hauteurs 3‘30’’ minutes
George Crumb – Makrokosmos
I. Primeval Sounds (Genesis I) (Cancer)
II. Proteus (Pisces)
VII. Music of Shadows (for Aeolian Harp) (Libra)
X. Spring-Fire (Aries)
Filippos Raskovic αλας
The aim of this performance is to portray a version the visible universe surrounding us into one limited space, resulting in a fabricated dimension. Ancient civilisations, such as the Greeks or Indians, believed that we are all connected with the universe, ‘as above, so below; as below, so above’, through vibrations, also known as Musica Universalis (the musical harmony of the universe/Pythagoras). Musica Universalis and its aesthetics are recreated using specific sounds and visuals (chosen repertoire and installation of an astrological chart/sky map). The individual/the performer becomes the microcosm, the little world, whom is a part of the surrounding audience/divine energy, the macrocosm/surrounding cosmos. Both dependent on each other, this symmetry between the microcosm and macrocosm (analogos) creates a universal harmony, an exploration of human beings and our space within the universe, as well as an exploration of our space in the performing world as 'classical musicians' for a deeper connection with music.
Astronomy is the study of the heavenly bodies (the sun, moon, planets, and stars); astrology is the belief that the position and movement of the heavenly bodies (planets/stars) influence life on earth. The word astrology (and astronomy) is derived from the Greek word for "star." and the name "planet" comes from the Greek term planētēs, meaning "wanderer", as ancient astronomers noted how certain lights moved across the sky in relation to the other stars.
The two were not always sharply separated, however. In ancient times, they were often closely linked and regarded with equal respect. Astrology originated in Babylon, the Egyptians refined the Babylonian system and the Greeks shaped it into its modern form (today). The ancient Greeks examined the sky very closely. They did more than simply observe and record the movements of the planets, they sought to understand why and how those bodies moved in such an orderly and predictable way. They wanted to find a logical, orderly system for predicting the movements of the sun, moon, and planets, and looked to mathematics and geometry to help discover such a system. Around 270 B.C., the mathematician and astronomer Aristarchus correctly suggested that the sun, not the Earth, is at the centre of the planetary system. He also suggested that the Earth moves around the sun like the other planets, and that it rotates, or spins, on an axis.
Astrology was based on the belief that the heavens and the Earth were connected in an invisible way, and the ancient Greeks believed if the Gods in the heavens ruled a man’s fate, the stars could reveal fortunes, and the motions and location of the stars and planets control the fate of humans. Astrologers, such as Ptolemy, believed that each person’s destiny is determined from birth, that celestial movement shapes human lives, using numbers. Casting horoscopes required considerable astronomical knowledge and mathematical skill. It certainly helped keep astronomy alive, since both astronomy and astrology used the same framework of observation and theories about the heavens.
Astronomy was a branch of mathematics and astronomers sought to create geometrical models that could imitate the appearances of celestial motions. Pythagoreans placed astronomy among the four mathematical arts known as the Quadrivium/study of numbers, (astronomy, arithmetic, geometry, and music), the arts and astrology sharing the common language of mathematics.
Musica Universalis (Universal Music)
An inaudible continuous cosmic music of a rare and exquisite sound (only Pythagoras alone was known to hear it), this music is present everywhere and governs all temporal cycles, such as seasons, biological cycles, and rhythms of nature. At the time, the sun, moon, and planets were thought to revolve around Earth in their proper spheres. The spheres were thought to be related by the whole-number ratios of pure musical intervals, creating musical harmony. Together with its fundamental mathematical laws of proportion it is the sound of the harmony of the created being of the universe.
Johannes Kepler was convinced "that the geometrical things have provided the Creator with the model for decorating the whole world." He attempted to explain the proportions of the natural world, particularly the astronomical and astrological aspects, in terms of music. Kepler discovered physical harmonies in planetary motion. He found that the difference between the maximum and minimum angular speeds of a planet in its orbit approximates a harmonic proportion. For instance, the maximum angular speed of the Earth as measured from the Sun varies by a semitone (a ratio of 16:15). At extremely rare occasions all of the planets sing together in "perfect concord”.
One of the most famous discoveries of Pythagoras is that the chief musical intervals are expressible in simple mathematical ratios between the first four integers; thus, the "Octave=2:1, the fifth=3:2, and the fourth=4:3. These ratios harmonize, not only mathematically but musically - they are pleasing both to the mind and to the ear. They add up to 10, the perfect number, and can be displayed in a triangle; a set of numbers whose relationship with each other seemed to summarize all the inter-dependent harmonies within the universe of space and time.
Pythagoras believed that every planet had a peculiar sound of its own. The celestial bodies (planets, Moon and stars) move according to mathematical equations, producing, by their orbit, a particular note according to its distance from the still centre, Earth (now the Sun). He represented this sound using numbers, more specifically the distance in each case was the same as the ratios of the intervals, and called it the “harmony of the spheres” (Musica Universalis).
(Below) The chart I have created is derived from an astrological chart, divided in 12 equal sections. These sections are then divided by different sized circles, and into half, thirds, and sixths (which represent the exact positions of the cosmic bodies in relation to time). The mathematical proportions created in the chart can also be represented as the intervals of the universe. This chart is to be created through light projections, visible onto the ground, in which the seating will be set up in each section, in exact numbers, according to the size of the space available. The centre is the ruling energy, where the performer/piano is positioned. This is highlighted by a spotlight in the shape of the inner circle of the chart. The rest of the space is to be in complete darkness, creating an illusion of the infinite space.
The repertoire I have chosen reflects on different aspects of aesthetics of this ‘fabricated’ universe. Starting off with Bartok’s Mikrokosmos, a series written for the development of the pianist, from the very beginning; here is the start, the inner development of the individual, which then goes on to Macrocosmos by Crumb, the surrounding cosmos absorbed by the individual. In further depth we then explore Ligeti, whose compositions reflect his obsession with math and musical proportions, the proportions of the universe, and later Messiaen, whose timbre and colours are a unique language in the musical world, the unseen colours of the universe. Philip’s final piece brings us to a final release/conclusion, using a more contemporary sound in which all aesthetics are combined.
NEW STAGES SERIES: ANALOGOS
Performance: February 1st 2019, Angela Burgess Recital Hall, Roya Academy of Muscic