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Aristoxenos
Aristoxenus of Tarentum ( el, Ἀριστόξενος ὁ Ταραντῖνος; born 375, fl. 335 BC) was a Greek Peripatetic philosopher, and a pupil of Aristotle. Most of his writings, which dealt with philosophy, ethics and music, have been lost, but one musical treatise, ''Elements of Harmony'' (Greek: Ἁρμονικὰ στοιχεῖα; Latin: ''Elementa harmonica''), survives incomplete, as well as some fragments concerning rhythm and meter. The ''Elements'' is the chief source of our knowledge of ancient Greek music."Aristoxenus of Tarentum" in ''Chambers's Encyclopædia''. London: George Newnes, 1961, Vol. 1, p. 593. Life Aristoxenus was born at Tarentum, and was the son of a learned musician named Spintharus (otherwise Mnesias). He learned music from his father, and having then been instructed by Lamprus of Erythrae and Xenophilus the Pythagorean, he finally became a pupil of Aristotle, whom he appears to have rivaled in the variety of his studies. According to the ...
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Elementa Harmonica
''Elementa harmonica'' is a treatise on the subject of musical scales by Aristoxenus, of which considerable amounts are extant. The work dates to the second half of the 4th century BC. It is the oldest substantially surviving work written on the subject of music theory. Title The work is known variously as Aristoxenou (or Aristoxenoy) Armonika (or Harmonika) Stoicheia ''i.e.'' Aristoxenou Armonika Stoicheia, Aristoxenou Harmonika Stoicheia etc. All of these translate as ''The Harmonics of Aristoxenus''. ''Elementa harmonica'' translates as Elements of Harmonics. ''Oxford Paperback Reference''(anWorld Cat The work is otherwise rendered as The Elements, or Elements, the latter translates into Greek as Στοιχεία. Subject Historical context The Elements is held to be the work founding a tradition of the study of music based on practice, which is, to understand music by study to the ear. Musicology as a discipline achieved nascency with the systematic study undertaken in the w ...
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Peripatetic School
The Peripatetic school was a school of philosophy in Ancient Greece. Its teachings derived from its founder, Aristotle (384–322 BC), and ''peripatetic'' is an adjective ascribed to his followers. The school dates from around 335 BC when Aristotle began teaching in the Lyceum. It was an informal institution whose members conducted philosophical and scientific inquiries. After the middle of the 3rd century BC, the school fell into a decline, and it was not until the Roman era that there was a revival. Later members of the school concentrated on preserving and commenting on Aristotle's works rather than extending them; it died out in the 3rd century. The study of Aristotle's works by scholars who were called Peripatetics continued through late antiquity, the Middle Ages, and the Renaissance. After the fall of the Western Roman Empire, the works of the Peripatetic school were lost to the Latin West, but they were preserved in Byzantium and also incorporated into early Islamic phil ...
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Pythagoreanism
Pythagoreanism originated in the 6th century BC, based on and around the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans. Pythagoras established the first Pythagorean community in the Ancient Greece, ancient Greek colony of Crotone, Kroton, in modern Calabria (Italy). Early Pythagorean communities spread throughout Magna Graecia. Pythagoras' death and disputes about his teachings led to the development of two philosophical traditions within Pythagoreanism. The ''akousmatikoi'' were superseded in the 4th century BC as a significant mendicant school of philosophy by the Cynicism (philosophy), Cynics. The ''mathēmatikoi'' philosophers were absorbed into the Platonic Academy, Platonic school in the 4th century BC. Following political instability in Magna Graecia, some Pythagorean philosophers fled to mainland Greece while others regrouped in Rhegium. By about 400 BC the majority of Pythagorean philosophers had left Italy. Pythagorean ideas exercised a m ...
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Archestratus (music Theorist)
Archestratus ( grc-gre, Ἀρχέστρατος ''Archestratos'') was a harmonic theorist in the Peripatetic tradition and probably lived in the early 3rd century BC. Little is known of his life and career. Athenaeus' reference (XIV.634d) to an Archestratus who wrote ''On auletes'' (Περὶ αὐλητῶν) in two books is perhaps to him; it is a "rather remote" possibility that he is identical with Archestratus of Syracuse. Harmonic theory The most substantial evidence for Archestratus' ideas is in a passage of Porphyry'commentaryon Ptolemy's ''Harmonics'', pp. 26–27 Düring (the "" are from the original): The ''pyknon'' is a structure located within a tetrachord. Despite the forbiddingly technical and "arid" appearance of the doctrines ascribed to Archestratus, Andrew Barker has argued that in fact "they engage with issues of real significance to musicians, and to anyone seeking to understand the resources and strategies of melodic composition." Connections w ...
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De Architectura
(''On architecture'', published as ''Ten Books on Architecture'') is a treatise on architecture written by the Roman architect and military engineer Marcus Vitruvius Pollio and dedicated to his patron, the emperor Caesar Augustus, as a guide for building projects. As the only treatise on architecture to survive from antiquity, it has been regarded since the Renaissance as the first book on architectural theory, as well as a major source on the canon of classical architecture. It contains a variety of information on Greek and Roman buildings, as well as prescriptions for the planning and design of military camps, cities, and structures both large (aqueducts, buildings, baths, harbours) and small (machines, measuring devices, instruments). Since Vitruvius published before the development of cross vaulting, domes, concrete, and other innovations associated with Imperial Roman architecture, his ten books give no information on these hallmarks of Roman building design and technology ...
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Vitruvius
Vitruvius (; c. 80–70 BC – after c. 15 BC) was a Roman architect and engineer during the 1st century BC, known for his multi-volume work entitled ''De architectura''. He originated the idea that all buildings should have three attributes: , , and ("strength", "utility", and "beauty"). These principles were later widely adopted in Roman architecture. His discussion of perfect proportion in architecture and the human body led to the famous Renaissance drawing of the ''Vitruvian Man'' by Leonardo da Vinci. Little is known about Vitruvius' life, but by his own descriptionDe Arch. Book 1, preface. section 2. he served as an artilleryman, the third class of arms in the Roman military offices. He probably served as a senior officer of artillery in charge of ''doctores ballistarum'' (artillery experts) and ''libratores'' who actually operated the machines. As an army engineer he specialized in the construction of ''ballista'' and '' scorpio'' artillery war machines for sieges. ...
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Philolaus
Philolaus (; grc, Φιλόλαος, ''Philólaos''; ) was a Greek Pythagorean and pre-Socratic philosopher. He was born in a Greek colony in Italy and migrated to Greece. Philolaus has been called one of three most prominent figures in the Pythagorean tradition and the most outstanding figure in the Pythagorean school. Pythagoras developed a school of philosophy that was dominated by both mathematics and mysticism. Most of what is known today about the Pythagorean astronomical system is derived from Philolaus's views. He may have been the first to write about Pythagorean doctrine. According to August Böckh (1819), who cites Nicomachus, Philolaus was the successor of Pythagoras. He argued that at the foundation of everything is the part played by the limiting and limitless, which combine in a harmony. With his assertions that the Earth was not the center of the universe (geocentrism), he is credited with the earliest known discussion of concepts in the development of heliocent ...
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Archytas
Archytas (; el, Ἀρχύτας; 435/410–360/350 BC) was an Ancient Greek philosopher, mathematician, music theorist, astronomer, statesman, and strategist. He was a scientist of the Pythagorean school and famous for being the reputed founder of mathematical mechanics, as well as a good friend of Plato. Life and work Archytas was born in Tarentum, Magna Graecia and was the son of Mnesagoras or Hadees. For a while, he was taught by Philolaus, and was a teacher of mathematics to Eudoxus of Cnidus. Archytas and Eudoxus' student was Menaechmus. As a Pythagorean, Archytas believed that only arithmetic, not geometry, could provide a basis for satisfactory proofs. Archytas is believed to be the founder of mathematical mechanics.: ''Vitae philosophorum'' As only described in the writings of Aulus Gellius five centuries after him, he was reputed to have designed and built the first artificial, self-propelled flying device, a bird-shaped model propelled by a jet of what was probably st ...
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Pythagoras
Pythagoras of Samos ( grc, Πυθαγόρας ὁ Σάμιος, Pythagóras ho Sámios, Pythagoras the Samos, Samian, or simply ; in Ionian Greek; ) was an ancient Ionians, Ionian Ancient Greek philosophy, Greek philosopher and the eponymous founder of Pythagoreanism. His political and religious teachings were well known in Magna Graecia and influenced the philosophies of Plato, Aristotle, and, through them, the Western philosophy, West in general. Knowledge of his life is clouded by legend, but he appears to have been the son of Mnesarchus, a gem-engraver on the island of Samos. Modern scholars disagree regarding Pythagoras's education and influences, but they do agree that, around 530 BC, he travelled to Crotone, Croton in southern Italy, where he founded a school in which initiates were sworn to secrecy and lived a communal, asceticism, ascetic lifestyle. This lifestyle entailed a number of dietary prohibitions, traditionally said to have included vegetarianism, although m ...
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Plato
Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was a Greek philosopher born in Athens during the Classical period in Ancient Greece. He founded the Platonist school of thought and the Academy, the first institution of higher learning on the European continent. Along with his teacher, Socrates, and his student, Aristotle, Plato is a central figure in the history of Ancient Greek philosophy and the Western and Middle Eastern philosophies descended from it. He has also shaped religion and spirituality. The so-called neoplatonism of his interpreter Plotinus greatly influenced both Christianity (through Church Fathers such as Augustine) and Islamic philosophy (through e.g. Al-Farabi). In modern times, Friedrich Nietzsche diagnosed Western culture as growing in the shadow of Plato (famously calling Christianity "Platonism for the masses"), while Alfred North Whitehead famously said: "the safest general characterization of the European philosophical tra ...
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