I study the riches of song complexes (dialects, sub-dialects etc) of Chaffinch (Fringilla coelebs) in Ukraine. But I did not found studies of numerical separation of these complexes and numerical description of their riches.
And in general, it's worth pointing out that whatever components you measure from an acoustic signal like bird song are multivariate measures. Therefore, it's most efficient and helpful to analyse them together and not singly. Furthermore, where the components are correlated (as is likely), the analysis needs to account for the correlation structure.
I'd therefore use ordination and scaling to demonstrate clusters associated with categories such as individual or song type. And I'd use ordination loadings or random forest mean decrease in accuracy values to determine exactly which element in each of the song groups is primarily responsible for the clustering.
I do agree, there are different approaches. Some attempting to give the most possible of the analysis to some software, while others give more weight to the scientist itself. I am in between. I do use and code software to support my acoustics studies but only on those areas where repetitive actions may be done better by a computer rather than a human. For activities like signal analysis, I use Baudline as a fast DSP but I prefer to collect data from each signal by myself instead of having a software "reading" it for me. There is still so much that our brains do when looking at a signal spectrogram than what a piece of code can do by only searching for some distinct variables.
I have found a good source to both inspiration and solutions when reading about similar challenges experienced by other areas of science. On that spirit, I recommend you to check the methods used and discribed by the attached study to see a "different" approach in also a different and complex taxon.
With kind regards
Article Study of Whistle Spatio-Temporal Distribution and Repertoire...
Best to use song analysis software, numerically quantifying song characteristics based on spectrograms. The above mentioned SASLab Avisoft is great, alternatives are Raven (Cornell), Audacity or Syrinx.
Hey Eugenia, you may find useful this paper below to compare different ways to analyze your data. Good luck on your project!
Nowicki, S., & Nelson, D. A. (1990). Defining Natural Categories in Acoustic Signals: Comparison of Three Methods Applied to ‘Chick‐a‐dee’Call Notes. Ethology, 86(2), 89-101.
You may use Shannon entropy measurements to calculate note disorder within the song. Please take o look in:
SILVA, M. L. ; VIELLIARD, Jacques Marie Edme ; PIQUEIRA, J. R. C. 2000. Using shannon entropy on measuring the individual variability in the Rufous-bellied Thrush Turdus rufiventris vocal communication. Journal of Theoretical Biology, 207(1): 57-64,