Professional

Composition Pro

The spectral analyser

Subjects covered:

• What is an audio spectrum?
• The spectral analysis window
• Working on the harmonics of a sound

What is an audio spectrum? [Professional] [Composition Pro]

Sound is just a vibration of the air or of the matter in which it propagates (water, wall,...). This vibration starts for instance in a music instrument when the player makes his instrument vibrate, by picking up a string, hitting a drum,... This vibration is then transmitted to the air around the instrument and it comes to the auditor's ear and gets registered as a sound impression to him.

So, to represent a sound signal, you need to measure the air pressure at specific regular intervals and memorize these values. This is what is done when you register a concert with a microphone and a digital recorder. By playing this sequence back into a loudspeaker, you can reproduce the exact sound that was recorded. Because of the frequency band to which the ear is sensible, to have a good reproduction quality, you must sample the sound signal 44100 times per second, with a sufficient precision level. This series of values is called the time representation of the sound. It gives the pressure value at any given time of a music concert. Here is how it appears for instance in the audio editor window of Pizzicato:

A mathematician called Joseph Fourier, established in the 19th century that such a signal could always be decomposed as a sum of sine and cosine waves of fixed frequencies and amplitudes. Practically, this means that the sound of a full orchestral symphony may be reduced to the sum of a series of simple sine waves with specific amplitudes and phases, with no variation in time for the full duration of the symphony. When you think about it, it is quite fascinating! But do not change a few of the frequencies or amplitudes, as the symphony may become an obscure sound confusion.

This way of representing a sound of a given time duration is called the frequency representation, or the frequency spectrum of the sound. In theory, you can switch back and forth between the time representation and the frequency spectrum representation and lose no information in the process (which means, keep the sound exactly the same). In practice, you can not make this process with an infinite number of frequencies, so you have to quantize the frequencies you will analyse and this precision may affect the sound result.

Pizzicato lets you analyse a portion of a sound signal to see what it represents in terms of frequency. You can then edit these frequencies (delete some, add some others, modify the spectrum, filter it,...) and then synthesize the signal back to the audio window. This is a way of experimenting sound design and manipulations. We will see now how to do that practically.

The spectral analysis window [Professional] [Composition Pro]

When you select some portion of a sound in the audio window (see the lesson on the audio editor window), you can right click the background of the window and reach the contextual menu item Spectral analysis...

• Open a WAV sound file with the File, Open an audio file... menu item. You can open one of your own file or if you have a Pizzicato license (not in demo mode), you will find several audio files in the DataEN / Libraries / Music libraries / Audio / Papelmedia. Be sure however not to modify these files, as it may have an impact on the sounds generated by Pizzicato. To be sure, make a copy of one of these file and open it.

• Select some portion of the file, for instance a segment of 1 or 2 seconds. Right click on the background of the window and select the contextual menu item Spectral analysis... The spectral analysis windows appears:

• Click the Analyse button and Pizzicato will now analyse the selected portion of the signal and display its frequencies. According to the duration of the signal and the frequency precision needed, this operation may take some time. A colored bar at the bottom of the window shows you the progress of the computation. Then Pizzicato will display the spectrum, for instance:

• When you move the mouse over the window, you can see the exact frequency and amplitude pointed to by the mouse, at the bottom left of the window.

• Just above the spectrum, you will see a scale with the frequencies. Below the window, you have a scroll bar so that you can see the rest of the spectrum (to the right).

• To the left of the tool bar of the window, you can select an horizontal zoom value to see frequencies more precisely or on a larger spectrum.

• The next 3 text boxes specify the frequency range and precision of the analysis. By default, the first frequency analysed is 20 Hz and the highest frequency is 4000 Hz. In that range, the step used is 1 Hz. This means that the frequencies analysed will be [ 20 - 21 - 22 - 23 - ... 3998 - 3999 - 4000 Hz]. You may change these values and click again on Analyse to see a more precise spectrum. Be aware that the larger the range and the precision step, the longer the analysis will take.

• This window may also be used for a special case. If you select one period of a sound in the audio window (which means a full up and down of a periodic sound like flute, violin,...), you can then use the Harmonics button and Pizzicato will analyse the harmonic values (integer multiples of the frequency of the note) and display them on the window. To select only one period of the sound, you should zoom in in the audio window so as to see the individual signal path, then select for instance from one zero value up to the next similar zero value of the signal. When zooming in, you will notice that most sounds have a repetitive pattern. You must then select the duration of just one such pattern.

• The Synthesize button let you reverse the process. Pizzicato will create the signal again from the spectrum analysis to the audio window selection. Notice that you can change the selection before doing this, for instance to place the modified copy somewhere else in the audio file. The text box just to its right specifies the amplitude of the synthesized signal, by default 50 %.

• You will find three tools that you can use to modify the spectrum: a pen, an eraser and a line drawing tool. Select one of these tools and use it inside the window to modify the spectrum. Be aware that a small change in the spectrum may create unexpected changes in the audio signal. You can easily experiment with this. One application is for instance to filter some frequencies in a signal. Analyse the signal with sufficient precision, erase the frequency range you do not want, then synthesize the signal back. You can transform for instance voices very amusingly.

• With a right click in the window, you can reach a contextual menu to save or load a spectrum as a file. This can be useful if you work some sound design and want to remodel its spectrum shape. You can save it and open it again later as a spectrum file.

• You will find a menu called Amplitude on the tool bar. It contains 4 items that can be displayed: Cosine, Sine, Amplitude, Phase. We will not get here into the exact mathematical meaning of these graphs. Roughly, the signal can be represented as a sum of cosine and sine waves, OR, as amplitude and phase. The phase is the moment at the beginning of the signal, when a sine wave starts. Working on the amplitude is the most easy way to change the signal, but you may try to affect its phase also. Or you can try to work directly on the sines and cosines, but the result will probably much more random than just filtering. By changing the phase of a signal you can really distort the original signal. Try and see.

• To design a new spectrum, select its range and precision and then click on the New button. The spectrum is then reset to zero and you can draw a new one.

Working on the harmonics of a sound [Professional] [Composition Pro]

You can design a new spectrum based on the harmonic series and then synthesize the corresponding sound.

• Create a new spectrum by clicking on the New button. Click on the Filter... button. The following dialog appears:

By enabling the first check box, Pizzicato will apply a filter on the spectrum, based on the note you select in the above dialog (you can also enter any frequency). This filter will act to display and use only the integer multiples of the note frequency. For instance, if you have a note of 220 Hz, Pizzicato will only enable the harmonics of this note, which are [220, 440, 660, 880,...].

The Inharmonic factor can be used to detune the all harmonic construction, as this number will be used to multiply frequencies. For instance, if you enter 1.1 for that value, the harmonic will become [220, 220+220*1.1=462, 462+220*1.1=704,...].

The Enlargment of harmonic peak will in fact extend slightly each harmonic. For instance, if the value is 1 and the precision is 1 Hz in the spectral window, there will be the presence of the above harmonics but for harmonic 440, there will also be 439 and 441 frequencies, etc...

By clicking OK, Pizzicato will filter out any frequency of the current spectrum that is not in these specifications. You can then use the pen, eraser and line drawing tools to design a spectrum and you will see that only the harmonics as specified in that dialog will appear. You can for instance draw a spectrum like this, around C1, with a peak enlargment of 4 :

You can then synthesize it back in the audio window and hear how it sounds like. Then modify, synthesize and hear again. You may combine this kind of manipulation with the design of a virtual and modular synthesizer to create and modify samples of your own sounds.

Professional

Composition Pro