Now let's see another way to control the cycle~
frequency. Get two number box, one integer and the other floating from
the palette and put on the patcher window. Connect with a cycle~ and
connect the cycle~ with a dac~.
Note that I don't write a frequency value on the cycle~. This means
that the cycle~ will start using its default frequency that is 0, i.e.
don't play until a valid frequency value is received from the controls.
Add the usual start and stop messages to the dac~ as in figure and go
to play mode.
In play mode, click on the integer number box and drag the mouse on
high. You'll see the value in the box rapidly changing. When the number
will reach an audible frequency (e.g. 20-30, but could be more,
depending on the quality of your speakers; remember that the little
computer speakers often don't work at all under 100 Hz), you will begin
to hear a glissato moving from low to high frequencies.
Now, you see, the number box don't act as button, like messages. It
works as a slider that you can control dragging the mouse up and down.
Now try the floating point number. This one works as the former, but a
little difference: if you click on the left part of the box (near the
little triangle) only the integer part of the number change; if you
click on the right, the fractional part also change. So clicking on the
left you have a coarse control and clicking on the left you get a more
fine control.
You can also change the box dimension to be sure to see all the number:
in edit mode, move the mouse near the lower right corner of the box
until the cursor become a cross, then click and drag.
Now,
it is very important
that you are always aware of the
patch data flow.
You must be able to figure in your mind how and when
the data flow in a Max/MSP patch.
It could be a little difficult for beginners, but only by this way you
can understand
the more complex patches.
So let's stop just a moment to understand exactly what's happening in
this
simple patch.
- When the number changes (and only when the number changes)
a message start from the number box, runs through the wire and reach
the cycle~. This number is not a frequency, it's a pure number.
Its only meaning are its value and its format (integer or float).
- The cycle~ receive this number in its left inlet and uses it
as a
frequency value only because on the left inlet a frequency value is
expected. If you connect the number box to the cycle~'s right
inlet,
you'll hear no frequency change because on the right inlet a phase
value (not frequency) is expected.
- So it's the cycle~ that gives the number a meaning,
depending on the inlet the number reach. Note that the cycle~ don't
mind about the number format because a frequency can be written both
way (with or without fractional part), but, with other objects, the
right format also is requested by some inlet. On the computer, the
number 50 is different from the number 50.0 so the right number with
the wrong format could be seen as an error.
The Floating Inspector
As you see, while dragging on a number box, you can go up and down with
no limits. You can also output negative numbers. Of course, setting
minimum and maximum to some meaningful value should be better.
To do so, go to edit mode, select the number object and click the menu
Windows → Show Floating Inspector.
This dialog allows you to set many options for the current selected
object. Note that the floating inspector options are not the same for
all objects, because any object has its own distinctive features. Some
objects have no floating inspector at all.
For number box, integer or floating, the most important feature is the
range. Here you can set minimum and maximum values.
Now we are using this number to control a frequency, so set the range
to reasonable values in Hertz e.g. min 20-30, max 4000-5000 (the lower
note on the piano is 27.5 Hz, the higher is 4186 Hz). Be sure the “No
Min” and “No Max” check boxes are unchecked. Now you can freely drag
the mouse.
By the floating inspector you can also set the colors of the number
object, the display format and a bunch of options:
- Bold: display the value in bold
- Draw Triangle: display/hide the little triangle on the left of
the number box
- Output Only on Mouse-Up: this is an important option (try it). If
you check it, you'll hear no glissato while changing the value with the
mouse. The value will change only when you leave the mouse button. It
means that, while playing, you can change a number with no acoustical
effect until you reach the right value.
- Can't Change: make the number box read only. Useful when it is
used only to show a number (r.g. the result of a computation)
- Transparent: hide the box displaying the number only.
Amplitude Control
The cycle~ has no amplitude control in itself. It always output the
wave at the maximum amplitude value.
To control the sound amplitude we must insert an amplifier between the
signal generator (the cycle~ in our example) and the dac~.
To understand how an amplifier works on a digital signal, remember that
a digital sound wave is a stream of number running at SR speed (e.g.
44100 numbers per second). Each number is an amplitude sample of
the sound wave. So the wave in this figure
is in fact a stream of numbers like this one
0 72 144 215 285 352 417 479 538
593 644 690 732 769 801 828 849 865
875 880 879 873 862 846 825 799 769 736 699 659 616 571 524 476 426 377
327 278 229 182 136 92 51 12 -23 -56 -85 -111 -133 -151 -165 -175 -182
-184 -184 -179 -171 -161 -147 -131 -113 -92 -71 -48 -24 0 24 48 71 92
113 131 147 161 171 179 184 184 182 175 165 151 133 111 85 56 23 -12
-51 -92 -136 -182 -229 -278 -327 -377 -426 -476 -524 -571 -616 -659
-699 -736 -769 -799 -825 -846 -862 -873 -879 -880 -875 -865 -849 -828
-801 -769 -732 -690 -644 -593 -538 -479 -417 -352 -285 -215 -144 -72 0
72 144 215 285 352 417 479 538 593 644 690 732 769 801 828 849 865 875
880 879 873 862 846 825 799 769 736 699 659 616 571 524 476 426 377 327
278 229 182 136 92 51 12 -23 -56 -85 -111 -133 -151 -165 -175 -182 -184
-184 -179 -171 -161 -147 -131 -113 -92 -71 -48 -24 0 24 48 71 92 113
131 147 161 171 179 184 184 182 175 165 151 133 111 85 56 23 -12 -51
-92 -136 -182 -229 -278 -327 -377 -426 -476 -524 -571 -616 -659 -699
-736 -769 -799 -825 -846 -862 -873 -879 -880 -875 -865 -849 -828 -801
-769 -732 -690 -644 -593 -538 -479 -417 -352 -285 -215 -144 -72 0 72
144 215 285 352 417 479 538 593 644 690 732 769 801 828 849 865 875 880
879 873 862 846 825 799 769 736 699 659 616 571 524 476 426 377 327 278
229 ...
where
each number represent the amplitude of the wave at a given
instant like a graph with the time on x-axis and the amplitude on
y-axis.
So, to change the wave's amplitude we can simply multiply each number
for a given value. If that value is greater that 1, the amplitude
increase. If it is lower that 1, the amplitude decrease. In the
following image, a plotted digital wave (red) is multiplied by 2.0
(blue) and by 0.5
(yellow). Here is the result. You can clearly see that only amplitude
is
affected.
Applying amplitude
control to a signal
To apply amplitude control to a signal we only need a multiplier
between the signal generator(s) and the dac~ (see patch on the left).
Be sure to pick the MSP multiplier (with tilde: *~) from the MSP
Operators group, not the Max multiplier (with no tilde).
To set the amplitude value we can use a floating point number. Now we
must set the range of the amplitude control.
In MSP, the maximum amplitude a dac~ can handle is 1, that is, when
reaching the dac~, a wave must run between ±1 to avoid clipping and
distortion. Of course a zero amplitude is no signal.
The cycle~ generator already output a wave at maximum amplitude, so our
amplifier is in fact a damper and will have the range 0 - 1 (here the
reason we must use a floating point number).
If the amplitude control would reach a value greater that 1, a wave
with range > ±1 would reach the dac~ and be clipped: you would hear
no amplitude increment, but harmonic distortion (try a value > 1).
Amplitude evaluation
Measuring the amplitude of an incoming signal could be very important
when you work with external signals. Now we'll see different ways to do
it using standard Max/MSP objects.
To make it simple, we'll apply the measurement to the cycle~ sine wave
for now. Look at the the patch 03.
Here you can see and try different ways to evaluate a signal's
amplitude.
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This is not a real measument.
Here we convert the given amplitude value to dB for control purposes
only and see if the real evaluations match.
By the way, here you can find the atodb object that convert a number to
deciBels. It is taken from the Max "Math" section on the object list.
The atodb output is connected to a number object to show the resulting
dB. The number object is made read-only (check the option in the
floating inspector).
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Here is the first real signal
amplitude evaluation.
You can find the peakamp~ object on the "MSP Analysis" section. This
object accept a signal in its left inlet and output the maximum
absolute amplitude every k milliseconds, where k is the argument (100
in figure). You can also control the k value sending an integer number
to the right inlet.
The peakamp~ object is very accurate and it's a good and simple way to
evaluate the peak amplitude of a signal.
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In the palette you can find two
graphic objects to evaluate and show a signal amplitude.
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The peak level meter accept a
signal in its left inlet and display the amplitude by the usual led
line. It also output the evaluated absolute amplitude.
The object appearance can be fully edited using the floating inspector.
Running the patch you'll see that when the input signal has a low
frequency (set the frequency control to 50 Hz or lower) the result is
rapidly changing. This is not a bug. It does not happens with natural
sounds. Here it happens because:
- The peak level meter has a little buffer. When the wave
frequency is low it see only a section of the wave cycle, but, more
important:
- Here we supply a single sine wave without harmonics. In
nature the signals have harmonics whose frequencies are higher than the
fundamental, so the wave is more complex and the peak amplitude can be
evaluated also with a little buffer.
This object's MSP name is meter~. If you to know more about it search
for meter~ on the MSP Reference manual.
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This level meter seems like the
previous one, with needle in place of leds, but it has some important
differences.
It is not a peak level meter. It computes the RMS (root-mean-square) of
the signal's amplitude. This is very important because the peak value
is meaningful with a simple harmonic wave, but it makes little sense to
talk about a peak
amplitude when describing a complex sound (e.g. a drum stroke) or a
noise. This is because there are many peak
amplitudes and any one is not representative of the overall amplitude.
So, how should we measure the amplitude of a complex signal? We can't
take the average of the instantaneous amplitudes since negative and
positive
values always cancel yielding an average value of zero. To prevent
this we square each amplitude making all values positive. We then take
the
square root of the average of the squared values to get back to an
amplitude
measure. The resultant measure is referred to as the root-mean-square
or
RMS
amplitude. The RMS amplitude is a more commonly accepted measure of
amplitude
because it applies to periodic sounds like sinusoids as well as to
noise.
This object output the RMS amplitude value in dB, so there is no need
of the atodb object.
This object's MSP name is levelmeter~. If you to know more about it
search for levelmeter~ on the MSP Reference manual.
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Now that you know more about the amplitude, you can set 0 dB on your
mixer.
If you connect Max/MSP to a professional mixer with measurement leds on
input and output, you can easily set the 0 dB. On the computer, play a
test frequency (about 1000 Hz). Then set the
board output to the maximum (or the level you normally use, but a good
board should work well at the maximum with no distortion). Then set the
amplitude control of the patch to the maximum (i.e. 1.0). This is the
MSP 0 dB (you should see 0 dB on all the meters).
On the mixer, set the input slider to 0 dB and turn the input
sensitivity control (if any) until the input signal level show 0 dB. Do
the same for the mixer output.
Why the dac~ maximum amplitude is 1?
It's a good question. Why 1 and not 100 or 1000 or a power of 2, like
1024 or the real amplitude of the sound board? Is there some technical
reason to set the range to 0 - 1? The answer lead us to the realm of
computer arithmetic, so it could be a little complex business. This
notes are for more
advanced (or curious) users.
- Max/MSP must work with many different sound
boards and the sound boards currently on the market can have different
dac types, typically 16 or 24 bit. Maximum values are 32767 for 16 bit
(2(16-1) - 1)
and 8388607 for 24 bit (2(24-1) - 1).
But the software can't work with absolute amplitude values simply
because the patches you make, must work with all the sound boards, even
if you change machine or the board itself. So a conventional maximum
amplitude value has to be set. When sending sound data to the sound
board all values will be scaled according to the maximum value the
board support.
- MSP works with 32 bit floating point
numbers. This is a very accurate way to make calculations on a computer
because 32 bit floating point numbers can hold until 18 digits after
the decimal point.
Floating point is more accurate than 24 or 32 bit integer arithmetic. People
often think that every operations on digital signals are noiseless, but
with integer arithmetic it's not really true. A very simple
example: suppose you are working with 24 bit integer arithmetic on a
digital wave with amplitude 8388607 (the maximum). Now suppose you are
mixing, and this signal's amplitude is lowered multiplying by, say, a
0.731 factor. The resulting amplitude is 6132071.717. OK: where do you
think this 0.717 goes? It get lost because this is integer arithmetic
and by this way every multiply you make creates a very little sampling
error.
An experienced digital user can argue that with integer arithmetic you
never multiply by floating point numbers. You multiply by an integer
number creating a double precision result that will be truncated to
simple precision, but it's the same because here are the lower bits
that get lost.
The meaning of the story is: always try to work with 32 bit floating
point when making computations on digital signals. You can't avoid the
final rounding error, when data are sent to the board's dac or are
written on audio CD in the usual format (44100, 16 bit, stereo), but at
least you save the accumulation of little sampling errors. The current
debate is about 48 bit integer versus 32 bit floating arithmetic (see this
James A. Moorer's paper), but under the 48 bit integer arithmetic,
32 bit float is surely better.
- But why 0 - 1? Even with floating point arithmetic, a
conventional amplitude of, say, 1000 could be easiest to understand.
Because of the problem of floating point arithmetic: while number
increase, you lose precision after the decimal point. This is normal
business on real world. If someone owes you $10.95 all the digits are
significant, but if someone owes you $100000.95 you could apply a
little
discount and save the $0.95.
So, to hold the maximum accuracy, MSP choose to work with little
numbers.
A useful patch: Hear the Fletcher/Munson Effect
Important note: to hear the Fletcher/Munson effect you must work
with hi-fi speakers. This is because this effect is evident at low
frequencies (under 100 Hz) and the little computer speakers are not
effective at this frequencies. You can use haedphones but
be careful.
Never turn on a patch without controlling its loudness or the volume of
your equipment. Set amplitude/loudness to 0, turn on the patch and then
raise the volume.
Let's do this trial.
- Return to patch 02 (single cycle~ with frequency and amplitude
controls).
- Set the frequency at (about) 1000 Hz.
- Be sure to
turn off the loudness control of your amplifier (if any) and the
equalizer (if any; remember that many mixers have filters). The
frequency response of your equipment must be flat (as much as
possible).
- Set the amplitude control to 0 (no sound).
- Turn on the patch and set a suitable amplitude (not disturbing
but
clearly audible).
Now begins to lower the frequency (click on the left part of the
control box to change the integer part only, going down faster). Never
change the amplitude. Move down the frequency only.
Under 500 Hz, the loudness will be a little lower. About and under 100
Hz the loudness will be very low. Very low frequencies (60 Hz and
lower) will be barely audible
even if the amplitude is the same!.
Why? It's your speakers? Maybe, but the real answer is that the human
ear frequency response (or better, the ear\brain combination response)
is not
the same for whole audible area. The ear works better
approximately from 500 to 5000 Hz. Outside this area it needs more
amplitude to hear equal loudness.
This effect has been first studied in 1937 by Fletcher
&
Munson who traced the human ear response curves. In 1956 Robinson
& Dadson refined the Fletcher/Munson curves and today the
Robinson/Dadson curves are generally preferred over the Fletcher/Munson
curves owing to their more reliable measurement results. The
International Standards Organization agreed and adapted the
Robinson/Dadson curves as the basis for ISO 226:1987; Normal
Equal-Loudness
Level Contours (ELLC) (see image on the left; the MAF line is the
Minimum Audible Field).
This chart say that humans don't hear all frequencies at the
same level. That is, our ears are more sensitive to some frequencies
and less sensitive to other frequencies. Not only that, but the
sensitivity changes with the sound pressure level (SPL), too. Take a
look at the chart. You'll notice it's marked horizontally with a scale
denoting the frequency of sound. Vertically it's marked in SPL. On the
chart are a number of curved lines, each with a number (loudness level)
marked.
Let's begin by looking at the lowest solid line marked with a loudness
level of 10 phons. (The loudness level in phons is a subjective
sensation--this is the level we perceive the sound to be at.) From
about 500Hz to roughly 1,500Hz the line is flat on the 10dB scale. This
means that for us to perceive the sound being a loudness level (LL) of
10 phons, (the overall curved line), frequencies from 500Hz to 1,500 Hz
must be 10dB. Make sense so far? OK, now look further into the higher
frequencies, say 5,000Hz. Notice the line dips here--this says we
perceive 5,000Hz to be 10 phons when the source is actually only 6dB.
To perceive 10,000Hz at the same level (10 phons), it would need to be
about 20dB. From this we can clearly see the ear is more sensitive in
the 2,000Hz to 5,000Hz range, yet not nearly as sensitive in the
6,000Hz and up range.
Lets take a look down at the lower frequencies now, say 100Hz. For us
to perceive 100Hz as loud as we do 1,000Hz (when the source is at
10dB), the 100Hz source must be at 30dB–that's 20dB higher than the
1,000Hz signal! Looking even farther down, a 20Hz signal must be nearly
75dB (65dB higher than the 1,000Hz signal)! We can clearly see our ears
are not very sensitive to the lower frequencies, even more so at lower
SPL levels.
Why is this? A simply physical explanation is that resonance in the
ear-canal amplifies frequencies between 1500 Hz and 5000
Hz with a peak around 3000 Hz. In addition, the response in the range
between 500 and 1500 is flat. All other frequencies are damped. Note
that the main communication
area lies in the range 500 - 5000. In this range we find human and
animal voices and in the upper part of this range we find the children
voices.
Now you know why the double-bass sound box is so big. Looking at the
musical instruments construction, we can see many ways to compensate
the Fletcher/Munson effect. For instance, the mechanical device of
piano lower keys is adjusted to struck the string a little harder with
respect to medium and high registers. So the player can achieve about
the same loudness using the same force.
OK. We heard the Fletcher/Munson effect and we also know what is and
why it happens. But now we can also measure it. Load the fletcher patch.
Here you can see two versions of the Fletcher patch. Now look at the
simplest and not hidden (left). There is a reference frequency fixed at
1000 Hz on right channel and a second cycle~ that can be set to various
frequencies (8ve distance) on the left channel.
To measure the Fletcher/Munson effect you must choose a frequency on
the left, then move the amplitude control of the 1000 Hz (up on the
right), until you hear the two frequencies have equal loudness. Then
you read the amplitude difference in dB in the read-only number box
down on the right.
The atodb object convert the amplitude from absolute value to dB value.
This value is negative because it say how much the 1000 Hz must be
damped to hear equal loudness.
The second patch version is the same with a more pleasant user
interface, but two main differences:
- it uses a slider as amplitude control: note that the slider range
is 0-100 (set by the floating inspector); then is multiplied by 0.01 to
achieve the 0-1 range. This is because the slider object can't output
floating point numbers (integers only). This kind of number trick is
common on Max. We'll see more on the next lesson.
- the converted dB value is multiplied by -1 to see a positive
number.
Numbers as Sliders
