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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.

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30 melodies

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30 melodies

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

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


30 melodies

P. Yale CtYBR inv. 4510

the sort of musical notation sometimes used

by professional singers in antiquity


Notation

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

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.


30 melodies

P. Mich. 1205r,


Papirus on internet

Papirus on internet

  • http://classics.uc.edu/music/index.html


Scales

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

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

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

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

Combinations of tetrachords

  • the melody seems to move among a series of closely related tetrachords


Pythagoras and tetrachord

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

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

Lydian notation-key(disjunt: form an octave)


A conjunct tetracord a seventh

A conjunct tetracord: a seventh


30 melodies

  • I. Dorian mode (scale), resembling the scale of D minor


Mathematical mysticism

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

Pytagoras of Samos

  • Pythagoras of Samos is a semimythicalPhilosopher (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

The Pythagoras Theorem

  • It was known to the Babylonians centuries before Pythagoras!


Daemons of the gong

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

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

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

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

Numerical-musical universe

  • Since numbers were for the Pithagoreans not abstractions but quantities with real, spatial, existence,

  • the discovery of numericalmusical laws governing the whole of creation, and especially the starry universe,

  • was an intoxicating one!


Musical planets

Musical Planets

  • According to the doxographerHippolytus, Pythagoras is said to have taught that

  • the universe is put togetherby 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

Parabolic hearing!

  • The very enthusiastic Neo-Pythagorean Iamblichus went so far as to claim thatPythagoras could actually hear the cosmic music inaudible to other mortals!


Plato republic

Plato ”Republic”

  • Er the Pamphylian, a hero slain in battle, was given the privilege of seeingthe next world and then returning to life to describe what he had seen.


Singing planets

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

Harmony of the sphere as music

  • Thus for Plato the universe was designed according to harmonious proportions, and thisintellectual harmony could be described, in the metaphoric languageof a dream-vision, as sounding music.


Cicero s somnium scipionis

Cicero's SomniumScipionis

  • For Cicero it is the motion of the spheres that produces the “great and pleasing sound” of the universe.

  • Mortal beings, accustomed frombirth 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

All is music!

  • But the sublunary world also partook of thismusical 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

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

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 behavioris governedby analogy with, or dependence upon, celestial (musical) harmony.


Music to heal the soul

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

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

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

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

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

Xenocrates

  • Used instrumental music to cure hysterics


Modes

Modes

  • Dorian (lyre):

  • steady, dignified, without frills (preferred by the Pithagoreans and Aristotle)

  • Phrigian (aulos):

  • emotional, cathartic


Phrigian aulos

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


30 melodies

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

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 GiorgioAnselmi of Parma (Dialoghi, 1434) and Marsilio Ficino


The modal glyph

The Modal Glyph


Heptagram

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

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

Ptolemy

  • The planets have powers , and are connected to the 4 elemets (fire, earth, water, air)

  • the qualities or powersof the planets -- warm, moist, etc. - are given by Ptolemy, Tetrabiblos


Eight mode fixed stars

Eight mode: fixed stars

  • In later times an eighth mode was added:

  • the Hypomixolydian, corresponds to the Fixed Stars

  • Octagon


Muses and modes

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 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

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

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.


Modes humor

Modes-Humor

  • Music in a particular mode amplifies or weakens a humor


Phlegmatic humor water cool and moist

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

Dorian scale, resembling the scale of D minor


Hypo dorian scale resembling the a minor scale

Hypo-dorian scale, resembling the A minor scale


Fire warm dry

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

Phrygian scale, resembling the scale of E minor


Hypo phrygian mode resembling the b minor scale

Hypo-phrygian mode, resembling the B minor scale


Air moist warm

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

  • Hypolydiandraws down the power of Venus, the results are Erotic sadness


Guardians

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

Lydian mode, resembling the scale of F sharp minor


Hypo lydian scale resembling the c sharp minor scale

Hypo-lydian scale, resembling the C sharp minor scale


Earth dry cool

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

  • 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 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

Mixolidian Guardians

  • The guardians associated with Mixolydian are Artemis (Sagittarius) and Hera (Aquarius)


Mixo lydian mode resembling the g minor scale

Mixo-lydian mode, resembling the G minor scale


Hypomixolydian

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

Hypomixolydian mode


Fixed stars

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


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