Dear Roberto,

The spectrogram is just a representation of the audio signal in the time-frequency domain. The information content of the spectrogram can be as high as for the signal in the time-domain. In their paper, George and Shamir obtain the spectrogram, and after that a complete set of features that are used for classification. It is reasonable that to classify music stiles you use frequency contents information and the time related information. The features set contains both, time and frequency related features, that are used for classifying the audio signals. Therefore, I suggest you to focus on the features meaning, and not in the spectrogram, because it is just a representation from which the features can be obtained easily.

Hello Roberto, Ya it is better to do from feature extraction to classification with this you can show better classification accuracy.

Thank you Dr. Rosa and Dr. Merugu for your answers. The main subject of Shamir article is to obtain features of partial spectrograms of fixed number of measures. I think that this segmentation is arbitrary because the spectrogram features must be classified as a whole, because the variation of a musical piece is less than a second. The results are interesting but the weigthing of the features described could be a imposibilitation to identify the real features given by the spectrogram. What do you think about the segmentation done by Shamir of the spectrogram of the songs?

What is your purpose of classification? i.e. for whom/why?  I do think both time domain and frequency domain features are necessary for audio classification. It can depend on the application and the purpose will decide the possible features to be used for classification. i.e. on what basis you want to classify the audio as classification can be done in many ways based on different high level features or low level features.

I agree with your opinion Dr. Velankar. The purpose is the central issue in the ellaboration of a classification criteria. I was working on biological effects (Electrodermal activity, Startle Reflex, Respiratory rate) trying to ellaborate a classification criteria of music. This work implies a measure of the average meter of the songs, centered on time domain features. But, the spectrogram is a tool for working on other known effects like the use of high frequencies and the pressence of noise. Is valuable the spectrogram in this context?   

Thank yor Dr. Rivera. Yes, we are considering to use pink noise as an alternative to music in the paradigm. Thank you for the suggestion of SWIPE, it seems to be an interesting tool for the proyect. 

Anyone consider the use of the cepstrum a better tool than the spectrogram? 

Thanks for the further elaboration. As I understand you are interested in finding meter i.e. perceived tempo of music. It is time domain feature measured as BPM i.e. Beats per minute . Various algorithms are proposed for same such as  based on kalman filtering or hybrid multiband approach. I suggest you to refer to different papers on musical beat tracking for same. 

BPM is not an objective indicator. If you know the score of the music, then you can "easily" find out the tempo because the composer defined the meter of the music. If you take Afro Blue it is commonly written as a waltz (3/4), but especially in higher tempos it is perceived as an 6/8 (or 6/4), two bars of waltz being one in the 6/8 . This decision between the two meters has a big effect on the tempo. Waltz in 240 BPM would be 6/8 in 80 BPM ( three 1/8 counting as one beat), if I haven't made a logical or calculation error.

Spectrogram is based on Fourier series which states that only periodic signals can be represented by a finite number of sinusoidal components. As sound is never truly periodic, the resulting representation in the frequency domain will always be an approximation (there are other limitations, specially related to the discrete domain). Some feature extractors (as they are dedicated algorithms to retrieve one specific acoustic feature) sometimes work better (more precisely) than spectrogram, but are also incomplete. I think we are still far from the moment when algorithms will accurately pinpoint specific acoustic features as our brain is able to effortlessly perform.

Thank you ME Velankar and  Rr. Kauflin for your answers. I agrre that BPM is a difficult measure and there is not consensus about its use. I am not agree with the  use of the indcation on the music sheet, because the variations on figures duration change itself the tempo of the music play. Probably an average approach of this features could help about the global impact of the piece, but a very short temporal horizon must be considered for obtain better results.

The spectrogram is useful in that it describes the signal in terms of time, frequency and magnitude. It is used as the basis for calculation of many useful features describing the music in terms of rhythm, timbre and intensity, and the frame-based nature of the overlapping STFT allows us to examine how these features change over time, study statistical patterns of features etc. I'd recommend the MIR Toolbox (developed by Olivier Lartillot) as a means of extracting many useful music features.

One point regarding the association of music features and physiological responses in the listener. In music perception studies, care must be taken with using physiological responses as they may be due to a variety of factors, and it's difficult to be sure about associations between particular parameters and participant responses. Also there are things like personal associations the participant may have with a given piece of music and so-on. Look at the work of Alf Gabrielsson, Tuomas Eerola for example

Hope this is of some use.

the spectrogram is a powerful tool to identify sound features either in real-time or in post-processing on recorded materials. Its utility however strongly depends on the type of audio material to be examined and on the accurate tuning of the analysis parameters. In some cases it is powerful enough to recognize the features of interest more accurately and objectively than human hearing, however, in other cases, it can't rival with our ears and brain in recognizing complex features. 

It is very important for determining the tone quality of low instruments like the tuba, contrabassoon, contrabass saxes & clarinets. Most of these instruments play slowly enough that Fourier analyses is good enough to characterize their sound. Unfortunately these low instruments produce very little sound on the fundamentals of the notes they play in their lower registers. For example a typical symphonic CC tubist may think he is really helping the orchestra in his playing of the low A at 55 hertz in the beginning of the Prelude to Die Meistersinger by R. Wagner. Actually less than 1% of his sound is at 55 hertz whilst the rest of his sound is centered around middle C# at 293.7 hertz. That is the 5th harmonic of the A and is flat to the well tempered scale. Imagine a string player wondering what is wrong as his instruments beats against tuba garbage. Harmonic analyses shows that most of these low instruments are fake and sound like bad harmonicas. Only because of the nonlinearity of the human ear and the wonderful human brain are these instruments tolerable! Their tone quality is poor because they are not scaled properly from trumpets. The tubing through the trumpet valves is about 0,5 inches in diameter. The tuba should be 2 inches there if scaled in accordance with the Buckingham PI Theorem.

Clearly music is a spectral theory because pitch in music theory can no more be defined by frequency than light can be a theory of waves.  So first we need a definition of a musical spectrum.

We shall say that a spectrum is a count that tallies how often a particular frequency is observed in a field of values.

It is understood here that the frequencies are related as a system of overtones of a fundamental mode of vibration, so that only the simple multiples of the system fundamental are allowed.

A musical spectrum can be determined in any field of values by counting how often the elements of a defined set occur.

According to affine theory the probability of each overtone in a 12-tone set is 1/12 so that when there is a characteristic probability distribution is observed this proves there is a nontrivial order.  That is, we can line the elements in their natural order of pitch, but there is a second order that is reveal as a characteristic fingerprint in the spectrum.

Here is an example.  Suppose we have a collection of songs on guitar that use the musical keys of G, C, E, A, and A minor, sometimes D or rarely F.  But never E-flat or B-flat or A-flat.  It would be a reasonable conclusion that the guitar tuning used is the standard tuning because these keys are the signature of this popular tuning.

This means that a histogram of the favored musical key signatures used is a fingerprint characteristic of the device-specific, pitch-independent language of the musical instrument.  (That is, if the capo is used, the spectrum just shifts so the guitar intonation is irrelevant to the choice of keys on guitar, but the tuning is determinative).

In affine theory every guitar tuning is the same, but in practice there is a spectrum of about a dozen tunings that are cherished and conserved for centuries.  And then there are thousands of guitar tunings with no known use.  The existence of these golden sets show that there is a higher order in music that is defined by how the sets are constructed.

Now look at the musical keys the Beatles are using and ask yourself, is the Beatles cannon all in standard tuning?  The published music and the recording do not have the same spectral fingerprints.

The specrogram is a signal analysis tool where the signal waveform x(t) in time time domain is segmented and converted to an equivalent representation in frequency domain based on the Fourier transform or Fourier analysis. A waveform is analysed into a sum of sinusoidal waves with specific frequency. So, physically the analysis is the frequency content of the waveform called the frequency spectrum of the signal. Concerning sound, any complicated sound waveform can be analysed using DFT or FFT to get its frequency content where the complex sound is thought to be composed of simple harmonic vibrations. So, such frequency content is rich with intelligible information that cab be used to differentiate between the signal sources by working out the differences between them.

The response of the ear to the sound is the audio signal. So, when one speaks about the audio signal means how far the ears will respond to this signal. May one multiply the sound signal by the ear frequency response and then compare the output of the audio signals and how they are different from each other.

This is just a conceptual view hope it may be useful.

Best wishes

Spectrogram presented not only the frequency content of the signal but also its energy. The spectrogram's vertical axis represents frequency, with the lowest frequencies at the bottom and the highest frequencies at the top, while the horizontal axis represents time; it runs from left to right of the axis. The colors enrich the spectrogram representation as its third dimension; different colors represent different energy levels . so if you combine it with classifier such as CNN which is manly image classifier it might give good results