2«* S. No 94., Oct. 17. '57.] 



NOTES AND QUERIES. 



31t 



The above musical intervals are supplied bj 

 Batteux from the following table, taking as his 

 basis the number 384 from Timseus, who fol- 

 lowed Eudorus and Grantor, the object being to 

 avoid fractions by means of a lai'ge integer.* 

 E 384, D 432, C 486, B 512, A 576, G 648, 

 F 729, E 768, D 864, C 972, B 1024, A 1152, 

 G 1296, F 1458, E 1536, D 1728, C 1944, B 2048, 

 B flat 2187, A 2304, G 2592, F 2916, E 3072, 

 D 3456, 3888, B flat 4374, A 4608, G 5184, 

 F5832, E 6144, E flat 6561, D 6912, C 7776, 

 B flat 8748, A 9216, G 10368 : making a total of 

 114,695, being 36 intervals. (Plato, Timse. Locr., 

 96 C.). It is worthy of observation that the first 

 number of Timseus, 384, very nearly corresponds 

 with Mercury's distance from the sun, and is 

 equal to 3 X 2^ and its octave, 768, is equal to 

 3 X 28 ; also that 384 happens to be the double 

 of Uranus's distance, 192, as above ; which last is 

 Plato's integer number, according to Plutarch 

 (Anim. Proc, xvi.). The number 384 is also the 

 product of 4 • 8 • 12, an arithmetical progression 

 whose common difference is 4. Saturn is 25 times 

 the distance of Mercury from the sun, whilst the 

 corresponding musical interval A, 9216, is equal 

 only to 24 times E, 384, a difference of one in- 

 teger exactly, but making a concord ; whilst the 

 analogy is very close in the other intervals re- 

 quired for the "music of the spheres." 



An inspection of the actual musical intervals 

 given by Batteux shows no correspondence .with 

 Bode's empirical 28 00, or the true distances 23 73, 

 26-67, and 27-67, of the split planet, as De Stael 

 supposes. 



Newton thought that the colours of the pris- 

 matic spectrum corresponded with musical inter- 

 vals, which thought is now regarded as merely 

 fanciful. (Lardner's Neu-t. Opt. U. K. S. 32.) 



With the same integer, Newton's scale (Brew- 

 ster's Optics, U. K. S. 23.) gives, — Violet, 384 ; 

 indigo, 614; blue, 902; green, 1190; yellow, 

 1382 ; orange, 1512 ; and red, 1728. 



The above will furnish examples of the truth of 

 the Pythagorean axiom, " robs apidixovs alTiovs ehai 

 rys oixrias" (Aristot. Met., i. 6.), meaning that the 

 Creator works by weight and measure. 



T. J. Bdckton. 



Lichfield. 



Uneda may rest assured that no ancient author 

 bears out the assertion that Pythagoras " predicted 



* The ratio of the semitones in the octave being 

 4* : 3S, or 256 : 243 = l^i,!, to get rid of the 3 in ^^, and 

 to allow of adding J for the perfect notes, he took 3 as his 

 base multiplied by 8 = 24, and 24 x 8 = 192, or 24 x 16 = 

 384, more than sufiicient to avoid fractions, for which 

 Plato's number, 192, suffices. In decimals | = "125, and 

 Jjij = •0535, showing that the semitone is not the exact 

 half, or it would be •0625 instead of '0535 : hence the ex- 

 traordinary diversities in harmony. 



the new planet discovered between Mars and Ju- 

 piter." Nor does Mde. De Stael's expression bear 

 out the assertion. She merely says " Ton affirm© 

 qu'il a pressenti les nouvelles planetes qui ont ete 

 decouvertes entre Mars et Jupiter." The verb 

 a pressenti does not mean " predicted," — but 

 merely had a presentiment. Her authority is a 

 brochure by M. Prevost of Geneva, a work which. 

 I have not seen, and therefore cannot decide how 

 far she was justified even in using that expression. 



All that can possibly be affirmed of Pythagoras 

 is that he seems to have had a correcter idea of 

 the solar system than any of the ancients, inas- 

 much as he maintained that the earth is not with- 

 out motion, nor situated in the centre of the 

 " spheres," but is one of those planets which make 

 their revolution about the " sphere of Fire." He 

 was also tolerably correct in estimating some of 

 the times of sidereal revolution: but the centre of 

 his system was not the Sun. He said " Fire holds 

 the middle place in the universe ; or, in the midst 

 of the four elements is placed the fiery globe of 

 unity." Round this "sphere of Fire, he made 

 the Sun itself revolve, and in the same time as 

 Mercury and Venus ! " 



Madame De Stael's " seven chords of the lyre " 

 does not express his theory as to the distances. 

 He conceived that the " celestial spheres " in which 

 the planets move, striking upon the ether through 

 which they pass, must produce a sound ; and that 

 this must vary according to the diversity of their 

 magnitude, velocity, and relative distances ; and 

 therefore argued that the distance of the several 

 celestial spheres from the earth correspond to the 

 proportion of notes in the musical scale — the dia- 

 tonic (of which he is said to be the inventor) pro- 

 ceeding by tones and semitones. Now, although 

 there is an obvious and necessary analogy between 

 sound and light — the diatonic scale being as it 

 were the prism of sound — it is evident that there 

 is no analogy whatever between such musical in- 

 tervals and the distances of the planets.* He be- 

 lieved that the moon and other planetary globes 

 are habitable, — that.the earth is a globe and ad- 

 mitted of antipodes. Philolaus of Crotona, one of 

 his followers, and the first who divulged his doc- 

 trine, announced that the universe, the Cosmos, 

 is one whole, which has a fiery centre, Hestia, 

 about which the ten celestial spheres revolve, — 

 heaven, the Sun, the planets, the earth, and the 

 moon ; that the sun has a vitreous surface, whence 

 the fire diffused through the world is reflected, 

 rendering the mirror from which it is reflected 



* This theory of musical intervals occtipied Kepler's 

 mind for many years in investigating the mean distances 

 of the planets and their revolutions; until, at length, 

 after seventeen years of useless experiment, he discovered 

 that " the squares of the times are proportional as the 

 cubes Qf the greater axes of the orbits." — La Place, vi, 

 414, - 



