How to find seamless loops in audio files (with a little bit of math and programming)
When making instrument sample sets (e.g. church organ sample sets used with Hauptwerk or GrandOrgue, see my project Jeux d'orgues), we need to set looping points in WAV audio files:
such that when playing the part [a, b] in loop, we don't hear any click or pop when the sample reaches the end of the loop.
Example 1: bad loop with audible clicks
Example 2: seamless loop with no click, that's what we are looking for! The loop has a ~ 2.670 second period, can you hear where are the looping points?
Finding looping points can be done manually but this is a very long and tedious task. A few programs exist to do this process automatically such as Extreme Sample Converter (it has an excellent autolooping algorithm), LoopAuditioneer (open source), ZeroX Seamless Looper, SampleLooper, etc.
Here we'll look at a homecooked algorithm that works well to detect looping points.
First of all, let's load the audio file (downloadable here) with Python:
from scipy.io import wavfile
import numpy as np
import itertools
sr, x = wavfile.read('060.wav')
x0 = x if x.ndim == 1 else x[:, 0] # let's keep only 1 channel for simplicity, but we could easily generalize this for 2 channels
x0 = np.asarray(x0, dtype=np.float32)
Let's say the audio file's sustain part (this is precisely where we're looking for a loop!) begins at t=2 sec and finishes at t=9 sec. We will now subdivide the timeinterval [2 sec, 9 sec] into a 250 milliseconds grid: 2, 2.25, 2.5, 2.75, 3, 3.25, ..., 8.75, 9.
From this sequence, we now create "loop candidates" (a, b) of length at least 1 second, example: (2.5, 7.5), (3.25, 5.75), (6.0, 8.75), etc.
Then, for each loop candidate, we'll improve the loop (this is the core of the algorithm, it will be discussed in the next paragraph) and compute a distance d
.
We finally keep the loop that has the minimal distance (among all loop candidates). Finished!
A = [int((2 + 0.25 * k) * sr) for k in range(29)] # the grid 2, 2.25, 2.5, ... 8.75, 9
dist = np.inf
for a, b in itertools.product(A, A): # cartesian product: pairs (a, b) of points on the grid
if b  a < 1 * sr:
continue
a, B, d = improveloop(x0, a, b, sr=sr)
print 'Loop (%.3fs, %.3fs) improved to (%.3fs, %.3fs), distance: %i' % (a * 1.0 / sr, b * 1.0 / sr, a * 1.0 / sr, B * 1.0 / sr, d)
if d < dist:
aa = a
BB = B
dist = d
print "The final loop is (%.3fs, %.3fs), i.e. (%i, %i)." % (aa * 1.0 / sr, BB * 1.0 / sr, aa, BB)
Finished? Not yet! We need to explain what we mean by improving a loop, as that's the crucial part of the algorithm. More precisely, we'll now explain how to transform a loop (3.25, 5.75) with points taken on the grid (this random loop probably "clicks" like in Example 1 before!) into a "good loop" (3.25, 5.831). Let's zoom on the junction point to understand what's going on:
How to measure if a loop is good or not? Ideally, if the loop (a, b) is perfect/seamless, x[a:a+10 ms]
should be very close to x[b:b+10 ms]
.
Measuring how close two arrays x
and y
are can be done by computing sum((x[n]y[n])^2)
, and if the sum is small, x
and y
are close.
Finding k
such that np.sum(np.abs(x0[a:a+W1]x0[k+b:k+b+W1])**2)
is minimal can be obtained by noting that
(x[n]  y[n+k])**2 = x[n]**2  2*x[n]*y[n+k] + y[n+k]**2
and by using numpy.correlate. We can now define this function:
def improveloop(x0, a, b, sr=44100, w1=0.010, w2=0.100):
"""
Input: (a, b) is a loop
Output: (a, B) is a better loop
distance (the less the distance the better the loop)
This function moves the loop's endpoint b to B (up to 100 ms further) such that (a, B) is a "better" loop, i.e. sum((x0[a:a+10ms]  x0[B:B+10ms])^2) is minimal
"""
W1 = int(w1*sr)
W2 = int(w2*sr)
x = x0[a:a+W1]
y = x0[b:b+W2]
delta = np.sum(x**2)  2*np.correlate(y, x) + np.correlate(y**2, np.ones_like(x))
K = np.argmin(delta)
B = K + b
distance = delta[K]
return a, B, distance
That's it, in less than 50 lines of Python code!
This audio file
(looped 4 times here but we could loop it forever) has been obtained with the algorithm described here. Not too bad, n'estce pas?
Example of output:
Loop (2.000s, 3.000s) improved to (2.000s, 3.009s), distance: 1003724800
Loop (2.000s, 3.250s) improved to (2.000s, 3.340s), distance: 839278592
Loop (2.000s, 3.500s) improved to (2.000s, 3.559s), distance: 1281863680
[...]
Loop (2.000s, 8.500s) improved to (2.000s, 8.544s), distance: 1092337664
Loop (2.000s, 8.750s) improved to (2.000s, 8.789s), distance: 964747264
Loop (2.000s, 9.000s) improved to (2.000s, 9.004s), distance: 2488913920
[...]
Loop (7.750s, 9.000s) improved to (7.750s, 9.004s), distance: 1167093760
Loop (8.000s, 9.000s) improved to (8.000s, 9.001s), distance: 1710333952
The final loop is (6.750s, 8.322s), i.e. (297675, 366989).
Note: Wouldn't it be possible to save these loop markers inside the WAV file's metadata instead of just printing them on screen? Sure it is, but as Python's standard library doesn't support WAV markers editing, you'll have to use these techniques to do this.
Get the reverb impulse response of a church
I recently recorded an impulse response of the reverb of a 14thcentury church (more or less the footprint of the sound ambiance of the building). Here is how I did it.
 First I installed a loudspeaker (a studio monitor Yamaha HS80M) in the church, quite high from the ground. I played, rather loud, a sound called a frequency sweep, that contains frequencies from 20Hz to 20000Hz, i.e. the entire human hearing range.
 Then, in the middle of the church, I recorded this with 2 microphones. Here is what I got:
Quite a lot of reverb, that's exactly what we want to catch with an IR!

Now, let's use some Digital Signal Processing to get the IR. All the source code in Python is here. If you're into math, here is the idea:
a
is the input sweep signal,h
the impulse response, andb
the microphonerecorded signal. We havea * h = b
(convolution here!). Let's take the discrete Fourier transform, we havefft(a) * fft(h) = fft(b)
, thenh = ifft(fft(b) / fft(a))
.  Here is the result, the Impulse Response of the church:
Then, of course, we can do some cleaning, fade out, etc.
But what is this useful for? You can use this Impulse Response in any music production software (the VST SIR1 is quite good and freeware) , and make any of your recordings (voice, instrument, etc.) sound like if they were recorded in this church. This is the magic of convolution reverb!
Useful trick when you record your own IR: play sweep0.wav
in the building instead of sweep.wav
. The initial "beep" is helpful to see exactly where things begin. If you don't do that, as the sweep begins with very low frequencies (starting from 20 Hz), you won't know exactly where is the beginning of your microphonerecording. Once your recording is done, you can trim the soundfile by making it begin exactly 10 seconds after the short beep.