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30 melodies
• 30 melodies or fragments of melodies
come down to us
• A couple are passed down through the
medieval tradition
• Five are preserved on stone inscriptions
• The rest, however, survive on the waste
paper of antiquity -- papyrus
Musical Papirus
• Among the many extraordinary treasures
that have been dug from the sands of Egypt
are the musical papyri: scraps of papyrus
(the ancient equivalent of paper)
containing musical notation.
• Most are very fragmentary, preserving
only a few notes here, a couple of phrases
there
P. Yale CtYBR inv. 4510
the sort of musical notation sometimes used
by professional singers in antiquity
Notation
• the notation is represented by an ancient
Greek alphabet
• ancient musicians had two separate
systems of musical notation, the one meant
for voice, and the other for instruments
P. Mich. 1205r
• This Roman era papyrus contains the sort
of musical notation used by instrumental
musicians in antiquity.
• The papyrus is a fragment from what was
probably a collection of melodies for
performance, perhaps intended for the
ancient aulos, a woodwind not unlike a
modern oboe; or, less likely, the ancient
kithara, the performance version of a lyre.
P. Mich. 1205r,
Papirus on internet
• http://classics.uc.edu/music/index.html
Scales
• In order to have a musical system, scales
were discovered, and from these
foundations the musical systems of all
nations have sprung.
• The scales differed greatly.
Chinese pentatonic system
• The Chinese, for instance, had a scale known to
us as the pentatonic, or five-toned scale, which
sounded very much like this:
Chinese note names
• To each of these notes they gave a name,
thus: "emperor", "prime minister",
"subject people", "state affairs", and
"picture of the universe".
Tetrachords
• Ancient Greek theorists and composers
thought not so much in terms of octaves,
as in terms of sequences of fourths, which
they called "tetrachords".
Combinations of tetrachords
• the melody seems to move among a series
of closely related tetrachords
Pythagoras and tetrachord
• Pythagoras invented a system of four tones
known as the tetrachord (or series of four
notes), which led to the first scale of one
octave. The following are tetrachords:
Disjunct or conjunct
• When two tetrachords are disjunct, that
is, when the top note of one is separated
by a tone from the bottom note of the
next, the two combine to form an octave
• When two tetrachords are conjunct, that is,
when the top note of one overlaps with
the bottom note of another, two
tetrachords combine to form a seventh-whence the famous seven-toned lyre
Lydian notation-key
(disjunt: form an octave)
A conjunct tetracord: a seventh
• I. Dorian mode (scale), resembling the
scale of D minor
Mathematical mysticism
• System of 4 (tetrachord, kosmos)
• 4 wind (N, S, W, E)
• 4 forces (earth, wind, water, fire)
• System of 7 (notes, 7 modes, planets, days)
• System of 8 (octave, 8 modes, 4x2 =
infinite, perfection)
Pytagoras of Samos
• Pythagoras of Samos is a semimythical
Philosopher (late sixth century B.C.)
• He left no writings
• his followers (Pithagoreans) were in the
habit of ascribing all sort of their own
ideas to him
The Pythagoras Theorem
– It was known to the Babylonians centuries
before Pythagoras!
Daemons of the gong
• For the Pithagoreans, the sound made when
a bronze gong is struck was the voice of
one of the demons imprisoned in the
bronze
Mystic numbers
• Pithagoras was a sort of ancient guru, who
beguilled his followers with exotic doctrine
of the trasmigration of the souls
• The interest in number of the pitagoreans
was more mystical than mathematics
• The number was the key to the universe
Musical concords
• Pithagora is credited by Diogenes Laërtius
with having discovered that the basic
musical concords, the octave, the fifth, and
the forth, corresponded to numerical ratios:
1:2, 2:3 and 3:4 respectly
Aristotle (Metaphysica A 5 986a)
• The Pithagoreans “saw that the modifications
and the ratios of the musical scales were
expressible in numbers;
• since, then, all other things seemed in their whole
nature to be modelled in numbers, and numbers
seemed to be the first things in the whole of
nature,
• they supposed the elements of numbers to be the
elements of all things, and the whole heaven to
be a scale (music) and a number”
Numerical-musical universe
• Since numbers were for the Pithagoreans not
abstractions but quantities with real, spatial,
existence,
• the discovery of numerical musical laws
governing the whole of creation, and especially
the starry universe,
• was an intoxicating one!
Musical Planets
• According to the doxographer
Hippolytus, Pythagoras is said to have
taught that
• the universe is put together by means of
harmonic laws and so produces, through
the motion of the seven planets, rhythm
and melody (see Diels, Doxographi Graeci
[1879], p. 555).
Parabolic hearing!
• The very enthusiastic Neo-Pythagorean
Iamblichus went so far as to claim that
Pythagoras could actually hear the
cosmic music inaudible to other mortals!
Plato ”Republic”
• Er the Pamphylian, a hero slain in battle,
was given the privilege of seeing
the next world and then returning to life
to describe what he had seen.
Singing planets
• The vision of Er includes a model of the
universe, a set of concentric rings or
whorls—the planets—hung on the spindle
of Necessity.
• on the upper surface of each circle
(planet) is a siren, who goes round with
them, hymning a single tone or note.
• The eight circles together form one
harmony (melody, octave)
Harmony of the sphere as music
• Thus for Plato the universe was designed
according to harmonious proportions,
and this intellectual harmony could be
described, in the metaphoric language
of a dream-vision, as sounding music.
Cicero's Somnium
Scipionis
• For Cicero it is the motion of the spheres
that produces the “great and pleasing
sound” of the universe.
• Mortal beings, accustomed from
birth to the sound of the cosmos (!),
cannot ordinarily hear it!
• only in a vision, or after death, does its
sublime harmony, of which terrestrial
music is an imitation, reveal itself.
All is music!
• But the sublunary world also partook of this
musical harmony: the elements of fire, air,
water, and earth (4)
• the seasons; the days of the week (7)
• the flow of rivers and the tides of the sea;
• the direction of winds (4);
• the growth of plants.
Plato
• The soul has circuits and revolution
analogous to those of the heavenly bodies
• The music, the soul and the whole universe
were governed by the same mathematical
order and proportion
Musical Macrocosm-Microcosm
• An elaborate set of these correspondences is
given by the late Greek theorist Aristides
Quintilianus.
• Man, the microcosm, shares in this
harmony: everything from the gestation
period of the human embryo and bodily
proportions to the smallest details of
human behavior is governed by analogy
with, or dependence upon, celestial
(musical) harmony.
Music to heal the soul
• Also the ”human” music could alter the
disposition of the hearers
• Theories about the moral and emotional
effect of different musical modes, rhytms,
instruments
Music to purifying the soul
• The Pythagoreans use ”medicine to purify the
body, music to purifying the soul”
• Pythagoras used to sing to his disciples,
accompaining himself on the lyre, to bring them in
a serene mood.
• For example, special melodies were used at night
to calm their minds and to ensure peaceful sleep
and good (and prophetic) dreams
• others were used in the morning to bring
alertness.
Musical burning
• In one case, a young man was about to
burn down the house of an unfaithful
girlfriend.
• Pythagoras realized that he was being
agitated excessively by the music played
nearby, and so he told the musician to
play in a different mode, which
immediately calmed the young man.
Damon
• Some musical patterns would shape a
boy’s caracter, or bring out a man’s latent
trait
• Some rythms expressed agression
• He addressed his essay to the Council of the
Aeropagus: he was seriuosly proposing
some sort of state control over music as a
public health measure
Plato (Timaeus)
•
•
•
•
The right melody is an aid
”to bringing our soul circuit,
when it has got out of tune (!),
into order and armony with itself”
Xenocrates
• Used instrumental music to cure hysterics
Modes
• Dorian (lyre):
• steady, dignified, without frills (preferred
by the Pithagoreans and Aristotle)
• Phrigian (aulos):
• emotional, cathartic
Phrigian - aulos
• The dancing overcomes the wild internal
jerkings of the soul and creates order and
calm (Plato)
• Aulos could cure: panic, epilepsy, sciatica,
snakebites
• The performance made the ”painful places”
palpitate, as dancing in response to the
music, and the pain had gone away
Pean
• The hymn Pean was associated with the
purification from injourios element
• When Sparta suffered from a plague,
Thaletas delivered the city from the
pestilence by means of his music
• The performance of 720 peans released the
women of Locri from madness
A long tradition
• For the Church Fathers Pythagorean
beliefs were acceptable as long as biblical
parallels could be found for them
• The great revival of Neo-Platonism among
fifteenth-century humanists led to some
imaginative restatements of Pythagorean
cosmic belief by such men as Giorgio
Anselmi of Parma (Dialoghi, 1434) and
Marsilio Ficino
The Modal Glyph
Heptagram
• First consider the Heptagram, the star of
seven points connected by red
arrows. Around these points are the letters
C-B, which represent notes in a C-major
scale (CDEFGAB)
Note, planet, day, mode
• Each note is corresponds to a day of the
week and to the corresponding planet
• each planet (note, day) corresponds to a
mode (scale)
• each mode (note, day, planets) corresponds
to one or more astrological symbols
• The signs are also associated with parts of
the body
Ptolemy
• The planets have powers , and are
connected to the 4 elemets (fire, earth,
water, air)
• the qualities or powers of the planets -warm, moist, etc. - are given by Ptolemy,
Tetrabiblos
Eight mode: fixed stars
• In later times an eighth mode was added:
• the Hypomixolydian, corresponds to the
Fixed Stars
• Octagon
Muses and modes
• Each mode is under the patronage of a
Muse: Clio, Calliope, Terpsichore,
Melpomene, Erato, Euterpe, Polyhymnia,
Urania
• The ninth Muse, Thalia is assigned the
Terrestrial Sphere and governs Silence
• "Thalia remains silent, like the Earth."
Each mode have a different
pattern
• Each mode has a different Form, or
pattern of tones and semitones, which
determines the character of the mode and is
of central importance in applying music
to therapeia (cure and care) for the soul
Therapeia
• The therapeia of the soul is based to is
based on the influence that the modes
have on the four humors:
• the subtle fluids that influence our
psychical and bodily state, and which must
be in harmony for proper mental, spiritual,
and bodily health.
• Their state of balance determines one's
temperament
Ramis de Pareja
• The mode-humor correspondences are
given in
• Ramis de Pareja, 1482. Musica Practica.
Bologna.
• A selection is translated in Godwin, Joscelyn,
1993. The Harmony of the Spheres: A Sourcebook
of the Pythagorean Tradition in Music. Rochester:
Inner Traditions.
• Music in a particular mode amplifies or
weakens a humor
Phlegmatic humor - water, cool
and moist
• Dorian imparts the fiery Solar power and
thereby dries the watery Phlegm, which
diminishes its tendency to lethargy
• Hypodorian, in contrast, imparts the
watery Lunar power, which reinforces the
Phlegmatic tendency, encouraging sleep
• The guardians associated with the Dorian mode
are Demeter (Virgo) and Aphrodite (Taurus), but
Hypodorian has only Hestia (Capricorn).
Dorian scale, resembling the
scale of D minor
Hypo-dorian scale, resembling
the A minor scale
Fire (warm, dry)
• Choleric humor, exuberance, and passion
• Phrygian invokes the power of Mars, which is
warm and dry, and therefore magnifies the
Choleric effects
• Hypophrygian invokes the power of Mercury,
which is neutral
• The guardians associated with Phyrigian are Hephaistos
(Libra) and Athena (Aries), but Hypophrygian has only
Hermes (Cancer, the Gate of the Moon), which
corresponds to its planet the Planet Mercury
Phrygian scale, resembling the
scale of E minor
Hypo-phrygian mode, resembling
the B minor scale
Air (moist, warm)
• influence the Sanguine humor, which imparts
good cheer, optimism, friendliness, and a
tendency to laughter, love, and song. Astral body.
• The Lydian mode invokes the power of Jupiter
(moist, warm), which reinforces the Sanguine
humor resulting in Jovial happiness
• Hypolydian draws down the power of Venus, the
results are Erotic sadness
Guardians
• The guardians associated with Lydian are
Ares (Scorpio) and Poseidon (Pisces)
• those with Hypolydian are Zeus (Leo) and
Apollo (Gemini).
Lydian mode, resembling the
scale of F sharp minor
Hypo-lydian scale, resembling
the C sharp minor scale
Earth (dry, cool)
• Melancholic humor, which is the most
complex humor in its effects; it is
associated with the physical body
• Because of its earthy nature, the
Melancholic humor imparts solidity,
firmness, and steadfastness, but also
therefore a certain indolence and tenacity
Mixolydian
• Mixolydian invokes the power of Saturn (dry,
cool), which magnifies the effect of the humor,
leading to Saturnine melancholy. This may
lead to paralyzing depression, but, if well
tempered, it may produce introspection,
artistic genius, good memory, a love of
scholarship, and the inclination to retire from
the world and devote oneself to spiritual
matters
Melancholia and genius
• Melancholia has been recognized as the
dominant humor in many people of
exceptional ability, for it provides the
sensibilities required to experience deeply,
and thereby to transcend the ordinary
Mixolidian Guardians
• The guardians associated with Mixolydian
are Artemis (Sagittarius) and Hera
(Aquarius)
Mixo-lydian mode, resembling
the G minor scale
Hypomixolydian
• The Hypomixolydian mode is associated with the
Celestial Sphere, which tempers the
Melancholic humor
• It represents the heavenly repose achieved when
one has ascended the planetary spheres; it is the
mode of Celestial bliss
• "More than any other, this mode has an innate
beauty and loveliness; it is free from all qualities
and suitable for every use" (Ramis, op. cit.).
Hypomixolydian mode
Fixed Stars
• since Hypomixolydian is the eighth mode,
it has no specific associated signs or
guardians, for it corresponds to all the
Fixed Stars and to the Thirteen Olympians