perm filename USEMUS.LCS[UP,DOC]1 blob
sn#107238 filedate 1975-05-17 generic text, type T, neo UTF8
00100 ******* WORK IN PROGRESS -- JUNE, 73 *********
00200
00300 ********** Using the Music System -- MUS10 **********
00400
00500 This manual is designed for use with the PDP10 at the Stanford AI lab.
00600 It is quite possible that several features discussed will not be
00700 operative on other installations. See appendix for some details.
00800
00900
01000 MUS10 is a complete sound generating package which exists on the
01100 disk. In its basic form it includes no storage area for sound output,
01200 so when the program is to be run, a number, establishing the core
01300 size, must be given following the program name.
01400
01500 For first attempts type:
01600
01700 R MUS10 10
01800 (All lines must be terminated with the 'RETURN' key.)
01900
02000 At this point the program will type the message:
02100
02200 INPUT?
02300
02400 Basically there are two responses possible. If the program is to
02500 receive further instructions from another file which has been
02600 prepared with an editing program, type:
02700
02800 NAME -- where NAME is the name of the file to be read.
02900 (If NAME has an extension, it must be used!)
03000
03100 If instructions are to be entered by means of the teletype keyboard
03200 (TTY mode), type carriage return (<CR>).
03300
03400 At this point a star (*) will appear which means the program is
03500 awaiting input.
03600
03700 Most complete statements to be read by MUS10 must end with a
03800 semicolon. Several complete statements may be entered on a single
03900 line but it is best not to have the lines too long. More than one
04000 line may be used for a single statement. If the less-than sign (<)
04100 appears everything following on that line will be ignored. Use this
04200 for entering comments.
04300
04400 ***** Note that the above rules DO NOT apply to the syntax
04500 of the SCORE program.
04600
04700 Already present in MUS10 is an "instrument" known as SIMP which has
04800 been set to play a test tone of 'A' (440 hz) for 1/2 second.
04900
05000 In order to play this tone, first get into TTY mode as described
05100 above, then type:
05200
05300 PLAY;SIMP;FINISH;
05400
05500 When the computation has finished the note 'A' will be heard if the
05600 various switches on the sound system are all in the right positions.
05700 (See appendix for this information and information regarding the
05800 filter settings.)
05900
06000 Assuming there were no typographical errors, you will know the comp-
06100 utation is done by the appearance of another star (*). The test tone
06200 may now be repeated several times by typing:
06300
06400 $P N where '$' indicates the 'ALT' key and 'N' is the
06500 number of times the note will play.
06600
06700 If no sound has been heard up to this point repeat the above, using
06800 some large number (e.g.20) for 'N' and go test the various switches
06900 until the tones are heard.
07000
07100 Occasionally a message will appear:
07200
07300 HUNG DEVICE AD
07400
07500 If this happens get expert help.
07600
07700 ******************************************************
07800
07900 The instrument SIMP has five parameters.
08000
08100 P1 = begin time of note (in seconds)
08200 P2 = duration of note " "
08300 P3 = pitch
08400 P4 = amplitude
08500 P5 = wave form (or timbre)
08600
08700 P1 and P2 will have the same significance in all instruments but all
08800 higher numbered parameters are assigned roles according to
08900 convenience. (However it will prove useful to consistently apply P3
09000 and P4 as above.)
09100
09200 Internally all pitch entries become numerical, however the twelve
09300 frequencies of the tempered chromatic scale, from middle C (261.62
09400 hz) up to B may be used in MUS10 by typing the letter names of the
09500 notes. The letter S = #; flats are not used in this program.
09600
09700 Since these letters merely represent the frequencies of each note,
09800 the octave range may be changed multiplying or dividing by multiples
09900 of two. Thus C or A in the octave below middle C would be entered
10000 as C/2 or A/2. In the octave above the basic middle octave these
10100 notes would be C*2 or A*2.
10200
10300 C -- 2 octaves down would be C/4
10400 C -- 3 octaves down would be C/8
10500 C -- 2 octaves up would be C*4
10600 C -- 3 octaves up would be C*8 etc.
10700
10800 To test the use of these letters try:
10900
11000 P3←C;PLAY;SIMP;FINISH;
11100
11200 Now instrument SIMP will play middle C instead of A. The left arrow
11300 (←) indicates that the value of C has been placed in P3, replacing
11400 any value that was previously there. (The left arrow and the equals
11500 sign[=] are interchangeable in this program.)
11600
11700 PLAY;SIMP;FINISH; must be typed so the new note will be computed.
11800 After it is first heard it may be repeated as indicated above.
11900
12000 If frequencies other than those of the tempered scale are to be
12100 played, a number may be used instead of a letter.
12200
12300 P3←1000;PLAY;SIMP;FINISH; will play a tone at 1000 hz.
12400
12500
12600 The amplitude scale available is the range of number from 0 to 2047.
12700 (This upper limit is set by the number of bits [12] used for the
12800 sound samples. See appendix.) P4 has been set at 1200 for the test
12900 tone. This may be reset using the same method as described before.
13000
13100 P4←100;P3←GS*2;PLAY;SIMP;FINISH;
13200
13300 This will play a G# above the middle octave at amplitude 100.
13400
13500 The duration of the tone may be changed be resetting P2.
13600
13700 P2←.1; etc. will play a note of 1/10 sec. duration.
13800
13900 If longer notes are desired the core being used must be expanded to
14000 allow for more storage space. At the established sampling rate
14100 (10000, see appendix.) 3.33k of core is needed for each second of
14200 sound. Since 1/2" may be played when MUS10 has 10k, 14k is needed
14300 for 1 1/2", 17k for 2 1/2", 20k for 3 1/2", etc. (Methods for
14400 playing much longer examples are described in SCORE.MAN.)
14500
14600 ********** SETTING CORE SIZE *********
14700
14800 To increase the core size type CALL, then C N where N is the core
14900 size desired. Then type CON (=continue) to return to where you
15000 previously were in the program.
15100
15200 When several parameters are to be changed at once the following
15300 type-in format should be used:
15400
15500 PLAY;SIMP 0 .2 FS/2 850;FINISH;
15600
15700 This will play F# below middle C for 2/10" at an amplitude of 850.
15800 (Please note that P5, the wave form for SIMP, will be dealt with
15900 later.)
16000
16100 ********** COMMAS **********
16200
16300 Commas may be used to separate the parameters and if nothing precedes
16400 a comma the contents of that parameter remains unchanged. Also any
16500 parameter numbers higher than the length of the list will not be
16600 affected.
16700
16800 PLAY;SIMP ,.3,,1200;FINISH; changes only P2 and P4.
16900
17000 ******************************************************
17100
17200 A string of notes may be played with the following input:
17300
17400 PLAY;SIMP 0 .2 C 1500;SIMP .2,,D;SIMP .4,,E;
17500 SIMP .6,,C;FINISH;
17600
17700 In this case P1 must be updated for each note. (Never overlap an
17800 instrument with itself. Distortion will occur.) P2, the note
17900 duration remains unchanged, so the commas suffice for the last three
18000 notes. P4, coming at the end of the list for the first note need
18100 only be stated once if it is not to change.
18200
18300 Rests are created by simply leaving some time between the end of one
18400 note (P1+P2) and the beginning of the next (the new P1).
18500
18600 PLAY;SIMP 0 .2 C;SIMP .5;FINISH; will play C for 2/10",
18700 rest for 3/10" and then play another C for 2/10".
18800
18900
19000 ********** FUNCTIONS **********
19100
19200 The wave form in P5 is entered by means of a name which is used by
19300 the program to locate a list, or array, of numbers (512) which
19400 describe the wave. The names used for this purpose will always be F
19500 followed directly by a number. These arrays will be called
19600 "functions."
19700
19800 Only one function is in MUS10, although more can be added. The
19900 function present is known as F1 and describes a sine wave. To see
20000 this wave on the CRT type:
20100
20200 SEE(F1);
20300
20400 To clear the screen, type 0.
20500
20600 Functions may be created with an external program called FUNC or
20700 within MUS10 itself by means of two routines called SYNTH and SEG.
20800 SYNTH is used to create composites made by adding various harmonics
20900 together. The form of F1 could be changed in the following manner:
21000
21100 SYNTH(F1); 1,1 2,1 3,.5 999;
21200
21300 In the three pairs of numbers the first of each pair represents the
21400 harmonic number and the second the relative amplitude of that
21500 harmonic. Thus the ratios of harmonics 1, 2 and 3 will be 1:1:.5 .
21600
21700 The size of the second number of each pair is important only in its
21800 relation to the other amplitude numbers. The number 999 is used to
21900 signal the termination of a string of entries.
22000
22100 Several pairs may entered and harmonic numbers up to 256 may be used
22200 but in practice great care must be taken to avoid the "foldover"
22300 effect which occurs when frequencies higher than one half the
22400 sampling rate are present. (See appendix.)
22500
22600 It should be pointed out that the fundamental (harmonic #1) need not
22700 be present in a wave.
22800
22900 SYNTH(F1); 10,1 12,1 15,1 999; will give the three notes of a
23000 minor chord. After this has been entered the following will cause a
23100 C minor chord to play:
23200
23300 PLAY;SIMP 0 .5 GS/8;FINISH;
23400
23500 While the lowest Ab (or G#) on the piano keyboard has been indicated,
23600 since the wave form includes only the 10th, 12th and 16th harmonics,
23700 the notes middle C, Eb and G will be heard.
23800
23900 Several experiments with different wave forms should be made. Be
24000 sure to SEE the waves so a visual-aural connection might be made.
24100
24200 A function may be changed in the middle of PLAY routine but it must
24300 be noted that the new wave definition must follow! the note which it
24400 is to affect.
24500
24600 In PLAY;SIMP 0 .3 D 1000;SIMP .3;SYNTH(F1); 1,.7 3,.2
24700 5,.1 999;SIMP .6,,E;FINISH; the newly defined wave
24800 will be heard in the second and third notes.
24900
25000
25100 If you wish to have several functions with different names available
25200 and you do not create them with the FUNC program, their names must be
25300 "declared" to MUS10. Suppose you wish to have F2, F3 and F4. You
25400 must type directly to MUS10 (or into an EDIT file which will be read
25500 by MUS10) the following:
25600
25700 ARRAY F2,F3,F4(512);
25800
25900 The "(512)" indicates that each function array will require 512 words
26000 of storage. Thus at this point the free storage left for sound
26100 samples has been reduced by 1 1/2K so you must increase the size of
26200 your core if you want to have the same amount of playing time as
26300 before.
26400
26500 The following example will play a sequence of notes wherein are heard
26600 the 10th, 14th and 18th harmonics of a low C, then the 10th, 13th and
26700 16th, and finally the 10th, 12th and 14th harmonics.
26800
26900 ARRAY F2,F3(512);
27000 SYNTH(F1);10,1 14,1 18,1 999;
27100 SYNTH(F2);10,1 13,1 16,1 999;
27200 SYNTH(F3);10,1 12,1 14,1 999;
27300 PLAY;SIMP 0 .3 C/4 2000 F1;
27400 SIMP .3,,,,F2;SIMP .6,,,,F3;FINISH;
00100
00200 A type of flow-chart diagram for SIMP would appear as follows:
00300
00400 P4 MAG*P3
00500 | |
00600 ↓ ↓
00700 ***************
00800 * * OSCIL
00900 * * U1 (UNIT GENERATOR ONE)
01000 * P5 *
01100 * *
01200 * *
01300 *********
01400 |
01500 ↓
01600 *****
01700 * OUT *
01800 * A *
01900 *****
02000
02100 The top left input, P4, serves simply as a multiplier for the numbers
02200 found in the wave form array, P5. The particular number from the
02300 array to be multiplied is determined by the number in the upper right
02400 input. The upper right input, in this case P3, when processed by
02500 "MAG" (the "magic" number) becomes the increment, the rate at which
02600 the wave form array is stepped through. The "magic" number is found
02700 by dividing the array length, 512, by the sampling rate, 10000.
02800
02900 512/SRATE=.0512 (Higher sampling rates will be discussed later.)
03000
03100 The maximum size of the numbers in the wave array is + or -1. Thus
03200 if P4 is set to 1000 the output of the OSCIL will be numbers in the
03300 range +1000 to -1000 which will describe the wave form put into P5
03400 cycling at the rate given in P3.
03500
03600
03700 The code for entering this instrument follows:
03800
03900 COMPILE;
04000 INSTRUMENT SIMP;
04100 OSCIL(P4,MAG*P3,P5);
04200 OUTA←OUTA+U1;
04300 END;
04400 FINISH;
04500
04600 Several instruments may appear between COMPILE; and FINISH;.
04700
04800
04900 This instrument has only one unit generator (the OSCIL) hence the
05000 output of U1 is added to the contents of OUTA. If there are several
05100 instruments the outputs of all the instruments will be combined in
05200 OUTA for each sample.
05300
05400 It will be noticed when playing instrument SIMP that the sound begins
05500 and ends quite abruptly. This is because no attack-decay envelope
05600 has been applied to the tone. The sound begins at the full amplitude
05700 of P4 and remains at that level for its total duration.
00100
00200 To apply an envelope, another unit generator must be added.
00300
00400
00500 P4 MAG/P2
00600 | |
00700 ↓ ↓
00800 ***************
00900 * * OSCIL
01000 * * U1 (UNIT GENERATOR ONE)
01100 * P5 *
01200 * *
01300 * *
01400 *********
01500 |
01600 | MAG*P3
01700 | |
01800 ↓ ↓
01900 ***************
02000 * * OSCIL
02100 * * U2 (UNIT GENERATOR TWO)
02200 * P6 *
02300 * *
02400 * * COMPILE;
02500 ********* INSTRUMENT TOOT;
02600 | OSCIL(P4,MAG/P2,P5);
02700 ↓ OSCIL(U1,MAG*P3,P6);
02800 ***** OUTA←OUTA+U2;
02900 * OUT * END;
03000 * A * FINISH;
03100 *****
03200
03300 Now that the instrument has been expanded you will note that it is
03400 the output of unit generator two (U2) which goes to OUTA.
03500
03600 P5 will now contain the envelope array. This array is best defined
03700 by the SEG routine. SEG defines the positions of line segments used
03800 to approximate a curve. With SEG several pairs of numbers may be
03900 entered. The first number of each pair is an amplitude, normally in
04000 the range of 0 to 1, and the second is the step number in the array.
04100 The step numbers 1 through 100 are used in SEG. (However internally,
04200 512 array locations are used.) Straight line segments are drawn
04300 between each of the points defined. The following would put a
04400 triangular envelope shape into F2:
04500
04600 ARRAY F2(512);
04700 SEG(F2); 0,1 1,50 0,100;
04800
04900 Note that the routine is terminated when step 100 is reached.
05000 DO NOT USE 999 with SEG.
05100
05200 After having typed in the code for instrument TOOT and the definition
05300 for an envelope in F2, the following will produce a note using that
05400 envelope:
05500
05600 SYNTH(F1);1,1 2,.4 3,.1 999;< Sets the tone color.
05700 PLAY;TOOT 0 .5 A 2000 F1 F2;FINISH;
05800
05900 If two envelopes are to be contrasted add another function and define
06000 it.
06100 ARRAY F3(512);
06200 SEG(F3); 0,1 1,7 .2,25 .1,60 0,100;< Staccato
06300 PLAY;TOOT 0 .2 1000 2000 F3 F1; < P5 has envelope
06400 TOOT .2 .5,,,F2;FINISH;<Plays stac. then sust.(F1 then F2)
06500
00100 In the next example a unit generator will be added above the right
00200 side of the bottom, tone producing unit generator. In this way a
00300 function may be used to describe fluctuations of pitch within the
00400 duration of a note -- much as the previous example gave the
00500 possibility for changing the amplitude during a single note.
00600
00700
00800 MAG*P7-MAG*P3 MAG/P8
00900 P4 MAG/P2 | |
01000 | | ↓ ↓
01100 ↓ ↓ ***************
01200 *************** * * OSCIL
01300 * * OSCIL * * U2
01400 * * U1 * P9 *
01500 * P5 * * *
01600 * * * *
01700 * * *********
01800 ********* MAG*P3 |
01900 | | _____________|
02000 |________ _↓___↓_
02100 | \ /
02200 | \ + /
02300 | \_/
02400 | |
02500 ↓ ↓
02600 ***************
02700 * *
02800 OSCIL * *
02900 U3 * P6 *
03000 * *
03100 * * COMPILE;
03200 ********* INSTRUMENT GLISS;
03300 | OSCIL(P4,MAG/P2,P5);
03400 ↓ OSCIL(MAG*P7-MAG*P3,MAG/P8,P9);
03500 ***** OSCIL(U1,MAG*P3+U2,P6);
03600 * OUT * OUTA←OUTA+U3; END; FINISH;
03700 * A *
03800 *****
03900
04000
04100 In order for this instrument to perform glissandos, a third function
04200 must be defined for P9 (the "shape" of the glissando). A straight
04300 line slope will suffice for a simple glissando. After typing in the
04400 instrument definition set up the three functions.
04500
04600 ARRAY F5,F6(512); <F1 is already present.
04700 SEG(F5);0,1 .8,7 1,12 1,90 0,100;<Envelope
04800 SEG(F6);0,1 1,100; <Slope
04900
05000 In the preceding, the ARRAY declaration is needed only when some new
05100 function names are to be used.
05200
05300 The following will play a glissando up two octaves, from C to C*4.
05400
05500 PLAY;GLISS 0 1 C 2000 F5 F1 C*4 1 F6;FINISH;
05600
05700 If P8←.5; (while P2 remains at 1) two glissandos will be heard.
05800
05900
06000 This same instrument may be used to produce a vibrato by putting a
06100 sine wave into P9, setting P8←1/7; (the vibrato rate will be 7 times
06200 per second) and making P7 some very small amount different from P3.
06300
06400 PLAY;GLISS 0 1 C 2000 F5 F1 C+2 1/7 F1;FINISH;
06500
06600 (It is assumed that F1 is a sine wave.)
00100 Various types of noise and other random fluctuations are
00200 produced by the two random number unit generators. These are called
00300 RANDH and RANDI. RANDH (H=hold) produces in effect a function made
00400 up of horizantal lines at various levels with a perpendicular jump
00500 from one level to the next. There are two inputs to RANDH. The
00600 first (left hand) gives the range, plus or minus, of random
00700 selection and the second (right hand) gives the rate (per second) at
00800 which the selections are to be made.
00900
01000 Care must be taken with the number in the first input. If
01100 the number 100 is given, the output of RANDH will fluctuate between
01200 +100 and -100. Thus if a range of 100 to 200 is desired, the input
01300 number should be 50 and the number 150 must be added to the output.
01400
01500
01600 MAG*P7 MAG*P8
01700 P4 MAG/P2 | |
01800 | | ↓ ↓
01900 ↓ ↓ ***************
02000 *************** * *
02100 * * OSCIL * RANDH * U2
02200 * * U1 ***************
02300 * P5 * |
02400 * * |
02500 * * |
02600 ********* MAG*P3 |
02700 | | _____________|
02800 |________ _↓___↓_
02900 | \ /
03000 | \ + /
03100 | \_/
03200 | |
03300 ↓ ↓
03400 ***************
03500 * *
03600 OSCIL * *
03700 U3 * P6 *
03800 * *
03900 * * COMPILE;
04000 ********* INSTRUMENT NOISE;
04100 | OSCIL(P4,MAG/P2,P5);
04200 ↓ RANDH(MAG*P7,MAG*P8);
04300 ***** OSCIL(U1,MAG*P3+U2,P6);
04400 * OUT * OUTA←OUTA+U3; END; FINISH;
04500 * A *
04600 *****
04700
04800 ARRAY F5(512); <F1 is already present.
04900 SEG(F5);0,1 .8,7 1,12 1,90 0,100;<Env.
05000
05100
05200
05300
05400 The following will produce white noise.
05500
05600 SRATE←25000;MAG←512/SRATE;SPEED←2;
05700 PLAY;NOISE 0 .5 C*8 1000 F2 F1 P3 P3*4;FINISH;
05800
05900 Actually P8 (given as P3*4) can probably be left at a number
06000 like 4000 for noise purposes. As P7 is changed the apparent
06100 band-width of the noise will be changed. As the band-width gets
06200 narrower the center frequency becomes more apparent. Thus if P7←P3/16
06300 and P3 is up in the range of C*8, something of the effect of blowing
06400 across an open tube will be produced. The pitch is clear -- but
06500 quite windy.
06600
06700 The SRATE (sampling rate) must be increased for noise
06800 production since very high frequencies are essential. At SRATE←25000
06900 the high frequency cut-off will be at 12500 hz.
07000
07100 If P8 is set to a low number (e.g. 8) individual random
07200 pitches, instead of noise, will be produced at that rate.
07300
07400
07500 If the random unit generator is replaced by a RANDI the
07600 random function produced will be made up of a series of slopes
07700 (I=incremental) up and down from one random point to another. In the
07800 case of noise production there is little difference between RANDI and
07900 RANDH. However RANDI is necessary for getting such things as random
08000 vibrato. The following will produce an acceptable, "human" sounding
08100 vibrato.
08200
08300 PLAY;NOISE 0 1 C*2 1000 F2 F1 P3*.01 16;FINISH;
08400
08500 The random rate of 16 per second (in P8) is considerably
08600 faster than the human vibrato rate of 5 to 8 per second. In this
08700 case however since the full band-width (in P7) is only seldom
08800 attained and the heard effect is that of a rate much slower than 16.
00100 ********** APPENDIX XXX NOT COMPLETE!!!XXX ************
00200
00300 The main program for sound generation is currently called MUSY.FAI or
00400 MUSEXP.FAI (EXP=export). The export version is designed to run on a
00500 standard PDP10 DEC system (which has a "FAIL" compiler.)
00600
00700 The main program must be loaded with two subroutine packages which
00800 are called NSCTPY.F4 (OR NSCEXP.F4) and MUSIO.FAI (or EXPIO.FAI.) The
00900 FORTRAN routines are for the creation of function arrays and for
01000 organizing the output of sound samples to tape or disk after they
01100 have been computed. The FAIL routines are for fast output of blocks
01200 of samples.
01300
01400 The STANFORD version can play sound from core or write all samples on
01500 an external device for playback with another program. The latter
01600 method is always used for sounds longer than about 10 seconds.
01700
01800 See SCORE.MAN for information on longplaying features (RCDFLG and
01900 BIGBIT) and much other information.
02000
02100
02200
02300 ********* SOME INFO RE. THE FUNC PROGRAM ***********
02400
02500 CRUNCH: Any two functions already in a single .DAT file may be
02600 "crunched" together. Also, a function may be created by either the
02700 SEG or SYNTH routines and then if instead of typing "F" for FINISH
02800 the letter "Z" is typed the program will jump immediately to "crunch"
02900 mode. At this point the new function may be combined with any
03000 function found in the file presently in core. Note however that once
03100 this new function is processed by any of "crunch" options its
03200 original form cannot be regained without going back to ordinary SEG
03300 or SYNTH mode.
03400
03500 PLOTTING: If "SP" (=see on the plotter) is typed single functions
03600 can be drawn on the Calcomp plotter. The size asked for is in
03700 inches. "SA" (=see all on plotter) will plot all the functions found
03800 in a single file. "SX" (=see all on the XGP) will draw all functions
03900 from a single file in the proper size for printing by the XGP. In
04000 order to use "SX" you must!!! follow the next steps exactly!!!
04100
04200 Before running FUNC type: A DSK PTP <CR>. This will cause the
04300 instructions FUNC sends to the plotter to be written in a
04400 file on the disk.
04500
04600 When FUNC asks you once more about what you want to do
04700 (you have already typed "SX" <CR> and then the appropriate
04800 file name) hit the "CALL" key.
04900
05000 Then type F <CR>. This finishes off the DSK file which
05100 has just been written.
05200
05300 Then type R X <CR>. This runs a program called X which
05400 converts plotter information to XGP commands.
05500
05600 X will ask you 5 questions. You should answer as follows:
05700
05800 PLOT.BIN <CR> (the file name)
05900 5 <CR> (shift 5 inches)
06000 <CR> (use default value of 11".)
06100 1 <CR> (1 inch from the left)
06200 Y (yes, delete the plot file)
06300
06400
06500
06600 Information re. WAVES. To run it type DO WAVES[LCS,MUS].
06700
06800 This will allow you to display the actual wave shapes of sound
06900 computed using RCDFLG←-1;. The MUSAA.DMD file thus produced is read
07000 by WAVES.
07100
07200 You may display up to 3072 samples at a time but since only 1024
07300 separate positions can be shown at once, larger numbers will cause
07400 some samples to be skipped over (but with no great loss.) After each
07500 group of samples is displayed a <CR> will move on to the next group.
07600 If a number is typed, that will set the extent of the next group. If
07700 the number -1 is given, the program will automatically cycle through
07800 all available samples by groups of the last given number. (When no
07900 more samples are to be found it will end with an error message.) In
08000 order to make the program go backwards type any number less than
08100 -2 for the number of samples you wish to back up.
08200
08300 This program should be of use in seeing the wave shapes produced by
08400 amplitude and frequency modulation as well as seeing the effects of
08500 foldover, etc. Composite waves from more than one voice may be
08600 displayed but as the complexity increases it may prove rather
08700 difficult to glean useful information from what is seen.