It should be noted that this analysis is just a generalized presentation for interest to the listeners. A thorough scientific acoustical analysis would require stringent experimental and analysis guidelines, which are beyond the scope of this particular article.
But some interesting facts are illuminated by the material presented, and may be interesting to those so inclined to search for more explanations of the similarities and differences between the sound of each cello.
Fast Fourier Forms
Fast Fourier Transforms have been generated of the open strings of each of the different cellos, played with their respective bows. These particular graphs plot the temporal evolution of the cello notes from background to foreground on one axis, and plot the various frequencies and amplitudes of the partials contained within each note on the other two axis. (amplitude on the vertical axis )
Although the partials exhibited by each of the different cellos are fairly similar in frequency, the amplitude relationships are quite different, which is largely responsible for the differing timbres of the cellos. You can click on the play button to see each illustration and to hear the actual recording of the cello note. You can also hear the difference between the various cellos by comparing the recordings.
Note that the Baroque cello samples and the Violoncello Piccolo samples sound approximately a semitone lower than the Carbonfibre and Mirecourt samples. This is because of the reference tuning frequency used to tune the cellos. Also, the Violoncello Picollo cello has a fifth string tuned at e'. For the more modern instruments, the Mirecourt and Carbon fibre, a is tuned at 440 Hz, while the two period instruments, the Baroque and Piccolo, are tuned to a = 415, the standard tuning reference used in their time.
Some observations which could be made are as follows:
In general, all cellos exhibit a characteristic decrease in amplitude as one goes up higher in the frequency spectrum of the partials of each note.
The Violoncello Piccolo has the least complicated spectrum of the four cellos, giving it its typically thinner sound.
The Carbon fibre cello and the Mirecourt cello produce the most overall energy, which distribute much of it in the lower 8 partials of the spectrum, giving them very rich and resonant sound.
The Baroque cello also produces a substantial amount of energy, but it is distributed more towards to lower partials of the spectrum, making it sound somewhat less resonant than the Mirecourt cello and Carbon fibre cello.
The upper partials of the Carbon fibre cello retain a lot of energy, and also seem to speak almost immediately as the note is bowed, which tends to give the sound a somewhat edgy timbre, compared to the other cellos.
Because the carbon fibre material itself is very different than the wood, (much denser) it seems to react quicker to stimulation, resonates longer, and generates a slightly different partial series.
Spectrographs
Figures "1", "2", "3" and "4" are Spectrographs of the four cellos.The open strings of each are first bowed, and then played pizzicato. The frequency of the partials are referenced on the vertical axis, while their intensity is represented by the colour, brighter being louder.
One can hear the files by pressing the play icon in the Spectograph section above.
Comparison
The last audio example, sample "5", is a comparison of the Mirecourt cello and Carbon fibre cello, alternately playing their open strings. The lower 3 partials of their harmonic spectrum have been filtered and reduced substantially in volume, to allow the listener to hear and observe the differences of the upper partials in their respective timbres.
