Length, tone and intonation can be distinctively used like phonemes, especially in the African languages. Therefore, they function as phonemes in such languages.
I think so, but there has to be some limits for this.
Indic languages are Alphasyllabaries. We have long and short vowels, with the difference being that the long vowel has double the length (in time) than the short vowel. We have separate letters for them too. For example, Malayalam, my language has a vowel repository of 16 vowels, and all of them can be written down and read. We use distinct diacritic marks along with consonants to mark each vowel. Some of the consonants sort of reflect the tone too. In addition, Malayalam has what are called chillus which are semivowels/semiconsonants.
Hi David! Whether these concepts are legit might depend on the theoretical framework one adopts. For example, if length is used as a phonological feature [+long], then the notion lengtheme and the feature would be synonymous and could be justified simply by providing a minimal pair. However, if one adopts a theoretical framework where length is derivate, say as a sequence of two segments, then the notion is redundant and because it is not a primative.
In the treatment of tone, some researchers have analysed them as being compositional (features High and Low, see Hyman 1993 or Bao 1999 for details). In such approaches, the toneme would really just be a feature. For some researchers, tones may not be thought of as compositional. In Chinese languages, a syllable [ma] is contrastive if it has a high flat tone, a rising tone, a low tone or a falling tone. If you think of rising and falling tones as non-compositional (i.e. cannot be stated as aa sequence of tonal features), then the toneme would include all the various tone melodies. In African languages, it seems that there is a lot of evidence for treating tones as sequences of H and L, as can be seen in the patterns found in Mende, Margi etc (see Peng 2013: Chapter 4).
In the treatment of intonation, it is possible also to use only tonal features H and L. One merely has to state the locus where they occur in relation to the utterance (either the syntactic structure or the prosodic structure). If that's the framework adopted, then there is no need for the notion intoneme.
Best,
Lian-Hee
References
Bao, Zhiming (1999) The Structure of Tone. Oxford University Press.
Hyman, Karry M. (1993) Register tones and tonal geometry. In van der Hulst, Harry and Keith Snider (eds.) The Phonology of Tone: the Representation of Tonal Register. Mouton de Gruyter. pp. 75-108.
Peng, Long (2013) Analyzing Sound Patterns: an Introduction to Phonology. Cambridge Univ. Press.