### Clone and Run VowSpace from Source

Source: https://github.com/alicagank/vowspace/blob/main/README.md

This snippet demonstrates how to clone the VowSpace repository from GitHub and run the application directly from the source code. It requires Git, Python 3.8+, and specific Python packages that can be installed using pip.

```Bash
git clone https://github.com/alicagank/VowSpace.git
cd VowSpace
python main.py
```

```Bash
pip install -r requirements.txt
```

--------------------------------

### VowSpace Data Table Format Example

Source: https://github.com/alicagank/vowspace/blob/main/README.md

Illustrates the minimum required columns for data input into VowSpace, including vowel, f1, f2, and speaker. It also mentions support for derived metrics like Bark, logarithmic values, and z-scores.

```Text
vowel   f1   f2   speaker
/æ/     123  1234 Markus
```

--------------------------------

### Lobanov Normalization Tutorial

Source: https://github.com/alicagank/vowspace/blob/main/tutorial/instructions.md

This tutorial guides users through normalizing vowel formants using the Lobanov method in VowSpace. It involves importing an Excel dataset, applying normalization via the 'Data Options' menu, and visualizing the results to minimize gender-based variation and reveal sociolinguistic patterns. The process includes steps for data import, visualization adjustments like Qhull and legend options, and saving the normalized plot.

```VowSpace
File -> Import Data from Spreadsheet
Data Options -> Normalize -> Lobanov Normalization
Visualization Options -> Connect with Qhull(s)
Visualization Options -> Legend Options -> Show Legend
Visualization Options -> Show Grids
File -> Save as...
```

--------------------------------

### Order Eigenvalues and Eigenvectors in Python

Source: https://github.com/alicagank/vowspace/blob/main/tutorial/instructions.md

This Python code snippet demonstrates how to order eigenvalues and their corresponding eigenvectors, typically from largest to smallest, using numpy's linear algebra functions. This is crucial for correctly interpreting the principal axes of data distribution when visualizing.

```python
#This ensures the eigenvalues and corresponding eigenvectors are ordered correctly, typically from largest to smallest eigenvalue.
eigvals, eigvecs = np.linalg.eigh(cov)
order = eigvals.argsort()[::-1]
eigvals, eigvecs = eigvals[order], eigvecs[:, order]
```

--------------------------------

### Bark-Scale Transformation Formula

Source: https://github.com/alicagank/vowspace/blob/main/README.md

Maps frequencies to the Bark scale, which is based on human auditory resolution and critical bands.

```Python
Z = 26.81 / (1 + 1960 / F) – 0.53
```

--------------------------------

### Audio Analysis with Parselmouth

Source: https://github.com/alicagank/vowspace/blob/main/README.md

Extracts audio information such as intensity, pitch, and vowel formant frequencies (f1-f4) from audio files using the Parselmouth library, an interface for Praat.

```Python
# Parselmouth library is used for audio analysis.
# Extracts intensity, pitch, and vowel formant frequencies (f1-f4).
```

--------------------------------

### VowSpace Input Data Format

Source: https://github.com/alicagank/vowspace/blob/main/paper/paper.md

This snippet illustrates the minimal input data format required by VowSpace for analyzing vowel formants. It includes the vowel, its first two formant frequencies (F1 and F2), and the speaker's name. VowSpace also supports columns for normalized formant values.

```plaintext
vowel f1 f2 speaker
/æ/ 123 1234 Markus
```

--------------------------------

### Vowel Plotting with Matplotlib

Source: https://github.com/alicagank/vowspace/blob/main/README.md

Visualizes vowel formant data using Matplotlib, employing a rectangular template with f1 and f2 values on axes and different colors for different sources.

```Python
# Matplotlib (3.8.2) is used for plotting.
# VowSpace utilizes a rectangular template with f1 on the rightmost side and f2 on the bottommost side.
```

--------------------------------

### Bark Difference Metric Formula

Source: https://github.com/alicagank/vowspace/blob/main/README.md

Calculates perceptual distance metrics using the Bark scale, transforming formant values and computing differences like Z3–Z1 and Z2–Z1.

```Python
Z_i = 26.81 / (1 + (1960 / F_i)) – 0.53
```

--------------------------------

### Log-Scale Transformation Formula

Source: https://github.com/alicagank/vowspace/blob/main/README.md

Applies a base-10 logarithmic transformation to raw formant values, reflecting the logarithmic nature of human auditory perception.

```Python
F_log = log10(F)
```

--------------------------------

### Mel-Scale Transformation Formula

Source: https://github.com/alicagank/vowspace/blob/main/README.md

Converts formant frequencies to the Mel scale, a common scale used in speech processing and auditory modeling.

```Python
F_mel = 2595 × log10(1 + F / 700)
```

--------------------------------

### ERB-Scale Transformation Formula

Source: https://github.com/alicagank/vowspace/blob/main/README.md

Transforms frequencies to the Equivalent Rectangular Bandwidth (ERB) scale, used in auditory models to simulate cochlear filtering.

```Python
F_erb = 21.4 × log10(1 + 0.00437 × F)
```

--------------------------------

### Nearey1 (Log-Mean Normalization) Formula

Source: https://github.com/alicagank/vowspace/blob/main/README.md

Applies vowel-intrinsic and vowel-extrinsic normalization by subtracting the log of the speaker-specific mean of all vowels from each log-transformed formant.

```Python
F_n[V] = log(F_n[V]) – log(mean(F_n_all_vowels))
```

--------------------------------

### Lobanov Normalization Formula

Source: https://github.com/alicagank/vowspace/blob/main/README.md

Implements the Lobanov normalization method (Z-score) to remove speaker-dependent anatomical differences by standardizing formant values.

```Python
F_n[V] = (F_n[V] – MEAN_n) / S_n
```

--------------------------------

### Nearey2 (Shared Log-Mean Normalization) Formula

Source: https://github.com/alicagank/vowspace/blob/main/README.md

A variation of Nearey1, this method subtracts a shared log-mean across all formants from each log-transformed formant to minimize intra-speaker variation.

```Python
F_n[V] = log(F_n[V]) – mean(log(F_1, F_2, ..., F_n))
```

--------------------------------

### Calculate Ellipse Scale Factor using Chi-Squared Distribution in Python

Source: https://github.com/alicagank/vowspace/blob/main/tutorial/instructions.md

This Python code calculates a scale factor for creating confidence ellipses using the chi-squared distribution. It specifically finds the value from a chi-squared distribution with 2 degrees of freedom corresponding to a 0.67 cumulative probability, which is then used to scale eigenvalues.

```python
scale_factor = chi2.ppf(0.67, df=2)
```

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