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 the contributions of "FV", the value of cash flow at time "t": Note that this series can be summed for a given value of "n", or when "n" is ∞. This is a very general formula, which leads to several important special cases given below. In this case the cash flow values remain the same throughout the "n" periods. The present value of an annuity (PVA) formula has four variables, each of which can be solved for by numerical methods: To get the PV of an annuity due, multiply the above equation by (1 + "i"). In this case each