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Contour tone diacritics with tipa?

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LaTeX allows for three level tones and two contours to be notated using the above-vowel diacritics: \'{} for the H tone (á), \`{} for L (à), \={} for M (ā), \v{} for LH (ǎ), and \^{} for HL (â).

The literature commonly uses above-vowel diacritics also for HM, ML, LM, MH, HLH and LHL, using sequences of the above level tones, for example a᷄ (MH) and a᷈ (LHL; note that this is not a tilde). TIPA, however, only offers tone bars for contours other than HL and LH.

Is there a way to combine diacritics in LaTeX for the combinations HM, ML, LM, MH, HLH and LHL, especially in a way available within \textipa{}?


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