fof2
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## 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
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. It uses the file fof2.csd.

Example 357. 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. It uses the file fof2-2.csd.

Example 358. 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>

## See Also

fof

## Credits

Author: Rasmus Ekman
fof2 is a modification of fof by Rasmus Ekman

New in Csound 3.45

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