Most appropriate spectral analysis method for a recording of a saxophone note? I'm currently doing an investigation where I am attempting to resonant frequencies of an Alto Saxophone at various different notes. I have taken audio recordings of the notes with a sample rate of $44100\textrm{ Hz}$, and exported them into CSV files. Now, I am attempting to analyze this data using the signal processing plugin for MATLAB, but I'm feeling a little bit overwhelmed with all the different options, as I'm not sure which spectral analysis method is most suitable for the my task.

In MATLAB, I'm seeing a number of spectral analysis methods including FFT, Burg Method, Welch Method, Multitaper Method, and more - but I'm not sure of their specific applications.

Again, my goal is to clearly identify the major spectral peaks (formants) which correspond to the resonant frequencies of the Saxophone bore. The data was taken with a condenser microphone at a sample rate of $44100\textrm{ Hz}$, with the Saxophone bore exactly 1 meter from the microphone. Ultimately, I'm looking to create a plot similar to the image I have attached. 

Please excuse my ignorance on this subject, this is my first time using MATLAB and I am not well-versed in digital signal processing. If anyone could help me with this, I would be extremely grateful.
The plot OP shared looks similar to log magnitude spectrum(black line) plotted with its envelope(red line). so from what OP says, OP need to plot log magnitude spectrum of recorded audio/signal. One thing to remember for this analysis is that same note should be played for entire duration of the signal to be analysed. if not, one should use proper windowing methods to ensure that signal remains stationary(in same note) for the entire duration of window under analysis. I am assuming that a note corresponds to a few particular frequencies. 

that is the way if you want to plot/analyse a graph similar to the one shared. are you also looking for other methods for determining the peaks corresponding to a particular note at a time?