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The most important operators are:
+ add - subtract * multiply (N.B. NOT x) / divide
These operators are used in expressions with numbers (sometimes called constants) or variables (which are simply a storage locations for numerical values). An expression using these operators may appear anywhere that a simple numerical constant can appear (i.e. as an argument in a function).
We assume the variables (kenv and asig) have been defined in a previous line.
14 / 9 2000 + kenv p3 - 1.0 asig * .5 p3 * .5
Parentheses ( and ) are used to control the order of computation in expressions. Without them, multiplication and division are performed before addition and subtraction, and similar operations are performed left-to-right.
6 * 4 + 5 ; result is 29 (6 * 4) + 5 ; result is 29 6 * (4 + 5) ; result is 54 ((6 + (2 * 4)) / 7) - 1 ; result is 1
Whenever in doubt, use cautionary parentheses.
ivar = 2000;
we should read this as " ivar gets-the-value-of 2000" and not as "ivar equals 2000". The reason for this is that the equal sign constitutes an assignment statement; the value on the right is passed to the variable on the left -- 2000 is passed to the variable ivar. Assignment statements can be used to set the contents of any i-, k- or a- variable to any numerical value. Most often, assignment statements are used to set up i- variables (when the instrument is first called) or to modify the contents of an existing variable:
ivar = 2000 ; ivar set to 2000 icps = cpspch(p5) ; icps set to cps value of pitch ivib = icps * .01 ; ivib (vibrato speed) is set to 1/100 of cps kenv linseg 1, p3, 0 ; ramp from 1 to 0 in duration p3 kenv = kenv * ivar ; increase the amplitude of the envelope
Essentially, GEN routines are mathematical procedures which create useful tables. The table size varies depending on how the function will be used, but it normally is a power of 2 or a power of 2 plus 1. (For now we will use power-of-two tables).
There are a wide range of GEN-types that are available for a wide range of uses within Csound. At present, we are concerned mainly with GEN routines that can be used to produce useful audio waveforms (i.e. that deal with sine waves). The two types in this category are GEN-9 and GEN-10.
The f- statement f1 0 256 9 1 1 0 is identical to f1 0 256 10 1.
Normally, you will want your envelopes to take place over the complete duration of the sound, and thus they will usually involve p3 in the duration arguments. There are two common types of envelopes:
1) those in which p3 is divided into fractions and placed in the various duration arguments:
In this type of envelope, the segments of time are all stretched and compressed uniformly as the duration (p3) is altered.
2) those in which values of time are placed in some of the duration arguments, and the remainder of the total duration in others:
In this type, some durations (the attack and first decay in the above example) are fixed (at .09 and .06 seconds). The last segment is specified as the remaining duration of the sound ( p3 - .15 OR p3 - (.09 + .06) ). In this type, the first two segments will take the exact durations specified and the final decay will be adjusted for longer or shorter note durations. Generally, this type of envelope is a better instrumental envelope since the speed of the attack does not normally vary with the duration of the note.
Of course, an amplitude envelope is only one of the many uses for the line, expon, linseg and expseg generators. Their output can be used as a control on almost anything.
variable function arguments.... comments
In the score file, a comment line should be inserted to list your parameters. This will become increasingly important as more parameters are used.
1) instrument 1 uses a single oscilator and has a envelope with an attack, initial decay, steady state and final decay. The longer the note as determined by p3 in the score, the longer the steady state should be.
2) instrument 2 is a percussive instrument to be used with a fixed duration. It uses a single oscilator with a waveform rich in harmonics. The instrument should be passed a parameter (or some parameters) from the score to control where it sounds in stereo space.
3) write a score (approx. 30 seconds) to demonstrate the two instruments. The score can be original or copied from an existing source.
Both orchestra and score should be fully documented (i.e. commented).
Index
GEN routines
The f1 0 512 10 1 statement that you have been writing in your scores is in fact a directive to the program to create (or Generate) a table of values which can be used by your orchestra. The values in the f- statement are:
GEN-10:
The parameters in Gen-10 (the values following the 10 in the f-statement) specify the relative strengths of harmonic partials. Normally, 1 is used as the largest value, and decimal values for weaker partials.
f1 0 256 10 1 ; a sine wave
f2 0 256 10 1 0 .4 0 .2 0 .1 0 .05 ; odd partials in diminishing strength
f3 0 256 10 .1 .2 .3 .4 .5 .6 .7 .8 .9 ; all partials with increasing strength
f4 0 256 10 1 0 0 0 1 0 0 0 1 0 0 0 1 ; only partials 1, 5, 9 and 13
GEN-9:
The parameters in Gen-9 (the values following the 9 in the f-statement) are groups of 3 values which specify the partial, the strength and the phrase (in degrees). If you are using harmonic partials and normal phrase, use Gen-10, but if you want ot specify phase differences in the partials, or you want inharmonic paritals use Gen-9.
f1 0 256 9 1 1 90 ; a sine wave out of phase
f2 0 256 9 1 .5 0 2.2 .5 90 ; fundamental and inharmonic partial
f3 0 256 9 1 .5 0 2 .5 180 ; waveform with destuctive interference
GEN-7:
Another useful Gen-routine is Gen-7 which can be used to create tables of linear ramps. It is easy to specify square waves, triangle waves, sawtooth waves etc. with this function. The parameters consist of a value followed by the number of points in the table to the next value and so on. The total number of points must be equal to the table size.
f1 0 256 7 1 127 1 1 -1 127 -1 1 1 ; a square wave
f2 0 256 7 0 64 1 128 -1 64 1 ; a triangle wave
f3 0 256 7 1 256 0 ; a sawtooth wave
Index
line, expon, linseg, expseg
One of the most powerful controls in Csound are the line, expon, linseg and expseg generators. Essentially they return values that are interpolated between fixed points in time. line and expon take as arguments a starting value, a duration, and a final value and produce values that would fall on a
straight line (line) or exponential curve (expon) between the two values. linseg (not lineseg) and expseg take as arguments a starting value, and a series of duration and next value pairs. (The number of arguments is always odd since they must have both a starting and ending value.
k1 line 1, p3, 0 ; moves linearly from 1 to 0 in the duration p3
k2 expon 1, p3, .0001 ; moves exponentially from 1 to (almost 0) in p3
k3 linseg 100, p3*.5, 0, p3*.5, 100 ; moves linearly from 100 to 0 and back to 100
k4 expseg 100, p3*.5, .0001, p3*.5, 100 ; moves exponentially from 100 to 0 and back to 100
k5 linseg 0, .25, 1, .25, .3, .5, .7, .5, .2, .75, .9, .75, .1 ; a complex linseg (3 seconds)
Using linseg and expseg in envelopes
Although there are many uses for these generators, an important one is as a control on the amplitude of an audio generator - in other words as an amplitude envelope. Although there are generators specially designed for generating envelopes, these routines are more flexible, and, I think, give better results. When linseg or expseg is used as amplitude envelope, the returned k- value is passed to the amplitude argument of the audio generating routine (i.e. oscil). For flexibily (and simplicity?) the maximum value of the envelope is set to 1.0, and the k- value is multiplied by the maximum amplitude (usually p4) later in the instrument (usually in the audio generator (i.e. oscil)).
For example, the following fragments produce exactly the same results:
1.
kenv linseg 0, .05, p4, p3-.05, 0 ; envelope with sharp attack
asig oscil kenv, cpspch(p5), 1 ; an oscilator outs asig, asig
2.
kenv linseg 0, .05, 1, p3-.05, 0 ; envelope scaled to 1
kenv = kenv * p4 ; envelope * max amplitude
asig oscil kenv, cpspch(p5), 1 ; an oscilator
outs asig, asig
3.
kenv linseg 0, .05, 1, p3-.05, 0 ; envelope scaled to 1
asig oscil kenv * p4, cpspch(p5), 1 ; amp argument has envelope multiplied
outs asig, asig ; by max amplitude
Scaling the amplitude envelope to 1, allows the envelope to be used more easily for other controls (i.e. to alter some other component of the sound).
kenv linseg 0, p3*.3, 1, p3*.5, .2, p3*.2, 0
kenv2 linseg 0, p3/2, 1, p3/2, 0
kenv linseg 0, .09, 1, .06, .6, p3-.15, 0
Index
Using Oscil
as an Audio Generator
We have already looked at using oscil as an audio generator -- it is one of the important building blocks of CSound. It takes three arguments (with an option 4th argument) to control its ampitude, frequency, and waveform (i.e. what wave table it uses). Normally, the frequency argument is passed from the score (often as a conversion of a from pch to cps representation with cpspch(p5) ) and the amplitude contains the maximum amplitude (passed from the score as p4) mulitplied by the envelope (which is a k- variable defined in a previous line). The waveform refers to the f- numbers defined in the score;
kenv line 1, p3, 0 ; envelope - ramp from 1 to 0
asig oscil p4 * kenv, cpspch(p5), 1 ; audio oscilator
outs asig, asig
Index
Formatting and Documenting Your Code
It is very important to organize your files so that you can understand them when you come back to them later, and so that others can understand what you are doing. Your code will be easier to read if it is formated (with Tabs) so that all variables, function names, and arguments are vertically aligned.
(TAB) kenv (TAB) linseg (TAB) 1, p3, 0 (TAB) ; a ramp from 1 to 0
(TAB) asig (TAB) oscil (TAB) kenv *p4, p5, 1 (TAB) ; an oscilator
;i# start dur amp ptch func
i1 0 .25 10000 9.00 1
Index
Suggested Assignment
Design the following instruments:
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