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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Արդյունքներ 28–ի 1-ից 3-ը:
Էջ 44
... highest in the enharmonic genus , for this in proportion to 1944 makes the 36:35 ratio , and in proportion to 1512 makes the 5 : 4 ratio.216 [ 31.13 ] 1701 will be the second highest in the diatonic genus for this with 1944217 makes the ...
... highest in the enharmonic genus , for this in proportion to 1944 makes the 36:35 ratio , and in proportion to 1512 makes the 5 : 4 ratio.216 [ 31.13 ] 1701 will be the second highest in the diatonic genus for this with 1944217 makes the ...
Էջ 135
... highest , so that the arrangement from the highest to the lowest through HGFE and ABCD is encompassed in a circle.43 [ 88.16 ] If on the aforementioned monochord we apply in succession to the notes for each part of the aforementioned ...
... highest , so that the arrangement from the highest to the lowest through HGFE and ABCD is encompassed in a circle.43 [ 88.16 ] If on the aforementioned monochord we apply in succession to the notes for each part of the aforementioned ...
Էջ 158
... highest . 192 [ 105.4 ] This is because the risings and settings 193 contain the beginning and end of appearance , the former as from the invisible , the latter as to the invisible ; the lowest and highest tunings contain the beginning ...
... highest . 192 [ 105.4 ] This is because the risings and settings 193 contain the beginning and end of appearance , the former as from the invisible , the latter as to the invisible ; the lowest and highest tunings contain the beginning ...
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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