Pythagorean tuning (Greek: Πυθαγόρεια κλίμακα) is a tuning of the syntonic temperament in which the generator is the ratio 3:2 (i.e., the untempered perfect fifth), which is 702 cents wide.Hence, it is a system of musical tuning in which the frequency ratios of all intervals are based on the ratio 3:2, "found in the harmonic series." This ratio, also known as the "pure" perfect fifth, is chosen because it is one of the most consonant and easiest to tune by ear.The system had been mainly attributed to Pythagoras (sixth century BC) by modern authors of music theory, while Ptolemy, and later Boethius, ascribed the division of the tetrachord by only two intervals, called "semitonium", "tonus", "tonus" in Latin (256:243 x 9:8 x 9:8), to Eratosthenes.