Lecture 8
Physical Modelling, Karplus Strong

Lecture Slides

A series of gif images of the lecture slides... (sorry, only accesible from within Stanford University)

Physical Modelling

Examples

singer.ins

Perry Cook's Singer physical modeling instrument in clm.

Here is the (very simple!) header of the instrument and a short description of its parameters:

(defcinstrument singer (beg amp data)

Mandatory parameters

beg

starting time in seconds

amp

amplitude

data

a list of lists that contains information for each synthesis "frame". Each component list has the following components (see the examples below):

dur: duration of the synthesis frame
shape: shape of the vocal tract
glot: glotal excitation
frequency: frequency of glotal source
glotamp: amplitude of the glotal component
noiseamp: amplitude of the noise component
vibramt: percentage of vibrato

The shape and glot parameters in the frame list can be a lisp variable containing a vocal tract shape or glotal excitation or can be a pointer to a file that contains it. If you compile and load the singer.ins instrument you will also load a default collection of shapes and glots. These are the available default definitions:

Glotal excitations:

test.glt
loud.glt
soft.glt
wide4.glt
wide5.glt
greekdefault.glt
lowbass.glt

Vocal Tract Shapes

aa.shp
hh2.shp
dhh.shp
aah.shp
hhh.shp
ohh.shp
ah.shp
oo.shp
ahh.shp
ee-.shp
hoo.shp
ooo.shp
ee.shp
ih.shp
ee2.shp
ihh.shp
open.shp
thh.shp
aw.shp
eee.shp
tt+.shp
aww.shp
eee2.shp
jjj.shp
ttt.shp
bb2.shp
eh.shp
kk+.shp
pipe1.shp
tzz.shp
bbb.shp
ehh.shp
kk2.shp
pp+.shp
uhh.shp
big.shp
euu.shp
kkk.shp
ppp.shp
uu.shp
fff.shp
ll2.shp
uuu.shp
lll.shp
rolledr.shp
vvv.shp
rolledrc.shp
mmm.shp
rolledro.shp
breath.shp
moo.shp
rr2.shp
chh.shp
gg2.shp
nng.shp
rrr.shp
wsp.shp
ggg.shp
nnn.shp
sh2.shp
xx2.shp
dd2.shp
ggg1.shp
noisahh.shp
shh.shp
xxx.shp
ddd.shp
gxx.shp
none.shp
sss.shp
zzz.shp

More definitions for both shapes and glots can be found in the following directories:

/dist/PRCStuff/SPASM/SPASM/glots
/dist/PRCStuff/SPASM/SPASM/shapes
/dist/PRCStuff/SPASM/BigLibrary/glots
/dist/PRCStuff/SPASM/BigLibrary/shapes

Some examples...

(with-sound () 
  (singer 0 .1 '((.4 ehh.shp test.glt 523.0 .8 0.0 .01) 
                 (.6 oo.shp test.glt 523.0 .7 .1 .01))))

(with-sound () 
  (singer 0 .1 '((.05 ehh.shp test.glt 523.0 0.8 0.0 .01) 
		 (.15 ehh.shp test.glt 523.0 0.8 0.0 .01) 
		 (.05 kkk.shp test.glt 523.0 0.0 0.0 .01) 
		 (.05 kkk.shp test.glt 523.0 0.0 0.0 .01) 
		 (.02 kk+.shp test.glt 523.0 0.0 1.0 .01) 
		 (.08 kk+.shp test.glt 523.0 0.0 0.2 .01) 
		 (.05 ooo.shp test.glt 523.0 0.8 0.0 .01) 
		 (.15 ooo.shp test.glt 523.0 0.8 0.0 .01) 
		 (.05 eee.shp test.glt 523.0 0.8 0.0 .01) 
		 (.15 eee.shp test.glt 523.0 0.8 0.0 .01) 
		 (.05 ehh.shp test.glt 523.0 0.8 0.0 .01) 
		 (.15 ehh.shp test.glt 523.0 0.8 0.0 .01) 
		 (.05 mmm.shp test.glt 523.0 0.8 0.0 .01) 
		 (.15 mmm.shp test.glt 523.0 0.8 0.0 .01)
		 (.10 mmm.shp test.glt 523.0 0.0 0.0 .01) )))

In the following example we are using a soundfile as an excitation function. In this case a gunshot would be processed by the vocal tract of the model. Highly unpleasant, I guess.

(with-sound () 
  (singer 0 .1 '((.05 ehh.shp "pistol.snd" 523.0 0.8 0.0 .01) 
		 (.15 ehh.shp "pistol.snd" 523.0 0.8 0.0 .01) 
		 (.05 kkk.shp "pistol.snd" 523.0 0.0 0.0 .01) 
		 (.05 kkk.shp "pistol.snd" 523.0 0.0 0.0 .01) 
		 (.02 kk+.shp "pistol.snd" 523.0 0.0 1.0 .01) 
		 (.08 kk+.shp "pistol.snd" 523.0 0.0 0.2 .01) 
		 (.05 ooo.shp "pistol.snd" 523.0 0.8 0.0 .01) 
		 (.15 ooo.shp "pistol.snd" 523.0 0.8 0.0 .01) 
		 (.05 eee.shp "pistol.snd" 523.0 0.8 0.0 .01) 
		 (.15 eee.shp "pistol.snd" 523.0 0.8 0.0 .01) 
		 (.05 ehh.shp "pistol.snd" 523.0 0.8 0.0 .01) 
		 (.15 ehh.shp "pistol.snd" 523.0 0.8 0.0 .01) 
		 (.05 mmm.shp "pistol.snd" 523.0 0.8 0.0 .01) 
		 (.15 mmm.shp "pistol.snd" 523.0 0.8 0.0 .01) 			      
		 (.10 mmm.shp "pistol.snd" 523.0 0.0 0.0 .01) )))

piano.ins

Scott Van Dyne's piano physical modeling instrument in clm.

Here is the header of the instrument and a short description of some of its parameters:

(definstrument (p :language :c :c-options "-c -O3")
  (&key
   (start 0.0)
   (duration 1.0)
   (keyNum 60.0)
   (strike-velocity 0.5)
   (pedal-down nil)
   (release-time-margin 0.75)
   (amp .5)
;;slider controls
   (detuningFactor 1.0)
   (detuningFactor-table '())
   (stiffnessFactor 1.0)
   (stiffnessFactor-table '())
   (pedalPresenceFactor .3)
   (longitudinalMode 10.5)
   (StrikePositionInvFac -0.9)
   (singleStringDecayRateFactor 1.0)
;; parameter tables indexed by keyNum
;; NB: you can override the loudPole-table by directly setting :loudPole to a value
   loudPole (loudPole-table default-loudPole-table)
   softPole (softPole-table default-softPole-table)
   loudGain (loudGain-table default-loudGain-table)
   softGain (softGain-table default-softGain-table)
   strikePosition (strikePosition-table default-strikePosition-table)
   detuning2 (detuning2-table default-detuning2-table)
   detuning3 (detuning3-table default-detuning3-table)
   stiffnessCoefficient (stiffnessCoefficient-table default-stiffnessCoefficient-table)
   singleStringDecayRate (singleStringDecayRate-table default-singleStringDecayRate-table)
   singleStringZero (singleStringZero-table default-singleStringZero-table)
   singleStringPole (singleStringPole-table default-singleStringPole-table)
   releaseLoopGain (releaseLoopGain-table default-releaseLoopGain-table)
   DryTapFiltCoefT60 (DryTapFiltCoefT60-table default-DryTapFiltCoefT60-table)
   DryTapFiltCoefTarget (DryTapFiltCoefTarget-table default-DryTapFiltCoefTarget-table)
   DryTapFiltCoefCurrent (DryTapFiltCoefCurrent-table default-DryTapFiltCoefCurrent-table)
   DryTapAmpT60 (DryTapAmpT60-table default-DryTapAmpT60-table)
   sustainPedalLevel (sustainPedalLevel-table default-sustainPedalLevel-table)
   pedalResonancePole (pedalResonancePole-table default-pedalResonancePole-table)
   pedalEnvelopeT60 (pedalEnvelopeT60-table default-pedalEnvelopeT60-table)
   soundboardCutoffT60 (soundboardCutoffT60-table default-soundboardCutoffT60-table)
   DryPedalResonanceFactor (DryPedalResonanceFactor-table default-DryPedalResonanceFactor-table)
   unaCordaGain (unaCordaGain-table default-unaCordaGain-table))

Some key parameters

start 0.0

start time in seconds

duration 1.0

duration in seconds of the note

keyNum 60.0

key number; middleC=60: can use the fractional part to detune

strike-velocity 0.5

corresponding normalized velocities (range: 0.0 ... 1.0)

pedal-down nil

set to t for sustain pedal down... pedal-down-times not yet implemented

release-time-margin 0.75

extra compute time allowed beyond duration to allow transients to decay to cero

amp .5

amp scale of noise inputs

detuningFactor-table '()

if there is a detuning table specified interpolate the detuning factor by using hte keyNum as input (the detuning factor is used in multiple string notes to slightly detune the second and third strings).

1.0 is nominal detuning
0.0 is exactly in tune (no two stage decay...)
> 1.0 is out of tune...

detuningFactor 1.0

if there is no detuning table specified then use this constant as the detuning factor

stiffnessCoefficient-table '()

lookup table for stiffness of strings (interpolated by keyNum). 0.0 to 1.0 is less stiff, 1.0 to 2.0 is more stiff...

stiffnessCoefficient 1.0

constant stiffness, used only if there is no stiffness table present

pedalPresenceFactor .3

longitudinalMode 10.5

StrikePositionInvFac -0.9

singleStringDecayRateFactor 1.0

DryPedalResonanceFactor .25

0 is no open string resonance; 1.0 is about full resonance of dampers raised; can be greater than 1.0

Some examples...

Normal...

(with-sound (:output (truename "/zap/thnormal.snd"))
   (loop for i from 0 to 7 do
      (p
       :start (* i .5)
       :duration .5
       :keyNum (+ 24 (* 12 i))
       :strike-velocity .5            ; 0 to 1, 0 is softest played note, 1 is loud note
       :amp .4			      ;overall volume level
       :DryPedalResonanceFactor .25   ;0 no open string resonance
				      ;1.0 is about full resonance of dampers raised
				      ;can be greater than 1.0
       )))

Detuning and stiffness...

(with-sound (:output (truename "/zap/thstiff.snd"))
   (loop for i from 0 to 7 do
      (p
       :start (* i .5)
       :duration .5
       :keyNum (+ 24 (* 12 i))
       :strike-velocity .5            ;0 to 1, 0 is softest played note, 1 is loud note
       :amp .4                        ;overall volume level
       :DryPedalResonanceFactor .25   ;0 no open string resonance
				      ;1.0 is about full resonance of dampers raised
				      ;can be greater than 1.0
    ;;modification to do detunedness
       :detuningFactor-table '(24 5 36 7.0 48 7.5 60 12.0 72 20 84 30 96 100 108 300)
          ;scales the above detuning values
	  ;  so 1.0 is nominal detuning
	  ;  0.0 is exactly in tune (no two stage decay...)
	  ;  > 1.0 is out of tune...

    ;;modification to do stiffness
       :stiffnessFactor-table '(21 1.5 24 1.5 36 1.5 48 1.5 60 1.4 72 1.3 84 1.2 96 1.0 108 1.0)
          ;0.0 to 1.0 is less stiff, 1.0 to 2.0 is more stiff...
       )))

Overdamped...

(with-sound (:output (truename "~/thdamped.snd"))
   (loop for i from 0 to 7 do
      (p
       :start (* i .5)
       :duration .5
       :keyNum (+ 24 (* 12 i))
       :strike-velocity .5              ;0 to 1, 0 is softest played note, 1 is loud note
       :amp .4                          ;overall volume level
       :DryPedalResonanceFactor .25     ;0 no open string resonance
					;1.0 is about full resonance of dampers raised
					;can be greater than 1.0
       
       ;;modifications to do damped sounds
       :singleStringDecayRate-table '(21 -5 24.000 -5.000 36.000 -5.4 41.953 -5.867 
                                      48.173 -7.113 53.818 -8.016 59.693 -8.875 66.605 -9.434 
                                      73.056 -10.035 78.931 -10.293 84.000 -12.185)
       :singleStringPole-table '(21 .8 24 0.7  36.000 .6 48 .5 60 .3 84 .1 96 .03 108 .03)
       :stiffnessCoefficient-table '(21.000 -0.920 24.000 -0.900 36.000 -0.700 48.000 -0.250 
                                     60.000 -0.100 75.179 -0.040 82.986 -0.040 92.240 .3 
                                     96.000 .5 99.000 .7 108.000 .7)
				     ;these are the actual allpass coefficients modified here
				     ;to allow dampedness at hig freqs
       )))

prc-toolkit95.lisp

Perry Cook's physical modelling toolkit translated to clm.

Karplus Strong synthesis

(defcinstrument plucky (beg dur freq amplitude &optional (maxA 1.0))

Mandatory and optional parameters

beg: starting time in seconds
dur: duration in seconds
freq: frequency in hertz
amplitude: amplitude (from 0 to 1)
maxA: amplitude of the initial noise component

Bowed string

(defcinstrument bow (beg dur frq amplitude &optional (maxA 1.0))

NOTE: freq is off in this one (in PRC's original also)

Mandatory and optional parameters

beg: starting time in seconds
dur: duration in seconds
freq: frequency in hertz
amplitude: amplitude (from 0 to 1)
maxA: maximum velocity

Wind instruments

(defcinstrument brass (beg dur freq amplitude &optional (maxA 1.0))

(defcinstrument clarinet (beg dur freq amplitude &optional (maxA 1.0))

(defcinstrument flute (beg dur freq amplitude &optional (maxA 1.0))

Mandatory and optional parameters

beg: starting time in seconds
dur: duration in seconds
freq: frequency in hertz
amplitude: amplitude (from 0 to 1)
maxA: maximum velocity

pluck.ins

The Karplus-Strong algorithm as extended by David Jaffe and Julius Smith

(definstrument pluck (start dur freq amp
			    &key
			    (weighting 0.9)
			    (lossfact 0.99)
			    (decaytime 6)
			    (attacktime 0.01))

Mandatory and key parameters

start: starting time in seconds
dur: duration in seconds
freq: frequency in hertz
amp: amplitude (from 0 to 1)
weighting 0.9: weighting is the ratio of the once-delayed to the twice-delayed samples. It defaults to .5=shortest decay. anything other than .5 = longer decay. Must be between 0 and less than 1.0.
lossfact 0.99: lossfact can be used to shorten decays. Most useful values are between .8 and 1.0.

Assignment (last!)

Make Sheila sing a tune (Sheila is the name of Perry Cook's virtual physically modelled singer).

Lecture 8 Physical Modelling, Karplus Strong

Lecture Slides

Physical Modelling

Examples

singer.ins

Mandatory parameters

piano.ins

Some key parameters

Normal...

Detuning and stiffness...

Overdamped...

prc-toolkit95.lisp

Karplus Strong synthesis

Mandatory and optional parameters

Bowed string

Mandatory and optional parameters

Wind instruments

Mandatory and optional parameters

pluck.ins

Mandatory and key parameters

Assignment (last!)

Lecture 8
Physical Modelling, Karplus Strong