This generates the log of a modified Bessel function of the second kind, order 0, suitable for use in amplitude-modulated FM.
size -- number of points in the table. Must be a power of 2 or a power-of-2 plus 1 (see f statement). The normal value is power-of-2 plus 1.
xint -- specifies the x interval [0 to +xint] over which the function is defined.
Note:
This subroutine draws the natural log of a modified Bessel function of the second kind, order 0 (commonly written as I subscript 0), over the x-interval requested. The call should have rescaling inhibited.
The function is useful as an amplitude scaling factor in cycle-synchronous amplitude-modulated FM. (See Palamin & Palamin, J. Audio Eng. Soc., 36/9, Sept. 1988, pp.671-684.) The algorithm is interesting because it permits the normally symmetric FM spectrum to be made asymmetric around a frequency other than the carrier, and is thereby useful for formant positioning. By using a table lookup index of I(r - 1/r), where I is the FM modulation index and r is an exponential parameter affecting partial strengths, the Palamin algorithm becomes relatively efficient, requiring only oscil's, table lookups, and a single exp call.
Here is a simple example of the GEN12 routine. It uses the files gen12.orc and gen12.sco. It generates the function ln(I0(x)) from 0 to 20. Here is its diagram:
Diagram of the waveform generated by GEN12.
Example 16-1. A simple example of the GEN12 routine.
/* gen12.orc */
; Initialize the global variables.
sr = 44100
kr = 4410
ksmps = 10
nchnls = 1
; Instrument #1.
instr 1
; Create an index over the length of our entire note.
kcps init 1/p3
kndx phasor kcps
; Read Table #1 with our index.
ifn = 1
ixmode = 1
kamp tablei kndx, ifn, ixmode
; Create a sine wave, use the Table #1 values to control
; the amplitude. This creates a sound with a long attack.
a1 oscil kamp*30000, 440, 2
out a1
endin
/* gen12.orc */
/* gen12.sco */
; Table #1: a modified Bessel function (using GEN12).
f 1 0 2049 12 20
; Table #2, a sine wave.
f 2 0 16384 10 1
; Play Instrument #1 for 2 seconds.
i 1 0 2
e
/* gen12.sco */