CHAPTER IV

_A--Sources_

PYTHAGORAS, the great philosopher of the sixth century B. C.

His teachings are known only through his pupils, especially Philalaos (ca. 540 B. C.), of whose writings fragments are preserved.

PLATO (427-347 B. C.).

In his 'Republic,' 'De legibus,' 'De furore poetico,' 'Timæus,' 'Gorgias,' 'Alcibiades Philebus,' there are copious references to music.

ARCHYTAS OF TARENT, a contemporary of Plato.

He was the first to recognize the transmission of tones by air vibration. His theories are cited by Theodore of Smyrna, Claudius Ptolemy, etc.

ARISTOTLE (383-320 B. C.).

In 'Polities' and 'Poetics' he makes frequent references to music.

ARISTOXENUS OF TARENT (ca. 320 B. C.), the most important musical theoretician of ancient Greece. His 'Rhythmics' and his 'Elements of Harmonics,' the greatest part of which is lost, have been many times translated and commented on.

EUCLID, the great mathematician, a follower of Pythagoras. His 'Sectio canonis' treats of the mathematical relation of tones.

HERON OF ALEXANDRIA (100 B. C.)

In his 'Pneumatica' he described the water organ (Hydraulis) invented by Ktebisius, his teacher.

ARISTIDES QUINTILIANUS (first to second century, A. D.) of Smyrna. His 'Introduction to Music' (μοὕσϛ ἁρ ονικἣϛ), completely preserved, except for corruptions by copyists, is especially notable for its tables of musical notation.

PLUTARCH, the celebrated writer of the comparative biographies (50-120 A. D.), wrote an 'Introduction to Music,' full of valuable information on the art.

CLAUDIUS PTOLEMY, the great Græco-Egyptian geographer, mathematician and astronomer (second century A. D.). His 'Harmonics'--in three books--is an exhaustive theory of the ancient scale system.

ALYPIUS (ca. 360 A. D.). His 'Introduction to Music' is valuable for the copious tables of notation (Alypian tables).

BOETHIUS (475-524 A. D.), the chancellor of Theodoric the Great. He was the chief exponent of Greek musical theory to the Middle Ages. His five books on music ('De Musica') are chiefly based on other works of the Roman period, notably on Ptolemy.

_B--Early Modern Writers on Greek Music_

VINCENZO GALILEO: Dialogo di Vincenzo Galileo ... della musica antica, et della moderna (Florence, 1581).

M. MEIBOMIUS (Meibom): Antiquæ musicæ auctores septem (Amsterdam, 1652).

_C--Modern Authorities_

AUGUST BÖCKH: De metris Pindari (Ed. of Pindar), 1811, 1819, 1821.

AUGUST BÖCKH: Die Entwicklung der Lehren des Philalaos (Berlin, 1819).

AUGUST BEGER: Die Würde der Musik im Griechischen Altertume (Dresden, 1839).

FR. BELLERMAN (ed.): Anonymi scriptio de musica (Berlin, 1841).

FR. BELLERMAN (ed.): Die Tonleitern und Musiknoten der Griechen (Berlin, 1847).

A. J. H. VINCENT: Notice sur trois manuscrits grecs relatifs à la musique (1847).

CARL FR. WEITZMANN: Geschichte der griechischen Musik (Berlin, 1855).

MARQUARD: Harmonische Fragmente des Aristoxenus (1868).

OSKAR PAUL: Boethius' fünf Bücher über die Musik (translated and elucidated, Leipzig, 1872).

FR. AUG. GEVAERT: Histoire et théorie de la musique de l'antiquité (Gand, 1875).

FR. AUG. GEVAERT: Les problèmes musicaux d'Aristote (_collab. w._ J. C. Vollgraf).

RUDOLPH WESTPHAL: Musik des griechischen Alterthumes (1883).

RUDOLPH WESTPHAL: Aristoxenus von Tarent (1883).

A. ROSSBACH und R. WESTPHAL: Theorie der musischen Künste der Hellenen (1885-89).

D. B. MONRO: The Modes of Ancient Greek Music (Oxford, 1894).

CARL VON JAN: Musicii Scriptores Græci (Leipzig, 1895).

H. S. MACRAN: The Harmonies of Aristoxenus (Oxford, 1902).

R. VON KRALIK: Altgriechische Musik (Stuttgart, 1900).

ARTHUR FAIRBANKS: The Greek Pæan (Cornell Studies XII, 1900).

LOUIS LALOY: Aristoxène de Tarente (1904).

A. J. HIPKINS: Dorian and Phrygian (Sammelbände der Int. Musik-Ges., Vol. IV, No. 3, pp. 371-81).

LITERATURE FOR