Music of ancient Greece in the context of "Western Classical music"

A sophist (Greek: σοφιστής, romanized: sophistēs) was a teacher in ancient Greece in the fifth and fourth centuries BC. Sophists specialized in one or more subject areas, such as philosophy, rhetoric, music, athletics and mathematics. They taught arete, "virtue" or "excellence", predominantly to young statesmen and nobility.

The arts of the sophists were known as sophistry and gained a negative reputation as tools of arbitrary reasoning. Protagoras, regarded as the first of the sophists, became notorious for his claim to "make the weaker argument the stronger".

An aulos (plural auloi; Ancient Greek: αὐλός : aulós, plural αὐλοί : auloí) or Latin: tibia was a wind instrument in ancient Greece, often depicted in art and also attested by archaeology.

Though the word aulos is often translated as "flute" or as "double flute", the instrument was usually double-reeded, and its sound—described as "penetrating, insisting and exciting"—was more akin to that of modern woodwind instruments such as oboes or bagpipes with a chanter and (modulated) drone.

The Spartan army was the principal ground force of Sparta. It stood at the center of the ancient Greek city-state, consisting of citizens trained in the disciplines and honour of a warrior society. Subjected to military drills since early manhood, the Spartans became one of the most feared and formidable military forces in the Greek world, attaining legendary status in their wars against Persia. At the height of Sparta's power—between the 6th and 4th centuries BC—other Greeks commonly accepted that "one Spartan was worth several men of any other state."

Tradition states that the semi-mythical Spartan legislator Lycurgus first founded the iconic army. Referring to Sparta as having a "wall of men, instead of bricks," he proposed reforming the Spartan society to develop a military-focused lifestyle following "proper virtues" such as equality for the male citizens, austerity, strength, and fitness. Spartan boys deemed strong enough entered the agoge regime at the age of seven, undergoing intense and rigorous military training. Their education focused primarily on fostering cunningness, practicing sports and war tactics, and also included learning about poetry, music, academics, and sometimes politics. Those who passed the agoge by the age of 30 achieved full Spartan citizenship.

Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are determined by choosing a sequence of fifths which are "pure" or perfect, with ratio ${\displaystyle 3:2}$. This is chosen because it is the next harmonic of a vibrating string, after the octave (which is the ratio ${\displaystyle 2:1}$), and hence is the next most consonant "pure" interval, and the easiest to tune by ear. As Novalis put it, "The musical proportions seem to me to be particularly correct natural proportions." Alternatively, it can be described as the tuning of the syntonic temperament in which the generator is the ratio 3:2 (i.e., the untempered perfect fifth), which is ≈ 702 cents wide.

The system dates back to Ancient Mesopotamia;. (See Music of Mesopotamia § Music theory.) It is named, and has been widely misattributed, to Ancient Greeks, notably Pythagoras (sixth century BC) by modern authors of music theory. Ptolemy, and later Boethius, ascribed the division of the tetrachord by only two intervals, called "semitonium" and "tonus" in Latin (256:243 × 9:8 × 9:8), to Eratosthenes. The so-called "Pythagorean tuning" was used by musicians up to the beginning of the 16th century. "The Pythagorean system would appear to be ideal because of the purity of the fifths, but some consider other intervals, particularly the major third, to be so badly out of tune that major chords [may be considered] a dissonance."

Classical music generally refers to the art music of the Western world, considered to be distinct from Western folk music or popular music traditions. It is sometimes distinguished as Western classical music, as the term "classical music" can also be applied to non-Western art musics. Classical music is often characterized by formality and complexity in its musical form and harmonic organization, particularly with the use of polyphony. Since at least the ninth century, it has been primarily a written tradition, spawning a sophisticated notational system, as well as accompanying literature in analytical, critical, historiographical, musicological and philosophical practices.

Rooted in the patronage of churches and royal courts in Europe, surviving early medieval music is chiefly religious, monophonic and vocal, with the music of ancient Greece and Rome influencing its thought and theory. The earliest extant music manuscripts date from the Carolingian Empire (800–887), around the time which Western plainchant gradually unified into what is termed Gregorian chant. Musical centers existed at the Abbey of Saint Gall, the Abbey of Saint Martial and Saint Emmeram's Abbey, while the 11th century saw the development of staff notation and increasing output from medieval music theorists. By the mid-12th century, France became the major European musical center: the religious Notre-Dame school first fully explored organized rhythms and polyphony, while secular music flourished with the troubadour and trouvère traditions led by poet-musician nobles. This culminated in the court-sponsored French ars nova and Italian Trecento, which evolved into ars subtilior, a stylistic movement of extreme rhythmic diversity. Beginning in the early 15th century, Renaissance composers of the influential Franco-Flemish School built on the harmonic principles in the English contenance angloise, bringing choral music to new standards, particularly the mass and motet. Northern Italy soon emerged as the central musical region, where the Roman School engaged in highly sophisticated methods of polyphony in genres such as the madrigal, which inspired the brief English Madrigal School.

Aristoxenus of Tarentum (Greek: Ἀριστόξενος ὁ Ταραντῖνος; born c. 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.