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of an Infinite PhasAr .
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Psychoacoustical Aspects and Musical Applications
As you recognize from the title of my today's presentation,
I am going to discuss the nsychoacoustical aspects and musical
applications of an infinite ohaser . However, since the infinite
ohaser has been preceded by other means and methods to produce
infinite effects, such as infinitely stepping and sliding tones,
I shall also briefly deal with the history of these phenomena .
In December 1964 a paper by Roger Shepard appeared in the
Journal of the Acoustical Society of America with the title
"Circularity in the Judgments of Relative Pitch" . In this paper
Shepard reported among other things about a sequence of ever ascen-
ding and descending half tone steps, which was generated at Bell
Labs on the IBM 7094 computer by a computer program developed by
M .V . Mathews for the synthesis of musical sounds .
In order to create the infinity effect, a cluster of tones
was Generated, consisting of sinusoidal components in one octave
intervals and covering a 10 octave range . The amplitudes were
largest in the center of the audio range and tapered off towards
the low and the high end to disappear below the threshold of per-
cention . This is illustrated in Fig . 1, where the "envelope" of the
sound levels is represented by a bell shaped curve . In this picture
the solid vertical lines represent the individual sinusoidal compo-
nents at a given time and the dotted vertical lines the sinusoidal
components in the following time increment . - Recording No . 1 -
For visually symbolizing this tonal sequence, Shepard used( M,!,ESCyE)R
the picture of a "circular"staircase, shown in Fig, 2, which gives
the optical illusion of being ascending when going counterclockwise
and descending, when going clockwise . In a slightly different form
this picture was presented by L .S . Penrose and R, Penrose in the
British Journal of Psychology (1958) under the title "Impossible
Cbjectsi A Special Type of Visual Illusion",the
Through the expedient of using/bell shaped loudness envelope
the tonal structure was the same at the beginning and the end of a
one octave cycle, so that the same computer program could be used
for going through each of the following octave sequences .
As reported by L .A . Hiller,"Risset, until recently on the
staff of IRCAM in Paris, also worked at Bell Laboratories in the
1960's, Among other tasks, he assembled a substantial compendium of
cemolex sounds that could be generated by the computer sound synthe-
sis techniques originated by Max Mathews and formalized as MUSIC5,"
In contrast to Shepard's restricted sets of discrete inter-
vals Risset generated complete tone sweeps, He found, that these
glissandi had at least "the same psychologically disturbing effect
cf Shepard's discrete note pattern," Like in the case of Shepard,
Risset's program "presents a little more than one octave of an endless
glissando, which could be pursued indefinitely since it is back to
its original point after an octave descent (or ascent)" .
After Risset :and other workers L .A . Hiller developed more
elaborate programs and compositions in collaboration with John Myhill
of the Department of Mathematics at SUA7YAB and Robert Brainerd, who
wrote an algorithm for their MUSIC5 program .
A major composition by Hiller evolved under the title
"Electronic Sonata and Midnight Carnival" in 1976 . one , of the key
elements of this composition was a complex set of glissandi with
octave and other changing intervals and . . . changing speed . Also
Juxtanositions of up and down glissandi were used .
As a working basis a so-called "normal set" of eleven
parallel glissandi was chosen, all one octave apart . The frequency
range from 20 Hz to 20,000 Hz was almost completely utilized with
the exception of using low pass filtering at the very high end to
avoid "foldover" or beat frequencies with the sampling rate, which
was chosen at 20 kHz . The production runs were made on a CDC-6400
computer utilizing a MUSIC5 program written substantially in COMPASS,
a fast assembly language .
- Recording No . 2 -
P/G,3 -
Within the framework of a larger composition still in progress
Jay Lee generates sliding tones in intervals of octaves, fifths and
triads to be compatible with classical harmonic structures . Lee also
uses the bell shaped amplitude envelope known from Shepard's work
tc enhance the infinity illusion .
He generated algorithms
written in PASCAL and encomnassing~one octave intervals . His work
was performed on a PDP-11 computer at a sampling rate of 20 kHz .
Dice to the use of the' bell shaped envelope there was no danger of
the high end of tl~e frequency range interf er$ing with - the sampling
frequency .
=-Recording No . 3 -
Now, after wp have learned a few things about the psycho-
acoustical aspects and effects of infinitely stepping and sliding
tones, it will be interesting to find out, what happens, if this
infinity phenomenon is moved from the domain of tone generation to
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sound modification, such as by selective filtering.
This is, where the so-called "infinite phasing" effect
comes in . In order to implement the infinite phasing, the "Barberpole
PhaserTM" was created as a multifunction sound modification device .
In the Barberpole PhaserTM the infinitely moving multiple filter
effect is combined with a number of complementary modulation capa--FIG. -!
bilities to optimize its versatility and effectiveness .%rinyafiu/ 7S
of /,,R/,-,It is the purpose of this presentation to stay within the
subject title of the "Psychoacoustical Aspects and Musical Applications«
� ,of an Infinite Phaspr . Therefore a description of the techical details
A
will follow in a later publication . - Also, I think ycu will be quite
anxious to hear, what infinitely moving filtering or phasing sounds
like, so I am going to give you a brief demonstration through the
means of tape recordings .
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(Recording No . 4) - First you will hear pink noise, which,
is filtered so that the peaks are approximately one octave and a
third apart .
(5) - Next you'hpar the same effect with prerecorded drums .
(6) - Now I am playing a complex chord on the Polymoog andprocessed through the Barberpole PhaserTM .
(7) - Next I am superimposing a sine wave modulation on topof the up sliding filter peaks .
(8) - Next I am superimposing a step function on top of thesliding filter peaks, first moving up and then down .
(9) - Next you hear a chord sequence phased up with a quasisaw tooth modulation and stereo panning.
(10)- Last you hear a Bass guitar phased up with a fastfrequency modulation superimposed upon the phasingeffect and with stereo panning .
I hope, that I have been able to demonstrate some of the
potential possibilities of infinite phasing.
In closing I want to thank those who have helped me make
this presentation possible . My special thanks go to Lejaren Hiller
and Jay Lee whop provided me with priceless literature information
and sound recordings and to Tom Rhea, who was instrumental in the
human engineering and appearance design of the Barberpole FhaserTM .
- Thank you -
List of Recordings of Infinite Sliding and SteppingTones and Infinite Phasing Effects .
1 .- Shepard's Tone by R .N. Shepard (around 1963.) .
2 .- Excerpt from Electronic Sonata by L .A . Hiller, 1976 .
3 .- Barberpoles by Jay Lee, 1981a) Cctave slides,b) Fifth slides,c) -Triad slides,
4 .- Infinite Phasing with pink noise (Bode, 1981, BarberpolePhaser)
5 .- Infinite Phasing with prerecorded drums .
6 .- Infinite Phasing with polyphonic synthesizer - UP .
7 .- Chord phased UP, sine wave superimposed upon infiniteup phasing.
8 .- Chord phased UP, then DOWN, with step function super-imposed upon phasing.
9 .- Chord sequence phased UP with saw tooth FM and stereopanning.
10 .- Bass guitar _phased up with fast sine FM and stereopanning.
11 .- Bass guitar phased DOWN with sine wave superimposedupon down phasing .
12 .- Electric guitar phased DOWN straight .
12b .- Electric guitar phased DOWN with FLIP feature,(switching back and forth between peaks .)
LOG FREQUENCY
PIG . 1 . Sound-pressure levels (in dB) of 10 simultaneouslysounded sinusoidal components spaced at octave intervals . (Thedotted lines correspond to an upward shift in the frequencies ofall components)
Plc. 2. "Circular"staircase illusion .
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Author sets up tonaleffects on synthesizer.Conventional tape deckat top, tape-loop re-verberation below, andplug-in modules atbottom
electronicsDecember 1, 1961
Sound Synthesizer CreatesNew Musical EffectsWell-known electronic circuits are used in system combinationsso that, unconventional sounds and patterns can be produced fromordinary audio. For example, a singer can generate his own stringbass accompaniment simultaneously with his voice
BV HARALD BODE The Wurlitzer Company, North Tonawanda, New York
Reprinted from electronics, December 1, 1961 © (All Rights Reserved) by McGraw-Hill Publishing Co ., Inc. / 330 W. 42nd Street, New York 36, N.Y .
INPUT I
10,000
5,000
2,000
1'000880500440
Z zoo100
50
20
10CPS
100
50 100
(B)
INPUT 1
50
(C)
100
NEW FRONTIERS IN ELECTRONIC MUSICMusic is the art of making pleas-
ing, expressive or intelligible com-binations of sounds and makingsuch combinations into composi-tions of definite structure and sig-nificance according to the laws ofmelody harmony and rhythm . It isalso the art of inventing, writingor rendering such compositions,whether vocal or instrumental.Ancient Greek music was limited
in expression by the primitive in-struments used, mostly of the lyreand flute types. However, it didestablish the diatonic scales basedon the tetrachord as a unit andgave us the rudiments of key rela-
200 300
350
7001050
200
300
500
1,000 1,500 CPS
INPUT 2
250 450
100 800950
1150
500
1,000 1,500 CPS
0U PUT
T
FIG. 1-Ring-bridge modulator (A) with input signals, (B) cord output (C)
FIG. 2-Output of ring-bridge modulator with gliding frequency appliedto one input and two harmonically related frequencies to the other
tionships.Early church music gave us the
neumes to indicate pitch, the de-velopment of staff notation, andthe superseding of the tetrachordunit by the hexachord. The practiceof descant, or simultaneous melody,gave rise to mensurable musicwhich in turn gave birth to counter-point.
Establishment of modern majorand minor scales with the octaveas a unit and of equal temperamentmade possible modulation into anykey and led to the development ofharmony.Great improvements in instru-
NEW SOUNDS and musical effects canbe created either by synthesizingacoustical phenomena, by process-ing natural or artificial (usuallyelectronically generated) sounds,or by applying both methods. Pro-cessing acoustical phenomena oftenresults in substantial deviationsfrom the original .
Production of new sounds or mu-sical effects can be made either byintermediate or immediate process-ing methods. Some methods of in-termediate processing may includepunched tapes for control of theparameters of a sound synthesizer,and may also include such tape re-cording procedures as reversal,pitch-through-speed changes, edit-ing and dubbing.Because of the time differential
between production and perform-ance when using the intermediateprocess, the composer-performercannot immediately hear or judgehis performance, therefore correc-tions can be made only after somelapse of time. Immediate process-ing techniques presents no suchproblems.Methods of immediate processing
include spectrum and envelopeshaping, change of pitch, change ofovertone structure including modi-fication from harmonic to non-harmonic overtone relations, ap-plication of periodic modulationeffects, reverberation, echo aindother repetition phenomena.The output of the ring-bridge
ment making marked the growth ofpurely instrumental music. Themodern symphony originated in thetime of Haydn and others about1770 .Recently, increasingly dissonant
linear counterpoint, Schoenberg asan example, is becoming popular.The French gave us polytonalityand the Russian composers havegiven us barbaric, dynamic rhythmswhile American jazz has contrib-uted to the music of the dynamicera in which we live .Modern proponents of musical
thought and expression have oftencomplained of being musically re-stricted by instrument range and,
Front panel of tape-loop reverberation and modular units (left) with top view of module chassis (right)
modulator shown in Fig. 1A yieldsthe sum and differences of the fre-quencies applied to its two inputsbut contains neither input fre-quency . This feature has been usedto create new sounds and effects.Figure 1B shows a tone applied toinput 1 and a group of harmonicallyrelated frequencies applied to input2. The output spectrum is shownin Fig. 1C .Due to operation of the ring-
bridge modulator, the output fre-
color ; thus most of their compost-~tions cannot express the emotionsthey feel and wish to communicate.New forms of music await, new typeinstruments or the development ofsound synthesizers that can pro-duce all possible audio tones, inany combination, at any amplitude,and with any form of envelopeshaping that will enable any imag-inable combination of tones to beplayed.Synthetically produced sound
offers a broad canvas upon whichall tones, regardless of their nature,can be painted, thus opening newavenues for the composers of to-morrow
quencies are no longer harmonicallyrelated to each other. If a groupof properly related frequencies wereapplied to both inputs and a percus-sive-type envelope were applied tothe output signal, a bell-like tonewould be produced .
In a more general presentation,the curves of Fig. 2 show the vari-ety of tone spectra that may be de-rived_,with a gliding frequency be-tween 1 cps and 10 Kc applied toone and two fixed 440 and 880 cpsfrequencies (in octave relationship)applied to the other input of thering-bridge modulator. The outputfrequencies are identified on the,graph.Frequencies applied to the ring-
bridge modulator inputs are notlimited to the audio range. Appli-cation of a subsonic frequency toone input will periodically modulate;a frequency applied to the other.Application of white noise to oneinput and a single audio frequencyto the other input will yield tunednoise at the output . Application ofa percussive envelope to one inputsimultaneously with a steady toneat the other input will result in apercussive-type output that willhave the characteristics of thesteady tone modulated by the per-cussive envelope .The unit shown in Fig. 3 provides
congruent envelope shaping as wellas the coincident percussive en-velope shaping of the program ma-terial . One input accepts the con-trol signal while the other input ac-cepts the material to be subjectedto envelope shaping . The processedaudio appears at the output of thegating circuit .To derive control voltages for the
gating functions, the audio at thecontrol input is amplified, rectifiedand applied to a low-pass filter .Thus, a relatively ripple-free vari-able d-c bias will actuate the vari-able-gain, push-pull amplifier gate .When switch St is in the gating po-sition, the envelope of the controlsignal shapes that of the programmaterial.To prevent the delay caused by
Ct and C. on fast-changing controlvoltages, and to eliminate asym-metry caused by the different out-put impedances at the plate andcathode of V� relatively high-valueresistors R:, and R, are inserted be-tween phase inverter V, and thepush-pull output of the gate circuit .These resistors are of the same or-der of magnitude as biasing re-sistors R, and R_ to secure a bal-ance between the control d-c signaland the audio portion of the pro-gram material.The input circuits of V. and V,
PIG . .3-Audio-controlled gate and percussion unit
act as a high-pass filter. The cut-off frequency of these filters exceedsthat of the ripple filter by such anamount that no disturbing audiofrequency from the control inputwill feed through to the gate. Thisis important for clean operation ofthe percussive envelope circuit. Thepulses that initiate the percussiveenvelopes are generated by Schmitttrigger V, and V, o . Positive-goingoutput pulses charge C., (or C.; plusCa or C, chosen by S,) with the dis-charge through R5. The time con-stant depends on the position of S,.
To make the trigger circuit re-spond to the beginning of a signalas well as to signal growth, differ-entiator C., and Re plus R, is usedat the input of Ve. The response tosignal growth is especially usefulin causing the system to yield to acrescendo in a music passage or toinstants of accentuation in the flowof speech frequencies .The practical application of the
audio-controlled . percussion devicewithin a system for the productionof new musical effects is shown inFig. 4. The sound of a bongo drum
triggers the percussion circuit,which in turn converts the sus-tained chords played by the organinto percussive tones . The outputsignal is applied to a tape-loop repe-tition unit that has four equallyspaced heads, one for record andthree for playback . By connectingthe record head and playback head2 in parallel, output A is produced .By connecting playback head 1 andplayback head 3 in parallel, outputB is produced, and a distinctiveABAB pattern may be achieved .Outputs A and B can be connected
FIG . 4-Organ chords are given drum envelope to produce musical drum effect. Other instruments, including voice,way be substituted for the organ
to formant filters having differentresonance frequencies.The number of repetitions may
be extended if a feedback loop isinserted between playback head 2and the record amplifier. The out-put voltages of the two filters andthe microphone preamplifier are ap-plied to a mixer in which the ratioof drum sound to modified percus-sive organ sound may be controlled .A presentation dealing more spe-
cifically with the tape-loop deviceand the sound-processing modulesused in the synthesizer is shown inFig. 5.The program material originat-
ing from the melody instrument isapplied to one of the inputs of theaudio-controlled gate and percus-sion unit . There it is gated by theaudio from a percussion instru-ment. The percussive melodysounds at the output of the gate areapplied to the tape-loop repetitionsystem . Output signal A-the di-rect signal and the informationfrom playback head 2-is appliedthrough amplifier A and filter 1 tothe mixer. Output signal B-thesignals from playback heads 1 and3-is applied through amplifier Bto one input of the ring-bridgemodulator. The other ring-bridgemodulator input is connected to theoutput of an audio signal generator.The mixed and frequency con-
verted signal at the output of the
PERC INSTR
MELODYINSTR
ring-bridge modulator is appliedthrough filter 2 to the mixer. Atthe mixer output a percussiveARAB signal (stemming from asingle melody note, triggered by asingle drum signal) is obtained . Inits A portion it has the originalmelody instrument pitch while itsB portion is the converted nonhar-monic overtone structure, both af-fected by the different voicings ofthe two filters . When the directdrum signal is applied to a thirdmixer input, the output will soundlike a voiced drum with an intricateaftersound . The repetition of theABAB pattern may be extended bya feedback loop between playbackhead 2 and the record amplifier.When applying the human sing-
ing voice to the input of the funda-mental frequency selector, the ex-tracted fundamental pitch may bedistorted in the squaring circuitand applied to the frequency divider(or dividers) . This will derive amelody line whose pitch will be oneoctave lower than that of thesinger . The output of the frequencydivider maythen be applied througha voicing filter to the program inputof the audio-controlled gate andpercussion unit . The control inputof this circuit may be actuated bythe original singing voice, afterhaving passed through a low-passfilter of such a cutoff frequencythat only vowels-typical for syl-
WRITE
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TAPE LOOP
DISTRIBUTER
lables-would trigger the circuit .At the output of the audio-controlled gate, percussive sounds withthe voicing of a string bass will beobtained mixed with the originalvoice of the singer . The humanvoice output signal will now be ac-companied by a coincident stringbass sound which may be furtherprocessed in the tape-loop repeti-tion unit.The arbitrarily selected elec-
tronic modules of this synthesizerare of a limited variety and couldbe supplemented by other modules.A system synthesizer may find
many applications such as explora-tion of new types of electronic mu-sic or as a tool for composers whoare searching for novel sounds andmusical effects. Such a device willpresent a challenge to the imagina-tion of composer-programmer.The modern approach of synthe-
sizing intricate electronic systemsfrom modules with a limited num-ber of basic functions has provensuccessful in the computer field .This approach has now been madein the area of sound synthesis .With means for compiling any
desired modular configuration, anaudio system synthesizer could be-come a flexible and versatile tool forsound processing and would besuited to meet the evergrowing de-mand for exploration and produc-tion of new sounds .
FIG. 5-Overall synthesizer system with tape-loop device and sound and envelope shapingtions of shaping circuits can be patched together to generate desired tonal effects
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units. Various combina-