# Mapping Phonation Types by Clustering of Multiple Metrics
### Definitions and Metrics  
The basic concepts of voice mapping are presented by [PERSON] and [PERSON] [14]. Here, we briefly recapitulate an example of visually representing multiple metrics across the 2D voice field. Its dimensions are the fundamental frequency \(f_{\mathrm{o}}\) (horizontal axis, in semitones) and the signal level in dB (vertical axis, SPL re 20 uPa at 0.3 m), which serve as the two independent variables. Note that both axes are on a logarithmic scale. Each metric is represented as a scalar field or curved surface above the plane of SPL \(\times f_{\mathrm{o}}\) and has the role of a dependent variable. In this study, all metrics were analyzed for voiced segments only, the criterion for voicing being that the autocorrelation of the acoustic signal at one cycle delay must exceed a threshold of 0.96. The metric is sampled at integer values of semitones and decibels, i.e., in the 'cells' of the map. Each cell contains the average of the metric for all visits to that cell (Figure 1). Each metric is visualized on its own 'layer' in a multi-layer map. The six metrics selected for this example and for the present study are the following. The first three are metrics of the EGG signal, and the last three pertain to the acoustic signal. The _quotient of contact by integration_ (\(Q_{\text{ci}}\)) is the area under the EGG pulse that has been normalized to 1 in both time and amplitude. The \(Q_{\text{ci}}\) was computed according to [16]. Like other metrics of the contact quotient, \(Q_{\text{ci}}\) can vary from nearly zero for a narrow EGG pulse to nearly 1 for a broad EGG pulse. The \(Q_{\text{ci}}\) thus represents the relative amount of contacting during a cycle. The exception is when the vocal folds are oscillating _without_ contacting, in which case, the EGG becomes a low-amplitude sine wave, and so the area under the normalized pulse (\(Q_{\text{ci}}\)) approaches 0.5. This commonly happens in a soft and/or breathy voice. The _normalized peak derivative_ (\(Q_{\Delta}\)) is the maximum derivative of an EGG signal; it represents the maximum rate of contacting during closure. \(Q_{\Delta}\) was computed as in [16]:  
\[Q_{\Delta}\approx 2\delta_{max}\left/\left[A_{p-p}\cdot\sin\left(\frac{2\pi}{ T}\right)\right]\right. \tag{1}\]  
where \(T\) is the period length in integer samples, \(A_{p-p}\) is the peak-to-peak amplitude, and \(\delta_{max}\) is the largest positive difference observed over the period between two consecutive sample points in the discretized EGG signal. In phonation without vocal fold collision, the EGG becomes a low-amplitude sine wave. Hence, the minimum value that \(Q_{\Delta}\) can assume is the peak derivative of a normalized sine wave, which is 1. The _cycle-rate sample entropy_ (CSE) metric is low for a regular, self-similar signal and high when a signal is transient, erratic, or noisy. A threshold parameter is set to keep  
Figure 1: Six layers of a voice map, each layer showing values of one metric, averaged per cell. In the top row are three EGG metrics, and in the bottom are three acoustic metrics. An amateur choir baritone sang _messa di roce_ on the vowel /a:/, with increasing and decreasing SPL on tones spanning just over one octave. Data from [PERSON] and [PERSON] [15]. its value at zero when the phonation is stable, even with pitch changing. When something 'abnormal' happens, such as a voice break between falsetto and modal voice, the CSE peaks. CSE represents the cycle-to-cycle instability of the EGG waveform. The CSE was computed as described in [17]. The audio _crest factor_ is computed as the ratio of the peak amplitude of the RMS amplitude for every phonatory cycle. It is a simple indicator of the relative high-frequency energy of the voice signal [18]. It increases with the abruptness of glottal excitation and is indirectly related to the maximum first derivative of glottal flow (the maximum flow declination rate, or MEDR).