Astronomy
Although a considerable knowledge of astronomy is evident from examination of Egyptian and Central American pyramids, for the purposes of this presentation, we will start our comparison somewhat later with the fact that the all-important beginnings of music and astronomy were well known to Pythagoras (-581 to -497) and to his surroundings. As a matter of fact, it is quite difficult to separate the person from the school here because Pythagoras left us no writings directly. However we are quite certain of the fact that he was aware that (a) the earth revolved around the sun and that its revolution on itself gave the appearance of the sun revolving around it,

Music
and (b) that the fifth was the interval of simplest proportion to produce a new note (the octave merely displacing the same note to another range). This fundamental position of the fifth for Pythagoras is so firmly ingrained into our collective memory that the form of tuning which uses only this interval bears his name (Pythagorean Tuning).

Astronomy
In astronomy, the culprit was certainly Ptolemy (Claudius Ptolemaeus 90-168) whose geocentric theory of astronomy placed the earth at the center of the universe with all the heavenly bodies circumnavigating it. This theory dominated academic and popular thinking for a millennium and a half.

Music
In music, the culprits are not as easy to spot but two of them deserve particular notice.
     1. Guido d'Arezzo (1000-1050) a Benedictine monk who provoked a revolution by inventing a new method of musical notation based on the first syllables of the lines from the Hymn to Saint John the Baptist. This precision of nomenclature was considered an affront and a menace to the existing habit of memorizing by rote.
     2 Gioseffo Zarlino (1517-1590) priest and organist, established the mathematical proportions between the degrees of the scale. Although his theoretical propositions were refuted by Vincenzo Galilei (father of Galileo), Zarlino (and to a certain extent Guido) succeeded in establishing the principle that the proximity of notes (a horizontal manifestation, as in the scale) was more fundamental than the simplicity of the mathematical relationship of the fifth (a vertical manifestation, as in chords). Music (especially harmony) was being led astray from the original Pythagorean concepts.

Astronomy
The battle to re-establish the Pythagorean heliocentric model (later endorsed by Aristarchos of Samos, -310 to -230) is a well documented saga. The patient, persistent observations by Nicolaj Kopernik (1473-1543) to replace the sun in its rightful, central position, the trial of Galileo Galilei (1564-1642), the additions and precisions of Johannes Kepler (1571-1630), of Isaac Newton (1642-1727), and more recently of Albert Einstein (1900-1955), have gradually accumulated an incontrovertible body of scientifically respectable astronomy. It is interesting to note that the path was not easy, neither rapid nor peaceful. The geocentric model was evidently a very egocentric one, humanity priding itself on inhabiting the central body of the universe. To maintain this glorified and preferential position, the "powerful" burnt Giordano Bruno (1548-1600) at the stake and, for the 100 years following the death of Galileo, 80% of "technical" papers on astronomy did not even mention the Pythagorean- Kopernican theory, and Bach probably still thought that the earth was the center of the universe. Astronomy painfully and slowly worked its way out of its erroneous past.

Music
Unfortunately, despite a few valiant efforts, music theory has not yet succeeded in establishing the truth.
     In his "Traité de l'harmonie" (1722), Jean-Philippe Rameau (1683-1764) proposed the daring (for the time) concept that harmony was more basic than melody. His first example of the dominant/tonic cadence is written in 5 voices (the 4 voice-leading lines, plus the fundamental bass) and he had the audacity to suggest that the subdominant (counter) chord would posses a sixth as fourth note. His work had no appreciable lasting influence and music theory remained proximity-oriented.
     In his "Traité d'Harmonie" (1907), François-Auguste Gevaert (1828-1908), after the usual painful presentation of harmony in triads, established light and order with progressions of tetrads by fifths, considering the seventh a true chordal tone, with its own clear and definite function. Unfortunately, he did not go back over the first section to differentiate the different categories of triads, real and deceptive, as incomplete tetrads. Very few academic theoreticians have even heard of Gevaert.
     In his "Handbuch der Harmonielehre" (Simplified Harmony, 1887), Hugo Riemann (1849-1919) presented in great detail the whole process of harmonic symmetrical inversion, the logical development of Rameau's symmetry between the dominant/tonic and sub-dominant/tonic progressions. However, Riemann still constructed his chords on a single note, the root (instead of in a 2-note frame), and, in the process of inversion, had the misfortune of calling the A minor chord the chord of E minor. The academic fraternity pounced on this weakness and threw out the precious baby with the relatively clean bath-water. Riemann is better known than Gevaert, but his influence was minimal and harmony remained unidirectional, with "seventh" chords only.
     It was not until the mid XXth century, in the 40s, 50s, and 60s, that a first generation of researchers presented a truly coherent and comprehensive view of harmony which is still largely unknown. Their concepts included the progressions of tetrads by fifths (from Gevaert) and the harmonic symmetry (from Riemann) to which they added the possibility of a chord possessing 2 functions, one with respect to the preceding chord, and another with respect to the following chord (what MusicNovatory now calls metamorphosis 4). They were also the first to perceive all the levels of rhythm. Needless to add that the resistance to these new concepts was violent.