Pythagoras as far back as 584–504 B.C., not only influenced the music in the classical Greek period (400 B.C.), but down to and throughout the Middle Ages to the Renaissance (1500s). To this day music is based on his mathematical discovery. He worked out a theory of numbers based on the idea that all nature was governed by the law of numbers and modern scientists have proven that he was correct in many of his ideas. In fact our orchestras and pianos are tuned in accordance with his theories. He invented an instrument called the monochord which consisted of a hollow wooden box with one string and movable fret. He discovered that when he divided the string exactly in half by means of the fret, the tone produced was an octave higher than the tone given out by striking the entire string; one-third of the string produced the interval of a fifth above the octave; one-fourth the length of the string produced a fourth above the fifth; one-fifth produced a third (large or major) above the fourth; one-sixth produced a third (small or minor); one-seventh produced a slightly smaller third and one-eighth produced a large second, three octaves above the sound of the entire string: [Illustration: (FUNDAMENTAL TONE)] The truth of Pythagoras’ theory of tone relationship has been proven by an experiment in physics showing that all of the above tones belong to the same tone family. An amusing experiment can be made by pressing silently any one of the tones marked 2, 3, 4, 5, 6, or 8, and striking the fundamental tone sharply, the key you are pressing silently will sound so that you can distinctly hear its pitch. The Greeks seem to have had no harmony (that is, combining of two or more tones in chords) outside of the natural result of men’s voices and women’s singing together. But they had groups of singers answering each other in what is called _antiphony_ (anti-against, phony-sound). Even our American Indians have their song leader and chorus answering each other. Greek rhythm followed the rhythm of the spoken word and was considered a part of their poetic system. GREEK INSTRUMENTS We have already spoken of the _syrinx_, Pan’s Pipes, the instrument of Pan, the satyrs and of the shepherds; the _monochord_, Pythagoras’ invention; the _lyre_ and _kithara_; and the flute or _aulos_. The lyre, of the family of stringed instruments, was the Greek national instrument. It was the first to be used in their musical competitions, and helped in the forming of the Greek modes. These were of two types, the lyre and the kithara. The first lyres which came down from the age of myths and fables were originally made of the shell of a tortoise and had four strings (the tetrachord) and later seven and even more strings. This form of the lyre was called _chelys_, or the tortoise, and was used for accompanying drinking songs and popular love songs.