 In 1868, Adolf von Thimus showed that an indication by a 1st-century Pythagorean, Nicomachus of Gerasa, taken up by Iamblichus in the 4th century, and then worked out by von Thimus, revealed that Pythagoras already had a diagram that could fill a page with interlocking over- and undertone series.Kathleen Schlesinger pointed out, in 1939, that since the ancient Greek aulos, or reed-blown flute, had holes bored at equal distances, it must have produced a section of the undertone series.She said that this discovery not only cleared up many riddles about the original Greek modes, but indicated that many ancient systems around the world must have also been based on this principle.