Harmonics of Aristoxenus

Harmonics of Aristoxenus

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1902 edition. Excerpt: ...at our conclusions unaided. In the first place then we shall assert that if any concord be added to the octave the sum is a concord. This property is peculiar to the octave. For if to an octave be added any concord, whether less than, equal to, or greater than itself, the sum is a concord. But this is not the case with the two smallest concords. For the doubling of a Fourth or Fifth does not produce a concord; nor does the addition to either one of them of the concord compounded of the octave and that one; but the sum of such concords will always be a discord. A tone is the excess of the Fifth over the Fourth; the 46 Fourth consists of two tones and a half. The following fractions of a tone occur in melody: the half, called a semitone; the third, called the smallest Chromatic diesis; the quarter, called the smallest Enharmonic diesis. No smaller interval than the last exists in melody. Here we have two cautions for our hearers; firstly, many have misunderstood us to say that melody admits the division of the tone into three or four equal parts. This misunderstanding is due to their not observing that to employ the third part of a tone is a very different thing from dividing a tone into three parts and singing all three. Secondly, from an abstract point of view, no doubt, we regard no interval as the smallest possible. The differences of the genera are found in such a tetrachord as that from Mese to Hypate, where the extremes are fixed, while one or both of the means vary. As the variable note must move in a certain locus, we must ascertain the limits of the locus of each of these intermediate notes. The highest Lichanus is that which is a tone removed from the Mese. It constitutes the genus Diatonic. The lowest is that which is two tones...
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Product details

  • Paperback
  • 182.88 x 241.3 x 7.62mm | 136.08g
  • Rarebooksclub.com
  • English
  • Illustrations, black and white
  • 1236930827
  • 9781236930828
  • 2,335,905