I plan on using equations in order to determine the standard distribution of frequencies that form a particular formant. For example, if I analyze each member of my group singing a particular vowel, I can collect the data of each formant, and create a distribution to analyze what the mean frequency is for each formant of that vowel. Since men and women have slightly different formants, I will also likely need to calculate the differences to see if blend among women differs from blend among men.
I will likely use these equations, which I’ve sources from http://integral-table.com/downloads/stats.pdf:
Mean: μ = (1/n)∑xi
Std. Deviation: sx = Sqrt[1/(n-1)∑[(xi −x bar)^2]
z-score: z = (x−μ)/σ
Correlation: r = 1/(n-1) ∑(from i=1 to n) [(xi −x bar)/sx ][(yi −y bar)/sy ]
In order to analyze the different frequencies present when a speaker says or sings a certain formant, I will be using a technology called Praat. Developed in Europe, this software allows a user to record a vocal sound and then analyze the different frequencies produced. I plan to utilize the function that creates a spectrogram and a waveform. It not only shows dark bands for different formants, but it also has the functionality to superimpose a line of best fit so the user can better visualize the formant’s change over time. There is also a feature that allows the user to break up the speech signal into phonemes, which creates readily understandable images to be presented with the data.
Here’s a screenshot of analyzing a word in Praat:
I plan on further analyzing the data I collect using Audacity. Audacity also allows for more intricate audio editing than Praat, so I will likely use it for filtering and trying to change formants in order to fix the blend on audio segments.
Things are still in the works, but I hope to have a component of my project that takes in audio samples and returns which vowel is being produced. If that is too difficult or not applicable enough to my project, I hope to find another way to be able to utilize Python in the way I analyze formants and calculate blend, in order to create a user interface in which a user who knows nothing about formants or the science of waves can still analyze blend. This will likely be in a Jupyter notebook, since that is such a great user interface.