## 4 Initial Attempts at Lightweight Machine Learning
### Features  
The bell shape is close to the normal distribution in terms of appearance. Unfortunately, the features used to portray the state of a normal distribution, such as skewness and kurtosis, are not applicable here since they are not used to determine whether a distribution is normal-like/bell-shaped in appearance or not.  
Besides our newly proposed feature for inscribing bell shape, Degree of Bell Shape (_DoBell_) (see Section 1.4), another appropriate classic feature we found and validated is negative turning (_NT_), which we utilized the _Time Series Feature Extraction Library_ (TS-FEL) [34] to compute. Treating the pitch histogram as a time series, _NT_ counts its number of violations during monotonic rise and fall, where adjacent equivalent values do not break the monotonicity. We found that _NT_ is ideally equal to the occurrence number of the local peaks throughout the histogram besides the highest peak. For example, in Figure 7(8), \(NT_{\text{pitch histogram equals 2}}\), while \(NT_{\text{merged pitch histogram equals 1}}\). A perfect bell shape's _NT_ equals 0. The _NTs_ for both basic and merged pitch histograms are usually small integers, most possibly between 0 and 3. Some songs with wide pitch ranges have relatively large _NTs_, such as _You Raise Me Up_ (both _NTs_ are 7).  
It is important to note that before calculating the _NT_ and the _DoBell_ features, the bins with zero height in all pitch histograms are removed.  
Applying the _NT_ and the _DoBell_ features to the pitch histogram and the merged pitch histogram produces four different features. It can be learned from Section 2.2 that for a Chinese anhemitonic pentatonic folk song where non-anhemitonic-pentatonic pitches occur, the anhemitonic pentatonic pitch histogram may allow better generation of the bell shape. Therefore, we also apply the _NT_ and the _DoBell_ to the anhemitonic pentatonic pitch histogram and the merged anhemitonic pentatonic pitch histogram to generate another four features. For instance, in Figure 3(1), after removing the bins of si\({}_{3}\) and si\({}_{4}\), the _NTs_  
Figure 10: The movable do solfgee-based basic and merged pitch histograms for two well-known traditional Korean and Japanese folk songs using the anhemitonic pentatonic scale without a perfect bell-shaped pitch distribution (_DoBell_\(<\) 1), with the languages/cultural groups of the original version in curved brackets.  
Figure 9: The movable do solfgee-based basic and merged pitch histograms for four well-known East Asian traditional folk songs from cultural groups other than (Han) Chinese, with the languages/cultural groups of the original version in curved brackets.  
of the basic/merged anhemitonic pentatonic pitch histograms drop from 2 to 0, and the _DoBells_ rise from 0.78 to 1.  
In the subsequent classification experiments, we generate eight types of features by taking various combinations of one from each of the three groups (\(NT\), _DoBell_), (all pitches, anhemitonic pentatonic pitches), and (pitch histogram, merged pitch histogram):  
* \(NT_{\text{pitch histogram}}\);
* \(NT_{\text{merged pitch histogram}}\);
* \(NT_{\text{anhemitonic pentatonic pitch histogram}}\);
* \(NT_{\text{merged anhemitonic pentatonic pitch histogram}}\);
* \(DoBell_{\text{pitch histogram}}\);
* \(DoBell_{\text{merged pitch histogram}}\);
* \(DoBell_{\text{anhemitonic pentatonic pitch histogram}}\);