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 is to emphasize that "u" is a "parameter" (fixed in any instance—the time when the cash flow will occur), while "t" is a "variable" (time). In other words, future cash flows are exponentially discounted (exp) by the sum (integral, formula_44) of the future discount rates (formula_45 for future, "r"("v") for discount rates), while past cash flows are worth 0 (formula_46), because they have already occurred. Note that the value "at" the moment of a cash flow is not well-defined – there is a discontinuity at that point, and one can use a convention (assume cash flows have already occurred, or