inations of Didymus (born at Alexandria, 63 B.C.) that the true
tuning of the first four tones of the scale occurs. This is it:

Diatonic (Didymus), 9/8 x 10/9 x 16/15 = 4/3.

Thus it appears that it was Didymus, and not Ptolemy, who proposed the
tuning of the tetrachord which is now accepted as correct. It is very
evident from the entire course of the discussion as conducted by
Ptolemy that his calculations were purely abstract. He is to be
reckoned among the Pythagoreans, who held that in time and number all
things consist. It was not until some centuries later that the happy
thought of Didymus came to recognition as the true statement of the
mathematical relation of the first four tones of the scale, and then
only through the ears of a race of musicians following the great
thesis of Aristoxenos, that in music it is always the ear which must
be the arbiter, and not abstract reasoning or calculation. The ratios
of the major and minor third also occur among the calculations of
Didymus; but here, again, they count for nothing in the history of
art, because these intervals derive their value and expressive quality
from their harmonic relation, while Didymus and all the Greeks
employed them as melodic skips only, and reckoned them in with a
multitude of other skips and progressions, without distinguishing them
in any way.

The one characteristic instrument of Greek music from the earliest to
the latest days was the lyre. In the oldest times, those of Homer and
Hesiod, it was called phorminx, which is believed to have been the
form so often represented on Greek vases of a turtle shell with side
pieces like horns, an instrument having but little effective
resonance. The later form was the so-called cithara, the most common
shape of which is that made familiar to all by the pedal piece of the
square pianoforte. This instrument rarely had more than six strings,
and as it had no finger board it could have had no more notes than
strings. Chappell, the English historian, attempts to demonstrate that
certain ones of these instruments had a bridge dividing the string
into two parts, thus largely increasing the compass, but the evidence
supporting this hypothesis is not satisfactory. Plato speaks of
instruments of many strings imported from Asia, which seem to have
been the fashion or fad in his day. He disapproved of them very
heartily, but the terms in which he speaks of them show that he cannot
have been very familiar wit