The Science of Harmonics in Classical Greece
The ancient science of harmonics investigates the arrangements of pitched sounds which form the basis of musical melody, and the principles which govern them. It was the most important branch of Greek musical theory, studied by philosophers, mathematicians and astronomers as well as by musical specialists. This 2007 book examines its development during the period when its central ideas and rival schools of thought were established, laying the foundations for the speculations of later antiquity, the Middle Ages and the Renaissance. It concentrates particularly on the theorists' methods and purposes and the controversies that their various approaches to the subject provoked. It also seeks to locate the discipline within the broader cultural environment of the period; and it investigates, sometimes with surprising results, the ways in which the theorists' work draws on and in some cases influences that of philosophers and other intellectuals.
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analysis Archytas argument Aristides Quintilianus Aristotle Aristotle’s Aristoxenian Aristoxenus arithmetic attributes attunement auloi Boethius Book brieﬂy Chapter chromatic Cleonides composition conclusions concords constructed context deﬁned deﬁnition demonstration diast»ema diast»emata diatonic diesis diezeugmenon difﬁculties discussion distinctions division dynameis earlier Elementa harmonica elements empirical harmonics enharmonic enharmonic genus Eratocles ethos evidence fact ﬁfth ﬁnd ﬁrst ﬁt ﬁxed fourth century frag genera genus Greek Harm harmonia harmonic science harmonic theory harmonikoi hypat»e hypothesis identiﬁed instance judgement later lichanos mathematical harmonics means melodic melos mes»e meson modulation movement multiple musical musicians notes numbers octave parames»e passage patterns perception perfect fourth Philolaus philosophers pitch Plato Plutarchan principles proposition Ptol Ptolemy Ptolemy’s pyknon Pythagoras Pythagorean quarter-tone reason recognised reference reﬂections relations relevant says scientiﬁc Sectio seems semitone sense sequence signiﬁcant Socrates sort sound speciﬁc string structure syst»ema syst»emata tetrachord Theophrastus theorems theorists thesis Timaeus tone tonoi topics treatise writer
Page v - Restore our fallen day; O re-arrange. O dear white children casual as birds, Playing among the ruined languages, So small beside their large confusing words, So gay against the greater silences Of dreadful things you did: O hang the head, Impetuous child with the tremendous brain, O weep, child, weep, O weep away the stain, Lost innocence who wished your lover dead, Weep for the lives your wishes never led. O cry created as the bow of sin Is drawn across our trembling violin.