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The solution we came up with to alleviate this problem is to average what the program thinks is the highest frequencies across multiple frames of data. We tested out different average lengths and found that averaging every 25 frames sounded the best. Our code will keep track of a variable-length list that contains the frequency of the highest peak per frame. At the start of every frame a new frequency value will be added to the list, and at the end of every frame the list is averaged to determine a single frequency. This list resets every 25 frames. In midst of this process, we also converted to linear frequency from FFT bins, which is done by multiplying by the ratio of the sampling frequency over half the chunk length. To further improve our results, we only added to the list frequencies if the magnitude of that particular frequency bin is above a particular value. This way our code will ignore the low amplitude noise and only record frequencies when a note is being played.
flag = 0
freq = []while(True):
data = stream.read(CHUNK)x = numpy.fromstring(data, dtype=numpy.float32)
x_filtered = scipy.signal.lfilter(taps, 1.0, x)X = numpy.fft.fft(x_filtered)
highest_freq = numpy.argmax(abs(X[0:511]))flag +=1
if (X[highest_freq]>5000):
freq.append(highest_freq*44100/(CHUNK/2))avg = (sum(freq)/len(freq))
if flag == 25:flag = 0freq = []
Once we have the correct frequency and the identity of the note, we proceed to figure out the frequency of the harmonizing note. We first create a Python dictionary of musical keys mapped to a list of the corresponding frequencies of that note at different octaves. For purposes of demonstration, we only added the key of C to the dictionary. However, other keys could easily be added. We then created a function that helps on determine which harmonic we are in given a musical key and the frequency of a note. We then apply the formula for finding the harmonizing frequencies describe in the previous section to the frequency we have and obtain the frequency of the third and fifth intervals from the note being played.
keys = {'c':[1636,1636/2,1636/4,1636/8]}sBuf = 50
def key_select(freq, key):for f in keys[key]:if freq>= f:
return freturn freq
def chord_freqs(key, note):n = 1200*numpy.log2(note/key)
if(500-sBuf<= n<=500+sBuf or 700-sBuf<= n<=700+sBuf or n<=sBuf):
f3 = note * math.pow(2, (400)/1200)f5 = note * math.pow(2, (700)/1200)
return f3 , f5elif (200-sBuf<n<200+sBuf or 400-sBuf<n<400+sBuf or 900-sBuf<n<900+sBuf):
f3 = note * math.pow(2, (300)/1200)f5 = note * math.pow(2, (700)/1200)
return f3, f5elif (1100-sBuf<n<1100+sBuf):
f3 = note * math.pow(2, (300)/1200)f5 = note * math.pow(2, (600)/1200)
return f3, f5else:
return 0,0
After obtaining the two harmony frequencies, we tried to take them into the time domain. We initially tried add triangles of frequency content centered at the desired frequencies and then taking the inverse transform, in hope to try to mimic a "real" sound. However, doing that caused the note to sound slightly off. Also we didn't add imaginary components to the frequency and the FFT library gave us warnings. So we decided to try out other approaches. The next thing we thought of was using the Karplus-Strong Plucked String algorithm to create a realistic decaying note. But we very quickly saw that the algorithm was not really meant to be used in real time. The algorithm works by creating the complete decaying signal. However, this is problem with other stream because we can only output 1024 samples at a time, which is not long enough to squeeze the whole decay in. We thought about storing the whole signal from the Plucked String algorithm and output it a frame at a time. But doing so not only slow down our system, but also would introduce problems if we played a different note half way through a output decaying note. We ended up deciding to just output pure sine waves and worry about making it sound less synthesized in the future.
def play_tone(stream, frequency=252, length=1, rate=44100):
chunks = []f3 , f5 = chord_freqs(key_select(frequency, 'c'), frequency)
chunks.append(sine(f3, length, rate)+sine(f5, length, rate))chunk = numpy.concatenate(chunks) * 0.25
stream.write(chunk.astype(numpy.float32).tostring(), CHUNK)def sine(frequency, length, rate):
length = int(length * rate)factor = float(frequency) * (numpy.pi * 2) / rate
return numpy.sin(numpy.arange(length) * factor)
Now that we were only outputting pure sine waves, we decided that it would be faster and save computation complexity but just creating the sine waves of the correct frequencies in the time domain directly. This would save computation time as now we don't need to compute an inverse FFT. To put it all together. We output the harmonies through the PyAudio stream. The UCA222 takes this and adds it to the guitar signal that it is already forwarding to the speakers.
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