HarmonicsBrill, 2000 - 192 էջ Ptolemy's comprehensive treatises on astronomy and geography were influential for nearly two millennia. Equally influential was his treatise on harmonics, the ancient science which combined and brought to completion the study of philosophy and science. This volume offers a comprehensive English translation and commentary of Ptolemy's Harmonics. The treatise begins with Ptolemy's study of pitches and intervals, for which he extracts both an idealized musical scale and a new acoustical tool. After discussing modulation, he expands his horizons by applying musical intervals to the human soul and celestial bodies, ultimately describing a cosmic harmony. The English translation faithfully reproduces Ptolemy's style and includes all the charts surviving in the manuscript tradition. The commentary offers a full exegesis of the text, loci paralleli, and citations of modern scholarly sources. |
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Էջ 50
... leading locus , while those contiguous greater ratios244 must be divided in the same way into the two following loci ; the 16:15 ratio is not found to be capable of standing in the leading locus . [ 35.18 ] For if we again triple the ...
... leading locus , while those contiguous greater ratios244 must be divided in the same way into the two following loci ; the 16:15 ratio is not found to be capable of standing in the leading locus . [ 35.18 ] For if we again triple the ...
Էջ 51
Ptolemy Jon Solomon. than that in the leading position , that is 16 : 15,245 and this would be contrary to clarity and to our original reasoning . [ 36.6 ] Once 8 : 7 is arranged as the leading position , the first numbers embracing the ...
Ptolemy Jon Solomon. than that in the leading position , that is 16 : 15,245 and this would be contrary to clarity and to our original reasoning . [ 36.6 ] Once 8 : 7 is arranged as the leading position , the first numbers embracing the ...
Էջ 56
... leading whole tones and the remaining interval , as they reckon it , a half tone , but as reason posits , that known as the leimma . [ 39.19 ] Their method succeeded for them because they did not differentiate by any substantial amount ...
... leading whole tones and the remaining interval , as they reckon it , a half tone , but as reason posits , that known as the leimma . [ 39.19 ] Their method succeeded for them because they did not differentiate by any substantial amount ...
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Common terms and phrases
according Ancient Greek Music Archytas Aristides Quintilianus Aristoxenian Aristoxenus arrangement Barbera beginning Book bridges called canon cause century chapter chromatic circle common compared consists consonances contain correct course demonstration derived described diapente diatessaron diatonic tonic diatonic diezeugmenon differences discusses disjunction distance divided divisions double diapason Düring emmelic enharmonic entire equal established example excesses four function genera genus greater half Harmonics hearing higher highest History homophones intense diatonic intervals leading length limits lower lowest magnitude manuscript Mathematics matter means mese method middle modulation nature nete notes observations offers original passage perception Perfect System pitch position Ptolemy Ptolemy's Pythagorean ratio reason refers relation remaining scale Science sense seven similar smaller soft diatonic soul sounds species strings superparticular tables tension term tetrachord Theory third tonic diatonic tonic tonoi tonos translation treatise tuned whole tone Winnington-Ingram