The Greek scales were based on tetrachords, from the Greek words tetra-four, chord-string that is, a group of four strings. If you play on the piano B C D E and C D E F and D E F G you will find the three tetrachords that formed the primary modes of the Greeks:—Dorian, Phrygian and Lydian.
Perhaps you have heard in Greek architecture of the Doric column which came from Doria, a province in Greece, and the Ionic column, from Ionia, and so on. In the same way the scales were named for sections of the country from which they first came, Dorian mode, Ionian, Æolian, Phrygian, Lydian, etc.
The Greek tetrachord was formed on the interval of a fourth, for example from E to A—these were called standing tones, because the intervals between the two standing tones or permanent tones could be changed but the first and the fourth always remained the same—
By putting two tetrachords together all the other Greek scales were formed. These fell into two classes, and according to Cecil Forsyth in his History of Music these classes were called the join and the break. When the second tetrachord began on the fourth tone of the first tetrachord, Mr. Forsyth calls it the joining method, thus.
When the second tetrachord began on the tone above the fourth tone of the first tetrachord, he calls it the breaking method, thus:
By using the join and the break with each of the three modes, Dorian, Phrygian and Lydian, you can see to what a great variety of scales and names this would lead. The Greeks spoke of their scales from the top note down, instead of from the lowest note up, as we do.
The first kithara was supposed to have been an instrument of four strings that could be tuned in any of these different ways, with the half-step either between the first and second strings, or between the second and third, or between the third and fourth. Two instruments tuned differently formed the complete scale, but it did not take long to add strings to their lyres and kitharas so that they could play an entire scale on one instrument.