The Manual of Harmonics of Nicomachus the Pythagorean
In ancient Greek thought, the musical scale discovered by the philosopher Pythagoras was seen as a utopian model of the harmonic order behind the structure of the cosmos and human existence. Through proportion and harmony, the musical scale bridges the gap between two extremes. It encapsulates the most fundamental pattern of harmonic symmetry and demonstrates how the phenomena of nature are inseparably related to one another through the principle of reciprocity. Because of these relationships embodied in its structure, the musical scale was seen as an ideal metaphor of human society by Plato and other Pythagorean thinkers, for it is based on the cosmic principles of harmony, reciprocity, and proportion, whereby each part of the whole receives its just and proper share.
This book is the first ever complete translation of The Manual of Harmonics by the Pythagorean philosopher Nicomachus of Gerasa (second century A.D.) published with a comprehensive, chapter-by-chapter commentary. It is a concise and well-organized introduction to the study of harmonics, the universal principles of relation embodied in the musical scale. Also included is a remarkable chapter-by-chapter commentary by the translator, Flora Levin, which makes this work easily accessible to the reader today. Dr. Levin explains the principles of Pythagorean harmony, provides extensive background information, and helps to situate Nicomachus' thought in the history of ideas.
This important work constitutes a valuable resource for all students of ancient philosophy, Western cosmology, and the history of music.
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according to Nicomachus air-column ancient heptachord Aristotle Aristoxenian Aristoxenus arithmetic attunement auloi aulos Barker Boethius called canon chromatic commentary composed concord conjunction consonance D'Ooge diatonic genus diesis difference dioxeian disjunction Dorian duple eighth string enharmonic Excerpt fact fifth fourth geometry Greater Perfect System Greek harmonia hemiolic heptachord Hermes higher pitch hole hypate hypate meson instruments inverse proportion Kronos lamblichus leimma length Levin lichanos lowest lyre mathematical melodic mese meson middle note monochord motion musical notes musical pitch musicians nete nete diezeugmenon nete hyperbolaion nete synemmenon Nicomachus explains Nicomachus of Gerasa Nicomachus says Notes to Chapter octachord octave paramese paranete parhypate Pherecrates Philolaus pipe planets Plato position produced proslambanomenos Ptolemy Pythagoras Pythagorean quarter-tone raise the interval ratio relation Rios scale semi-tone sesquioctave sound syllaba tension Terpander tetrachord Teubner theorists things Thrasyllus three genera Timaeus tion tone treatise vibration voice weight whole whole-tone words