## 4 Physical Audio Features Extraction Techniques
### Frequency Domain Physical Features
#### 4.2.4 Tonality-Related Physical Frequency Features  
The fundamental frequency is defined as the lowest frequency of an harmonic stationary audio signal, which in turn can be qualified as tonal sound. In music, tonality is a system that organizes the notes of a musical scale according to musical criteria. Moreover, tonality is related to the notion of harmonicity, which describes the structure of sounds that are mainly constituted by a series of harmonically related frequencies (_i.e._, a fundamental frequency and its multiples), which are typical characteristics of (tonal) musical instruments sounds and voiced speech. The following paragraphs describe the most widely employed tonality-related features that do not incorporate specific auditory models for their computation. * **Fundamental frequency:** it is also denoted as F0. The MPEG-7 standard defines audio fundamental frequency feature as the first peak of the local normalized spectro-temporal autocorrelation function [45]. There are several methods in the literature to compute F0, e.g., autocorrelation-based methods, spectral-based methods, cepstral-based methods, and combinations ([PERSON] [87]). This feature has been used in applications like musical onset detection ([PERSON] _et al._[57]), musical genre classification ([PERSON] and [PERSON] [28]), audio retrieval ([PERSON] _et al._[88]) and environmental sound recognition ([PERSON] and [PERSON] [47], [PERSON] and [PERSON] [48]). In the literature F0 is sometimes denoted as _pitch_ as it may represent a rough estimate of the perceived tonality of the signal (e.g., pitch histogram and pitch profile). * **Pitch histogram:** instead of using a very specific and local descriptor like fundamental frequency, the pitch histogram describes more compactly the pitch content of a signal. Pitch histogram has been used for musical genre classification by [PERSON] and [PERSON] [28], as it gives a general perspective of the aggregated notes (frequencies) present in a musical signal along a certain period. * **Pitch profile:** this feature is a more precise representation of musical pitch, as it takes into account both pitch mistuning effects produced in real instruments and also pitch representation of percussive sounds. It has been shown that use of pitch profile feature outperforms conventional chroma-based features in musical key detection, like in [PERSON] and [PERSON] [89]. * **Harmonicity:** this feature is useful for distinguishing between tonal or harmonic (e.g., birds, flute, _etc._) and noise-like sounds (e.g., dog bark, snare drum, _etc._). Most traditional harmonicity features either use an impulse train (like in [PERSON] _et al._[90]) to search for the set of peaks in multiples of F0, or uses the autocorrelation-inspired functions to find the self-repetition of the signal in the time- or frequency-domain (as in [PERSON] _et al._[91]). Spectral local harmonicity is proposed in the work by [PERSON] [92], a method that uses only the sub-regions of the spectrum that still retain a sufficient harmonic structure. In the MPEG-7 standard, two harmonicity measures are proposed. Harmonic ratio (HR) is a measure of the proportion of harmonic components in the power spectrum. The Upper limit of harmonicity (ULH) is an estimation of the frequency beyond which the spectrum no longer has any harmonic structure. Harmonicity has been used also in the field of environmental sound recognition ([PERSON] and [PERSON] [47], [PERSON] and [PERSON] [48]). Some other harmonicity-based features for music genre and instrument family classification have been defined, like harmonic concentration, harmonic energy entropy or harmonic derivative (see [PERSON] and [PERSON] [93]). * **Inharmonicity:** this feature measures the extent to which the partials of a sound are separated with respect to its ideal position in a harmonic context (whose frequencies are integers of a fundamental frequency).