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Ok, this is the end of the first section of the first chapter of this ear-training course. If you made until here, well done, but the way to trained ears is still long!

Let's summarise what we have learned so far.

Sound is physical phenomenon and can be defined as a perturbation of an elastic medium.

The vibrations of air determine an alternation of compression and rarefaction areas that propagates in longitudinal waves.

Sound waves can be of different shape, amplitude, frequency and wavelength.

Frequency, wavelength and period are related by mathematical proportions as follows:

lambda=C/ƒ where C is the speed of sound in air

Frequency (ƒ) is measured in Hertz (1Hz = 1 cycle/1s), period (T) in seconds, wavelength (lambda) in meters and the speed of sound in meters per second.

Higher values of amplitude mean more intense compression and rarefaction, meaning higher pressure exercised on our eardrums.

The loudness of a sound is measured in decibel (dB). So far we have only talked about dB(SPL) which are a measure of sound pressure, and dB(SIL) that measure sound intensity. Decibels express a relationship between a given value and its reference value, which is the '0dB' . For Sound Pressure Levels, 0dB is conventionally set at 20µPa, while for sound intensity it is set at 0,000000000001 W per square meter. Due to its logarithmic nature, doubling the number of dB does not mean doubling the sound pressure: a double amount of pressure is expressed by an increase of 6dB(SPL) and a double amount if intensity is expressed by an increase of 3dB(SIL).

Sound intensity is proportional to the square of the pressure, being the external conditions constant. Sound Pressure is inversely proportional to the distance from the sound source, while intensity is inversely proportional to the square of the distance.

Doubling the distance means:

1/2 of the pressure
1/4 of the intensity

Phase is related to two or more sound waves. Two sound waves completely in phase have peaks and zero crossing in the same point at the same time, while two sound waves completely out of phase will have the waveforms shifted by 180°.

Sine waves represent pure tones, but musical instruments generate much more complex sounds. Harmonics are sounds that are generated by a vibrating object and are whole multiples of the fundamental frequency. They contribute to give us the sense of timbre of an instrument. Overtones (sounds that are not mathematically related to the fundamental) also add to the sound spectrum of each instrument its own particular sound features.

Every complex sound, however, is nothing but a sum of simple sounds of different amplitude, frequency and phase relationship. The Fast Fourier Transform (FFT) allow us to switch from a waveform in the domains of time and amplitude, to the domains of frequency and amplitude in a given moment of time.

Sound waves of particular shape (square, triangular, sawtooth) embody very precise sound characteristics in terms of harmonic content, and are often used in synthesis. The proportionate frequency content and the periodicity is what we mostly use to differentiate sound and noise.

To complete overall perception of a sound, we also need to take into account its volume variations through time, or its envelope. The envelope consists of four stages: attack, decay, sustain and release; different combinations of these factors can affect heavily the way a sound is perceived.

Do not forget to practise with these concepts, especially if you are preparing for a proficiency test. In the free tests section you will find plenty of tests (with their keys) to test your progress.