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 on time value, and provides a simple introduction before considering more complicated and less familiar situations. This exposition follows . The fundamental change that the differential equation perspective brings is that, rather than computing a "number" (the present value "now"), one computes a "function" (the present value now or at any point in "future"). This function may then be analyzed—how does its value change over time—or compared with other functions. Formally, the statement that "value decreases over time" is given by defining the linear differential operator formula_37 as: This states that values decreases (−) over time (∂) at the discount