Division of Tone Space
The International Phonetic Association suggests using the tone letters to represent phonemic contrasts. For example, if a language has a single falling tone, then it should be transcribed as /˥˩/, even if this tone does not fall across the entire pitch range.
For the purposes of a precise linguistic analysis there are at least three approaches: linear, exponential, and language-specific. A linear approach is to map the tone levels directly to fundamental frequency (f0), by subtracting the tone with lowest f0 from the tone with highest f0, and dividing this space into four equal f0 intervals. Tone letters are then chosen based on the f0 tone contours over this region. This linear approach is systematic, but it does not always align the beginning and end of each tone with the proposed tone levels. Chao's earlier description of the tone levels is an exponential approach. Chao proposed five tone levels, where each level is spaced two semitones apart. A later description provides only one semitone between levels 1 and 2, and three semitones between levels 2 and 3. This updated description may be a language-specific division of the tone space.
Read more about this topic: Tone Letter
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