## follow up How to generate arbitrary waveforms

Using Nyquist scripts in Audacity.
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DERF
Posts: 217
Joined: Sun Jun 13, 2010 12:37 pm

### follow up How to generate arbitrary waveforms

Hello. I have a question to ask.

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0.05 1
0.3  0.4
0.5  0.4
1    0))
(setq wiggle 0.3)
(setq wigglerate 3)
(setf envelope
(sim (mult adsr (- 1 (* 2 wiggle)))
(mult adsr wiggle  (sum 1 (hzosc wigglerate)))))
(mult envelope s)
The operator' s manual say: "(sim [beh1 beh2 ...]) Returns a sound which is the sum of the given behaviors...)
my question is the following one:in this code

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(sim (mult adsr (- 1 (* 2 wiggle)))
(mult adsr wiggle  (sum 1 (hzosc wigglerate))))
_ the first behavior is:

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(mult adsr (- 1 (* 2 wiggle))
_ the second behavior is:

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(mult adsr wiggle  (sum 1 (hzosc wigglerate)))
Does it right?
Thank you.

steve
Posts: 47612
Joined: Sat Dec 01, 2007 11:43 am
Operating System: Linux *buntu
Contact:

### Re: follow up How to generate arbitrary waveforms

DERF wrote:Does it right?
Yes.

DERF
Posts: 217
Joined: Sun Jun 13, 2010 12:37 pm

### Re: follow up How to generate arbitrary waveforms

Thank you.
I would like to ask a second question.
She concerns the two behaviors exactly.
When we use without the function

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(sim
the second behavior, we obtain the sound wave n°2. If we use 2 behaviors, we obtain the sound wave n° 1.
We observe a small difference.The intensity decreased, and the wave is not altered in the same way all the time (the drawing of the wave is different) in the wave n° 2.The shape is more regular.
My question is the following one: is there an article which explains how the 1ier behavior acts on the second, and finally, which is the interest to combine behaviors, as in this precise example.

Attachments
BEHAVIORS .jpg (61.74 KiB) Viewed 1207 times

steve
Posts: 47612
Joined: Sat Dec 01, 2007 11:43 am
Operating System: Linux *buntu
Contact:

### Re: follow up How to generate arbitrary waveforms

I'll split up your code into sections, and demonstrate what each bit does:

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(setf adsr (pwlv 0 0.05 1 0.3  0.4 0.5  0.4 1 0))
This creates an "envelope", which is a low sample rate control signal.
A "control signal" is just a "sound", but at a low sample rate, and changing much more slowly that a normal audio waveform.

By default, "PWLV" creates control signals ("sounds") that have a sample rate 1/20th of the track sample rate.
If you return this kind of "sound", on it's own, back to the Audacity track, the length of the sound will be 1/20th of the length that you generated.
The sound returned by PWLV is assigned as the value of "adsr".

Example,

(pwlv 0 0.05 1 0.3 0.4 0.5 0.4 1 0) creates a signal that has length "1".
If this is in a "generate" type effect (in the Generate menu), then that is "1 second".
If this is in a "process" type effect (in the "Effect menu), then "1 unit" of time gets stretch to equal the length of the selection.

The "Nyquist Prompt" is, by default, a "process" type effect, so running this command in the Nyquist Prompt will return as sound that is 1/20th of the length of the selection:
firsttrack001.png (7.7 KiB) Viewed 1199 times

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(setq wigglerate 3)
(hzosc wigglerate)
HZOSC generates a sine wave at the specified frequency, which in this case is 3Hz. The sample rate of the Audacity track is used.
The default duration is 1 second, which when run in a process type effect is mapped to the length of the selection:
firsttrack003.png (11.47 KiB) Viewed 1199 times

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(setq wigglerate 3)
(sum 1 (hzosc wigglerate))
Adding "1" to the sine wave, offsets it vertically, so that it has a range of 0 to 2.
I have zoomed out vertically so that you can see the top part of the waveform:
firsttrack004.png (11.46 KiB) Viewed 1199 times

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(setq wiggle 0.3)
(setq wigglerate 3)
(setf adsr (pwlv 0 0.05 1 0.3  0.4 0.5  0.4 1 0))
(mult adsr wiggle  (sum 1 (hzosc wigglerate)))
Here we have generated a low frequency control signal "adsr", and a 3Hz sine wave which is offset vertically, and then we are combining them by multiplication.

Nyquist is clever here, because although the sample rate of adsr does not match the sample rate of the sine wave, Nyquist can handle that and uses the length in seconds, which in both cases is "1". However, if we are running this in the Nyquist Prompt, 1 second is mapped to the length of the selection.

Each sample in the sine wave is scaled (multiplied) by the value of adsr at the corresponding time.

Note that we are multiplying three things:
2) a constant value "wiggle", which is = 0.3
3) the sine wave (hzosc wigglerate)
firsttrack005.png (9.35 KiB) Viewed 1199 times

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(- 1 (* 2 wiggle))
This part is a bit of a distraction. "wiggle" is just the value 0.3, so the above expression simply evaluates to:
1 - (2 * 0.3)
= 0.4

so this:

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(mult adsr (- 1 (* 2 wiggle)))
could be written more simply as:

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which gives us:
firsttrack006.png (8.72 KiB) Viewed 1199 times

SIM is the same as SUM, and is simply a function for adding signals or numbers.

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(setf adsr (pwlv 0 0.05 1 0.3  0.4 0.5  0.4 1 0))
(setq wiggle 0.3)
(setq wigglerate 3)

(setf envelope
(sim
(mult adsr (- 1 (* 2 wiggle)))
(mult adsr wiggle  (sum 1 (hzosc wigglerate)))))
So here we are adding the envelope (mult adsr 0.4), with the wiggly line created in the final line, and assigning the result as the value if ENVELOPE:
firsttrack007.png (9.47 KiB) Viewed 1199 times
We can now multiply this envelope with any sound that we like. In the initial code, it multiplies the envelope by the sound from the Audacity track "S". Alternatively you could generate a sound, and multiply (scale) it with the envelope, for example, here I generate a 440 Hz sawtooth waveform, and multiply it by the envelope:

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(setf adsr (pwlv 0 0.05 1 0.3  0.4 0.5  0.4 1 0))
(setq wiggle 0.3)
(setq wigglerate 3)

(setf envelope
(sim
(mult adsr (- 1 (* 2 wiggle)))
(mult adsr wiggle  (sum 1 (hzosc wigglerate)))))

(setf my-saw-waveform (osc (hz-to-step 440) 1 *saw-table*))
(mult envelope my-saw-waveform)
firsttrack008.png (11.11 KiB) Viewed 1199 times

DERF
Posts: 217
Joined: Sun Jun 13, 2010 12:37 pm

### Re: follow up How to generate arbitrary waveforms

Thank you very much.
It is very interesting.

DERF
Posts: 217
Joined: Sun Jun 13, 2010 12:37 pm

### Re: follow up How to generate arbitrary waveforms

Hello.
It is necessary to begin with this code:

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(push (/ (+ 1.0 count) num) point-list )
My question is the following one: Is the following code identical to the first one?

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(setf point-list (cons (/ (+ 1.0 count) num) point-list))
It is right?
Thank you.

steve
Posts: 47612
Joined: Sat Dec 01, 2007 11:43 am
Operating System: Linux *buntu
Contact:

### Re: follow up How to generate arbitrary waveforms

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(setf a '(1)) ; A list containing the number 1
(setf b (push 2 a))
(setf c (cons 3 a))
(print a) (print b) (print c)

(setf a (cons 4 a))
(print a)
prints to the debug window:

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(2 1)
(2 1)
(3 2 1)
(4 2 1)
PUSH added "2" to the list A, modifying A, so A = (2, 1)
B = A, so B also = (2, 1)

CONS adds "3" to the list and returns the extended list, but does not modify the list,
C = (3, 2, 1), but A is still = (2, 1)

(setf a (cons 4 a)) adds "4" to the list, and sets A to the returned value of CONS, so A now = (4, 2, 1)

DERF
Posts: 217
Joined: Sun Jun 13, 2010 12:37 pm

### Re: follow up How to generate arbitrary waveforms

Thank you.
It is necessary to leave the following code:

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(setf point-list  '(list 0.1 0.5  1 0))
(setf amp-list (list 0.1  0.8  0.2  0.8   0.1  1 0))
(setf num (1- (length amp-list)))

(dotimes (count   num)
(setf a  (push (nth (1+ count) amp-list) point-list)))

(print a)
return : (0  1  0.1  0.8  0.2  0.8 LIST 0.1 0.5 1 0)
I tried to explain.
It seems to me that:
_ "num" take this "value": 6
_ "count" takes successively the "value" (0 - 1- 2- 3 - 4 - 5 )

My question is the following one:
Why does the evaluation proceed upside down?
[nth] takes successively the values 5 4 3 2 1 0.

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(push (nth (1+ 5) amp-list) point-list))
If you write this code

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(setf a (nth 6 '( 0.1  0.8  0.2  0.8   0.1  1 0    )))

(print a)

LISP return "0"
Then:

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(push (nth (1+ 4) amp-list) point-list))
return the value "1"
and so on.

steve
Posts: 47612
Joined: Sat Dec 01, 2007 11:43 am
Operating System: Linux *buntu
Contact:

### Re: follow up How to generate arbitrary waveforms

DERF wrote:Why does the evaluation proceed upside down?
It doesn't.

Let me give an example:

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(setf a-list (list "A" "B" "C" "D"))  ; a list containing letters
(setf num (length a-list))  ; set NUM to the length of the list
(print num)         ; prints 4 to debug window
(terpri)            ; new line
(setf new-list ())  ; an empty list

(dotimes (count num)    ; loop where "count" takes values 0 to 4
(setf val (nth count a-list))   ; set VAL to the nth item in A-LIST
(format t "Item ~a in a-list = ~a~%" count val) ; prints the value of the nth term in A-List
(push val new-list)   ; push the value to the begining of NEW-LIST
(format t "NEW-LISt = ~a~%" new-list) ; print NEW-LIST
(terpri))             ; new line
The debug window shows:

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4

Item 0 in a-list = A
NEW-LISt = (A)

Item 1 in a-list = B
NEW-LISt = (B A)

Item 2 in a-list = C
NEW-LISt = (C B A)

Item 3 in a-list = D
NEW-LISt = (D C B A)

Note that PUSH adds the value to the start of the new list, so the new list is the reverse of the original list.

DERF
Posts: 217
Joined: Sun Jun 13, 2010 12:37 pm

### Re: follow up How to generate arbitrary waveforms

Thank you.
It concerns the function [(format].
We can write:

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(format nil "~s ho ho" "o&&")
But, we can also write:

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(format t "~s ho ho" "o&&")
The answer of the nyquist prompt is identical.
My question is this: Is there a difference nevertheless?