A few words are necessary about 'Proportion.' This term was used in Elizabethan times exactly as we now use 'Time.' The 'times' used in modern music can practically be reduced to two—viz., Duple (two beats to the bar) and Triple (three beats to the bar). But in Elizabeth's day the table of various Proportions was a terribly elaborate thing. Of course many of these 'Proportions' never really came into practical use—but there was plenty of mystery left even after all deductions.
Morley (Introduction, 1597) gives Five kinds of proportions 'in most common use'—viz., Dupla, Tripla, Quadrupla, Sesquialtera, and Sesquitertia. The first three correspond to what we still call Duple, Triple, and Quadruple Time—i.e., 2 in the bar, 3 in the bar, and 4 in the bar. ['Bars' were not in general use till the end of the 16th century, but the principle was the same. The bars themselves are merely a convenience.]
Sesquialtera is more complicated, and means 'three notes are sung to two of the same kinde'; and 'Sesquitertia is when four notes are sung to three of the same kinde.' 'But' (Morley adds), 'if a man would ingulphe himselfe to learn to sing, and set down all them which Franchinus Gaufurius [1496] hath set down in his booke De Proportionibus Musicis, he should find it a matter not only hard but almost impossible.'
Ornithoparcus, in his Micrologus (1535), gives us an idea of the way this subject of proportion was treated by more 'learned' writers. He says (1) that music considers only the proportion of inequality, (2) that this is two-fold—viz., the greater and the lesser inequality. (3) The greater inequality contains five proportions, namely, multiplex, superparticular, superpartiens, multiplex superparticular, and multiplex superpartiens.
This is more amusing than instructive, perhaps. The three last lines of this passage refer to the various stories of real or pretended cure of disease by the use of particular pieces of music. One of the best known of these diseases is 'Tarantism,' or the frenzy produced by the bite of the Tarantula, in Italy.
Kircher, a learned Jesuit (1601-1680), gives an account, in his "Musurgia," of the cure of this madness by certain airs, by which the patient is stimulated to dance violently. The perspiration thus produced was said to effect a cure. In his "Phonurgia nova" (1673) Kircher actually gives the notes of the tune by which one case was cured.
In this connection, Kircher mentions King Saul's madness, which was relieved by David's harp playing. This is certainly to the point, and may well have been in Shakespeare's mind. [See George Herbert's poem, 'Doomsday,' verse 2.]
Our modern Tarantellas derive their name and characteristic speed from the old Tarantula.
Lear I, ii, 137. Edmund pretends not to see Edgar's entrance.
Edmund (aside). Pat he comes, like the catastrophe of the old comedy: my cue is villainous melancholy, with a sigh like Tom o' Bedlam.—O! these eclipses do portend these divisions. Fa, sol, la, mi.