24. rand, buzz and gbuzz

rand, buzz and gbuzz are three opcodes producing frequency rich signals. They usually have to be filtered to remove frequencies, a topic covered later.

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The rand opcode generates a random sequence. All the random values are between minus and positive of the first parameter, and the only required one.

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This String uses a rand opcode, to generate a sequence between negative .5 and positive .5.

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A noise signal will have a nearly uniform frequency spectrum.

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The buzz opcode uses a sine input frequency, to create a signal with many harmonics. In xcps we give the fundamental frequency, and then we give the number of harmonics we need.

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In this String using the buzz opcode, we request 3 harmonics of 440 Hz. The parameter value 1 indicates the table where the sine function is located, for our example.

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In the frequency spectrum, we can see that there are three frequencies, 440 Hz, 2 times 440 Hz, and 3 times 440 Hz. All three have the same magnitude.

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The gbuzz opcode creates a set of harmonics based on a cosine wave. We have to give it the fundamental frequency, number of harmonics in the output and the lowest harmonic that will be in the output. In addition, there is a parameter, kmul, which is a multiplying factor, controlling how harmonics increase or decrease.

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This Instrument String, uses gbuzz to create 3 harmonics of 440 Hz, but we start with the 2nd harmonic (2 times 440 Hz) and the higher frequencies damp off with a multiplying factor of 0.7. We use the cosine table, which is numbered 2, in our program.

# Main.py

from moduleCsound import *
addTag(startSyn,startOpt,stopOpt,startIns)
header()

# *** Instrument Strings ***

randStr="""
asig rand 0.5
out asig
"""

buzzStr="""
asig buzz 1, 440, 3, 1
out asig 
"""

gbuzzStr="""
asig gbuzz 1, 440, 3, 2, 0.7, 2
out asig
"""


instrument('rand',1,randStr)
instrument('buzz',2,buzzStr)
instrument('gbuzz',3,gbuzzStr)

addTag(stopIns,startSco)

# *** Table ***
table('1. Sine wave',1,0,8192,10,1)
table('2. Cosine wave',2,0,8192,11,1,1)

# *** Score ***
score(1,0,3)
score(2,3,3)
score(3,6,3)

addTag(stopSco,stopSyn)
writeRun('Tut24')

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This shows the three frequencies starting at 880 Hz (2 times 440 Hz) which are reducing at the rate of 0.7.

; Tut24.csd
<CsoundSynthesizer>
<CsOptions>
</CsOptions>
<CsInstruments>
sr = 44100
ksmps = 10
nchnls = 1
0dbfs = 1
; rand
instr 1
  asig rand 0.5
  out asig
endin
; buzz
instr 2
  asig buzz 1, 440, 3, 1
  out asig 
endin
; gbuzz
instr 3
  asig gbuzz 1, 440, 3, 2, 0.7, 2
  out asig
endin
</CsInstruments>
<CsScore>
; 1. Sine wave
f 1 0 8192 10 1
; 2. Cosine wave
f 2 0 8192 11 1 1
i 1 0 3
i 2 3 3
i 3 6 3
</CsScore>
</CsoundSynthesizer>

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You will find additional information at pythonaudio.blogspot.com, including the source code.

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This is the video of Tutorial 24:

23. Phase Modulation Example

A Phase Modulation example is presented.

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Instead of using the function that was named add() in our csound module, it will be renamed as addTag(), to make its meaning clear. Further, there are checks to see if the first and last character are the angle brackets.

# moduleCsound.py

from os import system
from time import sleep

L = []

startSyn,stopSyn='<CsoundSynthesizer>','</CsoundSynthesizer>'
startOpt,stopOpt='<CsOptions>','</CsOptions>'
startIns,stopIns='<CsInstruments>','</CsInstruments>'
startSco,stopSco='<CsScore>','</CsScore>'

def addTag(*b):
    """
    Adding Tag terms to csd file
    """
    for s in b:
        if s[0]!='<' or s[-1]!='>':
            raise Exception("AddTag only adds Tags")
    L.extend(b)
    return

def rem(remark):
    """
    Generates one line of comment
    """
    L.append('; %s' % remark)

def header(sr=44100,ksmps=10,nch=1,amp=1):
    """
    Generates 4 headers in the orchesta section
    """
    L.append('sr = %d' % sr)
    L.append('ksmps = %d' % ksmps)
    L.append('nchnls = %d' % nch)
    L.append('0dbfs = %d' % amp)
    return

def instrument(rem,instr,S):
    """
    Generates instrument code given a String
    in the orchestra section
    """
    tL = S.split('\n')
    if tL[0]!='' or tL[-1]!='' : raise Exception("Instr Str")
    tL = [' '*2 + tl for tl in tL]
    tL[0] = 'instr %d' % instr # (3)
    tL[-1] = 'endin'
    if rem!='': L.append('; ' + rem)
    L.extend(tL)
    return

def table(rem,tabNum,tabTime,tabSize,tabGEN,*tab):
    """
    Generates f line inside score section
    """
    tup = (tabNum,tabTime,tabSize,tabGEN)
    String = 'f %s %s %s %s' % tup
    LString1=[' ' + str(i) for i in tab]
    String1 = "".join(LString1)
    if rem!='': L.append('; ' + rem)
    L.append(String+String1)
    return

def score(instr,start,dur,*p):
    """
    Generates i line inside score section
    """
    String = 'i %s %s %s' % (instr,start,dur)
    LString1=[' ' + str(pf) for pf in p]
    String1 = "".join(LString1)
    L.append(String+String1)
    return
    
def writeRun(fname):
    """
    Write out the csd file and perform it
    """
    OutL=[Lu + '\n' for Lu in L]
    out = open('%s.csd' % fname,'w')
    out.writelines(OutL)
    out.close()
    sleep(1)
    cmd = 'csound -o %s.wav %s.csd' % (fname,fname)
    status=system(cmd)
    if status!=0: raise Exception ('Could not write wav file')
    return

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This equation shows what we are trying to do. In the csound program we have to prefix each variable with the letter a to indicate that it is an audio rate variable. First y3 is found as the output of an oscil with a frequency of f3. Then y2p is found, as a sum of phasor, of frequency f2, and the signal y3. The variable y2p, is a phase term. Using the table opcode, y2p, is decoded, to y2. Finally yp is found, which is the sum of a phasor of frequency f1, and the signal y2. Finally we decode the yp with the table opcode to get the y output.

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These steps are indicated in this Instrument String Template. There are 3 placeholders representing f3, f2 and f1. We have fixed the values of A, and B. After getting y, two envelopes are created for the left and right channels. There is a fast attack, and then the signal slowly decays, with fade-out, at the end.

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The ten instruments are created such that f3 equals 5 Hz, f2 equals 20 Hz, and f1 is going from 2200 Hz to 1300 Hz in steps of minus 100 Hz. Python knows we have a multi-line statement if there is a starting delimiter such as square brackets, until it finds a matching closing delimiter. The indentation level of a multi-line statement is that of the line that started the delimiter.

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Now the sine table is created and 10 scores are written, one for each instrument.

# PhaseEx.py

from moduleCsound import *
addTag(startSyn,startOpt,stopOpt,startIns)
header(nch=2)

# *** Instrument String Template ***
PhaseExTemplate="""
ay3 oscil .5, %s, 1 ; f3 (B=.5)
ay2p phasor %s ; f2
ay2p = ay2p + ay3
ay2 table ay2p, 1, 1, 0, 1
ay2 = ay2*2 ; A=2
ayp phasor %s; f1
ayp = ayp + ay2
ay table ayp, 1, 1, 0, 1
aenvL linseg 0,.01,.5,.19,.2,p3-.3,.2,.1,0
aenvR linseg 0,.01,.6,.19,.2,p3-.3,.2,.1,0
aL = ay*aenvL
aR = ay*aenvR
out aL, aR
"""

N = 10

PhaseExStr=[
  PhaseExTemplate % (5,20,2200-100*i)
    for i in range(N)]
for i in range(N):
  instrument('HaHa',
             i+1,
             PhaseExStr[i])

addTag(stopIns,startSco)

# *** Table ***
table('1. Sine wave',1,0,8192,10,1)

# *** Score ***
rem('Phase Mod Score')
for i in range(N): score(i+1,0.4*i,0.4)

addTag(stopSco,stopSyn)
writeRun('Tut23')

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The wav file shows the effect of the envelope.

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This is the frequency spectrum of the first score using the first instrument.

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You will find additional information at pythonaudio.blogspot.com, including the source code.

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This is the video of Tutorial 23: