The ancient musicians and mathematicians KNEW about and were fluent with the √2. They proved that to us with the ancient Babylonian cuneiform tablet known as from ~1800 BC.YBC 7289Or from the ancient Indian Vedic perspective ~1000 BC - In the Baudhayana sutra it appears as: The measure is to be increased by its third and this [third] again by its own fourth less the thirty-fourth part [of that fourth]; this is [the value of] the diagonal of a square [whose side is the measure]. mathematical formula for this musical TRITONE interval would be the geometric mean of √(AB), where A=1, and the next octave B=2, thus 1.414 = √2. |