Music Machinery

This is the second in a series of posts exploring the Million Song Dataset.

Every few months you’ll see a query like this on Reddit – someone is looking for songs that slowly build in intensity.  It’s an interesting music query since it is primarily focused on what the music sounds like.  Since we’ve analyzed the audio of millions and millions of tracks here at The Echo Nest we should be able to automate this type of query.   One would expect that Slow Build songs will have a steady increase in volume over the course of a song, so lets look at the loudness data for a few Slow Build songs to confirm this intuition.  First, here’s the canonical slow builder: Stairway to Heaven:

The green line is the raw loudness data, the blue line is a smoothed version of the data.  Clearly we see a rise in the volume over the course of the song.  Let’s look at another classic Slow Build – The Hall Of the Mountain King – again our intuition is confirmed:

Looking at a non-Slow Build song like Katy Perry’s California Gurls we see that the loudness curve is quite flat by comparison:

Of course there are other aspects beyond loudness that a musician may use to build a song to a climax – tempo, timbre and harmony are all useful, but to keep things simple I’m going to focus only on loudness.

Looking at these plots it is easy to see which songs have a Slow Build.  To algorithmically identify songs that have a slow build, we can use a technique similar to the one I described in The Stairway Detector.  It is a simple algorithm that compares the average loudness of the first half of the song to the average loudness of the second half of the song.  Songs with the biggest increase in average loudness rank the highest.   For example, take a look at a loudness plot for Stairway to Heaven.  You can see that there is a distinct rise in scores from the first half to the second half of the song (the horizontal dashed lines show the average loudness for the first and second half of the song). Calculating the ramp factor we see that Stairway to Heaven scores an 11.36 meaning that there is an increase in average loudness of 11.36 decibels between the first and the second half of the song.

This algorithm has some flaws – for instance it will give very high scores  to ‘hidden track’ songs.  Artists will sometimes ‘hide’ a track at the end of a CD by padding the beginning of the track with a few minutes of silence.  For example, this track by ‘Fudge Tunnel’ has about five minutes of silence before the band comes in.

Clearly this song isn’t a Slow Build, our simple algorithm is fooled.  To fix this we need to introduce a measure of how straight the ramp is.   One way to measure the straightness of a line is to calculate the Pearson correlation for the loudness data as a function of time.  XY Data with correlation that approaches one (or negative one) is by definition, linear. This nifty wikipedia visualization of the correlation of different datasets shows the correlation for various datasets:

We can combine the correlation with our ramp factors to generate an overall score that takes into account the ramp of the song as well as the straightness of the ramp.   The overall score serves as our Slow Build detector.  Songs with a high score are Slow Build songs.   I suspect that there are better algorithms for this so if you are a math-oriented reader who is cringing at my naivete please set me and my algorithm straight.

Armed with our Slow Build Detector, I built a little web app that lets you explore for  Slow Build songs.   The app – Looking For The Slow Build – looks like this:

The application lets you type in the name of your favorite song and will give you a plot of the loudness over the course of the song, and calculates the overall Slow Build score along with the ramp and correlation.  If you find a song with an exceptionally high Slow Build score it will be added to the gallery.  I challenge you to get at least one song in the gallery.

You may find that some songs that you think should get a high Slow Build score don’t score as high as you would expect.  For instance, take the song Hoppipolla by Sigur Ros.  It seems to have a good build, but it scores low:

It has an early build but after a minute it has reached it’s zenith. The ending is symmetrical with the beginning with a minute of fade. This explains the low score.

Another song that builds but has a low score is Weezer’s  The Angel and the One.

This song has a 4 minute power ballad build – but fails to qualify a a slow build because the last 2 minutes of the song are nearly silent.

Finding Slow Build songs in the Million Song Dataset

Now that we have an algorithm that finds Slow Build songs, lets apply it to the Million Song Dataset.   I can create a simple MapReduce job in Python that will go through all of the million tracks and calculate the Slow Build score for each of them to help us find the songs with the biggest Slow Build.  I’m using the same framework that I described in the post “How to Process a Million Songs in 20 minutes“.  I use the S3 hosted version of the Million Song Dataset and process it via Amazon’s Elastic MapReduce using mrjob – a Python MapReduce library.  Here’s the mapper that does almost all of the work, the full code is on github in cramp.py:

    def mapper(self, _, line):
        """ The mapper loads a track and yields its ramp factor """
        t = track.load_track(line)
        if t and t['duration'] > 60 and len(t['segments']) > 20:
            segments = t['segments']
            half_track = t['duration'] / 2
            first_half = 0
            second_half = 0
            first_count = 0
            second_count = 0

            xdata = []
            ydata = []
            for i in xrange(len(segments)):
                seg = segments[i]
                seg_loudness = seg['loudness_max'] * seg['duration']

                if seg['start'] + seg['duration'] <= half_track:
                    seg_loudness = seg['loudness_max'] * seg['duration']
                    first_half += seg_loudness
                    first_count += 1
                elif seg['start'] < half_track and seg['start'] + seg['duration'] > half_track:
                    # this is the nasty segment that spans the song midpoint.
                    # apportion the loudness appropriately
                    first_seg_loudness = seg['loudness_max'] * (half_track - seg['start'])
                    first_half += first_seg_loudness
                    first_count += 1

                    second_seg_loudness = seg['loudness_max'] * (seg['duration'] - (half_track - seg['start']))
                    second_half += second_seg_loudness
                    second_count += 1
                else:
                    seg_loudness = seg['loudness_max'] * seg['duration']
                    second_half += seg_loudness
                    second_count += 1

                xdata.append( seg['start'] )
                ydata.append( seg['loudness_max'] )

            correlation = pearsonr(xdata, ydata)
            ramp_factor = second_half / half_track - first_half / half_track
            if YIELD_ALL or ramp_factor > 10 and correlation > .5:
                yield (t['artist_name'], t['title'], t['track_id'], correlation), ramp_factor

This code takes less than a half hour to run on 50 small EC2 instances and finds a bucketload of Slow Build songs.   I’ve created a page of plots of the top 500 or so Slow Build songs found by this job. There are all sorts of hidden gems in there. Go check it out:

Looking for the Slow Build in the Million Song Dataset

The page has 500 plots all linked to Spotify so you can listen to any song that strikes your fancy.  Here are some my favorite discoveries:

Respighi’s The Pines of the Appian Way

I remember playing this in the orchestra back in high school. It really is sublime. Click the plot to listen in Spotify.

Maria Friedman’s Play The Song Again

So very theatrical

 Mandy Patinkin’s Rock-A-Bye Your Baby With A Dixie Melody

Another song that seems to be right off of Broadway – it has an awesome slow build.