Musical Pitch and the Measurement of Intervals Among the Ancient Greeks |
Other editions - View all
Popular passages
Page 20 - The first fact that we meet with in the music of all nations, so far as is yet known, is that alterations of pitch in -melodies take place by intervals, and not by continuous transitions.
Page 38 - A greater magnitude is said to be a multiple of a less, when the greater is measured by the less, that is, ' when the greater contains the less a certain number of times exactly.' III. " Ratio is a mutual relation of two magnitudes of the same kind to one another, in respect of quantity.
Page 4 - stroke transmitted through the ears by the air and passed through the brain and the blood to the soul.
Page 20 - ... I have described.2 The building of the scale must have been a matter of gradual accretion through ages and ages, though I suppose that its origin might possibly be conceded to lie in the sex cries of the anthropoid animal.3 "At the very bottom of the process of development," says Hubert H. Parry,4 "are those savage howls which have hardly any distinct notes in them at all. Many travelers record such things, and try to represent them in the European musical stave. For instance, the natives of...
Page 9 - The difference, then, between musical and nonmusical sounds seems to lie in this, that the former are constant, while the latter are continually varying. The human voice can produce sounds of both classes. In singing a sustained note it remains quite steady, neither rising nor falling. Its conversational tone, on the other hand, is perpetually varying in height even within a single syllable ; directly it ceases so to vary, its non-musical character disappears, and it becomes what is commonly called...
Page 10 - On the other hand, the motion to which noise is due is irregular and flitting, alternately fast and slow, and creating in the mind a bewildering and confusing effect of a more or less unpleasant character." The object we wish to attain, therefore, is to divide the sound wave in such a manner that it may always be reflected evenly and regularly from the surfaces with which it comes in contact. For this purpose we must examine the way in which the air vibrates in pipes, and draw our conclusions by...
Page 9 - Besides the three qualities above mentioned (amplitude, timbre and pitch) there exists another point in which sounds can be distinguished from each other, and which, though perhaps reducible to difference of timbre, requires some special remark, viz: that by which sounds are characterized either as noises or as musical notes. A musical note is the result of regular periodic vibrations of the air particles acting on the ear, and therefore also of the body whence they proceed, each particle passing...
Page 10 - OcUve. periodic vibrations of the air-particles acting on the ear, and therefore also of the body whence they proceed, each particle passing through the same phase at stated intervals of time. On the other hand, the motion to which noise is due is irregular and flitting, alternately fast and slow, and creating in the mind a bewildering and confusing effect of a more or less unpleasant character. Noise may also be produced by combining in an arbitrary manner several musical notes, as when one leans...
Page 9 - ... notes. A musical note is the result of regular periodic vibrations of the air-particles acting on the ear, and therefore also of the body whence they proceed, each particle passing through the same phase at stated intervals of time. On the other hand...