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FUNCTION TABLES
Note: This chapter has been written before arrays have been introduced in Csound. Now the usage of arrays is in many cases preferable to using function tables. Have a look in chapter 03E to see how you can use arrays.
A function table is essentially the same as what other audio programming languages might call a buffer, a table, a list or an array. It is a place where data can be stored in an ordered way. Each function table has a size: how much data (in Csound, just numbers) it can store. Each value in the table can be accessed by an index, counting from 0 to size-1. For instance, if you have a function table with a size of 10, and the numbers [1.1 2.2 3.3 5.5 8.8 13.13 21.21 34.34 55.55 89.89] in it, this is the relation of value and index:
| VALUE | 1.1 | 2.2 | 3.3 | 5.5 | 8.8 | 13.13 | 21.21 | 34.34 | 55.55 | 89.89 |
| INDEX | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
So, if you want to retrieve the value 13.13, you must point to the value stored under index 5.
The use of function tables is manifold. A function table can contain pitch values to which you may refer using the input of a MIDI keyboard. A function table can contain a model of a waveform which is read periodically by an oscillator. You can record live audio input in a function table, and then play it back. There are many more applications, all using the fast access (because function tables are stored in RAM) and flexible use of function tables.
How to Generate a Function Table
Each function table must be created before it can be used. Even if you want to write values later, you must first create an empty table, because you must initially reserve some space in memory for it.
Each creation of a function table in Csound is performed by one of the GEN Routines. Each GEN Routine generates a function table in a particular way: GEN01 transfers audio samples from a soundfile into a table, GEN02 stores values we define explicitly one by one, GEN10 calculates a waveform using user-defined weightings of harmonically related sinusoids, GEN20 generates window functions typically used for granular synthesis, and so on. There is a good overview in the Csound Manual of all existing GEN Routines. Here we will explain their general use and provide some simple examples using commonly used GEN routines.
GEN02 and General Parameters for GEN Routines
Let's start with our example described above and write the 10 numbers into a function table with 10 storage locations. For this task use of a GEN02 function table is required. A short description of GEN02 from the manual reads as follows:
f # time size 2 v1 v2 v3 ...
This is the traditional way of creating a function table by use of an "f statement" or an "f score event" (in a manner similar to the use of "i score events" to call instrument instances). The input parameters after the "f" are as follows:
- #: a number (as positive integer) for this function table;
- time: at what time, in relation to the passage of the score, the function table is created (usually 0: from the beginning);
- size: the size of the function table. A little care is required: in the early days of Csound only power-of-two sizes were possible for function tables (2, 4, 8, 16, ...); nowadays almost all GEN Routines accepts other sizes, but these non-power-of-two sizes must be declared as negative numbers!
- 2: the number of the GEN Routine which is used to generate the table, and here is another important point which must be borne in mind: by default, Csound normalizes the table values. This means that the maximum is scaled to +1 if positive, and to -1 if negative. All other values in the table are then scaled by the same factor that was required to scale the maximum to +1 or -1. To prevent Csound from normalizing, a negative number can be given as GEN number (in this example, the GEN routine number will be given as -2 instead of 2).
- v1 v2 v3 ...: the values which are written into the function table.
The example below demonstrates how the values [1.1 2.2 3.3 5.5 8.8 13.13 21.21 34.34 55.55 89.89] can be stored in a function table using an f-statement in the score. Two versions are created: an unnormalised version (table number 1) and an normalised version (table number 2). The difference in their contents will be demonstrated.
EXAMPLE 03D01_Table_norm_notNorm.csd
<CsoundSynthesizer>
<CsInstruments>
;Example by Joachim Heintz
instr 1 ;prints the values of table 1 or 2
prints "%nFunction Table %d:%n", p4
indx init 0
loop:
ival table indx, p4
prints "Index %d = %f%n", indx, ival
loop_lt indx, 1, 10, loop
endin
</CsInstruments>
<CsScore>
f 1 0 -10 -2 1.1 2.2 3.3 5.5 8.8 13.13 21.21 34.34 55.55 89.89; not normalized
f 2 0 -10 2 1.1 2.2 3.3 5.5 8.8 13.13 21.21 34.34 55.55 89.89; normalized
i 1 0 0 1; prints function table 1
i 1 0 0 2; prints function table 2
</CsScore>
</CsoundSynthesizer>
Instrument 1 simply reads and prints (to the terminal) the values of the table. Notice the difference in values read, whether the table is normalized (positive GEN number) or not normalized (negative GEN number).
Using the ftgen opcode is a more modern way of creating a function table, which is generally preferable to the old way of writing an f-statement in the score.1 The syntax is explained below:
giVar ftgen ifn, itime, isize, igen, iarg1 [, iarg2 [, ...]]
- giVar: a variable name. Each function is stored in an i-variable. Usually you want to have access to it from every instrument, so a gi-variable (global initialization variable) is given.
- ifn: a number for the function table. If you type in 0, you give Csound the job to choose a number, which is mostly preferable.
The other parameters (size, GEN number, individual arguments) are the same as in the f-statement in the score. As this GEN call is now a part of the orchestra, each argument is separated from the next by a comma (not by a space or tab like in the score).
So this is the same example as above, but now with the function tables being generated in the orchestra header:
EXAMPLE 03D02_Table_ftgen.csd
<CsoundSynthesizer>
<CsInstruments>
;Example by Joachim Heintz
giFt1 ftgen 1, 0, -10, -2, 1.1, 2.2, 3.3, 5.5, 8.8, 13.13, 21.21, 34.34, 55.55, 89.89
giFt2 ftgen 2, 0, -10, 2, 1.1, 2.2, 3.3, 5.5, 8.8, 13.13, 21.21, 34.34, 55.55, 89.89
instr 1; prints the values of table 1 or 2
prints "%nFunction Table %d:%n", p4
indx init 0
loop:
ival table indx, p4
prints "Index %d = %f%n", indx, ival
loop_lt indx, 1, 10, loop
endin
</CsInstruments>
<CsScore>
i 1 0 0 1; prints function table 1
i 1 0 0 2; prints function table 2
</CsScore>
</CsoundSynthesizer>
GEN01: Importing a Soundfile
GEN01 is used for importing soundfiles stored on disk into the computer's RAM, ready for for use by a number of Csound's opcodes in the orchestra. A typical ftgen statement for this import might be the following:
varname ifn itime isize igen Sfilnam iskip iformat ichn giFile ftgen 0, 0, 0, 1, "myfile.wav", 0, 0, 0
- varname, ifn, itime: These arguments have the same meaning as explained above in reference to GEN02. Note that on this occasion the function table number (ifn) has been defined using a zero. This means that Csound will automatically assign a unique function table number. This number will also be held by the variable giFile which we will normally use to reference the function table anyway so its actual value will not be important to us. If you are interested you can print the value of giFile (ifn) out. If no other tables are defined, it will be 101 and subsequent tables, also using automatically assigned table numbers, will follow accordingly: 102, 103 etc.
- isize: Usually you won't know the length of your soundfile in samples, and want to have a table length which includes exactly all the samples. This is done by setting isize=0. (Note that some opcodes may need a power-of-two table. In this case you can not use this option, but must calculate the next larger power-of-two value as size for the function table.)
- igen: As explained in the previous subchapter, this is always the place for indicating the number of the GEN Routine which must be used. As always, a positive number means normalizing, which is often convenient for audio samples.
- Sfilnam: The name of the soundfile in double quotes. Similar to other audio programming languages, Csound recognizes just the name if your .csd and the soundfile are in the same folder. Otherwise, give the full path. (You can also include the folder via the "SSDIR" variable, or add the folder via the "--env:NAME+=VALUE" option.)
- iskip: The time in seconds you want to skip at the beginning of the soundfile. 0 means reading from the beginning of the file.
- iformat: The format of the amplitude samples in the soundfile, e.g. 16 bit, 24 bit etc. Usually providing 0 here is sufficient, in which case Csound will read the sample format form the soundfile header.
- ichn: 1 = read the first channel of the soundfile into the table, 2 = read the second channel, etc. 0 means that all channels are read. Note that only certain opcodes are able to properly make use of multichannel audio stored in function tables.
The following example loads a short sample into RAM via a function table and then plays it. You can download the sample here (or replace it with one of your own). Copy the text below, save it to the same location as the "fox.wav" soundfile (or add the folder via the "--env:NAME+=VALUE" option),2 and it should work. Reading the function table here is done using the poscil3 opcode which can deal with non-power-of-two tables.
EXAMPLE 03D03_Sample_to_table.csd
<CsoundSynthesizer>
<CsOptions>
-odac
</CsOptions>
<CsInstruments>
;Example by Joachim Heintz
sr = 44100
ksmps = 32
nchnls = 2
0dbfs = 1
giSample ftgen 0, 0, 0, 1, "fox.wav", 0, 0, 1
instr 1
itablen = ftlen(giSample) ;length of the table
idur = itablen / sr ;duration
aSamp poscil3 .5, 1/idur, giSample
outs aSamp, aSamp
endin
</CsInstruments>
<CsScore>
i 1 0 2.757
</CsScore>
</CsoundSynthesizer>
GEN10: Creating a Waveform
The third example for generating a function table covers a classic case: building a function table which stores one cycle of a waveform. This waveform will then be read by an oscillator to produce a sound.
There are many GEN Routines which can be used to achieve this. The simplest one is GEN10. It produces a waveform by adding sine waves which have the "harmonic" frequency relationship 1 : 2 : 3 : 4 ... After the usual arguments for function table number, start, size and gen routine number, which are the first four arguments in ftgen for all GEN Routines, with GEN10 you must specify the relative strengths of the harmonics. So, if you just provide one argument, you will end up with a sine wave (1st harmonic). The next argument is the strength of the 2nd harmonic, then the 3rd, and so on. In this way, you can build approximations of the standard harmonic waveforms by the addition of sinusoids. This is done in the next example by instruments 1-5. Instrument 6 uses the sine wavetable twice: for generating both the sound and the envelope.
EXAMPLE 03D04_Standard_waveforms_with_GEN10.csd
<CsoundSynthesizer>
<CsOptions>
-odac
</CsOptions>
<CsInstruments>
;Example by Joachim Heintz
sr = 44100
ksmps = 32
nchnls = 2
0dbfs = 1
giSine ftgen 0, 0, 2^10, 10, 1
giSaw ftgen 0, 0, 2^10, 10, 1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9
giSquare ftgen 0, 0, 2^10, 10, 1, 0, 1/3, 0, 1/5, 0, 1/7, 0, 1/9
giTri ftgen 0, 0, 2^10, 10, 1, 0, -1/9, 0, 1/25, 0, -1/49, 0, 1/81
giImp ftgen 0, 0, 2^10, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1
instr 1 ;plays the sine wavetable
aSine poscil .2, 400, giSine
aEnv linen aSine, .01, p3, .05
outs aEnv, aEnv
endin
instr 2 ;plays the saw wavetable
aSaw poscil .2, 400, giSaw
aEnv linen aSaw, .01, p3, .05
outs aEnv, aEnv
endin
instr 3 ;plays the square wavetable
aSqu poscil .2, 400, giSquare
aEnv linen aSqu, .01, p3, .05
outs aEnv, aEnv
endin
instr 4 ;plays the triangular wavetable
aTri poscil .2, 400, giTri
aEnv linen aTri, .01, p3, .05
outs aEnv, aEnv
endin
instr 5 ;plays the impulse wavetable
aImp poscil .2, 400, giImp
aEnv linen aImp, .01, p3, .05
outs aEnv, aEnv
endin
instr 6 ;plays a sine and uses the first half of its shape as envelope
aEnv poscil .2, 1/6, giSine
aSine poscil aEnv, 400, giSine
outs aSine, aSine
endin
</CsInstruments>
<CsScore>
i 1 0 3
i 2 4 3
i 3 8 3
i 4 12 3
i 5 16 3
i 6 20 3
</CsScore>
</CsoundSynthesizer>
How to Write Values to a Function Table
As we have seen, GEN Routines generate function tables, and by doing this, they write values into them according to various methods, but in certain cases you might first want to create an empty table, and then write the values into it later or you might want to alter the default values held in a function table. The following section demonstrates how to do this.
To be precise, it is not actually correct to talk about an "empty table". If Csound creates an "empty" table, in fact it writes zeros to the indices which are not specified. Perhaps the easiest method of creating an "empty" table for 100 values is shown below:
giEmpty ftgen 0, 0, -100, 2, 0
The simplest to use opcode that writes values to existing function tables during a note's performance is tablew and its i-time equivalent is tableiw. Note that you may have problems with some features if your table is not a power-of-two size. In this case, you can also use tabw / tabw_i, but they don't have the offset- and the wraparound-feature. As usual, you must differentiate if your signal (variable) is i-rate, k-rate or a-rate. The usage is simple and differs just in the class of values you want to write to the table (i-, k- or a-variables):
tableiw isig, indx, ifn [, ixmode] [, ixoff] [, iwgmode]
tablew ksig, kndx, ifn [, ixmode] [, ixoff] [, iwgmode]
tablew asig, andx, ifn [, ixmode] [, ixoff] [, iwgmode]
- isig, ksig, asig is the value (variable) you want to write into a specified location of the table;
- indx, kndx, andx is the location (index) where you will write the value;
- ifn is the function table you want to write to;
- ixmode gives the choice to write by raw indices (counting from 0 to size-1), or by a normalized writing mode in which the start and end of each table are always referred as 0 and 1 (not depending on the length of the table). The default is ixmode=0 which means the raw index mode. A value not equal to zero for ixmode changes to the normalized index mode.
- ixoff (default=0) gives an index offset. So, if indx=0 and ixoff=5, you will write at index 5.
- iwgmode tells what you want to do if your index is larger than the size of the table. If iwgmode=0 (default), any index larger than possible is written at the last possible index. If iwgmode=1, the indices are wrapped around. For instance, if your table size is 8, and your index is 10, in the wraparound mode the value will be written at index 2.
Here are some examples for i-, k- and a-rate values.
i-Rate Example
The following example calculates the first 12 values of a Fibonacci series and writes them to a table. An empty table has first been created in the header (filled with zeros), then instrument 1 calculates the values in an i-time loop and writes them to the table using tableiw. Instrument 2 simply prints all the values in a list to the terminal.
EXAMPLE 03D05_Write_Fibo_to_table.csd
<CsoundSynthesizer>
<CsInstruments>
;Example by Joachim Heintz
giFt ftgen 0, 0, -12, -2, 0
instr 1; calculates first 12 fibonacci values and writes them to giFt
istart = 1
inext = 2
indx = 0
loop:
tableiw istart, indx, giFt ;writes istart to table
istartold = istart ;keep previous value of istart
istart = inext ;reset istart for next loop
inext = istartold + inext ;reset inext for next loop
loop_lt indx, 1, 12, loop
endin
instr 2; prints the values of the table
prints "%nContent of Function Table:%n"
indx init 0
loop:
ival table indx, giFt
prints "Index %d = %f%n", indx, ival
loop_lt indx, 1, ftlen(giFt), loop
endin
</CsInstruments>
<CsScore>
i 1 0 0
i 2 0 0
</CsScore>
</CsoundSynthesizer>
k-Rate Example
The next example writes a k-signal continuously into a table. This can be used to record any kind of user input, for instance by MIDI or widgets. It can also be used to record random movements of k-signals, like here:
EXAMPLE 03D06_Record_ksig_to_table.csd
<CsoundSynthesizer>
<CsOptions>
-odac
</CsOptions>
<CsInstruments>
;Example by Joachim Heintz
sr = 44100
ksmps = 32
nchnls = 2
0dbfs = 1
giFt ftgen 0, 0, -5*kr, 2, 0; size for 5 seconds of recording
giWave ftgen 0, 0, 2^10, 10, 1, .5, .3, .1; waveform for oscillator
seed 0
; - recording of a random frequency movement for 5 seconds, and playing it
instr 1
kFreq randomi 400, 1000, 1 ;random frequency
aSnd poscil .2, kFreq, giWave ;play it
outs aSnd, aSnd
;;record the k-signal
prints "RECORDING!%n"
;create a writing pointer in the table,
;moving in 5 seconds from index 0 to the end
kindx linseg 0, 5, ftlen(giFt)
;write the k-signal
tablew kFreq, kindx, giFt
endin
instr 2; read the values of the table and play it again
;;read the k-signal
prints "PLAYING!%n"
;create a reading pointer in the table,
;moving in 5 seconds from index 0 to the end
kindx linseg 0, 5, ftlen(giFt)
;read the k-signal
kFreq table kindx, giFt
aSnd oscil3 .2, kFreq, giWave; play it
outs aSnd, aSnd
endin
</CsInstruments>
<CsScore>
i 1 0 5
i 2 6 5
</CsScore>
</CsoundSynthesizer>
As you see, this typical case of writing k-values to a table requires a changing value for the index, otherwise tablew will continually overwrite at the same table location. This changing value can be created using the line or linseg opcodes - as was done here - or by using a phasor. A phasor moves continuously from 0 to 1 at a user-defined frequency. For example, if you want a phasor to move from 0 to 1 in 5 seconds, you must set the frequency to 1/5. Upon reaching 1, the phasor will wrap-around to zero and begin again. Note that phasor can also be given a negative frequency in which case it moves in reverse from 1 to zero then wrapping around to 1. By setting the ixmode argument of tablew to 1, you can use the phasor output directly as writing pointer. Below is an alternative version of instrument 1 from the previous example, this time using phasor to generate the index values:
instr 1; recording of a random frequency movement for 5 seconds, and playing it
kFreq randomi 400, 1000, 1; random frequency
aSnd oscil3 .2, kFreq, giWave; play it
outs aSnd, aSnd
;;record the k-signal with a phasor as index
prints "RECORDING!%n"
;create a writing pointer in the table,
;moving in 5 seconds from index 0 to the end
kindx phasor 1/5
;write the k-signal
tablew kFreq, kindx, giFt, 1
endin
a-Rate Example
Recording an audio signal is quite similar to recording a control signal. You just need an a-signal to provide input values and also an index that changes at a-rate. The next example first records a randomly generated audio signal and then plays it back. It then records the live audio input for 5 seconds and subsequently plays it back.
EXAMPLE 03D07_Record_audio_to_table.csd
<CsoundSynthesizer>
<CsOptions>
-iadc -odac
</CsOptions>
<CsInstruments>
;Example by Joachim Heintz
sr = 44100
ksmps = 32
nchnls = 2
0dbfs = 1
giFt ftgen 0, 0, -5*sr, 2, 0; size for 5 seconds of recording audio
seed 0
instr 1 ;generating a band filtered noise for 5 seconds, and recording it
aNois rand .2
kCfreq randomi 200, 2000, 3; random center frequency
aFilt butbp aNois, kCfreq, kCfreq/10; filtered noise
aBal balance aFilt, aNois, 1; balance amplitude
outs aBal, aBal
;;record the audiosignal with a phasor as index
prints "RECORDING FILTERED NOISE!%n"
;create a writing pointer in the table,
;moving in 5 seconds from index 0 to the end
aindx phasor 1/5
;write the k-signal
tablew aBal, aindx, giFt, 1
endin
instr 2 ;read the values of the table and play it
prints "PLAYING FILTERED NOISE!%n"
aindx phasor 1/5
aSnd table3 aindx, giFt, 1
outs aSnd, aSnd
endin
instr 3 ;record live input
ktim timeinsts ; playing time of the instrument in seconds
prints "PLEASE GIVE YOUR LIVE INPUT AFTER THE BEEP!%n"
kBeepEnv linseg 0, 1, 0, .01, 1, .5, 1, .01, 0
aBeep oscils .2, 600, 0
outs aBeep*kBeepEnv, aBeep*kBeepEnv
;;record the audiosignal after 2 seconds
if ktim > 2 then
ain inch 1
printks "RECORDING LIVE INPUT!%n", 10
;create a writing pointer in the table,
;moving in 5 seconds from index 0 to the end
aindx phasor 1/5
;write the k-signal
tablew ain, aindx, giFt, 1
endif
endin
instr 4 ;read the values from the table and play it
prints "PLAYING LIVE INPUT!%n"
aindx phasor 1/5
aSnd table3 aindx, giFt, 1
outs aSnd, aSnd
endin
</CsInstruments>
<CsScore>
i 1 0 5 ; record 5 seconds of generated audio to a table
i 2 6 5 ; play back the recording of generated audio
i 3 12 7 ; record 5 seconds of live audio to a table
i 4 20 5 ; play back the recording of live audio
</CsScore>
</CsoundSynthesizer>
How to Retrieve Values from a Function Table
There are two methods of reading table values. You can either use the table / tab opcodes, which are universally usable, but need an index; or you can use an oscillator for reading a table at k-rate or a-rate.
The table Opcode
The table opcode is quite similar in syntax to the tableiw/tablew opcodes (which are explained above). It is simply its counterpart for reading values from a function table instead of writing them. Its output can be either an i-, k- or a-rate signal and the value type of the output automatically selects either the a- k- or a-rate version of the opcode. The first input is an index at the appropriate rate (i-index for i-output, k-index for k-output, a-index for a-output). The other arguments are as explained above for tableiw/tablew:
ires table indx, ifn [, ixmode] [, ixoff] [, iwrap] kres table kndx, ifn [, ixmode] [, ixoff] [, iwrap] ares table andx, ifn [, ixmode] [, ixoff] [, iwrap]
As table reading often requires interpolation between the table values - for instance if you read k- or a-values faster or slower than they have been written in the table - Csound offers two descendants of table for interpolation: tablei interpolates linearly, whilst table3 performs cubic interpolation (which is generally preferable but is computationally slightly more expensive) and when CPU cycles are no object, tablexkt can be used for ultimate interpolating quality.3
Another variant is the tab_i / tab opcode which misses some features but may be preferable in some situations. If you have any problems in reading non-power-of-two tables, give them a try. They should also be faster than the table (and variants thereof) opcode, but you must take care: they include fewer built-in protection measures than table, tablei and table3 and if they are given index values that exceed the table size Csound will stop and report a performance error.
Examples of the use of the table opcodes can be found in the earlier examples in the How-To-Write-Values... section.
Oscillators
It is normal to read tables that contain a single cycle of an audio waveform using an oscillator but you can actually read any table using an oscillator, either at a- or at k-rate. The advantage is that you needn't create an index signal. You can simply specify the frequency of the oscillator (the opcode creates the required index internally based on the asked for frequency).
You should bear in mind that many of the oscillators in Csound will work only with power-of-two table sizes. The poscil/poscil3 opcodes do not have this restriction and offer a high precision, because they work with floating point indices, so in general it is recommended to use them. Below is an example that demonstrates both reading a k-rate and an a-rate signal from a buffer with poscil3 (an oscillator with a cubic interpolation):
EXAMPLE 03D08_RecPlay_ak_signals.csd
<CsoundSynthesizer>
<CsOptions>
-iadc -odac
</CsOptions>
<CsInstruments>
;Example by Joachim Heintz
sr = 44100
ksmps = 32
nchnls = 2
0dbfs = 1
; -- size for 5 seconds of recording control data
giControl ftgen 0, 0, -5*kr, 2, 0
; -- size for 5 seconds of recording audio data
giAudio ftgen 0, 0, -5*sr, 2, 0
giWave ftgen 0, 0, 2^10, 10, 1, .5, .3, .1; waveform for oscillator
seed 0
; -- ;recording of a random frequency movement for 5 seconds, and playing it
instr 1
kFreq randomi 400, 1000, 1; random frequency
aSnd poscil .2, kFreq, giWave; play it
outs aSnd, aSnd
;;record the k-signal with a phasor as index
prints "RECORDING RANDOM CONTROL SIGNAL!%n"
;create a writing pointer in the table,
;moving in 5 seconds from index 0 to the end
kindx phasor 1/5
;write the k-signal
tablew kFreq, kindx, giControl, 1
endin
instr 2; read the values of the table and play it with poscil
prints "PLAYING CONTROL SIGNAL!%n"
kFreq poscil 1, 1/5, giControl
aSnd poscil .2, kFreq, giWave; play it
outs aSnd, aSnd
endin
instr 3; record live input
ktim timeinsts ; playing time of the instrument in seconds
prints "PLEASE GIVE YOUR LIVE INPUT AFTER THE BEEP!%n"
kBeepEnv linseg 0, 1, 0, .01, 1, .5, 1, .01, 0
aBeep oscils .2, 600, 0
outs aBeep*kBeepEnv, aBeep*kBeepEnv
;;record the audiosignal after 2 seconds
if ktim > 2 then
ain inch 1
printks "RECORDING LIVE INPUT!%n", 10
;create a writing pointer in the table,
;moving in 5 seconds from index 0 to the end
aindx phasor 1/5
;write the k-signal
tablew ain, aindx, giAudio, 1
endif
endin
instr 4; read the values from the table and play it with poscil
prints "PLAYING LIVE INPUT!%n"
aSnd poscil .5, 1/5, giAudio
outs aSnd, aSnd
endin
</CsInstruments>
<CsScore>
i 1 0 5
i 2 6 5
i 3 12 7
i 4 20 5
</CsScore>
</CsoundSynthesizer>
Saving the Contents of a Function Table to a File
A function table exists only as long as you run the Csound instance which has created it. If Csound terminates, all the data is lost. If you want to save the data for later use, you must write them to a file. There are several cases, depending firstly on whether you write at i-time or at k-time and secondly on what kind of file you want to write to.
Writing a File in Csound's ftsave Format at i-Time or k-Time
Any function table in Csound can be easily written to a file using the ftsave (i-time) or ftsavek (k-time) opcode. Their use is very simple. The first argument specifies the filename (in double quotes), the second argument selects between a text format (non zero) or a binary format (zero) output. Finally you just provide the number of the function table(s) to save.
With the following example, you should end up with two textfiles in the same folder as your .csd: "i-time_save.txt" saves function table 1 (a sine wave) at i-time; "k-time_save.txt" saves function table 2 (a linear increment produced during the performance) at k-time.
EXAMPLE 03D09_ftsave.csd
<CsoundSynthesizer>
<CsInstruments>
;Example by Joachim Heintz
sr = 44100
ksmps = 32
nchnls = 2
0dbfs = 1
giWave ftgen 1, 0, 2^7, 10, 1; sine with 128 points
giControl ftgen 2, 0, -kr, 2, 0; size for 1 second of recording control data
seed 0
instr 1; saving giWave at i-time
ftsave "i-time_save.txt", 1, 1
endin
instr 2; recording of a line transition between 0 and 1 for one second
kline linseg 0, 1, 1
tabw kline, kline, giControl, 1
endin
instr 3; saving giWave at k-time
ftsave "k-time_save.txt", 1, 2
endin
</CsInstruments>
<CsScore>
i 1 0 0
i 2 0 1
i 3 1 .1
</CsScore>
</CsoundSynthesizer>
The counterpart to ftsave/ftsavek are the ftload/ftloadk opcodes. You can use them to load the saved files into function tables.
Writing a Soundfile from a Recorded Function Table
If you have recorded your live-input to a buffer, you may want to save your buffer as a soundfile. There is no opcode in Csound which does that, but it can be done by using a k-rate loop and the fout opcode. This is shown in the next example in instrument 2. First instrument 1 records your live input. Then instrument 2 creates a soundfile "testwrite.wav" containing this audio in the same folder as your .csd. This is done at the first k-cycle of instrument 2, by repeatedly reading the table values and writing them as an audio signal to disk. After this is done, the instrument is turned off by executing the turnoff statement.
EXAMPLE 03D10_Table_to_soundfile.csd
<CsoundSynthesizer>
<CsOptions>
-i adc
</CsOptions>
<CsInstruments>
;Example by Joachim Heintz
sr = 44100
ksmps = 32
nchnls = 2
0dbfs = 1
; -- size for 5 seconds of recording audio data
giAudio ftgen 0, 0, -5*sr, 2, 0
instr 1 ;record live input
ktim timeinsts ; playing time of the instrument in seconds
prints "PLEASE GIVE YOUR LIVE INPUT AFTER THE BEEP!%n"
kBeepEnv linseg 0, 1, 0, .01, 1, .5, 1, .01, 0
aBeep oscils .2, 600, 0
outs aBeep*kBeepEnv, aBeep*kBeepEnv
;;record the audiosignal after 2 seconds
if ktim > 2 then
ain inch 1
printks "RECORDING LIVE INPUT!%n", 10
;create a writing pointer in the table,
;moving in 5 seconds from index 0 to the end
aindx phasor 1/5
;write the k-signal
tablew ain, aindx, giAudio, 1
endif
endin
instr 2; write the giAudio table to a soundfile
Soutname = "testwrite.wav"; name of the output file
iformat = 14; write as 16 bit wav file
itablen = ftlen(giAudio); length of the table in samples
kcnt init 0; set the counter to 0 at start
loop:
kcnt = kcnt+ksmps; next value (e.g. 10 if ksmps=10)
andx interp kcnt-1; calculate audio index (e.g. from 0 to 9)
asig tab andx, giAudio; read the table values as audio signal
fout Soutname, iformat, asig; write asig to a file
if kcnt <= itablen-ksmps kgoto loop; go back as long there is something to do
turnoff ; terminate the instrument
endin
</CsInstruments>
<CsScore>
i 1 0 7
i 2 7 .1
</CsScore>
</CsoundSynthesizer>
This code can also be used in the form of a User Defined Opcode. It can be found here.
Other GEN Routine Highlights
GEN05, GEN07, GEN25, GEN27 and GEN16 are useful for creating envelopes. GEN07 and GEN27 create functions table in the manner of the linseg opcode - with GEN07 the user defines segment duration whereas in GEN27 the user defines the absolute time for each breakpoint from the beginning of the envelope. GEN05 and GEN25 operate similarly to GEN07 and GEN27 except that envelope segments are exponential in shape. GEN16 also create an envelope in breakpoint fashion but it allows the user to specify the curvature of each segment individually (concave - straight - convex).
GEN17, GEN41 and GEN42 are used the generate histogram-type functions which may prove useful in algorithmic composition and work with probabilities.
GEN09 and GEN19 are developments of GEN10 and are useful in additive synthesis.
GEN11 is a GEN routine version of the gbuzz opcode and as it is a fixed waveform (unlike gbuzz) it can be a useful and efficient sound source in subtractive synthesis.
GEN08
f # time size 8 a n1 b n2 c n3 d ...
GEN08 creates a curved function that forms the smoothest possible line between a sequence of user defined break-points. This GEN routine can be useful for the creation of window functions for use as envelope shapes or in granular synthesis. In forming a smooth curve, GEN08 may create apexes that extend well above or below any of the defined values. For this reason GEN08 is mostly used with post-normalisation turned on, i.e. a minus sign is not added to the GEN number when the function table is defined. Here are some examples of GEN08 tables:
f 1 0 1024 8 0 1 1 1023 0
f 2 0 1024 8 0 97 1 170 0.583 757 0
f 3 0 1024 8 0 1 0.145 166 0.724 857 0
f 4 0 1024 8 0 1 0.079 96 0.645 927 0
GEN16
f # time size 16 val1 dur1 type1 val2 [dur2 type2 val3 ... typeX valN]GEN16 allows the creation of envelope functions using a sequence of user defined breakpoints. Additionally for each segment of the envelope we can define a curvature. The nature of the curvature – concave or convex – will also depend upon the direction of the segment: rising or falling. For example, positive curvature values will result in concave curves in rising segments and convex curves in falling segments. The opposite applies if the curvature value is negative. Below are some examples of GEN16 function tables:
f 1 0 1024 16 0 512 20 1 512 20 0
f 2 0 1024 16 0 512 4 1 512 4 0
f 3 0 1024 16 0 512 0 1 512 0 0
f 4 0 1024 16 0 512 -4 1 512 -4 0
f 5 0 1024 16 0 512 -20 1 512 -20 0
GEN19
f # time size 19 pna stra phsa dcoa pnb strb phsb dcob ...
GEN19 follows on from GEN10 and GEN09 in complexity and control options. It shares the basic concept of generating a harmonic waveform from stacked sinusoids but in addition to control over the strength of each partial (GEN10) and the partial number and phase (GEN09) it offers control over the DC offset of each partial. In addition to the creation of waveforms for use by audio oscillators other applications might be the creation of functions for LFOs and window functions for envelopes in granular synthesis. Below are some examples of GEN19:
f 1 0 1024 19 1 1 0 0 20 0.1 0 0
f 2 0 1024 -19 0.5 1 180 1
GEN30
f # time size 30 src minh maxh [ref_sr] [interp]
GEN30 uses FFT to create a band-limited version of a source waveform without band-limiting. We can create a sawtooth waveform by drawing one explicitly using GEN07 by used as an audio waveform this will create problems as it contains frequencies beyond the Nyquist frequency therefore will cause aliasing, particularly when higher notes are played. GEN30 can analyse this waveform and create a new one with a user defined lowest and highest partial. If we know what note we are going to play we can predict what the highest partial below the Nyquist frequency will be. For a given frequency, freq, the maximum number of harmonics that can be represented without aliasing can be derived using sr / (2 * freq).
Here are some examples of GEN30 function tables (the first table is actually a GEN07 generated sawtooth, the second two are GEN30 band-limited versions of the first):
f 1 0 1024 7 1 1024 -1
f 2 0 1024 30 1 1 20
f 3 0 1024 30 1 2 20
Related Opcodes
ftgen: Creates a function table in the orchestra using any GEN Routine.
table / tablei / table3: Read values from a function table at any rate, either by direct indexing (table), or by linear (tablei) or cubic (table3) interpolation. These opcodes provide many options and are safe because of boundary check, but you may have problems with non-power-of-two tables.
tab_i / tab: Read values from a function table at i-rate (tab_i), k-rate or a-rate (tab). Offer no interpolation and less options than the table opcodes, but they work also for non-power-of-two tables. They do not provide a boundary check, which makes them fast but also give the user the resposability not reading any value off the table boundaries.
tableiw / tablew: Write values to a function table at i-rate (tableiw), k-rate and a-rate (tablew). These opcodes provide many options and are safe because of boundary check, but you may have problems with non-power-of-two tables.
tabw_i / tabw: Write values to a function table at i-rate (tabw_i), k-rate or a-rate (tabw). Offer less options than the tableiw/tablew opcodes, but work also for non-power-of-two tables. They do not provide a boundary check, which makes them fast but also give the user the resposability not writing any value off the table boundaries.
poscil / poscil3: Precise oscillators for reading function tables at k- or a-rate, with linear (poscil) or cubic (poscil3) interpolation. They support also non-power-of-two tables, so it's usually recommended to use them instead of the older oscili/oscil3 opcodes. Poscil has also a-rate input for amplitude and frequency, while poscil3 has just k-rate input.
oscili / oscil3: The standard oscillators in Csound for reading function tables at k- or a-rate, with linear (oscili) or cubic (oscil3) interpolation. They support all rates for the amplitude and frequency input, but are restricted to power-of-two tables. Particularily for long tables and low frequencies they are not as precise as the poscil/poscil3 oscillators.
ftsave / ftsavek: Save a function table as a file, at i-time (ftsave) or k-time (ftsavek). This can be a text file or a binary file, but not a soundfile. If you want to save a soundfile, use the User Defined Opcode TableToSF.
ftload / ftloadk: Load a function table which has been written by ftsave/ftsavek.
line / linseg / phasor: Can be used to create index values which are needed to read/write k- or a-signals with the table/tablew or tab/tabw opcodes.
- ftgen is preferred mainly because you can refer to the function table by a variable name and must not deal with constant tables numbers. This will enhance the portability of orchestras and better facilitate the combining of multiple orchestras. It can also enhance the readability of an orchestra if a function table is located in the code nearer the instrument that uses it.^
- If youŕ .csd file is, for instance, in the directory /home/jh/csound, and your sound file in the directory /home/jh/samples, you should add this inside the <CsOptions> tag:
--env:SSDIR+=/home/jh/samples. This means: 'Look also in /home/jh/sample as Sound Sample Directory (SSDIR)'
^ - For a general introduction about interpolation, see for instance http://en.wikipedia.org/wiki/Interpolation^