PANNING AND SPATIALIZATION
Simple Stereo Panning
Csound provides a large number of opcodes designed to assist in the distribution of sound amongst two or more speakers. These range from opcodes that merely balance a sound between two channel to ones that include algorithms to simulate the doppler shift that occurs when sound moves, algorithms that simulate the filtering and inter-aural delay that occurs as sound reaches both our ears and algorithms that simulate distance in an acoustic space.
First we will look at some 'first principles' methods of panning a sound between two speakers.
The simplest method that is typically encountered is to multiply one channel of audio (aSig) by a panning variable (kPan) and to multiply the other side by 1 minus the same variable like this:
aSigL = aSig * kPan
aSigR = aSig * (1 – kPan)
outs aSigL, aSigR
where kPan is within the range zero to 1. If kPan is 1 all the signal will be in the left channel, if it is zero all the signal will be in the right channel and if it is 0.5 there will be signal of equal amplitide in both the left and the right channels. This way the signal can be continuously panned between the left and right channels.
The problem with this method is that the overall power drops as the sound is panned to the middle.
One possible solution to this problem is to take the square root of the panning variable for each channel before multiplying it to the audio signal like this:
aSigL = aSig * sqrt(kPan)
aSigR = aSig * sqrt((1 – kPan))
outs aSigL, aSigR
By doing this, the straight line function of the input panning variable becomes a convex curve so that less power is lost as the sound is panned centrally.
Using 90º sections of a sine wave for the mapping produces a more convex curve and a less immediate drop in power as the sound is panned away from the extremities. This can be implemented using the code shown below.
aSigL = aSig * sin(kPan*$M_PI_2)
aSigR = aSig * cos(kPan*$M_PI_2)
outs aSigL, aSigR
(Note that '$M_PI_2' is one of Csound's built in macros and is equivalent to pi/2.)
A fourth method, devised by Michael Gogins, places the point of maximum power for each channel slightly before the panning variable reaches its extremity. The result of this is that when the sound is panned dynamically it appears to move beyond the point of the speaker it is addressing. This method is an elaboration of the previous one and makes use of a different 90 degree section of a sine wave. It is implemented using the following code:
aSigL = aSig * sin((kPan + 0.5) * $M_PI_2)
aSigR = aSig * cos((kPan + 0.5) * $M_PI_2)
outs aSigL, aSigR
The following example demonstrates all three methods one after the other for comparison. Panning movement is controlled by a slow moving LFO. The input sound is filtered pink noise.
EXAMPLE 05B01_Pan_stereo.csd
<CsoundSynthesizer>
<CsOptions>
-odac ; activates real time sound output
</CsOptions>
<CsInstruments>
; Example by Iain McCurdy
sr = 44100
ksmps = 10
nchnls = 2
0dbfs = 1
instr 1
imethod = p4; read panning method variable from score (p4)
;---------------- generate a source sound -------------------
a1 pinkish 0.3; pink noise
a1 reson a1, 500, 30, 1; bandpass filtered
aPan lfo 0.5, 1, 1; panning controlled by an lfo
aPan = aPan + 0.5; offset shifted +0.5
;------------------------------------------------------------
if imethod=1 then
;------------------------ method 1 --------------------------
aPanL = aPan
aPanR = 1 - aPan
;------------------------------------------------------------
endif
if imethod=2 then
;------------------------ method 2 --------------------------
aPanL = sqrt(aPan)
aPanR = sqrt(1 - aPan)
;------------------------------------------------------------
endif
if imethod=3 then
;------------------------ method 3 --------------------------
aPanL = sin(aPan*$M_PI_2)
aPanR = cos(aPan*$M_PI_2)
;------------------------------------------------------------
endif
if imethod=4 then
;------------------------ method 4 --------------------------
aPanL = sin((aPan + 0.5) * $M_PI_2)
aPanR = cos((aPan + 0.5) * $M_PI_2)
;------------------------------------------------------------
endif
outs a1*aPanL, a1*aPanR ; audio sent to outputs
endin
</CsInstruments>
<CsScore>
; 4 notes one after the other to demonstrate 4 different methods of panning
;p1 p2 p3 p4(method)
i 1 0 4.5 1
i 1 5 4.5 2
i 1 10 4.5 3
i 1 15 4.5 4
e
</CsScore>
</CsoundSynthesizer>
An opcode called pan2 exist which makes panning slightly easier for us to implement simple panning employing various methods. The following example demonstrates the three methods that this opcode offers one after the other. The first is the 'equal power' method, the second 'square root' and the third is simple linear. The Csound Manual alludes to fourth method but this does not seem to function currently.
EXAMPLE 05B02_pan2.csd
<CsoundSynthesizer>
<CsOptions>
-odac ; activates real time sound output
</CsOptions>
<CsInstruments>
; Example by Iain McCurdy
sr = 44100
ksmps = 10
nchnls = 2
0dbfs = 1
instr 1
imethod = p4 ; read panning method variable from score (p4)
;----------------------- generate a source sound ------------------------
aSig pinkish 0.5 ; pink noise
aSig reson aSig, 500, 30, 1 ; bandpass filtered
;------------------------------------------------------------------------
;---------------------------- pan the signal ----------------------------
aPan lfo 0.5, 1, 1 ; panning controlled by an lfo
aPan = aPan + 0.5 ; DC shifted + 0.5
aSigL, aSigR pan2 aSig, aPan, imethod; create stereo panned output
;------------------------------------------------------------------------
outs aSigL, aSigR ; audio sent to outputs
endin
</CsInstruments>
<CsScore>
; 3 notes one after the other to demonstrate 3 methods used by pan2
;p1 p2 p3 p4
i 1 0 4.5 0 ; equal power (harmonic)
i 1 5 4.5 1 ; square root method
i 1 10 4.5 2 ; linear
e
</CsScore>
</CsoundSynthesizer>
In the next example we will generate some sounds as the primary signal. We apply some delay and reverb to this signal to produce a secondary signal. A random function will pan the primary signal between the channels, but the secondary signal remains panned in the middle all the time.
EXAMPLE 05B03_Different_pan_layers.csd
<CsoundSynthesizer>
<CsOptions>
-o dac -d
</CsOptions>
<CsInstruments>
; Example by Bjorn Houdorf, March 2013
sr = 44100
ksmps = 32
nchnls = 2
0dbfs = 1
seed 0
instr 1
ktrig metro 0.8; Trigger frequency, instr. 2
scoreline "i 2 0 4", ktrig
endin
instr 2
ital random 60, 72; random notes
ifrq = cpsmidinn(ital)
knumpart1 oscili 4, 0.1, 1
knumpart2 oscili 5, 0.11, 1
; Generate primary signal.....
asig buzz 0.1, ifrq, knumpart1*knumpart2+1, 1
ipan random 0, 1; ....make random function...
asigL, asigR pan2 asig, ipan, 1; ...pan it...
outs asigL, asigR ;.... and output it..
kran1 randomi 0,4,3
kran2 randomi 0,4,3
asigdel1 delay asig, 0.1+i(kran1)
asigdel2 delay asig, 0.1+i(kran2)
; Make secondary signal...
aL, aR reverbsc asig+asigdel1, asig+asigdel2, 0.9, 15000
outs aL, aR; ...and output it
endin
</CsInstruments>
<CsScore>
f1 0 8192 10 1
i1 0 60
</CsScore>
</CsoundSynthesizer>
3-d Binaural Encoding
3-D binaural simulation is availalable in a number of opcodes that make use of spectral data files that provide information about the filtering and inter-aural delay effects of the human head. The older one of these is hrtfer. The newer ones are hrtfmove, hrtfmove2 and hrftstat. The main parameters for control of the opcodes are azimuth (the direction of the source expressed as an angle formed from the direction in which we are facing) and elevation (the angle by which the sound deviates from this horizontal plane, either above or below). Both these parameters are defined in degrees. 'Binaural' infers that the stereo output of this opcode should be listened to using headphones so that no mixing in the air of the two channels occurs before they reach our ears.
The following example take a monophonic source sound of noise impulses and processes it using the hrtfmove2 opcode. First of all the sound is rotated around us in the horizontal plane then it is raised above our head then dropped below us and finally returned to be straight and level in front of us.For this example to work you will need to download the files hrtf-44100-left.dat and hrtf-44100-right.dat and place them in your SADIR (see setting environment variables) or in the same directory as the .csd.
EXAMPLE 05B04_hrtfmove.csd
<CsoundSynthesizer>
<CsOptions>
-odac ; activates real time sound output
</CsOptions>
<CsInstruments>
; Example by Iain McCurdy
sr = 44100
ksmps = 10
nchnls = 2
0dbfs = 1
giSine ftgen 0, 0, 2^12, 10, 1 ; sine wave
giLFOShape ftgen 0, 0, 131072, 19, 0.5,1,180,1 ; U-shape parabola
instr 1
; create an audio signal (noise impulses)
krate oscil 30,0.2,giLFOShape ; rate of impulses
; amplitude envelope: a repeating pulse
kEnv loopseg krate+3,0, 0,1, 0.05,0, 0.95,0,0
aSig pinkish kEnv ; noise pulses
; -- apply binaural 3d processing --
; azimuth (direction in the horizontal plane)
kAz linseg 0, 8, 360
; elevation (held horizontal for 8 seconds then up, then down, then horizontal
kElev linseg 0, 8, 0, 4, 90, 8, -40, 4, 0
; apply hrtfmove2 opcode to audio source - create stereo ouput
aLeft, aRight hrtfmove2 aSig, kAz, kElev, \
"hrtf-44100-left.dat","hrtf-44100-right.dat"
outs aLeft, aRight ; audio to outputs
endin
</CsInstruments>
<CsScore>
i 1 0 24 ; instr 1 plays a note for 24 seconds
e
</CsScore>
</CsoundSynthesizer>
Going Multichannel
So far we have only considered working in 2-channels/stereo but Csound is extremely flexible at working in more that 2 channels. By changing nchnls in the orchestra header we can specify any number of channels but we also need to ensure that we choose an audio hardware device using -odac that can handle multichannel audio. Audio channels send from Csound that do not address hardware channels will simply not be reproduced. There may be some need to make adjustments to the software settings of your soundcard using its own software or the operating system's software but due to the variety of sound hardware options available it would be impossible to offer further specific advice here.
Sending Multichannel Sound to the Loudspeakers
In order to send multichannel audio we must use opcodes designed for that task. So far we have used outs to send stereo sound to a pair of loudspeakers. (The 's' actually stands for 'stereo'.) Correspondingly there exist opcodes for quadophonic (outq), hexaphonic (outh), octophonic (outo), 16-channel sound (outx) and 32-channel sound (out32).
For example
outq a1, a2, a3, a4
sends four independent audio streams to four hardware channels. Any unneeded channels still have to be given an audio signal. A typical workaround would be to give them 'silence'. For example if only 5 channels were required:
nchnls = 6
; --snip--
aSilence = 0
outh a1, a2, a3, a4, a5, aSilence
These opcodes only address very specific loudspeaker arrangements (although workarounds are possible) and have been superseded to a large extent by newer opcodes that allow greater flexibility in the number and routing of audio to a multichannel output.
outc allows us to address any number of output audio channels, but they still need to be addressed sequentially. For example our 5-channel audio could be design as follows:
nchnls = 5
; --snip--
outc a1, a2, a3, a4, a5
outch allows us to direct audio to a specific channel or list of channels and takes the form:
outch kchan1, asig1 [, kchan2] [, asig2] [...]
For example, our 5-channel audio system could be designed using outch as follows:
nchnls = 5
; --snip--
outch 1,a1, 2,a2, 3,a3, 4,a4, 5,a5
Note that channel numbers can be changed at k-rate thereby opening the possibility of changing the speaker configuration dynamically during performance. Channel numbers do not need to be sequential and unneeded channels can be left out completely. This can make life much easier when working with complex systems employing many channels.
Rendering Multichannel Audio Streams as Sound Files
So far we have referred to outs, outo etc. as a means to send audio to the speakers but strictly speaking they are only sending audio to Csound's output (as specified by nchnls) and the final destination will be defined using a command line flag in <CsOptions>. -odac will indeed instruct Csound to send audio to the audio hardware and then onto the speakers but we can alternatively send audio to a sound file using -oSoundFile.wav. Provided a file type that supports multichannel interleaved data is chosen (wav will work), a multichannel file will be created that can be used in some other audio applications or can be re-read by Csound later on by using, for example diskin2. This method is useful for rendering audio that is too complex to be monitored in real-time. Only single interleaved sound files can be created , separate mono files cannot be created using this method. Simultaneously monitoring the audio generated by Csound whilst rendering will not be possible when using this method; we must choose one or the other.
An alternative method of rendering audio in Csound, and one that will allow simulatenous monitoring in real-time is to use the fout opcode. For example:
fout "FileName.wav", 8, a1, a2, a3, a4
outq a1, a2, a3, a4
will render an interleaved, 24-bit, 4-channel sound file whilst simultaneously sending the quadrophonic audio to the loudspeakers.
If we wanted to de-interleave an interleaved sound file into multiple mono sound files we could use the code:
a1, a2, a3, a4 soundin "4ChannelSoundFile.wav" fout "Channel1.wav", 8, a1 fout "Channel2.wav", 8, a2 fout "Channel3.wav", 8, a3 fout "Channel4.wav", 8, a4
VBAP
Vector Base Amplitude Panning1 can be described as a method which extends stereo panning to more than two speakers. The number of speakers is, in general, arbitrary. You can configure for standard layouts such as quadrophonic, octophonic or 5.1 configuration, but in fact any number of speakers can be positioned even in irregular distances from each other. If you are fortunate enough to have speakers arranged at different heights, you can even configure VBAP for three dimensions.
Basic Steps
First you must tell VBAP where your loudspeakers are positioned. Let us assume you have seven speakers in the positions and numberings outlined below (M = middle/centre):
The opcode vbaplsinit, which is usually placed in the header of a Csound orchestra, defines these positions as follows:
vbaplsinit 2, 7, -40, 40, 70, 140, 180, -110, -70
The first number determines the number of dimensions (here 2). The second number states the overall number of speakers, then followed by the positions in degrees (clockwise).
All that is required now is to provide vbap with a monophonic sound source to be distributed amongst the speakers according to information given about the position. Horizontal position (azimuth) is expressed in degrees clockwise just as the initial locations of the speakers were. The following would be the Csound code to play the sound file "ClassGuit.wav" once while moving it counterclockwise:
EXAMPLE 05B05_VBAP_circle.csd
<CsoundSynthesizer> <CsOptions> -odac -d ;for the next line, change to your folder --env:SSDIR+=/home/jh/Joachim/Csound/FLOSS/audio </CsOptions> <CsInstruments> sr = 44100 ksmps = 32 0dbfs = 1 nchnls = 7 vbaplsinit 2, 7, -40, 40, 70, 140, 180, -110, -70 instr 1 Sfile = "ClassGuit.wav" iFilLen filelen Sfile p3 = iFilLen aSnd, a0 soundin Sfile kAzim line 0, p3, -360 ;counterclockwise a1, a2, a3, a4, a5, a6, a7, a8 vbap8 aSnd, kAzim outch 1, a1, 2, a2, 3, a3, 4, a4, 5, a5, 6, a6, 7, a7 endin </CsInstruments> <CsScore> i 1 0 1 </CsScore> </CsoundSynthesizer> ;example by joachim heintz
In the CsOptions tag, you see the option --env:SSDIR+= ... as a possibility to add a folder to the path in which Csound usually looks for your samples (SSDIR = Sound Sample Directory) if you call them only by name, without the full path. To play the full length of the sound file (without prior knowledge of its duration) the filelen opcode is used to derive this duration, and then the duration of this instrument (p3) is set to this value. The p3 given in the score section (here 1) is overwritten by this value.
The circular movement is a simple k-rate line signal, from 0 to -360 across the duration of the sound file (in this case the same as p3). Note that we have to use the opcode vbap8 here, as there is no vbap7. Just give the eighth channel a variable name (a8) and thereafter ignore it.
The Spread Parameter
As VBAP derives from a panning paradigm, it has one problem which becomes more serious as the number of speakers increases. Panning between two speakers in a stereo configuration means that all speakers are active. Panning between two speakers in a quadro configuration means that half of the speakers are active. Panning between two speakers in an octo configuration means that only a quarter of the speakers are active. And so on --- so that the actual perceived extend of the sound source becomes unintentionally smaller and smaller.
To alleviate this tendency, Ville Pulkki has introduced an additional parameter, called "spread", in a range from zero to hundred percent.2 The 'ascetic' form of VBAP we have seen in the previous example, means: no spread (0%). A spread of 100% means that all speakers are active, and the information about where the sound comes from is nearly lost.
As the kspread input to the vbap8 opcode is the second of two optional parameters, we first have to provide the first one. kelev defines the elevation of the sound - it is always zero for two dimensions, as in the speaker configuration in our example. The next example adds a spread movement to the previous one. The spread starts at zero percent, then increases up to hundred percent, and then decreases back down again to zero.
EXAMPLE 05B06_VBAP_spread.csd
<CsoundSynthesizer> <CsOptions> -odac -d ;for the next line, change to your folder --env:SSDIR+=/home/jh/Joachim/Csound/FLOSS/audio </CsOptions> <CsInstruments> sr = 44100 ksmps = 32 0dbfs = 1 nchnls = 7 vbaplsinit 2, 7, -40, 40, 70, 140, 180, -110, -70 instr 1 Sfile = "ClassGuit.wav" iFilLen filelen Sfile p3 = iFilLen aSnd, a0 soundin Sfile kAzim line 0, p3, -360 kSpread linseg 0, p3/2, 100, p3/2, 0 a1, a2, a3, a4, a5, a6, a7, a8 vbap8 aSnd, kAzim, 0, kSpread outch 1, a1, 2, a2, 3, a3, 4, a4, 5, a5, 6, a6, 7, a7 endin </CsInstruments> <CsScore> i 1 0 1 </CsScore> </CsoundSynthesizer> ;example by joachim heintz
New VBAP Opcodes
As a reaction to a number of requests, John fFitch has written new VBAP opcodes in 2012. Their main goal is to allow more than one loudspeaker configuration within a single orchestra (so that you can "switch" between them) and to give more flexibility to the number of output channels. This is an example for three different configurations which are called in three instruments:
EXAMPLE 05B07_VBAP_new.csd
<CsoundSynthesizer>
<CsOptions>
-odac -d ;for the next line, change to your folder
--env:SSDIR+=/home/jh/Joachim/Csound/FLOSS/audio
</CsOptions>
<CsInstruments>
sr = 44100
ksmps = 32
0dbfs = 1
nchnls = 7
vbaplsinit 2.01, 7, -40, 40, 70, 140, 180, -110, -70
vbaplsinit 2.02, 2, -40, 40
vbaplsinit 2.03, 3, -70, 180, 70
instr 1
aSnd, a0 soundin "ClassGuit.wav"
kAzim line 0, p3, -360
a1, a2, a3, a4, a5, a6, a7 vbap aSnd, kAzim, 0, 0, 1
outch 1, a1, 2, a2, 3, a3, 4, a4, 5, a5, 6, a6, 7, a7
endin
instr 2
aSnd, a0 soundin "ClassGuit.wav"
kAzim line 0, p3, -360
a1, a2 vbap aSnd, kAzim, 0, 0, 2
outch 1, a1, 2, a2
endin
instr 3
aSnd, a0 soundin "ClassGuit.wav"
kAzim line 0, p3, -360
a1, a2, a3 vbap aSnd, kAzim, 0, 0, 3
outch 7, a1, 3, a2, 5, a3
endin
</CsInstruments>
<CsScore>
i 1 0 6
i 2 6 6
i 3 12 6
</CsScore>
</CsoundSynthesizer>
;example by joachim heintz
Instead of just one loudspeaker configuration as in the previous examples, there are now three configurations:
vbaplsinit 2.01, 7, -40, 40, 70, 140, 180, -110, -70 vbaplsinit 2.02, 2, -40, 40 vbaplsinit 2.03, 3, -70, 180, 70
The first parameter (the number of dimensions) now has an additional fractional part, with a range from .01 to .99, specifying the number of the speaker layout. So 2.01 means: two dimensions, layout number one, 2.02 is layout number two, and 2.03 is layout number three. The new vbap opcode has now these parameters:
ar1[, ar2...] vbap asig, kazim [, kelev] [, kspread] [, ilayout]
The last parameter ilayout refers to the speaker layout number. In the example above, instrument 1 uses layout 1, instrument 2 uses layout 2, and instrument 3 uses layout 3. Even if you do not have more than two speakers you should see in Csound's output that instrument 1 goes to all seven speakers, instrument 2 only to the first two, and instrument 3 goes to speaker 3, 5, and 7.
In addition to the new vbap opcode, vbapg has been written. The idea is to have an opcode which returns the gains (amplitudes) of the speakers instead of the audio signal:
k1[, k2...] vbapg kazim [,kelev] [, kspread] [, ilayout]
Ambisonics
Ambisonics is another technique to distribute a virtual sound source in space. Although the practical use has some similarities to VBAP, Ambisonics follows a rather different approach. It has nothing to do with amplitude panning but establishs a sound field. So by default all speakers are active, and localisation results from effects other than just amplitude.
There are excellent sources for the discussion of Ambisonics online.3 We will focus here just on the basic practicalities of using Ambisonics in Csound, without going into too much detail of the concepts behind them.
Ambisonics works in two basic steps. In the first step you encode the spacial information of a virtual sound source (its localisation) in a so-called B-format. In the second step you decode the B-format to match your loudspeaker setup.
It is possible to save the B-format as its own audio file, to conserve the spacial information or you can immediately do the decoding after the encoding thereby dealing directly only with audio signals instead of Ambisonic files. The next example takes the latter approach by implementing a transformation of the VBAP circle example to Ambisonics.
EXAMPLE 05B08_Ambi_circle.csd
<CsoundSynthesizer> <CsOptions> -odac -d ;for the next line, change to your folder --env:SSDIR+=/home/jh/Joachim/Csound/FLOSS/Release01/Csound_Floss_Release01/audio </CsOptions> <CsInstruments> sr = 44100 ksmps = 32 0dbfs = 1 nchnls = 8 instr 1 Sfile = "ClassGuit.wav" iFilLen filelen Sfile p3 = iFilLen aSnd, a0 soundin Sfile kAzim line 0, p3, 360 ;counterclockwise (!) iSetup = 4 ;octogon aw, ax, ay, az bformenc1 aSnd, kAzim, 0 a1, a2, a3, a4, a5, a6, a7, a8 bformdec1 iSetup, aw, ax, ay, az outch 1, a1, 2, a2, 3, a3, 4, a4, 5, a5, 6, a6, 7, a7, 8, a8 endin </CsInstruments> <CsScore> i 1 0 1 </CsScore> </CsoundSynthesizer> ;example by joachim heintz
First to note is that for a counterclockwise circle, the azimuth now has the line 0 -> 360, instead of 0 -> -360 as was in the VBAP example. This is because Ambisonics usually reads the angle in the mathematical way: a positive angle is counterclockwise. Next, the encoding process is carried out in the line:
aw, ax, ay, az bformenc1 aSnd, kAzim, 0
Input arguments are the monophonic sound source aSnd, the xy-angle kAzim, and the elevation angle which is set to zero. Output signals are the spacial informations in x-, y- and z- direction (ax, ay, az), and also an omnidirectional signal called aw.
Decoding is performed by the line
a1, a2, a3, a4, a5, a6, a7, a8 bformdec1 iSetup, aw, ax, ay, az
The inputs for the decoder are the same aw, ax, ay, az, which were the results of the encoding process, and an additional iSetup parameter. Currently the Csound decoder only works with some standard setups for the speaker: iSetup = 4 refers to an octogon.4 So the final eight audio signals a1, ..., a8 are being produced using this decoder, and are then sent to the speakers in the same way using the outch opcode.
Different Orders
What we have seen in this example is called "first order" ambisonics. This means that the encoding process leads to the four basic dimensions w, x, y, z as described above.5 In "second order" ambisonics, there are additional directions called r, s, t, u, v. And in "third order" ambisonics again the additional k, l, m, n, o, p, q. The final example in this section shows the three orders, each of them in one instrument. If you have eight speakers in octo setup, you can compare the results.
EXAMPLE 05B09_Ambi_orders.csd
<CsoundSynthesizer> <CsOptions> -odac -d ;for the next line, change to your folder --env:SSDIR+=/home/jh/Joachim/Csound/FLOSS/Release01/Csound_Floss_Release01/audio </CsOptions> <CsInstruments> sr = 44100 ksmps = 32 0dbfs = 1 nchnls = 8 instr 1 ;first order aSnd, a0 soundin "ClassGuit.wav" kAzim line 0, p3, 360 iSetup = 4 ;octogon aw, ax, ay, az bformenc1 aSnd, kAzim, 0 a1, a2, a3, a4, a5, a6, a7, a8 bformdec1 iSetup, aw, ax, ay, az outch 1, a1, 2, a2, 3, a3, 4, a4, 5, a5, 6, a6, 7, a7, 8, a8 endin instr 2 ;second order aSnd, a0 soundin "ClassGuit.wav" kAzim line 0, p3, 360 iSetup = 4 ;octogon aw, ax, ay, az, ar, as, at, au, av bformenc1 aSnd, kAzim, 0 a1, a2, a3, a4, a5, a6, a7, a8 bformdec1 iSetup, aw, ax, ay, az, ar, as, at, au, av outch 1, a1, 2, a2, 3, a3, 4, a4, 5, a5, 6, a6, 7, a7, 8, a8 endin instr 3 ;third order aSnd, a0 soundin "ClassGuit.wav" kAzim line 0, p3, 360 iSetup = 4 ;octogon aw, ax, ay, az, ar, as, at, au, av, ak, al, am, an, ao, ap, aq bformenc1 aSnd, kAzim, 0 a1, a2, a3, a4, a5, a6, a7, a8 bformdec1 iSetup, aw, ax, ay, az, ar, as, at, au, av, ak, al, am, an, ao, ap, aq outch 1, a1, 2, a2, 3, a3, 4, a4, 5, a5, 6, a6, 7, a7, 8, a8 endin </CsInstruments> <CsScore> i 1 0 6 i 2 6 6 i 3 12 6 </CsScore> </CsoundSynthesizer> ;example by joachim heintz
In theory, first-order ambisonics needs at least 4 speakers to be projected correctly. Second-order ambisonics needs at least 6 speakers (9, if 3 dimensions are employed). Third-order ambisonics needs at least 8 speakers (or 16 for 3d). So, although higher order should in general lead to a better result in space, you cannot expect it to work unless you have a sufficient number of speakers. Of course practice may prove a preferable means of judgement to theory in many cases.
VBAP or Ambisonics?
Csound offers a simple and reliable way to access two standard methods for multi-channel spatialisation. Both have different qualities and follow different aesthetics. VBAP can perhaps be described as clear, rational, direct. It combines simplicity with flexibility. It gives a reliable sound projection even for rather asymmetric speaker setups. Ambisonics on the other hand offers a very soft sound image, in which the single speaker becomes part of a coherent sound field. The B-format offers the possibility to store the spatial information independently from any particular speaker configuration.
The composer, or spatial interpreter, can choose one or the other technique depending on the music and the context. Or (s)he can design a personal appraoch to spatialisation by combining the different techniques described in this chapter.
- First described by Ville Pulkki in 1997: Ville Pulkki, Virtual source positioning using vector base amplitude panning, in: Journal of the Audio Engeneering Society, 45(6), 456-466^
- Ville Pulkki, Uniform spreading of amplitude panned virtual sources, in: Proceedings of the 1999 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics, Mohonk Montain House, New Paltz^
- For instance www.ambisonic.net or www.icst.net/research/projects/ambisonics-theory^
- See www.csounds.com/manual/html/bformdec1.html for more details.^
- Which in turn then are taken by the decoder as input.^