The app controls are labelled in Italian: below, each label is given as it appears in the app, followed by its English meaning.

Changing the timbre of a sound: wave synthesis

1. Instructions
   • Click here to start the app and in the "Trasformazioni" (transformations) window select Cancella tutto (clear all)
   • Select Suono (sound) with the mouse;
   • Working directly on the amplitude palettes, build a complex sound (that is, one made of the superposition of several harmonics).
   • Change the weight of the various amplitudes, observe how the waveform changes and listen to the change produced in the sound. Do the same by changing the phases of the various harmonics.
   • Try building a sound with only the odd harmonics (you should get a "nasal" sound like that of the clarinet).
   • In any case, have fun changing all the possible parameters, trying to grasp the effects on the sound (and on the waveform) of what you are doing.
   • In the waveforms window select: Strumento: Flauto, Strumento: Oboe, Strumento: Clarinetto (Instrument: flute, oboe, clarinet)
   • Listen to the different timbres of the sounds produced: are you satisfied with the result?
2. Remarks
   • One has the impression that, with the "right recipe", that is, knowing the amplitudes and phases of the various harmonics, one could "synthesise" the sound of any musical instrument. (Indeed, the oboe, clarinet and flute waveforms were built in this way.)
   • This is only partly true: the app can analyse and synthesise only periodic functions, which in theory extend without limit in space and time. Every sound emitted by a musical instrument necessarily has, as explained on the page from sounds to music, an attack phase, a duration and a decay phase, and is therefore a non-periodic wave. In instruments (which we will call controlled-evolution instruments) in which the sound can be "sustained", in the sense that the player can supply energy to the oscillating system for a certain time (e.g. wind and bowed string instruments), the attack and decay phases matter less in determining the timbre than in "percussive" instruments (which we will call free-evolution instruments), in which the energy supplied to the oscillator is concentrated in a very short time.
   • In any case, even for the instruments reproduced (controlled-evolution ones), you will have found the timbre only vaguely similar to that of a real instrument. Clearly, the attack and decay phases of the sound cannot be ignored in determining the timbre. Moreover, a real sound (you will find many examples on the page perception of timbre) contains spurious harmonics generated by the mechanical "noises" of the moving parts of the instrument.
   • when players produce a sound, they can change, for the same note played (that is, with the frequency of the first harmonic fixed), the way the energy is distributed among the various harmonics (even suppressing some of them). One of the aims of playing technique (in an extremely reductionist view) is to acquire complete control of the timbre of the sound produced. Every musical instrument poses the player technical problems of its own, arising from the different way the sound is produced. Think of
     • the pianist's "touch";
     • the attack of a trumpet player's sound, which can be quick, producing a characteristic "click", or more spread out in time;
     • the different ways a violinist uses the bow to produce characteristic timbral effects;
     • the different timbre of a guitar depending on whether it is played with a plectrum or with the fingers;
     • the different timbre of the sound produced by a drum-kit cymbal depending on whether it is struck in the centre or near the edge.
3. Related topics: Fourier's theorem, uncertainty, perception of timbre

Relation between timbre and phase of the harmonics

1. Click here to start the app, choose the "seno" (sine) wave, switch the sound on, and repeatedly use the "cambia fase" (change phase) button.
   • After five clicks the function has turned into a cosine. The sound, however, does not change. We have changed neither frequency nor amplitude, only the waveform. Yet the timbre of the sound has not changed.
   • Why? The human ear is almost insensitive to the phase of sound waves, so signals that differ only in phase are perceived as identical (for an extended discussion see the sound wave and perception of timbre).
2. Choose a complex wave again, such as the sawtooth, and switch the sound on. For this experiment we recommend listening through headphones, but first adjust the volume, because this sound can be unpleasant if the volume is too high.
   • Now try changing the phases of the Fourier components freely by clicking and dragging the mouse.
   • This time you should hear slight changes in the timbre of the sound.
   • Why? This time you are not changing the overall phase of the whole signal, but the relative phases of the components. This produces a substantial change in the shape of the wave, which the ear can detect (for an extended discussion see the sound wave and perception of timbre).
3. Now choose a complex wave, and repeatedly use the "cambia fase" (change phase) button. In this case, note that all the Fourier components change phase.
   • A simple operation on the wave can become complex in Fourier space, but the reverse can also happen. This is why Fourier series are so widely used in physics.

Timbre and vowels

1. Click here to start the app and choose the "AAAA" wave. It simulates the vowel A pronounced by a male voice.
2. Switch to the "OOOO" waveform and compare the changes in the spectrum.
   • The human vocal apparatus can change the spectrum of the basic sounds emitted by the vocal cords by modifying the shape of the cavities of the mouth and pharynx (singers have developed sophisticated techniques to obtain a greater variety of effects, see human voice). The sound produced by the vibration of the vocal cords passes through a set of resonant cavities that enhance some of its harmonics and attenuate others, creating what we perceive as different vowels. For further details see resonance, resonant cavities