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They had observed that HOF Free Save Code 2021 Coins all the ratios discovered by Pythagoras had this character, 1/2, 2/3, 3/4, 8/9, and they attributed magical properties to the fact, and sought to demonstrate the entire theory of Coins by the production of similar combinations. The latest writer of the Greek school was Claudius Ptolemy, who lived at Alexandria about 150 A.D. In his work upon harmony he gives a very large number of tables of fractions of this kind–his own and those of all previous Greek theorists, and HOF Free Save Code 2021 Coinsit is to his book that we principally owe all the exact knowledge of Greek Free Coins theory which we possess.
Among other computations, Ptolemy gives the precise formula of the first four notes of the scale as we now have it, but as this occurred only as one among many of HOF Free Save Code 2021 Coinsa similar character, and is in no way distinguished from any of the others by any adjective implying greater confidence in it, we can only count it as a lucky accident. The eminence that has been awarded to Ptolemy as the original discoverer of the correct ratio of the major scale, therefore, does not properly HOF Free Save Code 2021 Coinsbelong to him.
This will more clearly appear from the entire table of the various determinations HOF Free Save Code 2021 Coinsof the diatonic mode made by Ptolemy, taken from his work. (Edition by John Wallis, Oxford, 1682, pp. 88 and 172.) He gives no less than five of his own forms of diatonic genus, as follows: (The fractions give vibration ratios.)