Music
Ptolemy also wrote an influential work, Harmonics, on music theory and the mathematics of music. After criticizing the approaches of his predecessors, Ptolemy argued for basing musical intervals on mathematical ratios (in contrast to the followers of Aristoxenus and in agreement with the followers of Pythagoras), backed up by empirical observation (in contrast to the overly theoretical approach of the Pythagoreans). Ptolemy wrote about how musical notes could be translated into mathematical equations and vice versa in Harmonics. This is called Pythagorean tuning because it was first discovered by Pythagoras. However, Pythagoras believed that the mathematics of music should be based on the specific ratio of 3:2, whereas Ptolemy merely believed that it should just generally involve tetrachords and octaves. He presented his own divisions of the tetrachord and the octave, which he derived with the help of a monochord. Ptolemy's astronomical interests also appeared in a discussion of the "music of the spheres". See: Ptolemy's intense diatonic scale.
Read more about this topic: Ptolemy
Famous quotes containing the word music:
“I cannot say what poetry is; I know that our sufferings and our concentrated joy, our states of plunging far and dark and turning to come back to the world—so that the moment of intense turning seems still and universal—all are here, in a music like the music of our time, like the hero and like the anonymous forgotten; and there is an exchange here in which our lives are met, and created.”
—Muriel Rukeyser (1913–1980)
“The first condition for making music is not to make a noise.”
—José Bergamín (1895–1983)
“Nearly all the bands are mustered out of service; ours therefore is a novelty. We marched a few miles yesterday on a road where troops have not before marched. It was funny to see the children. I saw our boys running after the music in many a group of clean, bright-looking, excited little fellows.”
—Rutherford Birchard Hayes (1822–1893)