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to the other as well as that of either part to the whole length.53 Ptolemy, however, a few generations later, found no continuing tradition of the monochord's use; and he considers it an inadequate instrument, though he does provide some detailed advice on how best to construct it.54 Elsewhere he recommends fitting out the kanon with eight or fifteen strings, equal in length and tuning, or (in the case of the fifteen-stringed version) with seven strings tuned to one pitch and the other eight an octave higher. There can be separate bridges, or just one crossing a bank of strings diagonally.55 |
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Ptolemy also describes a contrivance used by some theoreticians and poetically called the Helikon, after the mountain on which the Muses dwell. It had four strings and one diagonal bridge. The proportional lengths for the concords were constructed by geometrical procedures, given a square and the mid-points of its sides (Fig. 8.3). The verticals represent the strings; the position of the third |
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one on the horizontal axis is pinpointed by the intersection of the lines BD and AE. AE represents the bridge. The various vibrating lengths then available, 3, 4, 6, 8, 9, 12, will yield all the intervals contained in the note-series E A e a b e'.56 |
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53 Ptol. Harm. 2.13 p. 67.22ff. |
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54Harm. 1.8, 2.12. |
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55Harm. 1.11, 2.1-2, 13, 16, 3.1-2. See Barker, GMW ii. 300, 315, 319, 344, 356f., 362-70. |
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56 Ptol. Harm. 2.2 (Barker, GMW ii. 319f.), cf. Aristid. Quint. p. 99. 1ff. |
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