1. Here is a plot which we call a raster plot
Here is a plot which we call a raster plot. Each horizontal trace represents the amplitude plot of one phrase. The motifs are in order of appearance from top to bottom. In nature each phrase is separated by a silence. Red represents high amplitude (loud) sounds and blue represents low amplitude (quiet) sounds.

2. Next we turn each phrase into a point process, a series of all or nothing events (ones and zeros). Each event is represented by a white point on the above graph. These points are place at the time of most rapid amplitude change within the song (when color changes quickly from blue to red.) These points are localized by finding the peaks in the derivative of amplitude vector.

3. By removing the orginal amplitude raster we can view the series of phrases the bird sings as a series of point processes.

4. Next we use a spike sorting algorithm to sort the phrases (each now a point process or series of spikes) into clusters of similar phrases.

5. We can then run the clustering algorithm again, sorting each cluster into subclusters.

6. Now you can see the rows of amplitude data corresponding to the spike groupings.

7. Back to the original viewing format, amplitude.

8. We can also display this data using the colormap to indicate pitch.

9. We can also display this data using the colormap to indicate pitch.

10. High pitches are in red, low pitches are in blue.

11. In order to use the algorithm to cluster further we may have to select subsections or use offsets instead of onsets to define the spikes. For now, I did the remaining sorting by hand for this bird.

12. Here’s another of the five birds analyzed. Beasley.

13. Sorted using spike sorting.

22. After additional sorting by hand, I search for consistencies across the songs. Consider this graph a map of the song space for this bird’s current repretoir. We can begin to explain areas of that space by noticing that there are certain repeated elements.

23. Here’s a large and obvious repeated section at the beginning of a phrase which has several endings as options.

24. Here’s some motifs that can be used as both beginnings or endings
Here’s some motifs that can be used as both beginnings or endings. Notice that the beginning of the yellow motif overlaps with the end of the red motif.

25. One motif (brown) is an alternate beginning
One motif (brown) is an alternate beginning. Another motif (pink) can go in the beginning, end, or middle.

26. This (white) appears to be an ending motif that can be paired with three unique beginnings.

27. (light orange) Another beginning or ending motif that can be inserted into a small diversity of song types.

28. This motif (tan) is suprasegmental, it spans a connection junction between two motifs.

29. This motif (lime green) is an alternate ending for two types of beginnings. The song space is beginning to be explained by modular subunits that are shared across two or three songs.

30. The brown and beige motifs.

31. The neon green motif. We have explained most of the song space by large, modular elements that can each be found in a couple song types.

32. What Next?
The rhythmic template still appears to be present. Quantifiable?
Generative model of song from transitional probabilities between motifs?
We can now try to compute Euclidian distances between songs.
Use those distances and see if they inform the sequence of singing.