Psychoacoustical Aspects and Musical Applications of …Harald/Psychoacoustic.pdf · Psychoacoustical Aspects and Musical Applications ... Now I am playing a complex chord on the

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

- 3 -

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 .

f=/G.S_

(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

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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

READ I

-i

READ 2

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

READ 3

units. Various combina-