Longa (music) Longa (music) A longa (pl. "longe" or "longae"), long, quadruple note (Am.), or quadruple whole note is a musical note that could be either twice or three times as long as a breve (Am.: double whole note, or double note), four or six times as long as a semibreve (Am.: whole note), that appears in early music. The number of breves in a long was determined by the "modus" or "mode" of a passage. Sections in perfect mode used three breves to the long while sections in imperfect mode used two breves to the long. Imperfect longs, worth two breves,
Time value of money not already occurred), or simply not define the value at that point. In case the discount rate is constant, formula_47 this simplifies to where formula_49 is "time remaining until cash flow". Thus for a stream of cash flows "f"("u") ending by time "T" (which can be set to formula_50 for no time horizon) the value at time "t," formula_51 is given by combining the values of these individual cash flows: This formalizes time value of money to future values of cash flows with varying discount rates, and is the basis of many formulas in financial mathematics, such as the Black–Scholes