Conference napalm::commusic_v1

    You used to be able to do this with the SAD-1000 (analog delay IC,
    found in most analog delay stomp boxes) I had the spec sheets and
    notes on how to do this, if you're interested I'll see if they still
    live in my possessions somewhere....
    
    dave

    I have the same information.
    To see how it's done in charge-coupled devices or digitally, let's
    see how we would do it on magnetic tape..
    Problem: change the speed of something without changing its pitch.
    Well, we can change the speed of an audio recording on a variable-spped
    tape recorder by changing the tape speed.  However, this changes
    its pitch.  If we could change the pitch in the direction opposite
    to that that we changed the tape speed, we could correct for this.
    Therefore, the only new problem is pitch change.  How can we do
    pitch change on a tape recorder?
    Raising a pitch and lowering a pitch are separate problems.  Let's
    begin with lowering a pitch.
    
    1. Record a sound, say, me saying "record a sound." out loud.
     on 1/4" tape running at 15 inches per second. Let's say it took
    me 1 second of time to say that phrase.
    2. Using a razor blade, cut the tape every 1/4" along its length.
    This would require a great deal of skill and patience to actually
    do, of course.
    3. Throw away every other 1/4" length of tape, leaving half as many.
    4. Splice them together in sequence.
    5. Play the tape at half speed, or 7.5 ips.
    The result of this will be that my voice will be an octave lower,
    but that the phrase will be said in the same length of time, one
    second.                                
    If, instead, we had wanted to increase the speed without changing
    the pitch, just play it as the original speed, 15ips.  It will take
    .5 seconds.  The little 1/4" lengths of tape will merge together
    with some fluttering to reproduce the phrase with only half the
    original information.
    
    Now, let's try to raise a pitch an octave.  This is harder.
    1. Record a sound of me saying "record a sound." Duplicate this
    tape on another tape.  Splice both tapes into 1/4" sections,
    and insert corresponding pieces of tape (like, the "rd" sound in
    the word "record" on both tapes) next to each other.  Splice it
    all together.  The whole tape is now twice as long, 30 inches,
    as the original or the copy.  Play it at the original spped,
    which we said before was 15"/sec.  It will take 2 seconds for me
    to say "record a sound".  Now, play it at 30ips.  It will take 1
    second to say the words, as in the original, but will be an octave
    higher (munchkin land).
    
    2. Go to LEDS-BIM
    
    
    To make a digital version, replace the magnetic tape with digital
    memory.  Write a program that will adjust the amount of sound
    deleted or duplicated so that pitch can be moved over a continuous
    range.  
    To make a CCD version, read the data out at a different speed than
    it's read in.  Read data again if the player is reading faster than
    the recorder, and throw away data if the player is reading more
    slowly than the recorder.
    
    That should make it clear to people who already know how it works.
    Tom

    I did alot of work on this very thing a few years back. We were
    building a digital voice recorder system for Emergency 911 phone
    systems. We even go a few patents on the filtering & time conversion
    process that we can up with. Tom's explaination .34 is pretty accurate,
    but leaves out the important problems that must be dealt with, the
    filtering, and selection of fill data for the convertion to higher
    frequencies. We were most concerned with fast and slow playback
    with not fequency shift, but ended up with a system that handled
    both time shift with no frequency shift and frequency shift with
    no time shift.
    
    pcv

    I got bored reading the explaination, but it can probably be done
    the same way that CD players implement the cue fast-forward function,
    but on a finer grain.
    
    That is, actually play every N seconds of M seconds of your source
    program samples, and skip M-N of M seconds.  N must be less than M
    (obviously) and M is greater than the length of time required to
    audibly recognize the lowest frequency component in your source. Of
    course I'm sure this can introduce annomalies if N and M aren't chosen
    appropriately, but you get the idea.
    
    Steph

    >< Note 1225.4 by BOLT::BAILEY "Steph (stef') Bailey" >
>              -< Even cheap commercial electronics can do this. >-
>    That is, actually play every N seconds of M seconds of your source
>    program samples, and skip M-N of M seconds.  
>    N must be less than M (obviously)
I don't know what CDs do on fast forward, but this is not a reasonable
    
    description for changing.  N can be more than M if you want to raise
    pitch; you repeat a segment of audio.  A reasonable size for M
    has to be larger than your greatest period of your lowest frequency.
    It may be roughly 1/12 seconds.  Splicing the pieces together creates
    a problem; if the waves on either side of the juncture are at different
    levels or have very different slopes, a glitche or flutter can result.
    Perhaps commerical digital processors smooth the gulf with
    interpolation of a ramp across the two different levels.  I suspect
    that the Yam SPX90 looks for same-direction zero-crossing, because the
    pitch-change interval changes depending on the absolute pitch
    of the input; octaves are sometimes perfect, sometimes big, sometimes
    small, but always the same for a given absolute input pitch.
    
>     and M is greater than the length of time required to
>    audibly recognize the lowest frequency component in your source. Of
>    course I'm sure this can introduce annomalies if N and M aren't chosen
>    appropriately, but you get the idea.
>    
>    Steph
>
>
                                                                       tom

Thanks for the input, especially Tom.

So as I understand it, the input signal is somewhat altered (distorted)
by the application of the time compression algorithm.  Information is
in fact lost.

I've noticed that a sideband type of radio creates a munchkinization or
deathbooming if the frequency of reception is not exactly equal
to the frequency of the transmitted carrier.  What is happening here?

Todd.

    >< Note 1225.6 by HPSTEK::RHODES >
>I've noticed that a sideband type of radio creates a munchkinization or
>deathbooming if the frequency of reception is not exactly equal
>to the frequency of the transmitted carrier.  What is happening here?
>
>Todd.

    For cheap pitch change,
    Try a balanced modulator with a sine carrier, like the PAiA one;
    I also found a kit for one in a pulp electronics catalog.
    I think that in shortwave, 
    The frequency of the resulting signal is shifted by the difference
    between the carrier and the heterodyne tuner's signal. 
    The farthur apart they are, the higher the frequency difference,
    the munchkiner it gets.  
        Or roughly like that.
    Tom

    
    Re: .7
    
    This is correct.  When I used to work in communications, the microwave
    radio level metering sets had an audio monitoring output that had this
    frequency-shifting effect.
      

In Single Sideband modulation (which does in fact use a balanced modulator),
essentially only the harmonic structure of the sound is transmitted.  The
fundamental is reconstructed at the receiver.

When the receiver and transmitter are not using the same reference frequency
(caused by one of them being tuned wrong), the reconstruction in the receiver
is misled and it puts the fundamental back too high or too low in the audio
spectrum, off by the difference in the radio frequency carriers.  I think
the spacing of the harmonics remains the same, however, so it is not exactly a
perfect pitch change. 

Boy, it's been a long time since I fooled with this stuff.

    It's correct to say that balanced modulation does not offer real
    pitch change, linearly.  The arithmetic relationships distort
    harmonic content.  I use a balanced modulator to turn a piano
    into a prepard piano; it sounds like John Cage's technique of
    putting rubber wedges, screws, and other junk in between the 
    strings of a piano.  This works because the harmonic content of
    the sound changes.
    otm

    Exactly correct, Mr. Dickson...        
                                                                  
    	
    			DANGER - MATHEMATICS AHEAD - 
    
    
    --------Theory of Electromagnetic Communications Lecture 401.30-----
    
    On SSB (and in a ring modulator), the information that is passed
    through correctly can be described as a bunch of frequencies
    of the form 
    	
    	X+F1, X+F2, X+F3 ...
    
    where the Fn's are known, but X isn't.  X is the carrier frequency of
    the ring modulator (provided it's a sine wave), or the _difference_ in
    frequency of the SSB transmitter and reciever center frequencies. 
    
    So, SSB where the transmitter and reciever are "right on" reconstructs
    the signal correctly; likewise a ring modulator with carrier=0 doesn't
    alter the signal.
    
    
    What happens if X isn't zero:
    	
    	All of the frequencies are displaced by a constant number of
    Hz from their correct location- NOT a multiplicative constant.
    This (in general) results in a sound where the original harmonics
    (f, 2f, 3f, etc) are no longer in octave ratios- the distinctive
    ring modulator sound.
    
    	Second interesting effect: "negative frequency wrap-around":
    It really isn't fair to say a sound has harmonics at f, 2f, 3f,
    etc.  Really, it has harmonics at �f, �2f, �3f, etc.  The energy
    at frequency f is really split equally between a positive frequency
    at +f and a negative frequency at -f.
    
    	With normal (non-ring-modulative) processing, such as
    time-compression or time-expansion (via magnetic tape, sampler,
    or CCD) all harmonic frequencies are MULTIPLIED by some constant,
    but they are still integer multiples.
    
    Example:
    	Original:		�f, �2f, �3f 	
    					       	= �440, �880, �1320 Hz
    	speed up
    	playback by 1.3 :       �1.3f, �2.6f, �3.9f                
    						= �572, �1144, �1716 Hz
    
    but the harmonics are still in the ratios of 1:2:3 .  It just sounds
    like you're playing the same line a minor third or so higher.
    			                                  
    
    But with a ring modulator, the + and - freqencies don't shift equally-
    they both shift upwards.
    
    Example:
    	Original:               �f, �2f, �3f
                                                = 440, 880, 1320 Hz
    	Ring modulate with 400 Hz
    	carrier wave:		+f+400, -f+400,
    				+2f+400, -2f+400, 
    				+3f+400, -3f+400
                                        	= 840, 40,
    						  1280, 480,
    						  1720, 920  Hz
    
    What dows this sound like: Well, there's a low rumble (the 40 Hz), a
    slightly shifted original line (at 480 Hz), a pair of lines about an
    octave up and about a semitone apart <<yecch>> (at 840 and 920 Hz), and
    then a pair of rather thin high lines up at 1270 and 1720 Hz - a ratio
    of 1.35 to one, which is pretty close to a major third.
    
    It most certainly does NOT sound like a sampler in good working
    condition, nor like a sped-up tape loop.  
    					    
    Note that the low rumble is due to the -f component being shifted
    upwards from -440 Hz to -40 Hz.  Since the ear can't tell the
    difference between -f and +f, the output sounds like it has six, rather
    than three, positive frequencies. 
    
    More magick:  The new sound really has twelve freqencies: each of the
    six frequencies above is really a +/- pair again!  So, a second ring
    modulator after the first would give a signal with 12 positive
    frequencies (really 12 +/- pairs), etc.... 
    
    Even more majick: What if the modulator is NOT a sine wave??? This
    gets very complicated very quickly here.  Learn about Bessel functions
    if you're really interested.
                                              
    
    ----------------------------------
                                                                
    
    Do people really read these long mathematical notes of mine?
                                   

    re .11
    
    Yes! A mathematical discussion like this is always useful. I'd like
    to see a bit on the mathematics of how Lexicon's device does it's
    conversion. If I understand correctly, it converts the incoming
    signal in the time domain to the frequency domain. It then remaps
    that to a different time domain, and sends it out at the altered
    rate with close to the same frequency spectra intact. I'd like to
    see how all this is done on the fly. If your incoming data is being
    sampled at 44kHz, this gives you 22.7 �S between samples. Not a
    lot of time to do all this computation.
    
    dp

    
    I thought this notesfile was for frustrated musician computerpeople.
    
    Now I discover there are a few frustrated frustrated computerpeople
    musicians computerpeople.
    
    Richard.

    re .11: Yep, some of us read them.  Esp. those of us who miss our
    old modular systems with nice things like ring modulators!
    
    	Eirikur
    

    
    	A crude frequency shifter can be conceptualized by imagining
    samples clocked in at one rate and clocked out at another....
    
    	One of the problems with frequency shifters is that you dont
    get the product in real time. It comes later and it's noticable.
    This makes a difference if your trying to synthesize a bass guitar
    sound from a six string. Singing harmony with yourself, the problem
    can easily be lived with - you'd probably want a small time delay
    anyway.                                             
    
    	Has anyone ever evaluated the expression f(t)*f(t-T) as far
    as how it sounds? This is just a ring modulator with the carrier
    replaced by a delayed version of the input signal. Bet I know something
    you dont know! (Hint: f(t)*f(t)=f(2t), if f(t)=sinwt)        
    
    	Joe Jas
    

Now that I see the math, I notice a strong similarity with the formulas
for FM synthesis.  Both have that plus/minus stuff with wraparound, but
FM uses multiplicative modification of frequency while ring modulators
use additive modification.

    Re: .11 - Is it by any chance a comb filter with passbands at 
    f = N * 1/T for N=1,2,3... ?
    	
          
    Now, what's the response of 
    	
    	Vout(t) = Vin (t) * Vin (T - t)
    
    		(note that the second Vin term has time running BACKWARDS)
    	
    	:-)
    
    re .16:
    Both ring modulators and FM share a lot of common mathematics- and
    tend to sound similar too.  Bessel functions are the root of both
    matters.

Thanks all.

After reading Bill's first reply, I must say that I was saying to myself
"he's on to something here".  How about a multistage ring modulator digital
synth with outboard digital filtering?  Quick, let's build one along with
the ultimate drum machine...

RE: .12 (Lexicon device)

I was just venturing a guess at how the Lexicon machine works.  Probably
way off base.  Chances are they do just what Tom was saying - strech
the data (applying smoothing algorithms, of course) for time expansion, and
remove data (applying interpolatoin algorithms) for time conpression.

Todd.

Also note that the Lexicon machine samples an entire soundtrack (probably
direct to disk) before the compression or expansion algorithm is applied.
After the sampling has completed, the musical data is adjusted to fit 
into a desired time window.

Todd.

    
    re .15
    
    I did a little poking around in my math books the other night.
    
    First of all, (sin(x))^2 is not equal to sin(2*x).  This should be 
    readily apparent from the fact that
    
    	0 <= (sin(x))^2 <= 1
    
    while
    
    	-1 <= sin(2*x) <= 1
    
    What is true is that
    
    	d (sin(x))^2
    	------------ =  sin(2*x)
    	    dx

    which is kind of cute.    
    
    However, if you look at (sin(x))^2, you'll see that it looks a lot like
    cos(2*x), inverted and shifted up.
    
    In fact, a useful approximation of (sin(x))^2 is
    
    	(sin(x))^2  = (1 - cos(2*x) + ...)/2
    
    where "..." represents a bunch of terms I'm too lazy (or 
    mathematically inept) to figure out.  I couldn't find anything in 
    any of the sources available to me that discussed the Fourier 
    transform of (sin(x))^2, so I had to wing it.
    
    The following table is useful:
    
    	x	sin(x)	(sin(x))^2	cos(2*x)   (1 - cos(2*x))/2
    
    	0	  0	     0		   1	           0
    
       pi/6	 1/2	    1/4		  1/2		  1/4
    
       pi/4   sqrt(2)/2     1/2		   0		  1/2
    
       pi/3   sqrt(3)/2     3/4  	 -1/2		  3/4
    
       pi/2	  1	     1		  -1		   1
    
    So, it's a pretty good approximation at a couple of key points.
    
    Be that as it may, the point is, (sin(x))^2 has a prominent "2nd
    harmonic", i.e., a strong showing at 2*x, which is the point I 
    believe Joe was trying to make.
    
    Now, regarding ring modulating a signal with a delayed version of 
    itself:
    
    This is
    
    	sin(x)*sin(x+d)
    
    Using the trigonometric identity
    
    	sin(x+d) = sin(x)*cos(d) + cos(x)*sin(d)
    
    and observing that d is a constant, multiply it all out, use the
    trigonometric identity
    
    	sin(2*x) = 2*sin(x)*cos(x)
    
    and we get
    
    	sin(x)*sin(x+d) = k1*(sin(x))^2 + k2*sin(2*x) 	 

    where k1 and k2 are constants.
    
    We've already noted that (sin(x))^2 looks like cos(2*x), so the 
    bottom line (again, what I believe Joe was driving at), is that 
    ring modulating a signal with a delayed copy of itself effectively 
    frequency doubles it, subject to some phase wierdness (due to the 
    presence of both a sine and cosine term) and a DC offset.

    len.
    
    

    Does the deafening silence mean:
    
    	1) I got it all right?
    
    	2) I got it all wrong?
    
    	3) Nobody cares?
    
    	4) None of the above?
    
    I was hoping some young whippersnapper fresh out of school would tell me
    what the transform of (sin(x))^2 was. 
    
    And where'd Joe go?  What answer was *he* expecting?
    
    len (mildly abashed at having wasted all that effort).
    

    re:.21
    
    Give us a chance... You had the whole weekend to come up with it,
    I'll look it over tonight and give you a reply tomorrow morning...
    
    pcv

    re .22 - uhm, it was posted last Friday.  I figured everybody else
    had the whole weekend to find fault with my math.
    
    len.
    

    re: .23
    
    OK, so I'm slow... ;^)
    
    I looked over your equations, and they seem to look good (on paper).
    One of the things I noticed when I did alot of work on this subject
    was that we went down alot of ratholes trying to come up with a
    good sounding filter. I just wish I had the time to actually try
    this and hear how it sounds.
    
    pcv

    {yawn}
    
    neat stuff len.   
    
    when can I get the Fehskens Systems Inc. Doubler in a box?
    
    or you gonna license it to Yamaha and retire?