fof2
fof2 — Produces sinusoid bursts including k-rate incremental indexing with each successive burst.
Description
Audio output is a succession of sinusoid bursts initiated at frequency xfund with a spectral peak at xform. For xfund above 25 Hz these bursts produce a speech-like formant with spectral characteristics determined by the k-input parameters. For lower fundamentals this generator provides a special form of granular synthesis.
fof2 implements k-rate incremental indexing into ifna function with each successive burst.
Syntax
ares fof2 xamp, xfund, xform, koct, kband, kris, kdur, kdec, iolaps, \
ifna, ifnb, itotdur, kphs, kgliss [, iskip]
Initialization
iolaps -- number of preallocated spaces needed to hold overlapping burst data. Overlaps are frequency dependent, and the space required depends on the maximum value of xfund * kdur. Can be over-estimated at no computation cost. Uses less than 50 bytes of memory per iolap.
ifna, ifnb -- table numbers of two stored functions. The first is a sine table for sineburst synthesis (size of at least 4096 recommended). The second is a rise shape, used forwards and backwards to shape the sineburst rise and decay; this may be linear (GEN07) or perhaps a sigmoid (GEN19).
itotdur -- total time during which this fof will be active. Normally set to p3. No new sineburst is created if it cannot complete its kdur within the remaining itotdur.
iskip (optional, default=0) -- If non-zero, skip initialization (allows legato use).
Performance
xamp -- peak amplitude of each sineburst, observed at the true end of its rise pattern. The rise may exceed this value given a large bandwidth (say, Q < 10) and/or when the bursts are overlapping.
xfund -- the fundamental frequency (in Hertz) of the impulses that create new sinebursts.
xform -- the formant frequency, i.e. freq of the sinusoid burst induced by each xfund impulse. This frequency can be fixed for each burst or can vary continuously.
koct -- octaviation index, normally zero. If greater than zero, lowers the effective xfund frequency by attenuating odd-numbered sinebursts. Whole numbers are full octaves, fractions transitional.
kband -- the formant bandwidth (at -6dB), expressed in Hz. The bandwidth determines the rate of exponential decay throughout the sineburst, before the enveloping described below is applied.
kris, kdur, kdec -- rise, overall duration, and decay times (in seconds) of the sinusoid burst. These values apply an enveloped duration to each burst, in similar fashion to a Csound linen generator but with rise and decay shapes derived from the ifnb input. kris inversely determines the skirtwidth (at -40 dB) of the induced formant region. kdur affects the density of sineburst overlaps, and thus the speed of computation. Typical values for vocal imitation are .003,.02,.007.
kphs -- allows k-rate indexing of function table ifna with each successive burst, making it suitable for time-warping applications. Values of kphs are normalized from 0 to 1, 1 being the end of the function table ifna.
kgliss -- sets the end pitch of each grain relative to the initial pitch, in octaves. Thus kgliss = 2 means that the grain ends two octaves above its initial pitch, while kgliss = -3/4 has the grain ending a major sixth below. Each 1/12 added to kgliss raises the ending frequency one half-step. If you want no glissando, set kgliss to 0.
Csound's fof generator is loosely based on Michael Clarke's C-coding of IRCAM's CHANT program (Xavier Rodet et al.). Each fof produces a single formant, and the output of four or more of these can be summed to produce a rich vocal imitation. fof synthesis is a special form of granular synthesis, and this implementation aids transformation between vocal imitation and granular textures. Computation speed depends on kdur, xfund, and the density of any overlaps.
![[Note]](images/note.png)
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Note |
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The ending frequency of any grain is equal to kform * (2 ^ kgliss), so setting kgliss too high may result in aliasing. For example, kform = 3000 and kgliss = 3 places the ending frequency over the Nyquist if sr = 44100. It is a good idea to scale kgliss accordingly. |
Examples
Here is an example of the fof2 opcode. Play fof2.csd
Example 361. Example of the fof2 opcode.
See the sections Real-time Audio and Command Line Flags for more information on using command line flags.
<CsoundSynthesizer> <CsOptions> ; Select audio/midi flags here according to platform ; Audio out Audio in -odac -iadc ;;;RT audio I/O ; For Non-realtime ouput leave only the line below: ; -o fof2.wav -W ;;; for file output any platform </CsOptions> <CsInstruments> sr = 44100 ksmps = 128 nchnls = 2 ;By Andres Cabrera 2007 instr 1 ;table-lookup vocal synthesis kris init p12 kdur init p13 kdec init p14 iolaps init p15 ifna init 1 ; Sine wave ifnb init 2 ; Straight line rise shape itotdur init p3 kphs init 0 ; No phase modulation (constant kphs) kfund line p4, p3, p5 kform line p6, p3, p7 koct line p8, p3, p9 kband line p10, p3, p11 kgliss line p16, p3, p17 kenv linen 5000, 0.03, p3, 0.03 ;to avoid clicking aout fof2 kenv, kfund, kform, koct, kband, kris, kdur, kdec, iolaps, \ ifna, ifnb, itotdur, kphs, kgliss outs aout, aout endin </CsInstruments> <CsScore> f1 0 8192 10 1 f2 0 4096 7 0 4096 1 ; kfund1 kfund2 kform1 kform2 koct1 koct2 kband1 kband2 kris kdur kdec iolaps kgliss1 kgliss2 i1 0 4 220 220 510 510 0 0 30 30 0.01 0.03 0.01 20 1 1 i1 + . 220 220 510 910 0 0 30 30 0.01 0.03 0.01 20 1 1 i1 + . 220 220 510 510 0 0 100 30 0.01 0.03 0.01 20 1 1 i1 + . 220 220 510 510 0 1 30 30 0.01 0.03 0.01 20 1 1 i1 + . 220 220 510 510 0 0 30 30 0.01 0.03 0.01 20 1 2 i1 + . 220 220 510 510 0 0 30 30 0.01 0.03 0.01 20 0.5 1 i1 + . 220 220 510 510 0 0 30 30 0.01 0.05 0.01 100 1 1 i1 + . 220 440 510 510 0 0 30 30 0.01 0.05 0.01 100 1 1 e </CsScore> </CsoundSynthesizer>
Here is another example of the fof2 opcode, which generates vowel tones using formants generated by fof2 coinciding with values from the Formant Values appendix. Play fof2-2.csd
Example 362. Example of the fof2 opcode to produce vowel sounds.
<CsoundSynthesizer> <CsOptions> ; Select audio/midi flags here according to platform ; Audio out Audio in -odac -iadc ;;;RT audio I/O ; For Non-realtime ouput leave only the line below: ; -o fof2.wav -W ;;; for file output any platform </CsOptions> <CsInstruments> sr = 44100 ksmps = 128 nchnls = 2 ; Example by Chuckk Hubbard 2007 instr 1 ;table-lookup vocal synthesis iolaps = 120 ifna = 1 ;f1 - sine wave ifnb = 2 ;f2 - linear rise shape itotdur = p3 iamp = p4 * 0dbfs ifreq1 = p5 ;starting frequency ifreq2 = p6 ;ending frequency kamp linseg 0, .003, iamp, itotdur-.007, iamp, .003, 0, .001, 0 kfund expseg ifreq1, itotdur, ifreq2 koct init 0 kris init .003 kdur init .02 kdec init .007 kphs init 0 kgliss init 0 iforma = p7 ;starting spectrum iformb = p8 ;ending spectrum iform1a tab_i 0, iforma ;read values of 5 formants for 1st spectrum iform2a tab_i 1, iforma iform3a tab_i 2, iforma iform4a tab_i 3, iforma iform5a tab_i 4, iforma idb1a tab_i 5, iforma ;read decibel levels for same 5 formants idb2a tab_i 6, iforma idb3a tab_i 7, iforma idb4a tab_i 8, iforma idb5a tab_i 9, iforma iband1a tab_i 10, iforma ;read bandwidths for same 5 formants iband2a tab_i 11, iforma iband3a tab_i 12, iforma iband4a tab_i 13, iforma iband5a tab_i 14, iforma iamp1a = ampdb(idb1a) ;convert db to linear multipliers iamp2a = ampdb(idb2a) iamp3a = ampdb(idb3a) iamp4a = ampdb(idb4a) iamp5a = ampdb(idb5a) iform1b tab_i 0, iformb ;values of 5 formants for 2nd spectrum iform2b tab_i 1, iformb iform3b tab_i 2, iformb iform4b tab_i 3, iformb iform5b tab_i 4, iformb idb1b tab_i 5, iformb ;decibel levels for 2nd set of formants idb2b tab_i 6, iformb idb3b tab_i 7, iformb idb4b tab_i 8, iformb idb5b tab_i 9, iformb iband1b tab_i 10, iformb ;bandwidths for 2nd set of formants iband2b tab_i 11, iformb iband3b tab_i 12, iformb iband4b tab_i 13, iformb iband5b tab_i 14, iformb iamp1b = ampdb(idb1b) ;convert db to linear multipliers iamp2b = ampdb(idb2b) iamp3b = ampdb(idb3b) iamp4b = ampdb(idb4b) iamp5b = ampdb(idb5b) kform1 line iform1a, itotdur, iform1b ;transition between formants kform2 line iform2a, itotdur, iform2b kform3 line iform3a, itotdur, iform3b kform4 line iform4a, itotdur, iform4b kform5 line iform5a, itotdur, iform5b kband1 line iband1a, itotdur, iband1b ;transition of bandwidths kband2 line iband2a, itotdur, iband2b kband3 line iband3a, itotdur, iband3b kband4 line iband4a, itotdur, iband4b kband5 line iband5a, itotdur, iband5b kamp1 line iamp1a, itotdur, iamp1b ;transition of amplitudes of formants kamp2 line iamp2a, itotdur, iamp2b kamp3 line iamp3a, itotdur, iamp3b kamp4 line iamp4a, itotdur, iamp4b kamp5 line iamp5a, itotdur, iamp5b ;5 formants for each spectrum a1 fof2 kamp1, kfund, kform1, koct, kband1, kris, kdur, kdec, iolaps, ifna, ifnb, itotdur, kphs, kgliss a2 fof2 kamp2, kfund, kform2, koct, kband2, kris, kdur, kdec, iolaps, ifna, ifnb, itotdur, kphs, kgliss a3 fof2 kamp3, kfund, kform3, koct, kband3, kris, kdur, kdec, iolaps, ifna, ifnb, itotdur, kphs, kgliss a4 fof2 kamp4, kfund, kform4, koct, kband4, kris, kdur, kdec, iolaps, ifna, ifnb, itotdur, kphs, kgliss a5 fof2 kamp5, kfund, kform5, koct, kband5, kris, kdur, kdec, iolaps, ifna, ifnb, itotdur, kphs, kgliss aout = (a1+a2+a3+a4+a5) * kamp/5 ;sum and scale aenv linen 1, 0.05, p3, 0.05 ;to avoid clicking outs aout*aenv, aout*aenv endin </CsInstruments> <CsScore> f1 0 8192 10 1 f2 0 4096 7 0 4096 1 ;**************************************************************** ; tables of formant values adapted from MiscFormants.html ; 100's: soprano 200's: alto 300's: countertenor 400's: tenor 500's: bass ; -01: "a" sound -02: "e" sound -03: "i" sound -04: "o" sound -05: "u" sound ; p-5 through p-9: frequencies of 5 formants ; p-10 through p-14: decibel levels of 5 formants ; p-15 through p-19: bandwidths of 5 formants ; formant frequencies decibel levels bandwidths ;soprano f101 0 16 -2 800 1150 2900 3900 4950 0.001 -6 -32 -20 -50 80 90 120 130 140 f102 0 16 -2 350 2000 2800 3600 4950 0.001 -20 -15 -40 -56 60 100 120 150 200 f103 0 16 -2 270 2140 2950 3900 4950 0.001 -12 -26 -26 -44 60 90 100 120 120 f104 0 16 -2 450 800 2830 3800 4950 0.001 -11 -22 -22 -50 40 80 100 120 120 f105 0 16 -2 325 700 2700 3800 4950 0.001 -16 -35 -40 -60 50 60 170 180 200 ;alto f201 0 16 -2 800 1150 2800 3500 4950 0.001 -4 -20 -36 -60 80 90 120 130 140 f202 0 16 -2 400 1600 2700 3300 4950 0.001 -24 -30 -35 -60 60 80 120 150 200 f203 0 16 -2 350 1700 2700 3700 4950 0.001 -20 -30 -36 -60 50 100 120 150 200 f204 0 16 -2 450 800 2830 3500 4950 0.001 -9 -16 -28 -55 70 80 100 130 135 f205 0 16 -2 325 700 2530 3500 4950 0.001 -12 -30 -40 -64 50 60 170 180 200 ;countertenor f301 0 16 -2 660 1120 2750 3000 3350 0.001 -6 -23 -24 -38 80 90 120 130 140 f302 0 16 -2 440 1800 2700 3000 3300 0.001 -14 -18 -20 -20 70 80 100 120 120 f303 0 16 -2 270 1850 2900 3350 3590 0.001 -24 -24 -36 -36 40 90 100 120 120 f304 0 16 -2 430 820 2700 3000 3300 0.001 -10 -26 -22 -34 40 80 100 120 120 f305 0 16 -2 370 630 2750 3000 3400 0.001 -20 -23 -30 -34 40 60 100 120 120 ;tenor f401 0 16 -2 650 1080 2650 2900 3250 0.001 -6 -7 -8 -22 80 90 120 130 140 f402 0 16 -2 400 1700 2600 3200 3580 0.001 -14 -12 -14 -20 70 80 100 120 120 f403 0 16 -2 290 1870 2800 3250 3540 0.001 -15 -18 -20 -30 40 90 100 120 120 f404 0 16 -2 400 800 2600 2800 3000 0.001 -10 -12 -12 -26 70 80 100 130 135 f405 0 16 -2 350 600 2700 2900 3300 0.001 -20 -17 -14 -26 40 60 100 120 120 ;bass f501 0 16 -2 600 1040 2250 2450 2750 0.001 -7 -9 -9 -20 60 70 110 120 130 f502 0 16 -2 400 1620 2400 2800 3100 0.001 -12 -9 -12 -18 40 80 100 120 120 f503 0 16 -2 250 1750 2600 3050 3340 0.001 -30 -16 -22 -28 60 90 100 120 120 f504 0 16 -2 400 750 2400 2600 2900 0.001 -11 -21 -20 -40 40 80 100 120 120 f505 0 16 -2 350 600 2400 2675 2950 0.001 -20 -32 -28 -36 40 80 100 120 120 ;**************************************************************** ; start dur amp start freq end freq start formant end formant i1 0 1 .8 440 412.5 201 203 i1 + . .8 412.5 550 201 204 i1 + . .8 495 330 202 205 i1 + . .8 110 103.125 501 503 i1 + . .8 103.125 137.5 501 504 i1 + . .8 123.75 82.5 502 505 i1 7 . .4 440 412.5 201 203 i1 8 . .4 412.5 550 201 204 i1 9 . .4 495 330 202 205 i1 7 . .4 110 103.125 501 503 i1 8 . .4 103.125 137.5 501 504 i1 9 . .4 123.75 82.5 502 505 i1 + . .4 440 412.5 101 103 i1 + . .4 412.5 550 101 104 i1 + . .4 495 330 102 105 e </CsScore> </CsoundSynthesizer>