Presto Hindustani Music Alteration Analysis

4.4 Alteration
The second main rubette, the Alteration rubette, provides the functional¬ity for altering one composition to another. In this section, we generalize presto Hindustani Music’s alteration concepts (see Chapter 3, Section 3.2.1) for Power denotators. After the definition of alteration, we reconstruct some of the presto examples for better comprehension.
4.4.1 Definition of Alteration
For alteration we need:
• two compositions d1 : A@P(c11,. . . c1m) and d2 : A@P(c21,. . . c2n), cij being of form C, P being any form of type Power,
• d alteration dimensions with:
– S. = (S1,. . . Sd) altered Simple forms, Si 2 SP and Si =6 Sj for i=6 j and0 ~ i,j ~ d,
– (a1,b1),... (ad,bd),ai,bi 2 and – R. = (R1,. . . Rd) Simple forms, according to
. . ck) and c of form C so that n = ci, if δ(c, ci) ~ δ(c, cj) for j =6 i, 1 ~ i, j ~
These elements can just be calculated if Ri is embedded in R, which has been assumed above.
Then, the local alteration degree is calculated depending on the marginal alteration degrees (ai, bi). These degrees indicate, how much d1 is altered at its lowest and highest values on the Ri scale, whereby ai defines how much maxRiis altered and bi how much minRi. For ai, bi = 0, d1 remains unchanged and for ai, bi = 1, every element of d1 obtains the value in d2 with the smallest distance to it in dimension i, as we will see in the later definitions. If for example we choose d1 : A@Score, Ri = Onset, ai = 0 and bi = 1 the first Note of d1 in time is not changed at all, whereas the last note obtains a new onset, taken from the note in d2 that shows the least distance from it. For each note in between, the local alteration degree is calculated using linear interpolation, according to its position in time. We define the function for ck’s the local alteration degree degreei(SA(Ri, ck)) as follows: degreei(m) = ai + (ai -