Mensural notation recoverable from the modern text. While 19th and early 20th century editions of Renaissance music often preserved the large note values of the originals, including breves and longs, most modern editions will use scaled-down note values in order to match modern reading habits regarding tempo and beat structure. For 16th century music, a frequent scheme is diminution by a factor of 2 (i.e., rendering semibreves as modern minims), in a modern "alla breve" bar. Older music might be diminished by a factor of 4 (rendering semibreves as crotchets) or sometimes 8 (rendering breves as crotchets). For 13th-century pieces, diminution by
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