In pianos and harpsichords, generally less tension or thicker strings are used in the lower register to avoid the need for such large dimensions as demanded by a Pythagorean scale.
12.
Thus a Pythagorean scale is C D E F G A B, while the 5-limit Ptolemaic scale is C D E " 1 F G A " 1 B " 1.
13.
The Pythagorean comma shown as the gap ( on the right side ) which causes a 12-pointed star to fail to close, which star represents the Pythagorean scale; each line representing a just perfect fifth.
14.
A Pythagorean scale can be constructed " upwards " by wrapping a chain of perfect fifths around an octave, but it can also be constructed " downwards " by wrapping a chain of perfect fourths around the same octave.
15.
The "'Pythagorean scale "'is any tune tetrachords and the twelve tone Pythagorean system was developed by medieval music theorists using the same method of tuning in perfect fifths, however there is no evidence that Pythagoras himself went beyond the tetrachord.
16.
Beyond the well-known structural legacies of the Pythagorean scale, and the related mathematical developments it upheld to define western classical music, relatively little is understood about the precise character of music during this period; we do know, however, that it left, as so often, a strong mark on the culture of Rome.
17.
The Pythagorean scale of numbers was at once discovered to be perfect; but the poems of Homer we yet know not to transcend the common limits of human intelligence, but by remarking, that nation after nation, and century after century, has been able to do little more than transpose his incidents, new name his characters, and paraphrase his sentiments.
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