Muzika ir matematika

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Muzika ir matematika
Antika Viduramiai Barokas XX amius
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Muzika ir matematika

• Derinimas (akustika)
• Numerologija (teorija)
• Fraktalai (grynoji matematika)

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Antika
Pythagoras(c. 569 c. 475 B.C.)
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Derinimas(konsonansai)
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Derinimas (obertonai) aprayti Pythagoro
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Kvintu ratas
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Derinimas(disonansai - tritonis)
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Sferu harmonija
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Renesansas
Ars combinatorica permutacija ir
kombinacija Ritmo kombinacijos trukmes vieneto
pridejimaslaipsnikas trukmes vieneto
mainimassimetriku ritmo pieiniu formavimas
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Renesansas
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Fibonacci serijos
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Fibonacci seriju skaiciuoklishttp//www.mcs.surr
ey.ac.uk/Personal/R.Knott/Fibonacci/fibCalcX.html
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Skacius Phi
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Aukso pjuvis
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Barokas
Muzika skambanciu skaiciu menas(numerus
sonorus Gioseffo Zaelino) Muzika apibreiama
kaip matematikos mokslo aka
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Barokas
Skaiciu simbolika jungia kelias numerologines
tradicijas pitagorieciu sferu
harmonija viduramiu skaiciu mistifikacijas kri
kcionikaja numerologijos interpretacija
(tradicija)
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Muzikine paragrama
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Numerologija
Mokslas siekiantis nustatyti ryi tarp skaiciu ir
ju reikmes mogaus gyvenime. Pagrista mistiniu
skaitmens ir gamtos bei mogaus vibraciju raryiu.
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Barokas. Skaiciu reikmes
0 represents infinity, the frontierless
essence, source of all things, the universal egg,
the solar system as a whole, therefrom the
universal, the going around, but also 0 is the
universal paradox, the infinite large and
infinite small, the circle of infinity, but also
the centerpoint, the undividable small atom. 1
is symbol of perfection, the positive, active
principle, that gave birth to the entire
universe revelation and unity of the Cosmos.
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Barokas. Skaiciu reikmes
2 is duality of the creation heaven-earth,
mind-matter, light-darkness, moment-eternity,
positive-negative, good-evil, active-passive,
male-female, profits-losses etc. It is the number
of the composition and division of parts,
unifying and splitting, the concept of revelation
and obsurity. The deliberate outspoken and the
silent inner logic. 3 is symbol of the Holy
Trinity, (Father, Son Holy Spirit). Life,
substance intelligence. Power, matter and
conscience. Creation, maintainance and
resolvation. Birth, life, death. The family
father, mother and child. The thinker, the
thought and the subject of the thinking. The
past, the present and the future.
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Barokas. Skaiciu reikmes
4 is the number of reality and concretion, the
matter of the universe. The cube or quadrat, the
second power. Physical laws, logic, intellect,
knowledge, reasoning. The cross, intersection,
division, ordering, classification. 5
represents expansion, or spanning, understanding,
intelligence, judgement, increment, fertility,
propagation. Justice, mowing and harvest.
Reproduction of the ego in the material world.
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Barokas. Skaiciu reikmes
6 means cooperation. Marriage, interweaving, a
piece of a chain, relation, mutual influence,
counterbalance.. Also harmony, peace, redemption,
the interaction between the mental and physical
(Compare with the Jewish Star, a triangle
pointing upwards and one pointing downwards.) 7
is the number of fullfilment. Time and space,
duration, distance. Age, decay, death or
persistence. The seven eras, the days of the
week, the Seven Seals, the priciples of mankind,
the seven notes of the scale. The perfect human
being. The circular course of evolution, wisdom,
balance, equality, quietness.
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Barokas. Skaiciu reikmes
8 is the number of solution. The sublimating of
the natural in the spiritual, inhaling followed
by expiring. Giniality and inventions.
Revolution. Deformations and eccentricity,
capriciousness. 9 stands for the number of
rebirth. A new birth, ecclesiasticism, expansion
of senses, presentiments. Dreams, clairvoyance.
Reformation, nebulousness, pulsation, rhythm. The
stretching, travelling, distancing. 10 is the
synthesis of 0 and 1, of cosmos and creating
force. (But also of eg. the 10 Commandments, and
the Roman figure X, which often is used as a
pointer to Christ.)
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Skaitmeninio muzikos principo analize
Nustatomas pasirinktos atkarpos (temos, balso
linijos, akordo, frazes) garsu skaicius Key
stroke metodas realiai igaunamu (paspaudiamu)
garsu skaiciaus nustatymas Skaitmeninio modulio
ivedimas arba Modulis 9 Skaitmenines aknies
ir sumavimo veiksmai Skaiciaus diminucija ir
augmentacija
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Skaitmeninio muzikos principo analize
Laiko parametro organizavimas Tonacinio parametro
organizavimas Fakturinio parametro
organizavimas Skaitmeninis teminio parametro
organizavimas temos pravedimu skaicius temos
smulkesniu sintaksiniu dariniu skaicius temos
apimtis taktais (pustakciais) temos trukme
ritminiu aspektu temos ritminis pieinys
(ritmines formules) tema sudaranciu garsu
skaicius (key stroke) temos garsaeilis
(klasterinis skaitmuo) muzikos paskirstymas tarp
juodu ir baltu klaviu, tarp kaires ir deines
ranku (klavyrineje muzikoje)
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Bacho herbas
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Bacho skaiciu abecele
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Bacho Miios h-moll. Credo in unum Deo
129 taktai 43 x 3 (Credo, Credo, Credo) odis
Credo kartojamas 43 kartus CREDO
3175414 43
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J. S. Bach. Goldberg variacijos
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Kompozicija su skaiciu eilemis
XX amius
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Bulezo magikieji kvadratai(Structure Ia)
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Bulezo kompozicijaStructure Ia
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Iannis Xenakis Metastasis (partitura)
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Iannis Xenakis. Metastasis (schema)
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Iannis Xenakispaviljonas 1958 m. pasaulinei
parodai (sudarytas tik i tiesiu)
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Fraktalai
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