Mel scale

The message is the unit of the psychoacoustic size tonality with the symbols Z ( or z), and describes the perceived pitch of pure tones, so the pitch perception. The mel scale was proposed in 1937 by Stanley Smith Stevens, John Volkman and Edwin Newman. The name Mel derives from the English word melody.

Definitions of the critical band rate in Mel

There are two definitions of the mel scale, each differing in the reference value:

• Basis for the definition of the mel scale by Stanley Smith Stevens is the tone at the frequency f = 1000 Hz, it is assigned the critical band rate z = 1000 mel.

The mel scale in can be described by the following formula approximatively:

Complies with:

Transformed:

The rest of the article refers to the scale by Eberhard Zwicker.

• Eberhard Zwicker defined later a Mel - scale based on the Bark scale with the musical note C as a base. This tone with frequency f = 131 Hz is assigned to the critical band rate = 131 mel Z. Later it was changed again to 125 Hz.

In both definitions shall apply: a sound that is perceived twice as high, receives double Tonheitswert, a sound that is perceived as half as much, half Tonheitswert. With the help of psychoacoustic experiments can so the tonality scale can be determined.

Relationship between frequency and critical band rate

The relationship between tonality and frequency applies:

• For frequencies f up to about 500Hz, the logarithmic frequency scale and the logarithmic mel scale are nearly proportional.

A doubling of the frequency of 100 Hz to 200 Hz, thus leading to a doubling of the critical band rate of 100 formula 200 formula. A musical interval of an octave corresponds to a doubling of the perceived pitch here.

• For frequencies f greater than 500 Hz frequency and tonality are in a non-linear relationship. ( = 850mel 1000Hz, 8000Hz = 2100mel ) it must be raised to 10000 Hz, in order to achieve a doubling of the critical band rate of 1100 mel 2200 mel, for example, the frequency of a tone of 1500 Hz; It is here a musical interval of more than 2.5 octaves required to achieve a doubling of perceived pitch. That is, in this frequency range tone intervals are perceived less as they are seen it musically.

Auditory mechanisms for Tonheitsbestimmung

The auditory system uses different mechanisms to perceive pitch:

• In the low frequencies below 500 Hz 800 .. especially the time structure of the ear signals is evaluated and considered for pitch sensation approach. Here, the pitch sensation follows very closely the musical pitch.
• In the high frequencies above 1600 Hz, the hearing is no longer able to track the time structure of the ear signals. Here, the pitch sensation from the position of the excitation maximum is derived on the basilar membrane. Between the critical band rate and the location of maximum amplitude of vibration of the basilar membrane of the inner ear here, a linear relationship; that is, the same distances on the basilar membrane corresponding to the same Tonheitsdifferenzen.
• In the frequency range approximately 800-1600 Hz, the two mechanisms overlap.
• The perceived pitch of complex tones differs in the perception of pure tones and with slight variations generally proportional to the logarithm of the frequency. That's over a wide frequency range up to 5 kHz the case. This area is approximatively constant for complex tones, the " just noticeable difference " ( jnd ).

Sensation levels

It can be distinguished with a constant width of 3.9 mel 620 degrees of sensation of tonality. The entire hearing range of 16 Hz to 19000 Hz comprises 2400 mel.

Another measure of tonality is the Bark: Bark 1 = 100 or 1 mel mel = 0.01 Bark

For critical bands ( frequency groups ), there are two scales: The Bark scale ( mel scale ) and the ERB scale.