Thenceforward, the great task was to extend the tone-corpus into the infinity, or rather to _resolve it into an infinite space of tone_. Gothic had developed the instruments into families of definite timbre. But the new-born “orchestra” no longer observes limitations imposed by the human voice, but treats it as a voice to be combined with other voices—at the same moment as our mathematic proceeds from the geometrical analysis of Fermat to the purely functional analysis of Descartes.[295] In Zarlino’s “Harmony” (1558) appears a genuine perspective of pure tonal space. We begin to distinguish between ornamental and fundamental instruments. Melody and embellishment join to produce the Motive, and this in development leads to the rebirth of counterpoint in the form of the fugal style, of which Frescobaldi was the first master and Bach the culmination. To the vocal masses and motets the Baroque opposes its grand, orchestrally-conceived forms of the oratorio (Carissimi), the cantata (Viadana) and the opera (Monteverde). Whether a bass melody be set against upper voices, or upper voices be concerted against one another upon a background of _basso continuo_, always sound-worlds of characteristic expression- quality work reciprocally upon one another in the infinity of tonal space, supporting, intensifying, raising, illuminating, threatening, overshadowing—a music all of interplay, scarcely intelligible save through ideas of contemporary Analysis. From out of these forms of the early Baroque there proceeded, in the 17th Century, the sonata-like forms of suite, symphony and concerto grosso. The inner structure and the sequence of movements, the thematic working-out and modulation became more and more firmly established. And thus was reached the great, immensely dynamic, form in which music—now completely bodiless—was raised by Corelli and Handel and Bach to be the ruling art of the West. When Newton and Leibniz, about 1670, discovered the Infinitesimal Calculus, the fugal style was fulfilled. And when, about 1740, Euler began the definitive formulation of functional Analysis, Stamitz and his generation were discovering the last and ripest form of musical ornamentation, the four-part movement[296] as vehicle of pure and unlimited motion. For, at that time, there was still this one step to be taken. The theme of the fugue “is,” that of the new sonata-movement “becomes,” and the issue of its working out is in the one case a picture, in the other a drama. Instead of a series of pictures we get a cyclic succession,[297] and the real source of this tone-language was in the possibilities, realized at last, of our deepest and most intimate kind of music—the music of the strings. Certain it is that the violin is the noblest of all instruments that the Faustian soul has imagined and trained for the expression of its last secrets, and certain it is, too, that it is in string quartets and violin sonatas