Short answer: You may be interested in the chromagram and/or the Constant-Q transform.
From the links cited above:
In music, the term chroma feature or chromagram closely relates to the twelve different pitch classes. Chroma-based features, which are also referred to as "pitch class profiles", are a powerful tool for analyzing music whose pitches can be meaningfully categorized (often into twelve categories) and whose tuning approximates to the equal-tempered scale. One main property of chroma features is that they capture harmonic and melodic characteristics of music, while being robust to changes in timbre and instrumentation.
The transform exhibits a reduction in frequency resolution with higher frequency bins, which is desirable for auditory applications. The transform mirrors the human auditory system, whereby at lower-frequencies spectral resolution is better, whereas temporal resolution improves at higher frequencies. At the bottom of the piano scale (about 30 Hz), a difference of 1 semitone is a difference of approximately 1.5 Hz, whereas at the top of the musical scale (about 5 kHz), a difference of 1 semitone is a difference of approximately 200 Hz. So for musical data the exponential frequency resolution of constant-Q transform is ideal.
In addition, the harmonics of musical notes form a pattern characteristic of the timbre of the instrument in this transform. Assuming the same relative strengths of each harmonic, as the fundamental frequency changes, the relative position of these harmonics remains constant. This can make identification of instruments much easier. The constant Q transform can also be used for automatic recognition of musical keys based on accumulated chroma content.
Relative to the Fourier transform, implementation of this transform is more tricky. This is due to the varying number of samples used in the calculation of each frequency bin, which also affects the length of any windowing function implemented.
Some more data
I think what you're looking for is the Fourier Transform.
In mathematics, a Fourier transform (FT) is a mathematical transform that decomposes a function (often a function of time, or a signal) into its constituent frequencies, such as the expression of a musical chord in terms of the volumes and frequencies of its constituent notes. The term Fourier transform refers to both the frequency domain representation and the mathematical operation that associates the frequency domain representation to a function of time.
Specifically, you'd be working with the STFT (short time Fourier transform).
The Short-time Fourier transform (STFT), is a Fourier-related transform used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time. In practice, the procedure for computing STFTs is to divide a longer time signal into shorter segments of equal length and then compute the Fourier transform separately on each shorter segment. This reveals the Fourier spectrum on each shorter segment. One then usually plots the changing spectra as a function of time, known as a spectrogram or waterfall plot.
Those are the building blocks. Nevertheless, depending on what you need specifically, you'd probably want to dive into Music Information Retrieval (MIR).
Here there are introductory notes, in which basic concepts are presented.
Here is an article presenting a method of melody extraction, but it is more advanced.
I think these are the building blocks you need to understand to start thinking about the question you brought.
If you have further questions, I suspect they may be more thechnical, hence I'd recommend diving into some other stackExchange sites also: you may find some answers there, too.
As per the software, you may want to start with Librosa, but it's not the only option.