"O thou maker of the whele that bereth the sterres, which that art y-fastned to thy perdurable chayer, and tornest the hevene with a ravisshing sweigh, and constreinest the sterres to suffren thy lawe;"[15] The firmament, which in Chaucer is not restricted to the eighth sphere but generally refers to the whole expanse of the heavens, is many times mentioned by Chaucer; and its appearance on clear or cloudy nights, its changing aspects before an impending storm or with the coming of dawn, beautifully described.[16] 2. _The Harmony of the Spheres_ Some of the cosmological ideas reflected in Chaucer's writings can be traced back to systems older than the Ptolemaic. The beautiful fancy that the universe is governed by harmony had its origin in the philosophy of the Pythagoreans in the fourth century B. C., and continued to appeal to men's imagination until the end of the Middle Ages. It was thought that the distances of the planetary spheres from one another correspond to the intervals of a musical scale and that each sphere as it revolves sounds one note of the scale. When asked why men could not hear the celestial harmony, the Pythagoreans said: A blacksmith is deaf to the continuous, regular beat of the hammers in his shop; so we are deaf to the music which the spheres have been sending forth from eternity. In ancient and mediaeval cosmology it was only the seven spheres of the planets that were generally supposed to participate in this celestial music; but the poets have taken liberties with this idea and have given it to us in forms suiting their own fancies. Milton bids all the celestial spheres join in the heavenly melody: "Ring out, ye crystal spheres, Once bless our human ears, If ye have power to touch our senses so; And let your silver chime Move in melodious time, And let the base of heaven's deep organ blow; And with your ninefold harmony, Make up full consort to the angelic symphony."[17] Shakespeare lets every orb of the heavens send forth its note as it moves: "There's not the smallest orb which thou behold'st But in his motion like an angel sings, Still quiring to the young-eyed cherubins;"[18] Chaucer, too, makes all nine spheres participate: "And after that the melodye herde he That cometh of thilke speres thryes three, That welle is of musyke and melodye In this world heer, and cause of armonye."[19] Only in unusual circumstances can the music of the spheres be heard by mortal ears. In the lines just quoted the celestial melody is heard during a dream or vision. In _Troilus and Criseyde_, after Troilus' death his spirit is borne aloft to heaven whence he beholds the celestial orbs and hears the melody sent forth as they revolve: "And ther he saugh, with ful avysement, The erratik sterres, herkeninge armonye With sownes fulle of hevenish melodye."[20] 3. _The Cardinal Points and the Regions of the World_