Wednesday, May 23, 2012

Adjusting a Tuning Fork

I wanted something to help demonstrate the accuracy of my HotPaw music tuner apps for iPhone, iPad, and even Macs.  So I ordered a Concert A 440 tuning fork from Amazon.  It arrived in the mail a couple days later.  I quickly tried it out.  Big Problem!  The fork measured 9 cents sharp or 442 Hz.  Thinking something might be wrong with my tuners, I checked the tuning fork against 5 competing tuner apps.  But they all reported the pitch to be around the same amount sharp.  Was my iPhone broken?  To rule that out, I again checked the tuning fork with strobe tuner apps on a different iPhone and also an iPad.  Same result.

This tuning fork was out-of-tune.

But I found a quick-and-dirty fix.

As an online education forum suggested, a interesting school science experiment might be to see if adding weights and changing their position on a tuning fork will change the frequency of the fork. So I played science student, and tried the experiment.

Two big rubber bands on the tines clearly lowered the frequency... by way too much. Next I tried a couple strips of masking tape wrapped around the very end of the each tuning fork tine. That also lowered the frequency, by only a bit too much, to 20 cents flat. So I removed those pieces of tape and carefully measured them. Then I cut some tape strips about 9/29ths as long (actually a few mm longer). Wrapped the new lengths of tape on the fork tines, and the fork rang 3 cents flat. A little more fine trimming of the length of the tape with some sharp scissors, and I got the fork to measure within +-1 cent of 440 Hz, as measured against several calibrated iPhone tuners (both dial and strobe). The fork also now sounds good when played simultaneously with an mp3 of a 440 Hz tone to check for beats.

The tone probably isn't as pure, and tape will eventually age and wear, but this quick fix should work well enough until my next trip to a good music store for a better quality tuning fork.

Saturday, April 14, 2012

Drawing in iOS apps

New iOS programmers often ask how to draw a dot, line, or rect on the display, hoping for some simple method, such as drawDot(x,y), which works simply and immediately.

No such function exists in the iOS frameworks, and there are two big concepts needed to understand the reason why, and what to do instead.

The first concept is asynchronous event-driven programming.  In this software paradigm, an app doesn't tell the OS what to do (such as draw something now).  Instead your app has to declare a method, and requests the OS to call that method back at some later time.  The OS then calls back that method when it is good and ready, which is very often later, not now.

So, on iOS, your app doesn't just draw when it wants to draw.  You app has to instead politely request that the OS to call some a particular method, such as a drawRect, by doing a setNeedsDisplay request on the desired view or subview.  The OS usually complies with this request later, but only after you have exited the current code that your app is running.  And the OS won't comply with your request more often than the frame rate (usually 60 Hz).  Only at those times when the OS chooses to call your drawRect does a view's context actually exist for any drawing.

The second concept is the need to be able to redraw everything in view, even if one only wants to update one dot on top of something drawn a few seconds ago.  You can't just draw a dot or line and expect it to show up on top of much earlier content, stuff that which was drawn beforehand in another callback.  Even though you can see it on the display, nothing drawn one frame beforehand was actually saved for reuse as far as an iOS app is concerned.

In the old days of computing, when computers were the size of refrigerators or larger, there were no glass display screens.  All human readable output was via teletypes or line-printers, very often in another room from the computer. Your computer output was printed on paper, and then fed out the top.  If you needed to add a word, you didn't try to get the computer to somehow modify an existing printed sheet of paper with white-out or something, you just reprinted the entire page.  Or maybe you could stick a post-it note on top of the earlier printed page.  Whereas on early personal computers, a program might be able to change bits on a bitmapped memory display at any time.  That doesn't work under iOS.

iOS view drawing is more similar to the much older page printing model.  The display's bitmap isn't in the same memory as the app.  Your app sends a UIView's graphics contents off to the GPU somewhere else on the chip.  If you want any change anything, you need to send the entire view to the graphics logic again.  There's no way to directly add a pixel or line to an existing view that has already been displayed.  This is because an iOS device's display is connected via a really complicated GPU on another part of the chip, and this connection is pretty much opaque, e.g. write-only, just as if it were in another room via an output-only printer cable.

So how do you draw the usually procedural code way (e.g. add some dots and lines now, and some more dots and lines to that same view later)?  By having your app allocate its own bitmap memory and context, and drawing into that context using Core Graphics.  You can then send that entire bitmap to update a view as needed.

First, we need some instance variables in your view's interface declaration. (These could be global variables for a really tiny app where the code is not meant for reuse or code review.)

    unsigned char   *myBitmap;
    CGContextRef    myDrawingContext;
    CGRect          myBitmapRect;

Note that if you need more than one drawing context, each drawing context will require it's own bitmap.

Here's how to create your own bitmap drawing context:

- (void)makeMyBitMapContextWithRect:(CGRect)r {
    int     h = r.size.height;       
    int     w = r.size.width;
    int     bitsPerPixel = 8;
    int     rowBytes = 4 * w;       // for 32-bit ARGB format
    int     myBitmapSize = rowBytes * h;     // memory needed

    myBitmap  = (unsigned char *)malloc(myBitmapSize);

    CGColorSpaceRef colorspace = CGColorSpaceCreateDeviceRGB();
    if (myBitmap != NULL) {
        // clear bitmap to white
        memset(myBitmap, 0xff, myBitmapSize);     

        myDrawingContext = CGBitmapContextCreate(myBitmap, 
                              w, h, bitsPerPixel, rowBytes, 
                              kCGImageAlphaPremultipliedFirst );
        myBitmapRect = r;

Here's how to draw a dot in your bitmap context:

- (void)drawRedDotInMyContextAtPoint:(CGPoint)pt {
    float x = pt.x;
    float y = pt.y;
    float dotSize = 1.0;
    CGRect r1 = CGRectMake(x,y, dotSize,dotSize);
    CGContextSetRGBFillColor(myDrawingContext, 1.0, 0, 0, 1.0);
    // draw a red dot in this context
    CGContextFillRect(myDrawingContext, r1);    

But whatever drawing you do in your bitmap context will initially be invisible.  You still have to get the bitmap onto the iOS device's display.  There are two ways to do this. Here's how to draw your bitmap context into a view during the view's drawRect:

// call this from drawRect with the drawRect's current context
- (void)drawMyBitmap:(CGContextRef)context {     
    CGImageRef myImage = CGBitmapContextCreateImage(myDrawingContext);
    CGContextDrawImage(context, myBitmapRect, myImage  );

Call setNeedDisplay on your view (which needs to be an instance of your subclass of a UIView), and the OS will call the view's drawRect, which can then call the above update method.

If your bitmap drawing context is the exact same size as your view, here's how to update an entire UIView outside of a drawRect.

- (void)useMyBitmapContextAsViewLayer {
    CGImageRef myImage = CGBitmapContextCreateImage(myDrawingContext);
    // use the following only inside a UIView's implementation
    UIView *myView = self; 
    CALayer *myLayer = [ myView layer ];
    [ myLayer setContents : (id)myImage ]; 
//  notify OS that a drawing layer has changed
//  [ CATransaction flush ]; 

You only have to do a CATransaction flush if you are not calling setNeedsDisplay on your view, for instance, if you are doing drawing in a background thread.

Note that a view update isn't needed after every single item drawn.  Since the actual hardware display never changes more often than the frame rate, which is no more than 60 Hz, a view update is needed no more than once every frame time.  So don't call setNeedsDisplay, or the CALayer update method, more than once every 1/60th of a second. Perhaps use a timer method in an animation loop at a known frame rate to call this, and only if the bitmap is dirty.

Added (2012May22):

So why isn't this the regular paradigm to do drawing on iOS devices?  What's the disadvantage?

There are at least three big disadvantages of this method.  One is that the bitmap can be huge and use up a lot of memory, which is in limited supply to apps on iOS devices.  Second is that you may need to adapt your bitmap size to the resolution and scale of the device.  Or if you use an iPhone bitmap on an iPad, or a regular scale bitmap on a Retina device, the resulting image may look blurry or pixel-ly instead of sharp.  Lastly, this method can be very slow, resulting in a low frame rate or poor app performance, as a huge bitmap needs to be reformatted and copied to the GPU every time your app needs to update the display, which can take a lot longer than just sending a few line or point coordinates if your drawing isn't too complicated.  Apple has optimized their recommended graphics flow (drawing in a view's drawRect) for lower memory usage, better device independence, and good UI responsiveness, all of which benefit iOS device users, even if that makes things more difficult for an iOS app developer.

Tuesday, April 3, 2012

Musical Pitch is not just FFT frequency

In various software forums, including stackoverflow, I've seen many posts by software developers who seem to be trying to determine musical pitch (for instance when coding up yet another guitar tuner) by using an FFT. They expect to find some clear dominant frequency in the FFT result to indicate the musical pitch. But musical pitch is a psycho-perceptual phenomena.  These naive attempts at using an FFT often fail, especially when used for the sounds produced big string instruments and bass or alto voices.  And so, these software developers ask what they are doing wrong.

It is surprising that, in these modern times, people do not realize just how much of what they experience in life is mostly an illusion. There is plenty of recent research on this topic. One of my favorite books on this general subject is "MindReal" by Robert Ornstein. Daniel Kahneman won the 2002 Nobel Prize for ground-breaking research in a related area.

The illusion that our decisions are logical allows us to be susceptible to advertising and con men.  The illusion that we see what is really out there allows magicians and pick-pockets to perform tricks on us. The illusion that what we hear is actually the sound that a musical instrument transmits to our ear is what seems to be behind the misguided attempts to determine the pitch of a musical instrument, or a human voice, by using just a bare FFT.

One reason that frequency in not pitch is that many interesting sounds contain a lot of harmonics or overtones. This is what makes these sounds interesting.  Otherwise they would sound pretty boring, like a pure sine-wave generator might be. The higher overtones or harmonics, after being amplified or filtered by the resonance of the body of a musical instrument or the head of a singer, can often end up stronger than the original fundamental frequency.  Then the ear/brain combination of the listener, finding mostly these higher harmonics in a sound, guesses and gives us the illusion that we are hearing just a lower pitch.  In fact, this lower pitch frequency can be completely missing from the audio frequency spectrum of a sound, or nearly so, and still be clearly heard as the pitch.

So pitch is different from frequency, and musical pitch detection and estimation is different from just frequency estimation.  So pitch estimators look for periodicity, not spectral frequency.

But how can you have a periodic sound that does not contain the pitch frequency in its spectrum? 

It's easy to experiment and hear this yourself.  Using a sound editor, one can create a test sound waveform which shows this effect. Create a high-frequency tone, say a 1568 Hz pure sine wave (a G6). Chop this tone into a short segment, say slightly shorter than the 100th of a second. Repeat this high-frequency tone segment 100 times per second.  Play it.  What do you hear? It turns out you don't hear the high-frequency tone. An FFT will show most of the waveform magnitude in a frequency bin near 1568 Hz, since that's what makes up the vast majority of the waveform.  Even though the sound you created consist only of high frequency sine wave bursts, you'll actually hear the lower frequency of the repeat rate, or the periodicity.  A human will hear 100 Hz.

So to determine what pitch a human will hear, one needs a periodicity or pitch detector or estimator, not a frequency estimator.

There are many pitch detection or pitch estimation methods from which to choose, with varying strengths, possible weaknesses, as well as differing computation complexity.  Some of these methods include autocorrelation, or other lag estimators such as AMDF or ASDF.  A lag estimator will look for which next segment of waveform in time is the closest to being a copy of the current segment.  Lag estimators are often weighted, since periodic waveforms have multiple repetition periods from which to choose.  Other pitch estimation methods include, in no particular order,  Cepstrum or cepstral methods, harmonic product spectrum analysis, linear predictive coding analysis, and composite methods such as YAPT or RAAPT, which may even involved some statistical decision analysis.

It's not a simple as feeding samples to an FFT and expecting a useful result.